The Art Of Creating Doubt About Science

Quote from RobertBryant

electrical power to the grid following within 80 yearsfrom that 1 week, 24-7 run.

There have been a 24/7 runs from Brillouin and others already..

2020+80 =2100 is a long time .. how about 2020 +8 =2028?

Quote from RobertBryant

TER is experimental.... the WAY only.. it will never make xs heat

It is not a question of insufficient size or $..

However given enough TIME ,like dinosaur evolution..

the faithful say it will happen

A bit like LENR?

Quote from RobertBryant

There have been a 24/7 runs from Brillouin and others already..

I left out the Mizuno and Takahashi excess heat periods... hours... days... weeks.

Cold fusion in Japan 2019

The best hot fusion results are from the Chinese Tokamak 100 seconds of plasma 2017

not excess heat....far from it...

plasma only ,, and not cheap.

maybe there will be fusion for afew seconds in 2020 in Chengdu,Sichuan.

but xs heat is a few decades away.

https://www.popularmechanics.c…n-nuclear-fusion-reactor/

A story of obstruction and doubt from the eighties... academia/ professional profits/ bigpharma versus science.

Barry Marshall and the peptic ulcer cure..

for which he got the Nobel Prize

https://medium.com/doctoryak/c…rry-marshall-c80a873412a6

Quote from Curbina

is the concept of so called “planned obsolescence”. It became a part of industrial design, and there is a de facto silence agreement about it because there’s a widely held perception that it’s a necessary evil for maintaining of economic progress.

The first industrial mafia agreement was formed by Edinson's light bulb construction factory. All players (Phipps,Osram etc.) did meet and agreed that all classic light bulbs must die in average after 1000h. (you can find all details online) In reality is is easy to make them run for ever - just avoid leakage. So the art was to find a containing glass with a well defined leakage.

Why did nobody complain?

The same happens today with LED again. All agreed on high voltage and/or alternate current LED's that die due to rectifier death. You soon will be no longer able to buy useful cheap DC 12V LED's. Of course today all LED's are overprized by magnitudes as in fact the base diodes cost more or less nothing.

Quote from JedRothwell

Follow what? The links go in circles. I don't see what you are talking about.

If you are unable to follow two links, it's really a big problem.

Anyway, to make it easier for you, the links led to this warning by Shane D.: Fake&Succeed strategy in R&D. What about CF?

Quote

You are not supposed to add a message to the "No discussions please" thread! It says, "no discussions please."

Yes, I know. That's the reason why I've asked you (or the mods) to open a new thread, by quoting the same announcement that you posted in a protected area: Media/News/Video Library-No discussions please

Since then, you have kept inviting the L-F readers to look at your review of the F&P calorimetry (last time here: The Art Of Creating Doubt About Science ), but no one here can raise any objection, because there is no open thread where this topic can be freely discussed.

The BBC programm took its lead from a Scientific American

article 2005

https://www.researchgate.net/p…oubt-Is-Their-Product.pdf..

Although sellers are always interested to deny any harm from their products ... such as Merck with Vioxx

this article did not touch upon the warmongers' interest in denying harm in their weapons

NATO's defence of depleted uranium has enlisted panels of experts to this end for decades

eg2001 after the WHO was given a tour of Kosovo by NATO

"

Conclusions of the WHO Experts Team:

1. Depleted uranium is only weakly radioactive and emits about 40% less radioactivity than a similar mass of natural uranium.
2. Scientific and medical studies have not proven a link between exposure to depleted uranium and the onset of cancers, congenital abnormalities or serious toxic chemical effects on organs. Caution has been expressed by scientists who would like to see larger body of independent (i.e. non-military) funded studies to confirm the current viewpoint.

Recently a French widow won her battle against NATO

"The French court found that the cancer of the French gendarme is due to the radioactivity of depleted uranium used in the munitions of NATO forces.

https://en.news-front.info/202…-difficult-to-deny-guilt/

"

Quote from RobertBryant

"The French court found that the cancer of the French gendarme is due to the radioactivity of depleted uranium used in the munitions of NATO forces.

A single inhaled atom of Pu is enough to cause lung cancer. Today it is impossible to measure the Pu content of diluted uranium but it is easy to guess that one shot contains more than 10¹⁵...

Worst: These are kinetic projectiles that evaporate during insertion !!!!!

For me this is just a dirt cheap method to get rid of dangerous waste...

Just make movies like this

Lots of bubbles in the coils...outside coating them as the spark creates .. then stacking ect...

"User Can" was doing before he left..

Thinking he would brake the chain and stumble on to the processes at any time.

Quote from RobertBryant

I left out the Mizuno and Takahashi excess heat periods... hours... days... weeks.

Cold fusion in Japan 2019

The best hot fusion results are from the Chinese Tokamak 100 seconds of plasma 2017

not excess heat....far from it...

plasma only ,, and not cheap.

maybe there will be fusion for afew seconds in 2020 in Chengdu,Sichuan.

but xs heat is a few decades away.

https://www.popularmechanics.c…n-nuclear-fusion-reactor/

Display More

Hot fusion results are reproducible, clear, theoretically understood, and scaling factors have got better (not worse) than expected.

CF results are unreproducible or unclear. You are right - if Mizuno's claims were reproducible - and there is no reason why they should not be if real - CF is the engineering advance of the millenium.

Quote from Curbina

The whole chapter on depleted uranium ammunition is a testament of our insanity as species. And a painful example of how politics can completely and willfully ignore science (and basic common sense, for that matter).

The amount of natural uranium and thorium in the normal natural environment is much, much higher than the average person might think. For work, have found several dozens of radon springs, some well over 10000 CPS on a scintillometer. Some have been water wells for decades…

I also recently pulled a bottom Jenga piece on a geological map that is setting off a spreading wave of re-assigned rock units for 20+ km, and still is unfolding beyond, bumping things 50 Ma up and down all over to fit the new fact. Partially older tech is to blame, but sometimes just bad luck on a sample or two changes things a lot in a story that requires 100% compliance to the empirical chronology.

I'm still wondering if they already have a name for the thing..

PineSci Theory Finally

2022-07-06 Publication of EP3864671A4

EP3864671A4 - Methods and apparatus for facilitating localized nuclear fusion reactions enhanced by electron screening - Google Patents

[0276] THEORETICAL SUMMARY [0277] Electron screening plays a critical role in the overall efficiency of nuclear fusion events between charged particles. The kinetic energy transfer to fuel nuclei (D) by neutral particles, such as energetic neutrons or photons, is shown above to be far more efficient than by energetic charged particles, such as light particles (e , e⁺) or heavy particles (p , d, a). A theoretical framework is provided for d-D nuclear fusion reactions in high-density cold fuel nuclei embedded in metal lattices, with a small fraction of fuel activated by hot neutrons. Also established is the important role of electron screening in increasing the relative probability P_sc(ji/2 £ q < p) to scatter in the back hemisphere (p/2 < q < p), an essential requirement for subsequent tunneling of reacting nuclei to occur. This will correspondingly be reflected as an increase in the astrophysical factor S(E).

[0278] Also clarified is the applicability of the concept of electron screening potential energy U_e to the calculation of the nuclear cross section enhancement factor /(£) . It is demonstrated that the screened Coulomb potential of the target ion is determined by the nonlinear Vlasov potential and not by the Debye potential. In general, the effect of screening becomes important at low kinetic energy of the projectile. The range of applicability of both the analytical and asymptotic expressions for the electron screening lattice potential energy U_e is examined, which is valid only for E » U_e (E is the energy in the center of mass reference frame). It is demonstrated that for E < U_e, a direct calculation of Gamow factor for screened Coulomb potential should be performed to avoid unreasonably high values of the enhancement factor /(E) by the analytical and asymptotic formulae.

[0279] EXPERIMENTAL SETUP AND RESULTS [0280] Based on the results of the theoretical analysis, a highly screened environment in deuterated metals was selected. Such an environment features the fuel in a very high-density state, together with efficient screening by both shell and conduction electrons, or external ionization or Compton electrons from photon irradiation. Local fusion events were then initiated using hot neutrons that originate from photodisintegration of deuterons bombarded by photons above the 2.226 MeV level. The hot neutrons scatter and efficiently deliver nearly half of their energy to a relatively cold deuteron. The hot deuteron is then able to be scattered at a large angle with a nearby cold deuteron in a highly screened environment, leading to efficient nuclear tunneling and fusion.

[0281] This process is fundamentally different than other fusion processes in which all of the fuel nuclei are hot and reside in a weakly screened environment (e.g., in a Tokamak). Such an environment would be dominated by small angle nonproductive elastic Coulomb scattering with an inefficient tunneling probability. Maintaining one of the two fusing nuclei in a relatively cold and well-screened condition provides highly efficient large angle scattering and subsequent tunneling probabilities. Secondary processes following the initial fusion event include kinetically heated boosted fusion reactions, conventional secondary channels with ³He, ³H, alpha particles, etc., and potentially highly energetic interactions with the metal lattice nuclei, including Oppenheimer-Phillips stripping reactions. The goal in this experimentation was to explore fusion processes that make optimal use of highly electron screened environments with high density fuel in a manner conducive to process multiplication via effective secondary reactions. The experiments described herein were guided by the theoretical analysis. The experiments described below further illustrate the fundamental concepts of some embodiments of the present invention, namely, locally hot - globally cold fuel, process initiation and control by hot neutrons created in this particular case by photodistintegration of deuterons by gamma radiation, high density cold fuel, and highly screened fuel nuclei created from a combination of shell and conduction electrons and plasma channels from gamma irradiation.

[0282] d-D nuclear fusion events were observed in an electron- screened, deuterated metal lattice by reacting relatively cold deuterons with relatively hot deuterons (d*) produced by elastically scattered neutrons originating from Bremsstrahlung photodissociation. Exposure of deuterated materials (e.g., ErD₃ and TiD₂) to photon energies in the range of 2.5 to 2.9 MeV resulted in photodissociation neutrons below 400 keV and 2.45 MeV neutrons consistent with D(d,n)³He fusion. Additionally, neutron energies of approximately 4 and 5 MeV for TiD₂ and ErD₃ were measured, consistent with either“boosted” neutrons from kinetically heated deuterons or other capture processes.

[0283] Neutron spectroscopy was conducted using calibrated lead-shielded liquid (EJ309) and plastic (Stilbene) scintillator detectors. The data supports the subsequent theoretical analysis, predicting fusion reactions and subsequent reactions in highly screened environments. Such screening is naturally provided by shell and metal lattice electrons and by Compton scattering of the Bremsstrahlung radiation, providing plasma channels and further enhancing screening.

[0284] A. ELECTRON ACCELERATOR AND GENERAL LAYOUT [0285] Tests were performed using a Dynamitron electron accelerator having independent control of beam energy (450 keV to 3.0 MeV) and beam current (10 mA to 30 mA), as shown in experimental reactor 700 of FIG. 7A. Lead cave 710 is shown more clearly in FIG. 7B. The direct current-accelerated electron beam enters the beam room via an evacuated tube and is scanned over the braking target, utilizing the scanning magnet ~l m above the target. The beam was operated in photon mode for the current tests, utilizing a 1.2 mm-thick tantalum braking target. Samples in glass vials were placed on an aluminum exposure tray close to the tantalum braking target and were exposed while the electron beam scanned at a frequency of 100 Hz over the length of 0.91 m. FIGS. 7 A and 7B show the relative position of the 16 samples (total length 0.46 m) and lead cave 710, which housed the neutron detectors and is described below. FIG. 7C is a magnified view 720 of experimental reactor 700 illustrating the close proximity (11.2 mm distance) of the 20 ml sample vials relative to the braking target, which was cooled with ambient-temperature water flowing spanwise in a stainless-steel cooling channel. FIG. 8 shows a more general architecture 800 of the experimental setup, in which electrons are accelerated within a linear accelerator, impinging upon a high Z metal target from which Bremsstrahlung gamma radiation is emitted to impinge upon the sample, which includes a deuterated metal.

[0286] B. CAVE DESCRIPTION

[0287] Due to the intense gamma flux, the detectors (a), (b), (c) were placed in a thick lead cave 710 with the following dimensions: front wall - 30.5 cm (12 in); top and side walls - 15.3 cm (6 in); and base and rear walls - 10.1 cm (4 in). The distance from the sample centerline to the detectors was 0.76 m. Borated polyethylene (B-PE) was used to reduce the large flux of thermal neutrons entering from the sides of the cave to minimize the gamma signals from the reaction Pb(n, y) from the cave walls, thus improving signal quality. The B-PE thickness was 2.5 cm for the top, sides, and back and 2.5 cm B-PE plus 5 cm normal high-density standard PE for the base of cave 710.

[0288] C. BEAM CHARACTERISTICS

[0289] 1. PHOTON FLUX

[0290] The high Dynamitron beam current exposed the samples to intense photon flux. FIG. 9 is a graph 900 providing the photon spectrum N_g{E_g for the peak electron beam energy of 2.9 MeV at the top of the sample, as determined using the fitted 5-term interpolation formula, 450 mA of current (per vial):

[0291] where E^^ULX is the maximum photon energy per one incident electron and E_g is photon energy in MeV, with N_g{E_g in units of photon/second/MeV/Steradian. The constants used were c₀ =—3.187 X 10^-3 , c_x = 3.506 X 10^-3 , a₀ =—2.035 , a_x = —3.189 X 10^_2, and b = 6.327 X 10^-1. The peak photon energy was corroborated by the lanthanum bromide (LaBr₃) gamma detector (c) mounted in cave 700. The photon flux plotted in FIG. 9 was corroborated by a Monte Carlo (MCNP^®) analysis modeling the geometry noted in FIG. 7C.

[0292] 2. BEAM ENERGY MEASUREMENT

[0293] Beam energy was monitored by measuring a current through a linear stack of resistors to measure the terminal voltage on the electron accelerator. The beam voltage was recorded using a Labview Data Acquisition system and a high-speed triggering scope for short-term transients. The Dynamitron was very stable in beam energy (e.g., 2.9 MeV ± 100 keV ( 5s )). Current was also measured and was stable to within 2.5% (5s) of setpoint. During pre-test evaluation of the Dynamitron, the terminal voltage was checked by exposing beryllium near its photodissociation peaks of 1.76 and 2.42 MeV. By examining the change in the first and second derivatives of neutron production rates, it was determined that the photon beam energy was less than 50 keV of the specified set point, agreeing with the beam terminal voltage measurement method, which was used for all subsequent tests.

[0294] 3. PHOTODISSOCIATION NEUTRONS

[0295] With the beam operating above the deuteron photodissociation energy (2.226 MeV), photo-neutrons were produced. The peak and average photodissociation neutron energies were calculated, as shown in Table IV below.

TABLE IV: CALCULATED PHOTODISSOCIATION NEUTRON ENERGIES

[0296] D. NEUTRON DETECTION

[0297] 1. PROMPT NEUTRON DETECTION

[0298] Three different neutron detection systems were employed, as noted in Tables

V(A) and V(B) below.

TABLE V(A): NEUTRON DETECTION INSTRUMENT DETAILS

TABLE V(B): NEUTRON DETECTION INSTRUMENT DETAILS

[0299] The Eljen-309 liquid scintillator and the Stilbene single-crystal detector were used to detect prompt fast neutron counts and energies. The Eljen detector (5 cm diameter by 10 cm length) being larger than the Stilbene detector (2.5 cm diameter by 2.5 cm length), had a higher sensitivity to the fast neutrons, resulting in a greater signal. However, due to the unique single-crystal material, the Stilbene could measure slightly lower energy neutrons (0.3 MeV threshold) versus the EJ309 (0.5 MeV threshold). Both detectors pointed toward the specimens during radiation and were shielded from the intense gamma rays with the 30.5 cm front lead wall and surrounding cave. It was found that the Stilbene detector exhibited greater photon/neutron discrimination due to its material and design. A lanthanum bromide (LaBr₃) gamma detector was also placed in the cave (near the rear) and was used to measure gamma energies from both the beam and from thermal neutron capture on the lead walls, resulting in Pb(n, y) reactions.

[0300] A rough estimate of photo-neutrons interacting with the cave was determined by counting the 3 to 8 MeV gammas created during beam on conditions. It is previously noted that to reduce the gamma glow within the cave to acceptable levels, borated polyethylene was placed on all five sides of the cave (except the front), thus minimizing the captured thermal neutrons to reduce the ionizing radiation from the Pb(n, y). By using the B-PE around the cave, higher beam currents could be utilized, increasing the process signal-to-background noise for the fueled shots to meet the goal of accurately measuring fusion and other reaction neutrons.

0301] 2. PROMPT NEUTRON SIGNAL POSTPROCESSING

[0302] High -intensity primary Bremsstrahlung and secondary fluorescence x-rays from the Dynamitron beam were the most significant challenges for postprocessing the detector signal, even though the detectors were shielded in the lead cave. The strategy was to record all detector signals without any information loss with the fast data acquisition system (DAQ) throughout the beam exposure. A sophisticated model-based pulse-shaped discrimination (PSD) signal analysis procedure was developed for the postprocessing data analysis.

[0303] The detector photomultiplier tube (PMT) signal output was directly connected to a CAEN, 8-channel DT5730 desktop digitizer with 500-MHz sampling rate and 14-bit resolution, which is well suited for the signal from the organic scintillators. The pulse-processing-(DPP)-PSD firmware and control software, CoMPASS, of the digitizer were used for the on-line signal processing, data acquisition monitoring, and waveform recording. Each detector signal was triggered locally at the input channel and recorded independently with the DPP firmware. The Universal Serial Bus (USB) 2.0 interface of the digitizer allows data transfer at a speed of up to 30 MB/s. During the experiment, the data transfer speed was monitored, and data overflow was prevented by increasing the detection threshold, reducing the beam current, reducing the number of detector channels, or increasing the shielding materials. A total of 140 samples (280 ns long) of each signal waveform were recorded for the postprocessing.

[0304] 3. ENERGY CALIBRATION

[0305] The energy scales of the pulse height spectrum of the detector were periodically calibrated using Cs-l37, Co-60, and Th-232 check sources. The PMT gains and calibration stability were important for the PSD performance, the neutron spectrum unfolding, and combining and/or comparing separate sets of experimental data. The detector gain stability across the measurements was confirmed (and corrected) using the 511 keV line during off-line analysis. The neutron detection efficiency of the detector was determined from the known spectra of the AmBe and Cf-252 sources. Average detector efficiency was calculated to be approximately 13% for the Stilbene detectors and 11% for the EJ-309 detectors. Energy-dependent efficiency was used for the response matrix normalization and subsequently for the neutron flux calculation of the detector unfolding.

[0306] 4. SIGNAL FILTERING AND HYBRID PSD APPROACH

[0307] A two-stage process was used to process the scintillator data. First, the signal was filtered with a multistep approach to arrive at a series of clean wave forms. Second, a hybrid PSD technique was used to virtually eliminate false neutron counting. The most important filter to remove double peaks and false neutron counting is the Pile-Up signal rejection (PUR). If small peaks (spikes) with amplitudes exceeding 8% of the main peak were observed on the tail of the signal, the signal was rejected from further processing. The rejection criterion was set to 5% for the stronger signals above 1 MeV. The PUR criteria cannot be tighter because it is the delayed secondary scintillator phosphorescence light pulses that give the PSD information. Next, low-amplitude high- frequency noise filters incorporating a root- mean- square (RMS) approach were applied to remove the smaller x-ray signals (spikes) and delayed fluorescence, which may pass through the pile-up rejection criteria. Also, successive neutron recoils within the phosphorescence decay will alter PSD performance. These types of events were further reduced by the signal root-mean-square (RMS) and baseline shift filters. The pile-up rate increases with the beam energy and current. For example, at beam conditions of 2.9 MeV and 15 mA the filters rejected about 35% (passing 65%) of all triggered signals.

[0308] The clean wave forms were subsequently processed by the hybrid PSD algorithm. The PSD processing also consisted of a multistep approach. The signal was first processed through a frequency-gradient method with fast-Fourier transform (FFT) and wavelet analysis. Next, each signal was compared to a predetermined neutron or gamma template waveform. Finally, the charge integration method was then applied comparing the“tail” area to the overall area, resulting in the PSD parameter versus electron equivalent energy, as shown Section III (Experimental Results) below.

[0309] All signals that passed through those filters were subsequently plotted in the PSD spectrum. Due to the high gamma flux the neutron pulse height spectrum was accepted if the PSD parameter was above an 8s threshold of the gamma ray band. Therefore,“accepted” waveform shapes reliably resulted in neutron signatures. The PUR algorithm coupled with the 8s constraint on the PSD between neutron and gamma PSD parameter virtually eliminated neutron double hits (aliasing) and gamma signals being recorded as neutrons. The 8s constraint also reduced fast-neutron counts considerably, but significantly increased the fidelity of the overall data and the neutron energy measurement. For reference purposes, the peak photo neutrons produced were less than 400 keV. This was below the Eljen-309 threshold and was also below the Stilbene ability to measure on account of the 8s constraint window used to ensure separation of neutrons from gammas in the PSD.

[0310] 5. NEUTRON ENERGY DETERMINATION

[0311] As discussed above, the detectors were calibrated in electron-equivalent units, as were the measured neutron pulse height spectra. The steps used to unfold the detector response include the following. First, MCNPX-Polimi and MPPost postprocessing codes were used to generate the detector response matrix. Subsequently, the HEPROW computer code package obtained from Oak Ridge National Lab (RSICC), which used Bayes theorem and maximum entropy methods, was utilized for the spectrum unfolding.

[0312] Three different unfolding codes were evaluated: GRAVELW, UNFANAW, and MIEKEW. A calibration study was performed in which a 40-mCurie AmBe neutron source was placed near the scintillator detectors while data was collected. Good correlation was found across the energy range when comparing the AmBe unfolded results with the well-known AmBe spectrum. The best correlation was found using the GRAVELW unfolding code, which was subsequently used in the final reported results. [0313] The input files of the unfolding code were the experimental spectra and the detector response matrix. The response matrix is the ideal pulse height spectra with monoenergetic neutrons hitting the detector. Neutron count uncertainty is assumed to be the standard uncertainty assigned to contents in one channel assuming Poisson statistics hold, and is the square root of the number of counts. It is also assumed that no correlation exists between different channels. The neutron penetration through the cave (lead and B-PE) was simulated using the MCNP6 code. For reference purposes, the lead cave scattered approximately 80% of incoming fusion neutrons.

[0314] E. SAMPLE MATERIALS AND METHODOLOGY

[0315] 1. SAMPLE MATERIALS

[0316] The samples exposed in this study were created from prepared batches of either deuterated or bare (no-load) erbium or titanium metal material. Table IV below provides the materials, test shot identifier, shot durations, energy, and current settings that were used. In the test shot exposures, ErD₃ (480 g in 16 vials) and TiD₂ (216 g in plate and powder form) samples containing 5 X 10²⁴ deuterium atoms were used. No additional deuterium atoms were added to the samples.

TABLE VI: TEST SHOT SAMPLE EXPOSURES

[0317] In Table VI, black rows indicate baseline configuration, gray rows indicate beam energy study, and white rows indicate beam current study. Note that test shots TS1575 and 1576 were distinct samples made from ErD₃ and were exposed to evaluate reproducibility. These samples evaluated reproducibility of the process using specimens made from different material batches and exposed on different test days, and outcomes were comparable. Samples were tracked using meticulous records for custody control from material loading through exposure and posttest analysis using high-purity germanium (HPGE) gamma scans and liquid beta scintillator counting.

[0318] For each test, the samples were placed into glass vials and subsequently positioned at a close distance to the tantalum braking target (see FIG. 7C) to maximize the flux per unit area per unit time to evaluate the hypothesis that fusion events could be initiated with ionizing radiation in deuterated metal lattices where the deuterium fuel was in a stationary center-of-mass frame. Natural- abundance erbium (99% purity) and titanium (99% purity) were deuterated by gas loading using appropriate pressure, temperature, and time protocols. Erbium was chosen for this study for several reasons: (1) Erbium loads to ErD₃ have a high fuel number density (8 X 10²² D-atoms/cm³); (2) Erbium showed enhanced nuclear reactions via LINAC exposure in previous tests; (3) Erbium metal maintains a high deuteron stoichiometry between furnace D-loading and testing; and (4) Erbium (Z = 68) provides a mid-range of metal lattice screening without excessive metal lattice interaction reducing fusion reactions.

[0319] Titanium was also exposed under comparable conditions to examine the effect of a higher fuel number density (l x 10²³ D-atoms/cm³) and lower atomic mass (Z = 22), approximately 1/3 the positive nuclear charge of Er, which also contributed to fewer metal lattice screening electrons. The sample mass change (accuracy ±5%) from before until after gas loading was used to determine the D-loading of the sample materials. Note 99.999% ultra-high-purity gas was used to deuterate the samples. Although the vials were sealed during exposure, air was used as the cover gas.

[0320] 2. CASE-CONTROL METHODOLOGY

[0321] A case-control methodology was utilized, where identical tests were performed on fueled and unfueled samples, to isolate the fuel as the only experimental variable. For consistency between the ErD₃ and TiD₂, the same amount of fuel (5 X 10²⁴ D-atoms) was exposed. This amounted to 480 g of ErD₃ or 216 g TiD₂, respectively, exposed in 16 vials. For the unfueled case, a comparable mass of bare Er and bare Ti was exposed. As will be shown in the results below, during unfueled shots, there was some neutron activity above cosmogenic background. This activity is believed to have been caused by screened reactions from the naturally occurring deuterium (153 ppm) in various standard water-cooling passages in the Dynamitron that were exposed to either direct or indirect gamma irradiation. For reference, the braking target cooling channel contained 1.6 X 10²² D-atoms and the scanner side cooling passages contained 1.2 X 10²² D-atoms.

[0322] III. EXPERIMENTAL RESULTS

[0323] A. PULSED SHAPE DISCRIMINATION SPECTRA

[0324] FIG. 10A provides an example Pulse Shape Discrimination (PSD) plot 1000 relating PSD parameters versus electron equivalent energy recorded in the detector

(EJ309 HV) for TS 1576 ErD₃ with beam conditions of 2.9 MeV and 15 mA and a 6- hour exposure. It should be noted that FIG. 10A includes ellipses illustrating nominal energy ranges (ranges 1 and 2) corresponding to those counts from the PSD plot that, when unfolded, lead to the nominal 2.45 MeV and 4 MeV neutron energies discussed in Section III(B). As noted in the Neutron Detection section, an 8s constraint window was used to ensure separation of neutrons from gammas. Data points occurring above the 8s separator line were confidently counted as neutrons and not gammas.

[0325] B . COMPARISON OF FUELED VERSUS UNFUELED RESULTS

[0325] B . COMPARISON OF FUELED VERSUS UNFUELED RESULTS

[0326] As described above, a case-control methodology was followed where ErD₃ (fueled) samples and Er-bare (unfueled) samples were exposed in separate exposures, holding constant all other experimental parameters, including sample material type and mass, beam energy and current, sample placement under the beam, detector placement, and cave configuration. FIG. 10B is a graph 1010 that presents the EJ309 detector results for TS 1576 (fueled, black line above) and TS589 (unfueled, dark gray line below) in detector counts (PMT counts after filtered using the process noted earlier) versus electron energy equivalent units (keVee). The small spikes to the right of the peaks are all from the fueled results. FIG. 10C is a graph presenting a comparison of the net counts (TS 1576 (fueled) minus TS589 (unfueled) prior to unfolding with the HEBROW algorithms and shows the results of two relevant comparison cases. For reference purposes, the simulation results were scaled as follows: 2.45 MeV spectrum per neutron was scaled up by 17000 and the 4 MeV neutron spectrum was scaled up by 6000 to roughly match the area under the experimental curves. The 6-hour data shows significantly higher detector counts during the fueled exposures.

[0327] In the simulations, a monochromatic neutron source with neutron energies (E_n) of either 2.45 MeV or 4 MeV are used as the input to the MCNPX-Polimi model of the EJ-309 detector. The fusion energy neutrons result in simulated detector spectra centered on the main peak. The detector counts for 4 MeV neutrons have a broader energy response and correlate with the higher energy measured counts. It is noted that the shape of the curve for ErD₃ in the 0 to 800 keVee range bears significant resemblance to previous results by Lang, who used a similar scintillator/PSD approach to measure neutron energies for a 35-DD-W-S NSD/Gradel Fusion d-D fusion neutron generator.

[0328] C. NEUTRON SPECTRA AND REPRODUCIBILITY

[0329] Utilizing the methods for the detector modeling and neutron energy unfolding described earlier, the“net” (fueled minus unfueled) PSD data was converted into neutron spectra. Graphs 1100, 1110, 1120 of FIGS. 11A-C present data showing neutron spectra measured for the 6-hour aggregate data for two separate ErD₃ test samples. FIGS. 11A-C show evidence of (1) fusion neutron production (all); (2) neutrons with greater than fusion energies (EJ309); and (3) reproducibility of the process. The uncertainty bars represent 3s. Fusion energy neutron counts were scaled to sample location. TS1575 1.5 X 10³ neutron counts per second and TS1576 1.6 X 10³ neutron counts per second using EJ309 and 14 X 10³ neutron counts per second using the Stilbene detector. It should be noted that the Stilbene detector exhibits better gamma/neutron separation, and thus, fewer true neutrons are discarded during postprocessing, resulting in the higher neutron count rate.

[0330] FIG. 11A is for TS 1575 and FIG. 11B is for TS 1576. Both were corrected for background and unfueled exposure. The HEBROW unfolding algorithm incorporates the intrinsic detector efficiency. The unfolded neutron spectra showed a number of interesting features, including several primary neutron energy peaks of 2.45, 4, and to a lesser degree, 5 MeV, plus an apparent shoulder peak 4.2 MeV. The measured neutron energies were remarkably close, indicating process reproducibility. FIG. 10C shows the neutron spectra for TS 1575 measured using the solid-state Stilbene detector, showing the nominal 2.45-MeV fusion neutron peak, which was in the calibrated range of the detector. The higher energy peaks occur in the nonlinear range of the detector, and are not presented here.

[0331] D. AFTERNATE MATERIAF EXPOSURE: TITANIUM DEUTERIDE

[0332] Graph 1200 of FIG. 12 shows the neutron spectra for TiD₂ using the EJ309 detector for the“net” fueled (TS611-612) minus unfueled (TS631) PSD data. The unfolded neutron spectra showed a number of interesting features, including several primary neutron energy peaks of 2.45 (fusion energy), 4, and to a lesser degree 5 MeV, and an apparent shoulder peak at 4.2 MeV. It is noted that the fluence fusion-energy neutron peak (-2.45 MeV) is approximately 30% higher for the TiD₂ than for the ErD₃, accounting also for the exposure times. [0333] E. COMPARISON NEUTRON PRODUCTION IN TITANIUM

DEUTERIDE VERSUS ERBIUM TRIDEUTERIDE

[0334] Fusion Energy Neutrons: Comparing integrated fusion neutron counts of TiD₂ and ErD₃, one finds TiD₂ produces 1.31 times more neutrons than ErD3. Recall that fusion reaction rates are proportional to the D-fuel number density squared (n²). TiD₂ has slightly higher number density (lxlO²³ D/cm³) than ErD₃ (0.8xl0²³ D/cm³). Squaring the ratios of the number densities one would expect to measure approximately 1.56 times more fusion neutrons for TiD₂ than for ErD₃. It is recognized that if the number density of TiD₂ were just slightly less (0.92xl0²³ vs. lxlO²³ D/cm³), one could account for the small discrepancy.

[0335] Higher Energy Neutrons (-4 MeV): Higher counts of ~4 MeV neutrons were measured for ErD₃ as compared to the TiD₂. This general trend would be in alignment of screened Oppenheimer-Phillips reactions favoring higher Z base metals. However, because there are other factors at work (i.e., neutron energy boosting) occurring simultaneously, additional research may be beneficial to understand the differences in the 4 MeV neutron production found for TiD₂ and ErD₃.

[0336] F. MEASUREMENT UNCERTAINTY

[0337] The uncertainty bars for the neutron spectra in FIGS. 11A-C and 12 were determined based on the combined effect of detector energy resolution and the unfolding algorithm. The neutron energy uncertainty (horizontal band) was determined using the perturbation method. First the standard deviation in electron equivalent units was determined by examining the response of the detectors to established gamma peaks for standard check sources (Cs-l37 and Co-60) by fitting a Gaussian distribution resulting in a s~50 keVee. To obtain the plotted 3s, the original spectrum was“offset” by either +150 keVee or -150 keVee, corresponding to ±3s on the EJ309 detector energy resolution, (or ±120 keVee for the slightly better resolution Stilbene detector) prior to unfolding. Once unfolded, the shifts in the neutron energy peaks (e.g., fusion neutron peak at 2.4 MeV) were determined for both the plus and minus unfolded spectrum.

[0338] This perturbation analysis resulted in a slightly asymmetric neutron energy uncertainty band, biased toward the lower energy, as shown in the figures. The fluence uncertainty (vertical bands) were determined using the GRAVEL unfolding methodology using ±3s. Note that for clarity, the uncertainty bars were plotted on the figures for only select data points.

[0339] IV. DISCUSSION

0340] A. EVIDENCE OF FUSION AND FAST NEUTRONS

[0341] 1. FUSION NEUTRONS

[0342] As shown in FIGS. 11A-C, there are several distinct peaks corresponding to primary fusion neutrons as well as neutrons potentially resulting from subsequent fusion reactions. Kinematic derivations for neutron heating of the deuteron discussed in the theoretical section above were used to calculate the range of neutron energies caused by the heated fuel. See Table VII below.

TABLE VII: CALCULATED NEUTRON ENERGIES RESULTING FROM

KINETIC HEATING OF DEUTERIUM FUEL

Figure imgf000084_0001

Figure imgf000085_0001

[0343] Bremsstrahlung at 2.9 MeV gives rise to photoneutrons with an average neutron energy of 0.145 MeV. Neutron-deuteron recoil then causes a hot deuteron with average energy of 0.064 MeV. Given enhanced screening as described above, a hot deuteron may fuse with a cold deuteron. The separation angle of the (n, 3He) recoil products from 0° to 180° leaves the neutron with 2.2 to 2.76 MeV. This energy spread, coupled with the full-width at half maximum (FWHM) of the instrument, explains some of the broadening of the neutron peaks. A second generation fusion neutron heats a deuteron (n, d*), giving rise to neutron energies from 1.72 to 4.45 MeV. These energies bracket the span of the secondary peak and shoulder of 4 to 4.2 MeV, noted in FIGS. l lA and 11B.

[0344] 2. EFFICIENCY OF DETECTING FUSION NEUTRONS

[0345] From the point at which the fusion neutrons are created until they are counted in the detector, there are several loss mechanisms. Tables VIII(A) and VIII(B) below list the factors influencing detector efficiency for measuring fusion (2.45 MeV) neutron counts, where absolute detector efficiency equals the product of all columns.

TABLE VIII(A): FACTORS INFLUENCING DETECTOR EFFICIENCY

Figure imgf000086_0001

TABLE VIII(B): MORE FACTORS INFLUENCING DETECTOR EFFICIENCY

Figure imgf000086_0002

[0346] Per the above, these factors include detector intrinsic efficiency, three data postprocessing factors, a cave factor (i.e., neutrons passing through the cave), and a geometric factor. The data postprocessing factors account for effects of the filter, template-matching, and 8s cut. The final column tabulates absolute detector efficiency, which is the product of the above-noted factors for both the EJ-309 and Stilbene. Based on these analyses, for every lxlO6 fusion energy neutrons created, the following numbers would be detected and reported: EJ-309 -7 neutrons; stilbene -2 neutrons.

[0347] 3. OTHER ENHANCED NUCLEAR REACTIONS

[0348] FIGS. 11A-C and 12 show evidence of distinct peaks of neutrons having ~4 and ~5 MeV energies. The 4 MeV peak appears sharp, potentially indicating unique nuclear reactions and not simple energy boosting from hot fuel reactions ((n, d*) followed by or (d*, n)). Examining FIG. 10(a), these higher energy neutrons correspond to PSD counts in the -1000 to 1500 keVee range. To confirm that these counts were not caused by intense ( n, f) reactions with the surrounding materials, the LaBr3 spectrum was examined in this energy range and revealed a monotonically decreasing spectrum with no structure, which may raise concerns of gamma leakage into the neutron channel.

[0349] In the highly deuterated metal lattice, which provides shell and lattice screening coupled with temporal plasma filaments from the gamma radiation, it appears that other processes (for example, Oppenheimer-Phillips stripping processes in the highly screened environment) occurred where a fast neutron is ejected and the proton fuses with the metal nuclei. The theoretical section above calculated very large enhancement factors, on the order of 1013 above bare cross sections given 166Er shell and photon-induced plasma screening. Consequently, 50 to 60 keV deuterons may react with the lattice atoms.

[0350] Table IX below presents candidate reactions with the candidate host metal isotopes.

TABLE IX: POSSIBLE REACTIONS WITH BASE METAL RESULTING IN

FAST-NEUTRON EMISSIONS

Figure imgf000088_0001

[0351] Table IX also provides the resulting neutron energies for various“projectile” particles, with product energies consistent with either D(d*, p*)T or D(d*, n*)3He. One can see for erbium that several reactions may result in 4-MeV neutrons (e.g., 166Er(d, n)167Tm or 166Er(3He, n)168Yb) or 5-MeV neutrons (e.g.,™Er(d, n)171Tm or 168Er(3He, n)170Yb). For titanium, 4-MeV neutrons may result from 46Ti(d, n)47V and 5-MeV neutrons may result from 47Ti(d, n)48V. Table IX also indicates whether the product is stable and gives the decay half-life if unstable. The stable isotopes would not be seen during the posttest HPGE gamma scans, nor would the longer half-life isotopes. Post-exposure HPGE gamma analyses did not reveal isotopes other than ones obtained via neutron capture. [0352] Based on the above observations, it appears that both primary d-D fusion and Oppenheimer-Phillips stripping processes in the highly screened environment occurred. Evidence of these energetic neutrons indicates attractive nuclear processes are occurring with energetic products (n*, p*, t*, 3He*), which can result in subsequent nuclear processes.

[0353] B. COMPARISON OF EXPERIMENTAL DEUTERON HEATING TO PUBLISHED WORK

[0354] Mori conducted direct-drive ICF experiments with deuterated polystyrene spheres. See Mori et al.,“Fast heating of fuel assembled in a spherical deuterated polystyrene shell target by counter-irradiating tailored laser pulses delivered by a HAMA 1 Hz ICF driver,” Nucl. Fusion 57 116031 (2017). Using a three-step pulse, Mori observed that deuteron heating had occurred. Detailed time-of-flight neutron measurements along the axis (0°) and off-axis (90°) indicated both fusion energies (90°) and neutrons having greater than fusion energy. Although Mori doesn’t highlight it, there is evidence of 2.45-MeV neutrons even on the“on-axis” case in his work. Similarly, the peak at 1.8 MeV may be an example of neutrons which have“cooled” by deuteron heating. There is some evidence of neutrons in the 4 MeV range. In Mori, the nominal 4-MeV peak shows a relatively broad base and seems to be consistent with boosted neutrons resulting from deuteron heating with energy ranges consistent with those in Table VIII. However, note that the 4-MeV peak in Fig. 11A rises sharply, which suggests that there is a primary reaction, such as Oppenheimer-Phillips stripping processes, consistent with the candidate reactions in Table VIII. [0355] C. COMPARIS ION OF MEASURED AND THEORETICAL

CALCULATIONS

[0356] 1. d-D FUSION RATES, CALCULATION

[0357] Using the theoretical methods outlined herein, an estimate of the d-D fusion rates for the following conditions was determined: 2.9-MeV beam energy and 450-mA current for each of the 16 vials. The calculations were performed in Mathematica using the following steps: (1) calculation of the bremsstrahlung spectrum from 0 to 2.9 MeV using the five-term beta function approximation with a 2.9-MeV endpoint (see FIG. 9 for spectra); (2) calculation of the photoneutron energy spectra; (3) determination of the resulting deuteron energy spectra (from these calculations, it should be noted that the average photoneutron energy was 145 keV and average hot deuteron energy was 64 keV); and (4) determination of the number of d-D reactions per second per vial, utilizing shell and plasma screening. Of the total number of d-D reactions per second, half would have created neutrons via D(d,n)3He and the other half would have created protons via D(d,p)T. Utilizing both shell and plasma screening, with a screening length Asc = 4.16x10 10 cm, a total reaction rate of L2xl03 neutrons/s was calculated for all 16 samples. It should be noted that the calculations did not include any subsequent processes described above, nor were all theoretical considerations included at this time.

[0358] 2. d-D FUSION RATES, EXPERIMENTAL

0359] Fusion energy neutron counts scaled to the sample location were determined to be 1.5 ± 0.3xl0³ neutrons/s for TS 1575 and 1.6 ± 0.3xl0³ neutrons/s for TS 1576 via the EJ-309 detector, showing process reproducibility. These values were obtained by scaling the neutron counts integrated in the fusion energy range (nominally 2.0 to 2.6 MeV) to account for detector factors effecting detector sensitivity of measuring neutron counts as outlined in Table VII. The measured neutron rate for the fusion channel energies for all 16 vials compared favorably with the calculated value.

[0360] EXPERIMENTAL CONCLUSIONS

[0361] Per the above, it is demonstrated that efficient electron screening on localized fusion rates in a dense fuel environment can lead to a significant increase in reaction rates. Based on the theoretical analysis above, neutrons can be exploited to effectively heat deuterons in primary and subsequent reactions, with the well-screened cold target fuel providing screening by shell, conduction, and plasma electrons, resulting in d-D reactions measured by characteristic fusion energy neutrons. This fusion cycle is performed at a high fuel density inside a metal lattice to enable subsequent reactions with the host metal nuclei and other secondary processes.

[0362] More specifically, exposure of deuterated materials, including ErD₃ and TiD₂, to Bremsstrahlung photon energies (< 2.9 MeV) resulted in both photodissociation- energy neutrons and neutrons with energies consistent with D(d, n)³He fusion reactions. Furthermore, process reproducibility was demonstrated. Several key ingredients required for fusion reactions are also identified above. Deuterated metals present a unique environment with a high fuel density (10²² to 10²³ D-atoms/cm³), which further increases the fusion reaction probability through shell and lattice electron screening, reducing the d-D fusion barrier.

[0363] Exposing deuterated fuels to a high photon flux creates local plasma conditions near the cold D-fuel. This additional screening further increases the Coulomb barrier transparency and further enhances fusion reaction rates. In these experiments, deuterons were initially heated by photoneutrons with an average energy of 145 keV for the 2.9 MeV beam energy to initiate fusion. However, other neutron sources would also provide the necessary deuteron kinetic energy. Calculations in the theoretical section indicate that neither electrons nor photons alone impart sufficient deuteron kinetic energy to initiate measurable d-D reactions.

[0364] Neutron spectroscopy revealed that both d-D 2.45-MeV fusion neutrons and other processes occurred. The data also indicates that the significant screening enabled charged reaction products (hot d* or 3He*) to interact with the host metal. These interactions may produce the ~4 MeV and ~5 MeV neutrons, where the Oppenheimer- Phillips stripping processes occurred in the strongly screened environment. Some embodiments thus demonstrate the ability to create enhanced nuclear reactions in highly deuterated metals with the deuteron fuel in a stationary center-of-mass frame. This process eliminates the need to accelerate the deuteron fuel into the target with implications for various practical applications.

[0365] MEDICAL ISOTOPES

[0366] Medical isotopes are a critical aspect of many modem medical diagnostic techniques and procedures. Techniques for radioisotope production include various neutron activation and creation mechanisms to produce an isotope of a specific decay chain, as well as techniques for separation of the desired isotope from the source materials and any ancillary products also produced as part of the activation/creation processes. Activation of a source is typically accomplished by neutron activation in a nuclear reactor, and also by using energetic photons, electrons, protons, alpha particles, and others from a variety of machines specifically designed to accelerate these particles. Targets in many configurations, both fluids and solids, are impacted, and as a consequence of these impacts, a fraction of the original target material is transmuted, whether isotopic or elemental. Chemical post-processing of targets after activation results in the isolation of the desired radioisotope.

[0367] Isotope-specific systems, and often more than one system for most isotopes, have been designed and redesigned as the machinery used in the production processes has improved. As medical research is an ever-changing field, the number of isotopes of interest varies, and in some cases, the development of a new isotope production technique influences the usage of that isotope in medical procedures. Various radioisotopes may be used to treat cancer and other medical conditions, provide diagnostic information about the functioning of various organs, and sterilize medical equipment, among other applications. Tables X and XI below provide lists of isotopes, half-lives, and uses for conventionally produced reactor and cyclotron radioisotopes, respectively.

0086] Electron screening also increases the probability of fuel ions tunneling through the Coulomb barrier. Furthermore, screening significantly increases the probability of interaction between hot fuel and lattice nuclei due to Oppenheimer- Phillips processes, which could open potential routes to reaction multiplication. The applicability of the electron screening potential energy U_e for the calculation of the enhancement factor f(E ) to the nuclear fusion cross section is examined. The expression of U_e is also derived for general screening process using a unifying concept of a screening length _sc . It was found that energetic neutrons provide the most effective heating of fuel ions to initiate nuclear fusion reactions in condensed matter, in comparison with heating via energetic charged particles. The above effects were integrated into an overall analysis of a nuclear fusion process that could be used as a theoretical basis for understanding, designing, and optimizing of experiments, such as those discussed below.

[0087] I. NUCLEAR FUSION CROSS-SECTION OF BARE NUCLEUS IONS [0088] In the standard case of sub-barrier quantum tunneling through the Coulomb barrier between positive nucleus ions, the nuclear fusion cross-section of bare nucleus ions J_t,_are{E ) can be written as:

[0089] where E is the energy in the center of mass (CM) reference frame, G(E) is the Gamow factor, and S(E ) is the astrophysical 5- factor containing the details of nuclear interactions. In the non-relativistic case, the relation between energy E in the CM frame and the kinetic energy K_1¥ of the projectile nucleus ion in the laboratory (lab) frame takes the relatively simple form:

[0090] In the lab frame, the target nucleus ion with mass m₂ is at rest (i.e., v₂ = 0) and the projectile nucleus ion with mass

has a velocity of v_1¥ at infinity.

[0091] In Wentzel-Krammers-Brilloin (WKB) approximation, the Gamow factor G(E ) involves the evaluation of the following integral:

[0092] Here, h is the reduced Planck constant, U_c(r) is the Coulomb potential energy U_c(r)—Z_xe - Z₂elr (i.e., the Coulomb barrier) of a projectile nucleus with charge Z_xe in the Coulomb field Z₂e/r of the target nucleus, m = m₁m₂/(m₁ + m₂) is the reduced mass of the projectile and target nuclei, r₀ = (b_± + R₂) is the classical distance of closest approach with nuclei (effective) radii

and R₂ , and r_ctp is the classical turning point, determined from the following expression:

[0093] Evaluation of the integral in Eq. (7) gives the standard expression for the

Gamow factor:

[0094] where V_c = (Z₁e)(Z₂e)/r₀ is the full height of the Coulomb barrier, E_G = 2pc² (naZ₁Z₂)² is the Gamow energy, and a = e² /he.

[0095] In the limit of H- « 1 (what is usually the case), the Gamow factor reduces to the relatively simple Sommerfeld expression:

[0096] II. NUCLEAR FUSION WITH ELECTRON SCREENING

[0097] A. COULOMB BARRIER SCREENING BY LATTICE ELECTRONS

[0098] In experiments with deuteron beams and deuterated targets, when target deuterium nuclei ( D ) were embedded in insulators and semiconductors, a relatively small enhancement of nuclear reaction rates was found for D(d, p)t nuclear fusion reactions as compared to reactions with gaseous D₂ target experiments. These enhancements of reaction rates for D(d, p)T nuclear reactions in host insulators and semiconductors are naturally explained by the screening of interacting nuclei with static electron clouds localized in atomic shells of host materials. Collectively, shell electrons produce a negative screening potential for the projectile nucleus, effectively reducing the height and spatial extension of the Coulomb barrier between interacting nuclei. [0099] However, much larger effects have been readily measured with deuterated metal targets (excluding the noble metals, such as copper (Cu), silver (Ag), and gold (Au)). A large enhancement of the nuclear reaction rates for D(d, p)T fusion reactions in host metals could be considered as the result of an additional dynamic screening by free-moving conduction electrons, which are readily concentrated near the positive ions. These screening effects are collectively referred to as“lattice screening.”

[0100] Electron screening of target nuclei either by atomic shell electrons or conduction electrons are usually both approximated by a negative uniform shift—U_e of the Coulomb barrier U_c(r). Here, U_e is the electron screening potential energy and is given by the formula:

Z_xe Z₂e

U_e = (11)

[0101] where Z₁ and Z₂ are the atomic number of projectile and target nuclei, respectively, and _sc is the corresponding screening length. The standard derivation of Eq. (11) and the effect of electron screening can be straightforwardly estimated by recalculating the Gamow factor G{E) in Eq. (7) by replacing the Coulomb potential energy U_c(r ) with the general expression for the screened Coulomb potential energy

U_c,sc (r )

[0102] The radial distance r in Eq. (7) is less than or equal to the classical turning point r_ctp given by Eq. (8), which, in turn, is generally much smaller than the characteristic distance of electron cloud distribution from reacting nuclei, which is the corresponding screening length _sc. In other words:

[0103] One can expand (— -j—) = ( l—7-) in Eq. (12) to find that the screened

V ^sc' V ^sc '

Coulomb potential energy U_{C sc}(j ) (i.e., the screened coulomb barrier) can be rewritten as:

[0104] with the standard Coulomb barrier U_c(j ) as:

[0105] and the electron screening potential energy U_e determined as:

Z_xe Z₂e

Ue = (16)

[0106] Therefore, the concept of an electron screening potential energy U_e , introduced above in Eqs. (l l)-(l5), can be theoretically justified if the classical turning point r_ctp is much smaller than the corresponding screening length _sc. This condition, stated in Eq. (13), can be rewritten as:

E » U_e (17)

[0107] using the definition of the classical turning point given by Eq. (8).

[0108] For low energies, where E < U_e , the concept of an electron screening potential energy U_e given by Eqs. (l l)-(l5) is not applicable, and the direct numerical evaluation of the Gamow factor G(E) in Eq. (7) with the screened Coulomb potential energy U_{C sc}(j ) from Eq. (12) is required. [0109] It is known that the lowering of U_c( ) by U_e is equivalent to the increase of E by U_e , as can be seen in Eq. (7) - namely, [U_c(r)— U_e]— E = U_c(r)— (E + U_e). The uniform shift U_e is called the“electron screening potential energy.”

[0110] Therefore, the experimentally measured tunneling probability

a screened target at the ion energy E in the CM frame can be evaluated as the experimentally measured tunneling probability for bare ion collisions at higher energy ( + U_e

[0111] The experimental fusion cross-section s _exp(E) can be written as:

6 exp 00 = ®bare (E) - f(E) (19)

[0112] which is essentially the definition of the enhancement factor /(E).

[0113] From Eq. (5), the expression for an enhancement factor f_Ug ( E ) can be written as:

[0114] In the case of S E b

which is usually the general case, the enhancement factor fu_e(E ) can be written as:

[0115] In the limit « 1 , Eq. (20) is further reduced to the following

asymptotic formula:

[0116] following from Eq. (10).

0117] For low energy (when E < U_e), the concept of an electron screening potential energy U_e given by Eqs. (l l)-(l5) is not applicable, and the direct numerical evaluation should be used. For the Gamow factor Gdirect (E) in Eq. (7) with U_c (r ) ® U_{C SC} (r ,

[0118] where r_c ^* _tp is the modified classical turning point determined numerically from the following equation:

[0119] where the screened Coulomb potential energy U_{C sc}(r ) is obtained from Eq. (12).
[0120] The enhancement factor in this case is equal to:
f direct (E ) = exp [G_C (E) - Gdirect (25)
[0121] where G_C (E ) is determined from Eq. (9).
[0122] Table II presents the calculated values of enhancement factors for deuterated erbium (ErD₃) for various levels of energy of interest. Note that U_e was calculated using Eqs. (54) or (62) noted below and was found to be U_e = 347 eV.
TABLE II: ENHANCEMENT FACTOR VALUES FOR DEUTERATED ERBIUM

[0123] Note, for example, that the value of 3 U_e corresponds to a 2 keV kinetic energy of the projectile in the lab frame, illustrating that the analytical formula for fu_e(E ) is valid, but the asymptotic formula for the enhancement factor is still inappropriate. Since the electron screening effect becomes important at low kinetic energy of the projectile, direct numerical calculation of the Gamow factor should be used for accurate results.
[0124] The above equations show a sharp rise in enhancement factor /(£^") for deuterium interaction with host metals, especially at moderately low deuteron energies. The enhancement factor /(£^") further increases with Z and with decreasing projectile energy. This may enable Oppenheimer-Phillips stripping reactions, resulting in the production of energetic protons and neutrons, and providing a possible route for multiplication. Such Oppenheimer-Phillips stripping reactions appear to have been observed in the experimental work described below.
[0125] Measured U_e for Select Targets: The experimental values for electron screening potential energies are U_e = 25 ± lSeV for gaseous targets and U_e = 39 to 52eV for deuterated insulators and semiconductors targets. However, for deuterated metal targets, much larger values of electron screening potential energies U_e are measured, ranging from U_e = 180 ± 40 eV for beryllium to U_e = 800 ± 90eV for palladium. The exclusion is observed for deuterated noble metal targets, namely, U_e = 43 ± 20eV (Cu), U_e = 23 ± !OeV (Ag), and U_e = 61 ± 20eV (Au). [0126] Theoretical values for U_e, considering screening by static electron clouds localized in atomic shells of host materials, that are calculated in the adiabatic limit utilizing differences in atomic binding energies, correlate well with experimentally measured values for U_e for gaseous targets, as well as for deuterated insulators and semiconductors targets. In contrast, theoretically calculated values of screening potential energies U_e by static electron clouds in atomic shells of host most metals are almost one order of magnitude smaller than values of electron screening potential energies U_e experimentally measured for deuterated alkaline metal targets. These discrepancies require a different physical mechanism for theoretical clarification of the experimental results. The novel physical mechanism, which takes into account the presence of quasi-free-moving conduction electrons in metals as an additional source for screening of interacting nuclei, is discussed later herein.
[0127] B . COULOMB BARRIER SCREENING BY PLASMA PARTICLES
[0128] In deuterated materials exposed to ionizing radiation (g-quanta or energetic electron e-beam) dense plasma channels are created inside an irradiated sample including non-equilibrium two-temperature plasma with free moving hot electrons and free-moving cold deuteron ions. Energetic electrons in plasma cannot create a bound state with deuteron ions because the mean kinetic energy of hot electrons ( K_e~kT_e ) is much larger than the Coulomb interaction (U_ie~qi q_e/f) between them:
K_e » \U_ie \ (26)
[0129] The inequality in Eq. (22) represents the condition required for plasma existence, and can also be written as:
kT_e » e² · n¹/³ (27) [0130] using the fact that the mean distance r between ions is on the order of n¹/³ :
r~n¹/³ (28)
[0131] Introducing the Debye length A_De, which is defined as:

[0132] Eq. (27) can be rewritten in light of Eq. (28) as: 0.28 f (30)

[0133] Eq. (30) indicates that in plasma, the Debye length A_De is larger by order of magnitude than the mean distance f between ions.
[0134] It also follows from Eqs. (28) and (30) that the number of electrons in the electron Debye sphere N_De in plasma is much larger than one:

[0135] Therefore, the statement _De > 0.28 f as given by Eq. (30), and the equivalent statement N_De » 1 in Eq. (31), follow from the plasma existence requirement of K_e » \U_ie\, which is expressed in Eq. (26).
[0136] The undisturbed plasma in plasma channels is electroneutral, with the total electric charge density Q₀ being equal to zero in each unit volume:
Qo = qi Kio + q_e - n_e0 = 0 (32)
[0137] where n_i0 is the undisturbed mean ion number density, n_e0 is the undisturbed mean electron number density, qi is the ion electrical charge, and q_e is the electron electrical charge. It follows from Eq. (32) that the electron and ion undisturbed number densities n_e0 and n_i0, respectively, are equal to each other if q^— q_e = e: Qo = qr n_io + q_e - n_e0 = 0 ® n º n_e0 º n_iQ (33)
[0138] However, the long-range Coulomb forces between ions in the plasma act at distances that are much larger than the mean distance between plasma particles. The interaction between any two charged ions at such distances is influenced by the presence of a large number of charged particles. Consequently, the resulting effective field is collectively produced by many charged particles, and naturally described by the self- consistent Vlasov field, which is not a random one, but rather macroscopically certain. In other words, it does not cause the entropy of the system to increase.
[0139] In accord with the above description, each ion in the plasma can be considered as surrounded by a spherically symmetrical (on average) charged ion cloud with non-uniform charge density distribution Q(r):
Q(^r) = qi ⁿi(r) + q_e n_e(r) (34)
[0140] where r is the distance from the ion (located at r = 0). Here, n_e(r) is the electron number density and 7q(r) is the ion number density, both distributed in the self-consistent Vlasov potential field 0(r) around the ion in consideration.
[0141] Since in the Vlasov field 0(r) the potential energy of an electron is q_e 0(r) and the potential energy of the ion is
f(t ) , the corresponding electron number density n_e(r) and ion number density 7q(r) are both given by the corresponding Boltzmann’s distribution: n_e (r) = n_e0 exp 0⁾ (35)
kT_e qi
n-i (r) = n_i0 exp 0 (36)
kTi [0142] where T_e and 7) are the electron and ion temperatures, respectively. Here, n_e0 and n_i0 are the mean electron and ion number densities, respectively, in undisturbed plasma.
[0143] The Vlasov potential 0(r) in the ion cloud around any considered ion obeys the nonlinear electrostatic Poisson’s equation (the Vlasov equation):

[0144] where the total electric charge density Q(r) is the nonlinear function in 0(r), as given by Eq. (34) together with Eqs. (35) and (36).
[0145] The solution of the Vlasov equation in Eq. (37) should be used in the evaluation of the Gamow factor in Eq. (7) for the screened Coulomb barrier U_{C sc}. For the projectile nucleus with charge +e in the Vlasov potential field 0(r) of target nucleus with charge qi = +e, the screened Coulomb barrier U_{C sc} is by definition:
U_c,sc = e 0(r) (38)
[0146] At a large distance from the considered ion (located at r = 0), the Vlasov field goes to zero (0(r ® oo) ® 0) since it describes the deviation from reference potential of unperturbed plasma. Thus,
n_e(r ® oo) ® n º n_e0 (39)
n_t{r ® oo) ® n º n_i0 (40)
[0147] As the undisturbed plasma is electroneutral, the total electric charge density Q₀ is equal to zero in each unit volume:
Q(r ® ¥) ® Q₀ = q_t n_i0 + q_e n_e0 = 0 ® n º n_e0 º n_i0 (41)
[0148] See Eqs. (32) and (33). [0149] Since the Vlasov potential 0(r) is small at a large distance r from the ion (located at r = 0), the ion and electron charge density distributions can be reduced to linear expressions in terms of 0(r):

[0150] Leading to a linear expression in 0(r) for the total charge density t)( (r)):

[0151] Substitution of Eq. (44) into Eq. (37) gives the linearized electrostatic Poisson’s equation (Debye equation) for the Vlasov potential f(t):

0152] where A_D is the Debye screening length in two-component, two-temperature plasma:

D² = l₀ ² + _Dg (46)

[0153] where A_Di and A_De are the ion and electron Debye lengths, respectively. They are defined as:

[0154] If the electron temperature T_e Is much higher than the ion temperature 7) (i.e., hot electrons and cold ions), then the Debye screening length l_Ό for two-component, two-temperature plasma is determined by the ion Debye length _Di:

[0155] as it follows from Eqs. (46)-(48).

[0156] Near the ion with charge qi = +e (located at r = 0), the Vlasov potential 0(r) reduces to the Coulomb potential q r generated by this ion:

0(r ® 0) t (50)

r

[0157] The exact solution of the Debye equation, Eq. (45), for the Debye potential D(r) that satisfies the boundary condition expressed by Eq. (42), takes the following form known as the Debye potential:

[0158] The usual approximation of the Vlasov potential f(t) that obeys nonlinear Eq. (37) by the linear Debye potential _D(r) is expressed by Eq. (51) with the correct boundary condition from Eq. (50), which is extensively used in the nonlinear theory of plasma sheaths.

[0159] This approximation can also be used to obtain the analytical expression for the plasma-screened Coulomb barrier U_{C sc}. The Debye potential energy U_D(r ) of the projectile nucleus with charge +e in the Debye potential field _D(r) of the target nucleus with charge q^ = +e, given by Eq. (51), by definition is as follows:

[0160] In summary, the correct expression for the screened Coulomb barrier U_{C sc} is determined by the Vlasov potential and not by its linearized version, the Debye potential. The Vlasov potential is valid at any temperature and can be obtained by direct numerical solution of the nonlinear equation, Eq. (37), with the total electric charge density Q(r) given by Eqs. (34)-(36). Alternatively, as commonly done in an evaluation of the nonlinear plasma sheath problem, it is linearized to the Debye potential given by Eq. (51), with the correct boundary condition in Eq. (50), to merge with the Coulomb potential near the bare ion.

[0161] In dense non-equilibrium, two-temperature plasma channels created in deuterated metal by g-ionizing radiation, the electron temperature T_e is much higher than ion temperature 7) , and therefore the Debye screening length l_Ό is determined mainly by the ion Debye length A_Di, as it follows from Eqs. (46)-(48). Therefore, the Debye screening length l_Ό as given by Eq. (49) converts to:

[0162] since in deuterated erbium ErD₃ exposed to g-ionizing radiation n_i0 = n_e0 = = 8 X 10²²cm^-3 and 7) = 293 K (room temperature). Also, the plasma-particle screening potential energy U_e, which is given by Eq. (16) for deuterated erbium ErD₃, becomes equal to: 347 eV (54)

[0163] with A_D from Eq. (53).

[0164] C. COULOMB BARRIER SCREENING BY CONDUCTION ELECTRONS IN METAL LATTICE [0165] In order to scientifically explain the high values of electron screening potential U_g ^Xp experimentally measured for deuterated alkaline metal targets, it has been suggested to take into account the presence of quasi-free moving conduction electrons in metals for screening of interacting nuclei. Indeed, when atoms are tightly packed, such as in solid host metals, wave functions of valence electrons of individual atoms are overlapped, acquiring a considerable kinetic energy K_{e degeneracy} due to quantum degeneracy. The Fermi repulsion is large enough to liberate valence electrons from individual atoms into a sea of conduction electrons since they are identical particles and are truly indistinguishable.

[0166] The electron energy K_{e degeneracy} , also called the Fermi energy e_F, can be straightforwardly estimated from the Heisenberg uncertainty relation:

Ap_e Ar~h (55)

[0167] The root-mean-square of electron momentum p_e = /(pj ) is equal to the momentum uncertainty Ap_e if ( p_e ) = 0:

[0168] and Ar is of the order of the characteristic distance between electrons r which, in turn, is of the order

Ar~f = n^{~ 1}^³ (57)

[0169] where n_e is the electron number density. The value of p_e is obtained from Eqs. (37)-(39):

[0170] Then the Fermi energy e_F is estimated to be:

[0171] More precise calculation of the Fermi energy e_F for degenerate electron gas is given by:

[0172] It has been previously considered that differences between the Fermi-Dirac and classical (Boltzmann) distributions of the conduction electrons may be expected to be negligible for the electron screening at room temperature. In that simplified model, deuteron ions together with metal conduction electrons were treated as a one-component equilibrium classical plasma, which comprises metallic quasi-free moving conduction electrons (providing plasma screening) and singly -charged localized deuteron ions (not contributing to plasma screening). The Debye screening length in one-component, equilibrium ( T_e = 7)) classical (Boltzmann) plasma that approximates the screening by conduction electrons, _{De c}, is then reduced to the electron Debye screening length, _De:

0173] For deuterated erbium ErD₃ with material parameters n_e0 = n_i0 = 8 X 10²² cm^-3 and T_e = 293 K (room temperature), Eq. (61) gives l_Ώb = 4.15 X 10^-10 cm. Therefore, the conduction electron screening potential energy U_e, which is given by Eq. (16) for deuterated erbium ErD₃, is equal to: 347 eV (62)

[0174] with _{De c} from Eq. (61). It should be clear to the skilled artisan that a much better estimate of U_{e c} can be achieved with Fermi-Dirac statistics for the description of conduction electrons rather than with the classical (Boltzmann) statistics. It is noted that the screening potential values calculated for plasma and conduction electrons are identical, although for different reasons. Indeed, plasma formation may also contribute to screening in non- metal targets, e.g., in dense deuterium gas irradiated by ionizing radiation.

[0175] D. SCREENING OF REACTING HYDROGEN ISOTOPE NUCLEI BY ATOMIC SHELL (BOUND) ELECTRONS IN DEUTERATED METALS [0176] The screening of ions by atomic shell (bound) electrons is modeled by the Thomas-Fermi model. The Wentzel-Thomas-Fermi screened Coulomb atomic potential (energy) is:

[0177] where Z_x and Z₂ are the atomic numbers of projectile and target (host) nuclei, respectively, and for instance, the modified (to better fit experimental data) Thomas- Fermi screening length _TF (atom size) by atomic shell electrons of host material is given by the following relation:

1.4 a₀

l TF (64)

Z¹/ ³

[0178] where a₀ is the Bohr radius of a₀ = 5.29 10 ⁹ cm and Z is the atomic number of the host material.

[0179] III. GENERAL SCREENING CASE FOR REACTING HYDROGEN ISOTOPE NUCLEI [0180] In the general case, taking into account possible simultaneous screening of reacting hydrogen isotope nuclei by atomic shell electrons of the host material and by conduction electrons the total screening potential energy U_{e sc} can be estimated as: e²

U_e,sc = Y^~ (65)

Asc

[0181] where the screening length A_sc is given by one of the following general relations:

[0182] where A_TP is the modified Thomas-Fermi screening length by atomic shell electrons of the host material, A_{De c} is the screening length by conduction electrons, and A_D is the Debye screening length in plasma.

[0183] Since the inverse square of screening lengths A_pp , A^² _C , or A^² is proportional to the corresponding electron number density, the derivation of Eqs. (65) and (66) is similar to the derivation of Eqs. (46)-(48), as the summation of electron number densities was used in both cases to contribute to the total charge density is in electrostatic Poisson’s equation for the screened Coulomb interaction potential.

[0184] IV. COULOMB SCATTERING ON TARGET NUCLEI

[0185] A. ELASTIC COULOMB SCATTERING BY LIGHT PARTICLES

( e^~, e⁺ )

[0186] Coulomb scattering of energetic projectile particles on target nuclei is the principle process associated with the nuclear fusion reactions of interest. Fusion nuclear events are more likely under the condition of large-angle scattering, which brings the reacting ions to the classical distance of closest approach to successfully tunnel through the Coulomb barrier. However, the elastic scattering at small angles dominates the Coulomb scattering interaction. Generally, the electron screening of the Coulomb barrier could significantly reduce the small-angle elastic scattering, thus increasing the probability of large-angle scattering and correspondingly successful nuclear fusion events. Elastic scattering studies on Coulomb scattering of energetic projectiles on target nuclei are analyzed herein and extended to include the electron screening by plasma electrons, as well as by conduction electrons in deuterated metals. It is also found that the kinetic energy transfer (kinetic heating) to fuel nuclei is the most successful by energetic neutral particles, such as neutrons and g-quanta-producing photodissociation neutrons.

[0187] The Coulomb scattering of relativistic projectile electrons on target atoms (absorbing medium) is characterized by the projectile electron-target atom differential cross section da / dil\_e-a , which is determined as the sum of the projectile electron-target nucleus differential cross-section da/dH \_e-N and the projectile electron-target orbital electron differential cross section da/d . \_e-e multiplied by Z (the atomic number of target atoms). The projectile electron-target atom differential cross section is given by the following relation:

[0188] where 6hs the electron scattering angle, b = v_e/c (with v_e being the velocity of the projectile electron and c being the speed of light), and 9_min is the atomic screening parameter defined as:

[0189] where h is the reduced Planck constant and _TF is the modified Thomas- Fermi target atomic radius given by Eq. (25). The electron momentum p_e is determined by the following relations:

[0190] where E_e = E_e— m_e · c ² is the kinetic energy of the projectile electron (E_e is the total energy of projectile electron and m_e is the electron mass).

[0191] Eq. (67) was derived in the first Born approximation to the Dirac equation for the Wentzel-Thomas-Fermi screened Coulomb atomic potential (energy) given in Eq. (63):

[0192] where A_TF is the Thomas-Fermi screening length (atom size) by atomic shell electrons of host material given by Eq. (64).

[0193] The projectile electron-target atom elastic scattering characteristic distance D_e-a is determined from the following relation:

D_e ²__a = D_e ²__N + (Z - D_e ²__e) (71)

[0194] where the projectile electron-target nucleus characteristic scattering distance D_e-N is determined by:

with y = _1/yi b², and the projectile electron-target orbital electron characteristic scattering distance D_e-e given by Eq. (71) with Z = 1.

[0195] Here, r_e = e² /m_ec² is the classical radius of electron r_e = 2.82 femtometers (fm) = 2.82 X 10^-13 cm. Substitution from Eq. (72) and D_e-e into Eq. (71) yields:

2r_e - VZ(Z + l) 2e² - VZ(Z + l)

[0196] The total cross section a_e-a is obtained by integrating over dil the differential cross section for projectile electrons scattering on target atoms from Eq. (67):

[0197] where 9_min = ( h/p_e ) - /ί_t , given by Eq. (68). The expression for a_e-N follows from Eq. (68) with the substitution D²__a ® D^Z__N.

[0198] For E_e = 2 MeV and m_N = m_d (deuteron mass), the numerical value for a_e-d is as follows: 38.41 kb (75)

[0199] since p D²__d = 45.1 mb, but

1.17 x 10^-6.

[0200] The target nucleus recoil energy can be found from the conservation of the total momentum in the elastic projectile electron-target nucleus scattering process:

VN ⁼ Pe Pe (76)

[0201] Where p_N is the target nucleus recoil momentum, p_e is the momentum of incident electron, and p_e' is the momentum of the scattered electron. Since in elastic scattering p_e = \p_e\ » \p_e' \ (for the reason that small angle scattering is the most probable event), it follows from Eq. (76) that:

PN = PN = Pe + P'e - 2 Pe Pe ' ^cos Q « 2 p² (1 - COS Q) (77)

[0202] where Q is the scattering angle. Correspondingly, it follows from Eq. (77), with the help of Eq. (69) that the nucleus recoil energy E_N(Q) is:

[0203] where E_e = E_e— m_cc² is the kinetic energy of projectile electron, E_e is the total energy of the projectile electron, and m_e and m_N are the electron and nucleus masses, respectively.

[0204] The mean target nucleus recoil energy E_N in a single elastic projectile electron-nucleus (target) collision is obtained by averaging E_N ( Q ) over dPi:

da

[0205] Substitution of — dCL _e-N into Eq. (79) and taking the integral yields the expression for the mean target nucleus recoil energy E_N in a single elastic projectile electron-nucleus (target) collision:

(deuteron mass), the numerical value for the mean target nucleus recoil energy E_N— E_d in a single elastic projectile electron-target deuteron nucleus collision is as follows:

E_d = 24.75 meV (81) [0207] B . HEAVY PARTICLE ELASTIC COULOMB SCATTERING (d, p, a) [0208] The Coulomb scattering of the heavy projectile particles on target nuclei is characterized by the differential cross section of the heavy projectile particles and nuclei, which is given by Eq. (67) with the substitution D²__a ® D_p-NS, with b_r = v_p/c, and:

[0209] where p_p = ^J2 m_p E_p is the projectile momentum and m_p and E_p are the projectile mass and kinetic energy, respectively.

[0210] The projectile particle-target nucleus characteristic scattering distance D_p-N is determined by: z_{p '} Z_N e²

D p-N (83)

[0211] where z_p is the projectile particle atomic number (z_p = 1 for the proton and deuteron projectile, z_p = 2 for the a projectile), and Z_N is the target nucleus atomic number.

[0212] The total cross section s_r-N for a single scattering event can be obtained from Eq. (74) with the substitution D²__a ® D_p-N and with b ® b_r « 1, since the heavy projectiles are nonrelativistic:

[0213] since

[0214] For a non-particle projectile with E_p = 3 MeV and a deuteron target nucleus ( m_N = m_d), the numerical value for s_r-Ό (total scattering cross section) is as follows: f da p 2p m„ e⁴ l

s, p J άW r-R

-D = 5.76 Mb (85)

άW a 2

P-D ^{u u}min,p h ^{, L2} ^P

[0215] For a deuteron projectile with E_d = 3 MeV and a deuteron target nucleus ( m_N = m_d), the numerical value for a_d-D is as follows: f da p D_d-D 2p m_d e⁴ A_JF

°d-D J άW a ² = 11.51 Mb (86) άW d-D °min,d h² Ed

[0216] whereas for deuteron projectile with E_d = 10 keV and a deuteron target nucleus (jn_N = m_d), the numerical value for a_d-D is as follows: 3.45 Gb (87)

[0217] The relative probability P_sc(ji/2 £ q < p) to scatter in the back hemisphere (p/2 < q £ p) is equal to:

1 G^p da

P_sc (^?r/2 < q £ p) - - — 2p sin q d9 (88)

°d-D J- W d-D

[0218] For a deuteron projectile with E_d = 3 MeV and a deuteron target nucleus ( m_N = m_d), the numerical value of P_sc(ji/2 £ q < p) for screening by shell electrons (A_sc = A_TF = 1.4a₀ = 7.4 X 10^-9 cm) is equal to:

P_sc( p/2 £ q £ p) = 1.57 x IO^-10 (89)

[0219] and the value for screening by a metal conduction electron (T_sc = A_{De c} = 5 X 10^_1° cm) is equal to:

P_sc( p/2 £ q £ p) = 3.45 x 10 ⁸ (90)

[0220] In the case of conduction electron screening in Eq. (90), the screened Coulomb potential energy V_{C sc}(r) is defined by the same as in Eq. (70) with A_TF ® A_sc = A_{De c} = 5 x 10^_1° cm. [0221] For a deuteron projectile with E_d = 10 keV and a deuteron target nucleus ( m_N = m_d), the numerical value of the probability P_sc(ji/2 £ q < p) for screening by a deuteron shell electron (A_sc = A_TF = 1.4a₀ = 7.4 X 10^-9 cm) is equal to:

P_sc( p/2 £ q £ p) = 4.73 x 10 ⁸ (91)

[0222] and for screening by a metal conduction electron (l_sc = A_{De c} = 5 X 10^_1° cm) is equal to:

P_sc( p/2 £ q £ p) = 1.04 c 1(G⁵ (92)

[0223] Generally, the deep electron screening of the Coulomb barrier (with A_{De c} « A_TF) could significantly reduce small angle elastic scattering dominance, increasing the probabilities of large angle scattering (thus increasing the astrophysical factor S(E)) and successful nuclear fusion events.

[0224] For an a projectile with E_a = 3 MeV and a deuteron target nucleus ( m_N = m_d), the numerical value for a_a-D (total scattering cross section) is as follows: 91.48 Mb (93)

[0225] whereas for an a projectile with E_a = 1 MeV and a deuteron target nucleus ( m_N = m_d), the numerical value for a_a-D increases due to the inverse dependence on energy:

a_a-D = 274.5 Mb (94)

[0226] The target nucleus recoil energy could be found from the conservation of the total momentum in the elastic projectile particle-target nucleus scattering process:

PN = P_p - Pp (95) [0227] where p_N is the target nucleus recoil momentum, p_p is the momentum of the incident projectile particle, and p_p' is the momentum of the scattered projectile particle. Since in elastic scattering p_p = \p_p \ » \p_p \ (for the reason that small angle scattering is the most probable event), it follows from Eq. (95) that:

P_N = P_N = PP + P _p - 2 p_p p_p cos Q » 2 p² (1 - cos Q) (96)

[0228] where Q is the scattering angle. Correspondingly, the target nucleus recoil energy E_N(Q ) follows from Eq. (96):

[0229] where E_p = p_p /2 m_p is the kinetic energy of the projectile particle.

[0230] The mean target nucleus recoil energy E_N in a single elastic nonrelativistic projectile-target nucleus collision is obtained by averaging of E_N ( Q ) over dPi, and from Eq. (79) with the usual substitution a ® a_p =

it follows that:

[0231] since

[0232] C. COMPTON SCATTERING ON FREE DEUTERON

[0233] The differential Klein-Nishina (1929) cross section da_F ^N /d£l per unit solid angle dil for Compton scattering of an electron on a deuteron is given by the standard expression:

[0234] where r_D is the deuteron classical radius r_D = e²/m_Dc² , e_Ό = E_Y/m_Dc² , and E_g is the photon energy.

[0235] The total cross section s ^N is obtained by integrating the differential cross section for Compton scattering given by Eq. (99) over d .:

[0236] The above integration produces the standard known formula:

[0237] For E_g = 2 MeV and m_N = m_d, the numerical value for s ^N is as follows:

^KN

°c = 49.43 nb (102)

[0238] For small e_B ^cr

mpc « 1, the expression s ^N is reduced to:

133 1144

e ) (103)

10 ^' 35

[0239] For E_g = 2 MeV and (m_N = m_d), the numerical value for s ^N (e_D « 1), calculated with the help of Eq. (103), is almost as in Eq. (102), namely: s^^N(e_ΰ « 1) = 49.43 nb (104)

[0240] The deuteron recoil energy E_D(9 ), which is the kinetic energy transferred to a free (unbounded) deuteron by g-quanta with energy E_g, is given by the standard known expression:

[0241] where 9 is the photon scattering angle. When E_g « m_Dc² (i.e., e_D « 1), then Eq. (105) is reduced to:

[0242] Mean deuteron recoil energy E_D in a single Compton collision is obtained by averaging of E_D(9 ) from Eq. (104) with da_c/d . from Eq. (99) over d .:

[0243] The above integration produces the standard known expression:

- 3(3 - e₀)(1 + e₀)(1 + 2e₀)³ 1h(1 + 2e₀)]

÷ (6e_Z)(1 + 2e_ΰ) [2 + e_W (1 + e_ΰ)(8 + eo)]

- 3(1 + 2e_b)³ [2 + e_ΰ (2 - e_B)] 1h(1 + 2e₀)} (108)

[0244] When e_B « 1 (i.e., E_g « m_Dc²), then Eq. (108) is reduced to:

3931

e + ) (109)

350

[0245] For E_g = 2 MeV and m_N = m_d, the numerical value for E_[)(e_[) « 1) is as follows:

E_W(e_W « 1) = 2.13 keV (110)

[0246] In the case of Compton scattering on free electrons, when E_g = 2 MeV, then e_b = E_Y/m_ec ² = 3.914. It thus follows from Eq. (108) that in the case (r_D ® r_e), E_e = 1.062 MeV. For E_g, E_g = 1.022 MeV, e_b = E_Y/m_ec² = 2, and it follows from Eq. (108) that E_e = 0.453 MeV. Therefore, the kinetic energy transfer to fuel nuclei (D) by energetic photons is much more efficient than by other energetic, light charged particles (c , e⁺), or by energetic, heavy charged particles (p, d, a).

[0247] Table III provides a comparison of the mean target nucleus recoil energy E_N in single elastic nonrelativistic projectile-target nucleus collision for various projectiles and at different projectile energies. In Table III, the target is always a deuteron nucleus ( m_N = m_d), and the calculation provides a numerical value for E_D (b_r « l).

TABLE III: MEAN DEUTERON RECOIL ENERGIES FOR SOME REACTIONS

[0248] Thus, it can be concluded that the kinetic energy transfer to fuel nuclei D by either energetic light charged particles (e⁺, e^~) or by energetic heavy charged particles ( p , d, a) is a very inefficient process unless there is a mechanism to increase the probability of large-angle scattering, such as via a decreased mean-free path by increased ion and electron densities.

[0249] V. NEUTRON ELASTIC SCATTERING ON DEUTERON NUCLEI

[0250] Since the deuteron nucleus possesses just a single (ground) energy level, the neutron scattering on the deuteron is an elastic scattering process if the energy of the neutron is below the disintegration of the deuteron by the neutron (the deuteron disintegration threshold by a neutron is K^^h = 3.4 MeV). In this case, it is known that the neutron elastic cross section o_sc(e_CM) is isotropic in CM (the center of mass frame), that is:

[0251] where 9_CM is the neutron scattered angle in the CM frame and o_sc is the total neutron elastic cross section. The scattering angle 9_iab in lab frame is related to 9_CM as:

m_d sin 9_CM

tan 9_tab = (112)

m_n + m_d · cos 9_CM

[0252] where m_n and m_d are the neutron and deuteron masses, respectively.

[0253] Since the scattered angles 9_CM and 9_iab are different, the angular distributions of scattered particles in the CM and lab frames are also different. However, the number of scattered particles in the corresponding solid angle d .(9_CM ) in the CM frame and in solid angle d .(9_iab ) in the lab frame must be the same:

°_sci^i_ab)dil{9i_ab) = a_sc(9_CM)dCl(9_CM ) (113)

[0254] However, dCl(9_CM) = 2p sin 9_CM and dCl(9i_ab) = 2p sin(0_;a¾) d9i_ab . Therefore, Eq. (113) becomes:

<r_sM_ab) sin (9_lab) d9_lab = a_sc(9_CM ) sin(0_CM) d9_CM (114)

[0255] With the help of Eq. (112), it follows from Eq. (114) that the angular distribution of scattered particles in the lab frame can be determined from the corresponding angular distribution of scattered particles in the CM frame as follows:

[0256] The relation between scattered neutron velocities v'_{n CM} in the CM frame and v'_n.i_ab in the lab frame is given by the formula:

m_r

v r

n,lab — V n,CM ' V CM’ ^VCM v_n (116)

m_n + m_d [0257] where v_CM is the CM frame velocity and v_n is the neutron velocity in the lab frame. Correspondingly, the relation between neutron and deuteron velocities V_U,CM and v_{d CM} in the CM frame and v_n and v_d in the lab frame are as follows:

= 0 (117)

[0258] Since the magnitude of neutron velocity in the CM frame does not change after collision (i.e., v'_{n CM} = v_{n CM}), it follows with the help of Eq. (116) and Eq. (117) that:

[0259] Rewriting Eq. (118) in terms of the neutron kinetic energy Kή after and the neutron kinetic energy K_n before the collision yields:

[0260] It is convenient to introduce the new parameter a_n by the following definition:

( m_d - m_n )²

a_n = (120)

(m_d + m_n

[0261] Then, in terms of the new parameter a_n, Eq. (119) is reduced to:

[0262] From Eq. (121), one skilled in the art will recognize that the kinetic energy Kή is in the following limits (0 < 0_CM < p) : a_n - K_n £ £ K_n (122) [0263] The probability distribution P(K_n ® K^) dK^ is, by definition, the probability that the neutron with initial kinetic energy K_n will acquire kinetic energy in the energy gap

+ dK^) after the collision. The probability that the neutron will be scattered in the interval ( 9_CM , 9_CM + d9_CM ) is given by:

[0264] where o_sc(9_CM) is the neutron differential elastic cross section and o_sc is the total neutron elastic cross section in the CM frame. It is clear that they are the same probabilities:

[0265] since for d9_CM > 0 ® dK^ > 0 , thus providing the positivity of the probability P{K_n ® K^) > 0.

[0266] From Eq. (121), it follows that:

[0267] Substitution of Eq. (125) into Eq. (124) yields:

[0268] Since the neutron elastic cross section o_sc(9_CM) is isotropic in the CM frame, then substitution of o_sc(9_CM) = o_sc/4n from Eq. (111) into Eq. (126) yields:

[0269] Therefore, the kinetic energy probability distribution P(K_nl is independent on K' in the whole interval ( a_n K_n

< K_n). [0270] VI. NEUTRON ENERGY LOSS IN ELASTIC COLLISIONS WITH

DEUTERON NUCLEI

[0271] By definition, the average neutron energy

after elastic collision is obtained by averaging
with the probability distribution P(K_n ® K^) given by Eq.

(127):

[0272] The average kinetic energy transferred from the neutron to the deuteron nucleus in an elastic collision is equal to K_n—

(see also Eq. (120)):

[0273] which is equal to one half of the maximum energy transfer in a head-on collision:

[0274] for a neutron projectile on a deuteron target nucleus, with the total elastic cross section of the order of:

a_sc~ 3 bn (25 meV £ K_n £ 2MeV) (131)

0275] Consequently, the kinetic energy transfer to fuel nuclei (D) by energetic neutrons is the most efficient process compared to energy transferred by energetic light charged particles (e⁺, e^~), by energetic heavy charged particles (p, d, a), or even by energetic photons.

Quote from THHuxleynew

Hot fusion results are reproducible, clear, theoretically understood, and scaling factors have got better (not worse) than expected.

They are not easily reproducible judging by the escalating expense and delays in ITER. I cannot judge how well they are understood theoretically, but if they were well understood, I doubt there would be so many delays.

Tokamak hot fusion is tremendously difficult to reproduce. It takes billions of dollars and hundreds of experts to make a Tokamak reactor. Saying it is "reproducible" is like saying thermonuclear fusion bombs are reproducible. Yes, even the North Koreans managed to do it, although the first ones they made barely worked. But no one would claim they are easy to reproduce, even though they are well understood fusion reactions.

Quote from THHuxleynew

CF results are unreproducible or unclear.

CF results are difficult to reproduce compared to some other experiments, but compared to Tokamaks they are dead easy. They are very, very clear. As clear as Lavoisier's calorimetry of 1780. And as irrefutable. So clear that any scientist living after 1780 should instantly understand the results must be real. You do not, of course, and neither did Morrison, but you have no rational or technical reasons. Just emotion. You also deny the laws of thermodynamics, perhaps without realizing that is what you do. You cannot accept thermodynamics and reject cold fusion. Cold fusion is predicated on those laws. If it is wrong, the laws must also be wrong, and heat can go from a cooler body to a hotter body after all.

Its an interesting way to catalog the info..

o charging = discharge

and use of alternative... then z-wave ,,cave ?.. ect knowing what it is.

interesting, but its today's world..

Should do it..