Posts by Jarek

    Nuclear force has range ~1fm ( https://en.wikipedia.org/wiki/Nuclear_force ) so for fusion we would need to take two protons to approximately this distance - Coulomb says that it would require ke *e*e/r ~ 1.4 MeV.
    However, the temperature in the core of our sun is said to be 15 million Kelvins ( https://en.wikipedia.org/wiki/Solar_core ), what means only ~1.4 keV thermal energy - it is thousand times smaller than required to get nuclei to 1fm distance, could only get to 1pm distance.


    How is it explained that it is sufficient for fusion? If just as "tunneling", it should be compatible with Boltzmann distribution - giving ~exp(-1000) ~ 10^-435 scale of probability.
    Maybe it is already required to consider electron-assistance here: that there is electron remaining between the two collapsing nuclei?

    As Jarek ( and many papers) pointed too: An external field (shaped electron "cloud") may be able to polarize the nucleus, this might slightly change/ (de-) polarize the internal trajectories of so called B-electrons, which are assumed to be "banging around" inside the nucleus.


    I don't think electrons can "bang inside" a nucleus: while the largest diameter of nucleus is ~15fm, Lorentz force bends the trajectory of free-falling electron making the minimal distance ~100fm.
    This distance is sufficient for nuclear forces e.g. to capture electron or give it some energy in internal conversion, but not to directly enter the nucleus.


    I think I see where you’re going with this now. According to QM, the degrees of freedom of a nucleus are quantized. The speed of rotation, the number and energy of any nuclear phonons, the potential energy latent in arrangements of nucleons above the ground state, etc., all correspond to distinct energy levels of the nucleus. This picture does not seem to leave open the possibility of a kind of white noise that perturbations from orbital electrons could build on top of in order to move a nucleus into a higher energy level through some kind of stochastic resonance. Perhaps zero point energy provides such a noise floor. This is not an area where I can speak from a position of knowledge.


    The quantization corresponds to a discrete set of (dynamical) metastable states: local minima separated by energy barriers.
    For atomic orbitals, like in Couder's picture, the quantized states correspond to resonance with the field to get a standing wave to avoid bremsstrahlung.
    Changing the (dynamical equilibrium) state is rapid but not instant (e.g. delay in photoemission)


    For nucleus I also believe that we can ask about dynamics hidden behind effective quantum description (expanding liquid drop model) - some dynamical structure of fields, with a complex landscape of local minima - states between which we observe as transitions.
    The mainstream view is that we need some QFT to describe it - as there is a varying number of particles in this never-ending series of creations and annihilations of e.g. interaction bosons.
    However, there is also an alternative way to describe a varying number of particles: classical field theory with solitons (nonlinear) - it also supports varying number of particles.
    I believe there is a correspondence between classical FT with solitons and QFT - we could calculate effective parameters describing interactions of solitons and insert them into Feynman diagrams of perturbative QFT ... however, this is really hard to calculate.


    Anyway, I imagine nucleus as a (dynamical) spatial structure of a field - I have some candidate (it explains e.g. why proton is lighter than neutron, deuteron than p+n: because baryon structure requires some positive charge (less than e) - neutron has to compensate it what is costly, in deuteron baryons share the positive charge), but I am not insisting on the details.
    Transiting between its states is rapid (not instant) and due to Noether theorem it has to release the energy (and momentum and angular momentum) difference - as gamma.
    It is really surprising that these photons cannot disperse - have to be localized (be soliton).
    For optical photons my intuition for its reason is the angular momentum - they are created from changing spin of electron e.g. from -1/2 to +1/2: by rotation 180 deg.
    This rotation creates photons as twisting wave like behind marine propeller - in contrast to water, they don't disperse because EM field has no viscosity.


    For nucleus again the angular momentum might be what prevents this energy in EM field from dispersing.
    But there might be nuclear processes without any twisting, like symmetric p-e-p collapse. This symmetry should be maintained for the EM wave carrying the energy difference - no angular momentum preventing photon from dispersing its energy.


    Regarding experimental evidence - such EM impulse would convert this energy into thermal energy of surrounding atoms - it seems extremely difficult do directly detect.
    So lots of LENR claims: with silent detectors but excess heat might be seen as such experimental evidence.

    Regarding lack of gammas, you have written about 10MeVs - you would need a really long cascade of gammas (requiring semi-stable states of nucleus), electron of this scale from e.g. internal conversion would also be well seen, e.g. from bremsstrahlung gammas it would produce.


    What do you think about releasing this energy in a form of a less localized form - gammas "maintain their shape" while traveling, so technically they are solitons of EM field.
    Why this energy couldn't be released in a form of e.g. cylindrically-symmetric EM wave, like from line antenna - such wave would disperse this energy in 1/r way, converting it into local thermal energy.


    Regarding me being "a fan of Gryzinski", it is much more complex. So much earlier (~2008) I was working on Maximal Entropy Random Walk (MERW, my physics PhD) - showing that thermally perturbed trajectories average to quantum probability distributions (MERW has started in my physics MSc alongside ANS coding your data is written with if you use Apple or Facebook).
    MERW has also lead me to the question of the structure of particles (~2009), which should start with the question of charge quantization - it has a natural analogue in mathematics: topological charge. Using such picture for electron (started by Manfried Faber), a qualitatively trivial model (vector field with e.g. (||v||^2 - 1)^2 Higgs potential) recreates electrons as the simplest charges - with quantization, pair creation/annihilation, finite energy of charge (infinite for point charge), Coulomb force and the rest of electromagnetism. I have expanded it other particles and nuclei (slides, essay).


    Anyway, we finally need concrete trajectories for these solitons/electrons ... which in time average to quantum statistics due to MERW - and I know only Gryzinski who has made a solid work here - basing on agreement with experiments, many on them. But I am open for other reasonable approaches (?)
    His model doesn't cover the structure of nucleus (and he believed neutron was proton with electron, I disagree with) - I rather use intuitions from my model here, but only for this possibility of radiating energy as cylindrically-symmetric EM wave.


    Regarding shocks from PHz electron passing in ~10^-13m distance, it doesn't transfer energy, just kicks the structure of nucleus, shake it to speed up finding energy minimum.
    This nucleus can release abundant energy, what means it is in a local energy minimum, but there is a lower energy minimum behind a barrier.
    A single kick from the passing electron is not sufficient to cross this energy barrier, but many of them can help crossing it (decay), like in stochastic resonance ( https://en.wikipedia.org/wiki/Stochastic_resonance ).


    Regarding the webpage you cite ( http://math.ucr.edu/home/baez/…dNuclear/decay_rates.html ), it mainly discusses electron capture, but there is also:
    "A 1996 paper discusses this bound-state decay of bare-nucleus
    rhenium-187. Whereas neutral rhenium-187 has a half-life of 42 ×
    10^9 years, the authors measured fully ionised rhenium-187 to have a half life
    of just 33 years! They discuss the cosmological implications of the altered half
    life of rhenium-187 in various degrees of ionisation in stellar interiors, and what that
    implies for our knowledge of galactic ages."
    which surprisingly has an opposite effect - the presence of electrons prevents from decay - I will have to think about it, but these kicks from passing electron could have also stabilizing effect e.g. through a resonance: decay may require change of the frequency, while the regular kicks can stabilize nucleus in a different frequency.

    The lack of gammas is a big objection.
    As for fusion, EM impulse might be the answer: that instead of releasing the energy as EM soliton (gamma), the EM wave could have a different shape, e.g. a cylindrically-symmetric shape like in line antenna, dispersing the energy with 1/r.
    Or maybe nuclear processes could radiate energy in non-quantized portions, e.g. maintaining the power (released energy per second) for a longer time, instead or radiating it in nearly immediate steps (? spatial explanation seems more likely for me).


    Regarding mechanism for indirect action of shell electron on the nucleus, these frequent (~petahertz) electric and magnetic shocks from electrons passing in ~10^-13m distance seem quite a shaking of the nucleus - might be crucial for rate of releasing abundant energy.


    There is documented difference of rate for electron capture while ionizing the atom - are there more processes with observed such difference (nuclear process being affected by shell electrons) ?

    I don't have experience with such unconvential fission, alpha, beta ... but their standard versions are well seen in detectors.
    I understand it is not seen? What is experimental evidence of such events? Only excess heat?


    Regarding electrons affecting nuclear processes, free-fall atomic model has an interesting third option: it says that electrons are passing in ~femtometer distance from nucleus, ~10^15 times per second.
    Each such passing is a shock to the structure of nucleus from the huge electric and magnetic field of electron - such regular shocks might induce some internal process in nucleus, e.g. through stochastic resonance: https://en.m.wikipedia.org/wiki/Stochastic_resonance

    In the case of alpha decay/fission, there is in fact a Coulomb barrier that needs to be crossed, but from the other direction: the alpha particle must tunnel through the Coulomb barrier of the daughter nucleus, from the inside. The idea is that this process can be enhanced appreciably through electron screening. Alpha decay and fission are particularly sensitive to the width of the Coulomb barrier, and screening decreases that width and hence increases the tunneling rate.


    These are just fission, alpha and beta decay - a natural tendency of some isotopes to spontaneously release energy ... these seem to be conventional nuclear energy sources?


    By (screening) you mean that the presence of electron cloud affects the rate of these reactions?
    In other words, ionization of atoms reduces the rate.
    It is what they observe for electron capture: https://en.wikipedia.org/wiki/…_capture#Reaction_details
    "The electron that is captured is one of the atom's own electrons, and not a new, incoming electron, as might be suggested by the way the above
    reactions are written. Radioactive isotopes that decay by pure electron capture can be inhibited from radioactive decay if they are fully ionized ("stripped" is sometimes used to describe such ions). "


    So one reason might be presence of electrons traveling very close to the nucleus.
    A different reason can be indeed the screening - ionized atom is positive, attracting negatively charged particles.

    So please give an example of sequence of LENR reactions which could lead to a practical energy source without: fusion, crossing the Coulomb barrier, or just using decay of some isotopes (used e.g. to power satellites) ?

    The only thing what must be answered (hen egg problem): Is there first a current or the collapse or is it all together a well synchronized cascading event!


    As we agree that QM describes dynamical equilibrium, which is not the case here - we need to ask about concrete trajectories of electron to understand hypothetical CF.
    This trajectory is mainly affected by the Coulomb force - getting Kepler orbits in first approximation.
    As we have discussed, there are many arguments that these are very low angular momentum Kepler orbits (e.g. electron capture, magnetic dipole moment of atom, Helbig-Everhart scattering resonances etc.) - these are ellipses degenerated into nearly lines coming from the nucleus.
    There is some probability that another nucleus will be incoming from the direction of such very flat ellipse - if they are able to hold this electron during the collapse, they can get close enough for fusion.
    Earlier, to avoid torque from spin-spin interaction, they should align their spins.


    So this is a well synchronized three body event.

    As Hagelstein rightly says, the challenge is more about explaining the lack of expected radiations than how to achieve fusion.


    Their difficulty is hard to compare ;-) ... both crossing the Coulomb barrier and nearly lack of observed radiation needs to be explained, understood.


    In earlier posts of this thread you can find my proposal to explain this lack of radiation, e.g. first post here: Electron-assisted fusion
    So assuming CF if true, I believe we need e.g. p - e - p three body collapse: similar charge behavior like in linear antenna.
    They should earlier align their spins, getting a system with cylindrical symmetry - maintaining this symmetry while the collapse, the released energy should have also a form of a cylindrically symmetric EM impulse.
    The trick is instead of producing localized EM wave (gamma) - maintaining localized energy, release this energy in cylindrically-symmetric EM wave: which disperse this energy as 1/r - heating up a small neighborhood.



    Here are some cylindrically-symmetric EM waves from linear antenna ( http://ocw.upm.es/teoria-de-la…nnas_athens09_tuesday.pdf ) :

    Why the released energy has always to be produced as localized EM soliton (gamma)?
    Why releasing this energy in cylindrically-symmetric collapse, the result cannot be such cylindrically-symmetric EM wave? ... solving the Hagelstein's problem.


    Quote

    QM-electron (probability-) clouds are only useful in statistical environments, i.e. systems near equilibrium conditions. The formalism was not invented to handle sudden multidimensional changes. (...) They call this short period just tunneling... (= lack of explanation...)


    I completely agree here - QM describes dynamical equilibrium, we need a more suitable description for rapid changes - asking for the actual trajectory of electron.

    I thought there is this large interest in LENR becouse of bringing hope for amazing power source ... where I think we agree that


    1. We need fusion,
    2. Which needs crossing the Coulomb barrier (going through neutrons is nonrealistic),
    3. For which the only realistic explaination for being statistically non-negligible is electron staying between the two nuclei,
    4. For electron staying between two nuclei down to femtometer scale we need to ask about its trajectory - quantum probability clouds are not sufficiently localized.


    Do we agree here?

    Eric, regarding me being fixed on electron remaining between the two nuclei as the only reasonable explanation for hypothetical fusion in 1000K, so we had 260 posts in this thread and I honestly haven't seen any other reasonable explanation here (?)
    Chemistry, charge concentration, screening, topological defects etc. might be sufficient for taking two nuclei to picometer distance ... but fusion requires thousand times smaller distance, and so thousand times larger energy (V ~ 1/r).
    This is just far beyond such "electron-cloud-related" explanations - it is a completely different energy scale.
    If it's impossible for an electron to stay between the two nuclei, for this moment I don't see fusion in 1000K realistic - especially that it's hard to believe that nearly 30 years is not sufficient to get a single really clear demonstration.


    Regarding effective asymptotic treatment of atom as effective multipole, this is only one of many ways that can be used to test models of atoms in various scattering experiments.
    Scattering is nearly a direct way to ask nature about the structure of atom, and various scattering scenarios was the basic way for Gryzinski to infer and test his model - these his papers have >2000 citations: https://scholar.google.pl/scholar?hl=en&q=gryzinski

    Ok, as the title says, I am focusing here on fusion. Other nuclear reactions have different issues, but the main goal and claims are LENR as amazing energy source - I cannot imagine without fusion and crossing the Coulomb barrier (?)


    To your point about the asymptotic screening of the nucleus on the part of bound electrons, this is an interesting and valuable observation. I’ll add to it that what presents a barrier to the breakup of a nucleus by fission or alpha decay is not the core nuclear charge, but the Coulomb barrier, which surrounds the nucleus like a sheath that extends some picometers out. Hence the suspicion it is there (outside of the nucleus) that screening would need to take place for breakup to occur.


    We might take from your observation, however, the thought that perhaps beta decay processes, which require overlap of any electron charge with the nucleus itself (and not just the Coulomb barrier, outside of the nucleus) will be more likely with lighter nuclei unstable to beta decay/electron capture and less likely, all else being equal, with heavier nuclei.


    The best way to experimentally test effective asymptotic view of atoms as electric multipoles (static + oscillating) is exactly through scattering with low energy electrons - they are charged and very light.
    It was introduced not by me, but in Gryzinski's 1970 paper ( http://journals.aps.org/prl/ab…10.1103/PhysRevLett.24.45 , then extended in his 1975 papers) as classical explanation for Ramsauer effect, which was previously believed to be purely quantum ( https://en.wikipedia.org/wiki/…r%E2%80%93Townsend_effect )



    However, this is only asymptotic behavior - while crossing from pico- to femto-meter distance, which is the most crucial during nuclear fusion, the electron cloud of a given atom becomes nearly negligible - the incoming particle feels practically only the charge of the nucleus ... unless there is electron staying between them.


    To support that, I have cited the screening coefficients for shell electrons:
    Z_eff = Z - s

    As you can see - this screening quickly drops with the distance (shell number) from nucleus: for 1s orbital, the screening is between 1 and 2. So dozens of electrons in such atom, are felt by 1s electron as just a ~2 elementary charges.
    And 1s electron is ~10^-10m distance - getting to femtometer distance, this screening goes to practically 0.
    This vanishing of screening is a consequence of the shell theorem: https://en.wikipedia.org/wiki/Shell_theorem


    So screening of shell electrons is practically negligible during the most crucial part of fusion process (pico->femtomemter, Coulomb potential says that you need 1000x more energy to get to 1fm than to 1pm).
    The only hope for fusion in 1000K is that a single electron stays between these two collapsing nuclei.

    Sure, the assumption of spherical density has lots of disagreements with reality.
    Effectively, this nonsymmetry can be asymptotically described by higher electric moments (dipole, quadrupole, octupole) and their oscillations - what is the base of later Gryzinski's scattering models, e.g. explaining the Ramsauer effect ( https://en.wikipedia.org/wiki/…r%E2%80%93Townsend_effect ).


    However, average electron-nucleus distance is relatively large (~10^-10m), and orbitals focus on dynamical equilibrium - which is greatly affected by the incoming second nucleus, which needs to get to 10^-15m distance, where any interaction with shell electrons becomes nearly negligible.

    Eric,
    1) if you want high concentration of electrons, you can have a few dozens of them in a large atom - does increasing Z make LENR more probable?
    These electrons effectively screen the charge of nucleus down to zero ... but only asymptotically (and electric dipole/qudrupole/octupole may remain). While getting really close, this screening drops down to zero ( https://en.wikipedia.org/wiki/Shell_theorem ) - making essential only the single electron which remains between the two nuclei.

    Anions can have stronger screening, but again only asymptotically - it doesn't help when the two nuclei are really close.
    Electron concentration might be helpful in some initial stage, but the most of assistance is required in the final state - when the nuclei approach ~10^-15m distance so that nuclear force could take from here - in such distances there is just no place for a second electron due to tiny mass and huge Coulomb force.

    2) Applying external magnetic or electric field perturbs the dynamical equilibrium (Zeeman, Stark). Classically, the electron orbits became a bit shifted, and Gryzinski claims nearly perfect agreement for such calculations of diamagnetic properties ( http://www.sciencedirect.com/s…icle/pii/0304885387903337 for He, Ne, Ar, NaCl, KCl and CaCl2).
    Anyway, we are talking here about eV-scale of changes - very far from the required for nuclear transitions.


    3,4) I see you are talking about more general LENR, while I was thinking about the ones finally leading to excess energy - not from radioactive isotopes or fission.
    Neglecting situations with 782keVs for going through neutron, such excess energy requires crossing the Coulomb barrier - what, if true, requires electron staying between the nuclei for a sufficient time.


    Electron concentration, high energy electrons, external field applied, van der Waals force etc. might have some influence on the initial state.
    But the energy of Coulomb barrier is 1/r: crossing the last femtometers require more energy than getting to 10fm distance - this final state is the most crucial, and electron between the two nuclei seems the only factor which could really help.

    1. Electrons avoid concentration due to Coulomb repulsion ... assuming you could get 10x energy this way (flying hamster...), you just got from 0.1eV to 1eV scale ...
    2. Where this dynamic condition comes from?
    3. Sure beta decay is a good source for high energy electrons, but you need specific isotopes to produce it ... and such electrons produce high energy gammas ...
    4. Ok, some of these electron, you need a concrete source for, could allow for 3He + e -> t ... but still: so what? How tritium helps you with fusion?
    If you would like to fuse it with a different nucleus, you would still need to cross the Coulomb barrier ...


    The role of electrons is definitely crucial if LENR is true, but it's not about their high energy (unless reaching 782eV) or high concentration - high energy electron just pass by nucleus, high concentration of electrons repel each other.
    If true, LENR is an act of three actors: two nuclei and a low energy electron - attracted by both of them, what should be sufficient to stay for a long enough time near these sources of attraction, with noneligible probability.

    An other guy who investigated some aspects of electron resonances is heffner : mtaonline.net/~hheffner/DeflationFusion2.pdf


    He is writing exactly what this thread was supposed to be about (electron-assisted fusion):
    "D + e- + D ---> He + e- + energy
    D + e- + D ---> T + p + e- + energy
    D + e- + D ---> 3He + n + e- + energy"
    However, he hides electron dynamics behind "tunneling", "wavefunciton collapse" - these are popular QM terms used when we don't know what's happening there - we need to understand this hidden dynamics, finally calculate probabilities of such events.
    Eventually, he could present some quantum calculations, but I don't see anything like that in this paper.

    The question of induced beta decay reactions (including electron capture) involves a different but similarly interesting thought experiment. Re the p + e → n reaction, I find this one unlikely for the reason you mention. But what about 3He + e → t, which requires only ~ 19 keV?


    I have to admit that I still don't understand ...
    In 1000K for LENR, thermal average energy is below 0.1eV ... while 19keV indeed looks better than 782keV ... it still seems extremely unlikely, and I completely don't understand how tritium could help? You would still need crossing the Coulomb barrier to fuse it with a different nuclei.
    Could you give an example of the entire sequence (leading to excessive energy from nuclear reactions in ~1000K)?


    The only way to avoid crossing the Coulomb barrier I can imagine here is going through something neutral like neutron - but it would require investing these unimaginable large 782keV energy ... or dineutron, but it so exotic that it seems we probably don't even know its mass or lifetime: https://en.wikipedia.org/w/index.php?title=Dineutron


    So currently I don't see a way for realistic LENR without crossing the Coulomb barrier - and the only way for doing it seems by using assistance of electrons.
    And if radial trajectories of electrons dominate, Gryzinski has gathered dozens of arguments for, it seems reasonable that such radial trajectory "jumps" between the two nuclei for a sufficient time - Gryzinski has been considering this kind of trajectories for molecular bonds earlier and so 27th April 1989 he was able to publish response in Nature to F&P (23rd March): http://www.nature.com/nature/j…38/n6218/pdf/338712a0.pdf
    He has started working on CF back then, mentions some calculations in his book, but I couldn't get anything concrete.


    Here is his 1990 New Energy Times comment: http://newenergytimes.com/v2/archives/fic/F/F199007.PDF
    1991 theory conference, but I couldn't find text: http://adsabs.harvard.edu/abs/1991AIPC..228..717G
    4 papers here, but I could get only 1: http://www.ibiblio.org/pub/aca…sion/wais/cold-fusion.cat

    Wyttenbach,
    GUT is for explaining everything, while here we have a different case: in a situation covered by a given theory, it provides wrong predictions.
    Like predicting lack of shielding of inner shells by outer shells, or forbidding electron capture - these fundamentally wrong predictions make this theory just wrong.


    Regarding staying between two nuclei, here we just have a series of successive scatterings - electron falls on one nucleus with nearly zero angular momentum, scatters back nearly 180 deg (also in pure Kepler), falls on the second nucleus and so on - staying between them, screening their repulsion.
    There is absolutely no magic in such explanation, no additional resonances needed (resonances are for stable systems like atoms) - just asking about trajectory of electron.


    Eric, could you elaborate?
    I thought we are talking about e.g. nickel nuclei absorbing protons from hydrogen?
    How would you like to avoid crossing the Coulomb barrier here by induced alpha or beta decay, or induced fission?
    There is hypothesized p + e -> n reaction, but it requires to invest ~782keV first, which seems completely unachievable to localize in this point using only chemical or mechanical ways (?)

    I don't have access to this book of Ryde -
    does its experimental results agree with quantum predictions (equally spaced lines for Lyman gamma: 4 -> 1)
    or rather with Frerichs 1934 results (external lines are closer than predicted by QM)?


    Regarding Mills, I don't know about Stark, but the screening constant from my previous post is another clear argument against Bohr and Mills: outer shell electrons screen charge of nucleus for inner shell electrons.
    If electrons would stay in a circle or sphere, the shell theorem says that there would be no screening from outer shells: https://en.wikipedia.org/wiki/Shell_theorem


    Regarding LENR, it requires to understand how electron could stay between the two nuclei for a long enough time to screen the Coulomb barrier (like symmetric p - e - p initial system collapsing into deuteron) - it requires understanding dynamics of electrons inside atom - what we are currently discussing: should we be satisfied with quantum probability clouds (making LENR practically impossible), or maybe we can also ask for electron trajectories behind them - which average to these density clouds?
    How these trajectories shouo look like?
    Bohr's are excluded by many arguments, for example electron capture, magnetic dipole moment of hydrogen (orbital angular momentum), these screening constants ...
    Are low angular momentum (Gryzinski) also excluded?
    If they are allowed by experiments, such electrons could stay for a longer time between two nuclei - allowing for LENR.

    I hope the discussion about a magical membrane has ended here once for all ...


    Let's go back to real physics - screening constant.
    Gryzinski has written that in contrast to his classical calculations, QM has a real problem to get it right: http://gryzinski.republika.pl/teor6ang.html
    I a trying to test it against the physicsforum:
    https://www.physicsforums.com/…ants-slater-rules.887322/
    (the Stark problem remains unresolved there: https://www.physicsforums.com/…ory-vs-experiment.885330/ )


    "In multiple-electron atoms the effective charge of nucleus for a given electron, is reduced by the presence of other electrons (including those from more external shells, against the shell theorem):
    Z_eff = Z - s
    where the screening constant s depends on Z and the concerning orbital. It is usually calculated by semi-empirical so called Slater's rules: https://en.wikipedia.org/wiki/Slater%27s_rules


    I have tried to find some experimental values.
    On page 286 of 1936 English translation of Arnold Sommerfeld's "Atomic structure and spectral lines" there is a clear figure (on the left below) with dots suggesting experimental values (but I couldn't find it being explicitly written).
    Wikipedia article cites 1967 "Atomic Screening Constants from SCF Functions. II. Atoms with 37 to 86 Electrons" by Clementi, Raimondi, Reinhardt ( http://scitation.aip.org/conte…cp/47/4/10.1063/1.1712084 ) which contains Hartee-Fock calculations of screening constants (figure on the right) - unfortunately it doesn't seem to refer to any experiment (?)



    These two figures have some essential differences (including order!) - could anybody refer to some better experimental results?"