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128) Screening or something else?

Ludwik Kowalski (2/13/04)
Department of Mathematical Sciences
Montclair State University, Upper Montclair, NJ, 07043

Steven Jones thinks that the D+D coulomb barrier for ions embedded in metals may be lowered significantly due to the phenomenon of screening. This, he wrote to me in private, has been confirmed by a large team of German scientists [F. Raiola et al., European Physical Journal A (13:377-382, 202)]. I should read this article when I find it. It reminded me the paper of Kasagi mentioned in the unit #17. Fortunately, the site has a paper that Kasagi presented at the 7th International Conference on Cold Fusion. I downloaded this paper [J. Kasagi et al., “Anomalously Enhanced D(d,p)T Reaction in Pd and PdO Observed at Very-Low-Energy Bombardments.”] and read it critically. Here are my comments:

1) The idea of studying the enhancement of D(d,p)T cross section at very low energies in metals is great. Unfortunately, I have no access to earlier publications of Kasagi in which procedural details are said to be described in more details. What I have is not sufficient to be convinced.

2) The experiment was performed by using a thick target (d beam is stopped). Protons were counted by using the dE-E telescope of Si detectors; the first detector was only 50 microns thin. (Detectors of such thickness were not available when I was an active researcher.) Why the observed energy spectra of protons are not shown in the paper?

3) The target was thick and a large fraction protons was certainly not detectable. That fraction was energy-dependent; the lower the beam energy the larger the fraction. Some kind of procedure must have been used to correct for this effect. But I did not see the description of their procedure. Should I rule out a possibility that the so-called “enhancement” is due to the overcorrecting?

4) As indicated by the authors, the target itself (concentration of deuterons in metal) was not stable. This was probably due to large current beams (needed to observe rare protons). Is it conceivable that the so-called “enhancement” is due to target instabilities. The authors recognize this possibility and mention another possible source of a systematic error; the assume values of dE/dx for protons and deuterons at very small energies.

5) In the resume of Kasagi’s paper, presented at the 10th International Conference on Cold Fusion, I see a statement that screening alone is not sufficient to explain the enhancements. Some other phenomena, the authors say, must also be contributing.

6) I suppose that Raiola’s team was familiar with papers published by Kasagi’s team. It will be interesting to see what Raiola thinks about Kasagi’s papers.

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What is not possible in plasma (ionized gas), some say, might be possible in condensed matter. Let me illustrate this in terms of a coulomb barrier that prevents two ions from fusing at an ordinary temperature. To produce fusion in a gas one has two well known options: to increase the temperatures to millions of degrees or to electrically accelerate one of the ions. In a solid however one might imagine some additional scenarios. One of them is screening of positive ions by negative electrons, as suggested by Jones. And another is to produce some kind of a collective effect. Can the energy needed to overcome the coulomb barrier be supplied (to a pair of embedded ions) from atoms surrounding them? If the total number of contributing atoms is one billion, for example, then only 0.001 eV of energy per atom would provide 1 MeV needed to produce fusion. That is my naive way of understanding arguments presented in some theoretical papers. I am referring to papers presented by S, Chubb T.Chubb and P. Hegelstein at the 10th International Conference on Cold Fusion. (More recent papers of these authors are going to be presented at the March 2004 meeting of American Physical Society. The abstracts can be seen at the APS web site )

Not having an accepted theory is the major weakness of those who investigate various cold fusion (CF) fields. But arguments about models should not be confused with arguments about the validity of experimental data. It is worth recalling that no theoretical model existed when excess heat from radium was discovered by Pierre Curie. The discovery of neutrinos, on the other hand, followed the opposite path; the existence of these hard to detect particles was first predicted theoretically and then confirmed via experimental investigations. Pauli’s prediction, however, was triggered by calorimetric measurements of heat released in beta decay.

The major argument of those who rejected CF claims in 1989 was the fact that these claims could not be explained in terms of the accepted model of nuclear reactions. I think that it is OK to reject a model of a physical phenomenon on the basis of a conflict with experimental data but it is not OK to reject experimental data on the basis of a conflict with the model. Physical reality is much richer than man-made models. But that is a philosophical statement. In practice experimental findings conflicting with confirmed theories, as in the case of CF, should be scrutinized very carefully before being accepted.

In reading Kasagi’s paper I noticed that A. Lipson, from Russian Academy of Sciences, was one of the coauthors. Like Jones, Lipson et al. demonstrated that 3 MeV protons are emitted from metallic foils loaded with hydrogen. In their setup protons were accompanied by alpha particles. That investigation has already been described in the unit # 28. Another investigation of Lipson et al., was presented at the 10th International Conference on Cold Fusion. The major tool in that study was the glow discharge chamber of Karabut et al. (already described in the unit #13). The main question was “how does the rate of emission of charged particles depend on the applied voltage?” These particles were detected with CR-39 detectors placed inside the chamber. The paper, entitled “Enhancement of DD-reaction Accompanied by X-ray Generation in a Pulsed Low Voltage High-Current Deuterium Glow Discharge with a Ti-Cathode,” can be downloaded from the ICFF10 folder at

Here is the abstract of that paper: “Using noiseless solid state plastic track detectors (CR-39) and Al2O3:C thermo-luminescent (TLD) detectors, the yields of 3.0 MeV protons (from DD-reaction) and soft X-ray photons emitted from the cathode are studied in the pulsing-periodic deuterium glow discharge with Ti-cathode at low discharge voltages (ranging of 0.8-2.5 kV) and high current density (300 – 600 mA/cm2). Analysis of DD-proton yield versus accelerating voltages, allowed to estimate the deuteron screening potential value Us at the deuteron energy range of 0.8 < Ed < 2.45 keV. It was found a strong DD-reaction enhancement in glow discharge (the effective screening potential Ue = 610 ±150 eV) compared to that for accelerator experiments at higher deuteron energies (Elab >2.5 keV) and lower beam current density (50- 500 microA/cm2). X-ray measurements showed an intensive (Ix = 1013-1014 s-1-cm-2) soft X-ray emission (with a mean energy of quantum Ex = 1.2-1.5 keV) directly from the Ti cathode. The X-ray yield is strongly dependent on a deuterium diffusivity in the near -- the -- surface layer of cathode.”

Note that the energy range at which the D(d,p)T reaction was studied (down to 0.8 keV) is below the range explored , with traditional accelerators. Nine references to studies conducted by using accelerators are made by Lipson et. al. The authors emphasize that studies of reaction yields at very low bombarding energies are highly significant in the context of astrophysical and thermonuclear processes. Such investigations seem to bridge a gap between cold fusion and traditional nuclear physics. The authors show that at the bombarding energy of 1 keV the number of 3 MeV protons is by nine orders of magnitude higher than theoretically expected. This refers to deuterons embedded in a Ti cathode and to a theory which agrees with experimental data at higher energies. In other words, the authors show that the accepted theory is not necessarily valid at very low energies and when targeted nuclei are not free to recoil, as they are in a hot plasma. The authors argue that the observed enhancement of the D(d,p)T reaction cross section is consistent with the assumption that the coulomb barrier is lowered by 0.61 keV, for example, due to the screening by electrons.

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But what is screening?
How can all this be made meaningful to students in an introductory physics course? The concept of the coulomb barrier has already been described in the unit #40. To explain screening I would ask students to consider the following problem. Place two deuterons on the x axis, one at the origin and another at a distance x along the positive direction. Treat the second deuteron as a probe charge and calculate the electric potential as a function of x. This gives the familiar 1/x curve. If the attractive nuclear potential is very large at x<3 F and zero at all larger distances then the coulomb barrier is the same as the value of the electric potential at x=3. It is equal to 480 kV. Now place an electron at x=-5 F. The coulomb barrier is still electric potential at the location x=3 F. But it is now due to two point charges: the deuteron at x=0 and the electron at x=-5 F. The answer is 300 kV. Repeat the exercise when x2=-2 F. This time the coulomb barrier is 192 kV. Repeat it again to see the the coulomb barrier becomes zero when x2=0 (as one would expect without any calculations).

This simple numerical exercise is sufficient to convince students that presence of an electron,somewhere outside the two deuterons, has the effect on the coulomb barrier. Closer the electron smaller the barrier. Presence of two or more elections, as one can easily verify, would further reduce the coulomb barrier. This electric effect is can be called screening. Note that the value of x=3 was chosen because the range of nuclear forces was assumed to be 3 Fermis. The coulomb barriers would be considerably lower if the range of nuclear forces were larger. For the range of 4 fermis, for example, the coulomb barriers (with x2=-5 and -2 F) would be 200 and 120 kV, respectively. Even without screening the coulomb barrier would be 360 kV (with the range of 4 F) instead of 480 kV (with the range of 3 F).

It is clear that small distances between electrons and deuterons are extremely rare in a low pressure gas (plasma). But in condensed matter average distances between atoms are much shorter and a possibility of screening can be envisaged, especially in some metals. It is well known that in metals not all electrons orbit around atomic nuclei. It is possible to speculate that clouds of electrons are formed in some regions of metallic structures, perhaps near the boundaries of microcrystals where the D ions are trapped? Billions of Ti atoms would be involved to keep them there. Conditions for forming electron configurations which lower coulomb barriers significantly are probably rare. In some places the lowering of coulomb barriers might be very small in other it can be very large. According to Lipson et al., the average coulomb barrier lowering, in Ti, is about 0.6 kV. This is a small fraction of the two-body barrier, such as 200 kV. It is counterintuitive to think that by reducing the barrier from 200 to 199.4 kV, for example, one could increase the proton emission rate by the factor of one billion, as reported in the paper. But why should my intuition be trusted in the field about which I know so little? The purpose of this essay is nothing more than to clarify the meaning of the term “screening.”

It should be clear that one-dimensional setups of charges, and an arbitrarily chosen shape of the nuclear potential (rectangular with a given range, such as 3 F or 4 F) are not reliable for calculating coulomb barriers with or without screening. But they are sufficient to explain what screening is. To estimate the height of the coulomb barrier, without screening, one should look at the energy dependence of fusion cross sections. Most nuclear physics textbooks would show such experimental data. I am now looking at the curves for the DD reactions. They tell me that the coulomb barrier is probably omewher between 100 kV and 200 kV. The yields of neutrons and protons decrease very rapidly when kinetic energies of relative motion are less than 50 keV. (That is why thermonuclear reactions in gasses are studied at extremely high temperatures.)

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Here is a message, inspired by the above, that I just posted on the Phys-L list.

1) In electrostatic you might ask students to estimate the coulomb barrier preventing positive D ions from fusing at low temperatures. Here is my suggestion. First tell students that in addition to repulsive forces the ions attract each other by very strong nuclear forces. But these forces do not obey the 1/r^2 law. They are negligibly small when r is above a distance R (called range). For x<R the attractive nuclear forces are much larger than repulsive electric forces. That would be a sufficient justification for defining the coulomb barrier, CB, as the value of the electric potential at x=R.

The rest is trivial. Assume that R=3 F, for example, and calculate the CB. Note that F is the unit of length (femtometer or 10^-15 m). My answers were 480 kV and 360 kV, at R=3 F and 4 F, respectively. Depending on your predisposition, you may or may not like linking this problem with the cold fusion controversy.

2) If you do like this idea then consider addressing the screening effect. Some scientists say that screening is possible when D ions are embedded in metals, such as Pd or Ti. Simply stated, and without trying to argue about what causes screening (local clouds of electrons at crystal’s boundaries?) one can simply declare: screening consists of lowering of the coulomb barrier by nearby electrons.

To illustrate screening do the following. Place one deuteron at x=0 at treat the other deuteron, at x>0, as a probe charge. That is what I did to calculate coulomb barriers. Then place an electron at some negative value of x, for example, -2 F. The CB is now V=V1 + V2 (where V1 is the positive part due to the deuteron and negative V2 is the negative part due the electron). You will see that CB approaches zero when electron is approaching the origin, as it should be. My answer, for R=4 F, was CB=120 kV for the electron placed at x=-2 F. And nothing prevents you from introducing more than one screening electron.

Suppose a single electron at x=10 A =100000 F is replaced by a negative particle of variable charge. Assuming R=4 F, how does the magnitude of the negative charge affect the coulomb barrier? It turns out that the charge of only 250000*e is sufficient to eliminate the coulomb barrier. Here my results;

charge in 10^5*e QB in kV
2.1 0.0015
2.0 72
1.0 216
0.5 288
0.1 346
0.01 358
0.00 360 (an ideal two-body barrier)

I find them shocking. First because the distance of 10 A is about ten times larger than the distance between atoms in most metals. And second because the number of electrons needed to eliminate the barrier (for that distance) is a negligible fraction of free electrons in each cubic micron. But not being a solid state physicist I do not know how to explain the postulated clustering of free electrons.

4) Yes, I know that three or more particles would usually not be at rest on the x axis. And I know that the nuclear potential is not a rectangular well. My goal is to estimate the orders of magnitude of CB, and to illustrate the idea of screening.

5) By the way, we usually think that the so-called “free electrons” in metals are uniformly distributed, like in ionized gases. What evidence do we have for this? Yes,
I know that the physics of surfaces is very complex, even for something familiar, such as friction.

6) No, I am not trying to poison your mind with heretical pseudo science. This piece is essentially an attempt to show how a trivial electrostatic problem can be made relevant, even in an introductory course. Those who do not want to deal with the concept of screening in condensed matter might ask students "why do fusion reactions in ionized gasses occur at stellar temperatures only?" This will naturally lead to two interesting topics outside electrostatics: the QM tunneling and the Maxwellian distribution of kinetic energies of ions at various temperatures. Students love digressions but one must make sure that the main topic is electrostatics.


ADDED ON JULY 23, 2011

A stranger who read the unit 128 just sent me a private message. He wrote: "Just a couple comments on the above article. ... I agree that screening would seem to play a minor role and would not be able to change the Coulomb potential much in matter in which the electrons were disposed symmetrically around the nucleus. But asymmetries do occur. For instance in highly polarized matter. I've been studying dielectrics such as barium titanate which have been produced with permittivities in excess of 30,000. In such materials at high electric fields the local field on the charges in the material can be ~10TV/m. This would certainly introduce an asymmetry in the dispositions of electrons in the nucleus. It wouldn't be too difficult to set up an experiment to test this."

What kind of experiment can be performed with barium titanite [BaTiO3]? Suppose this dielectric is used as a target bombarded by 3 MeV protons. Suppose the cross section of a known Ti(p,n) reaction is measured. Then the same is done with a metallic Ti target. If the coulomb barrier for titanium in the dielectric is really lower than for the Ti in the metal then the cross section should be target-dependent. The cross section for the dielectric target, could be several times larger for the metallic target. Naturally, one needs a well equipped nuclear laboratory.

This was posted in the private discussion list for CMNS researcher. Then I added that such result would be the first demonstration, outside the CMNS field, that structure of condensed matter can have a dramatic effect on a nuclear process. The accepted textbook wisdom is that nuclear processes are not dependent on changes taking place at the atomic level (such as Ti metal versus Ti in a dielectric). A reproducible difference in cross sections, for example, by a factor of 2 or 10, would probably produce a dramatic change in the attitude of most scientists toward our CMNS field.

One researcher referred to Kasagi experiments. Responding to this, I wrote that Kasagi's energy region was several eV. Why did I suggest 3 MeV? Because the cross section at ~3 MeV should be many orders of magnitude larger (easier to measure) than at ~10 eV. On the other hand the 3 MeV is still below the region where the dependence of the cross section on energy becomes less steep. All this is based on what I remember, not on literature. Below are my additional reflection, also posted on the CMNS list.

1) For the most common (74%) isotope, 48Ti, the (p,n) reaction will not take place when the energy of protons is 3 MeV, as I suggested. Why not? Because the Q value is 4.7 MeV The needed energy should be at least 5 MeV. This still is less than the coulomb barrier (~ 7 MeV). I would not hesitate using 5.5 MeV protons.

2) The coulomb barriers are practically identical (about 7MeV) for all stable isotopes of titanium [46 (8%), 47 (6%), 48 (74%) 49 (6%) and 50 (5%)]. But the Q values are likely to be different for other isotopes.

3) Let me go back to the 48Ti target. The probability of Ti+p fusion (formation of an excited 49V compound nucleus) depends only on the height of the coulomb barrier. But the cross section for a particular reaction, such as the Ti(p,n), depends on how many other "output channels" are also open (energetically possible), at a given excitation energy of the compound nucleus. I am thinking about the (p,d), (p,t), (p,al), etc. The Q values of competing reactions must be known to theoretically estimate a particular cross section.

4) What is the Q value of the (p,al) reaction: 48Ti + p --> 45Sc + alpha ? It happens to be +2.6 MeV. In other words, the (p,al) reaction is exothermic; it would take place, even for 3 MeV protons, and below. Considering this fact I would measure the (p,al) cross sections, not the (p,n) cross sections, as initially suggested. And why not the (p,d) or (p,t) reaction? These reactions can also be used to show that the expected effect is real. To answer this question I would have to calculate the Q values of these reactions. Detecting and identifying energetic charge particles is likely to be easier (less costly) than detecting and identifying energetic neutrons.

5) The less demanding (lest costly) method of validation of the expected effect would be to measure the elastic scattering cross section, ES for alpha particles, for example, at 30 or 45 degrees. The formula for the ES is well known (and experimentally verified for thin metallic targets). The ES is inversely proportional to the square of the coulomb barrier. Once the ES is measured the barrier can be calculated. Why is this method less desirable than measuring a cross section of a nuclear reaction induced by protons? Because a sufficiently strong alpha source is much less expensive than a proton accelerator. The source could be placed into a small vacuum chamber and CR-39 chips could be used to detect scattered alpha particles.

But, as the saying goes, the devil is in the details. The most difficult part, for me, would be preparation of two thin targets, metallic and dielectric. The word "thin" stands for the "thin in comparison with the range of projectiles in it." Why is this important? Because the kinetic energy of projectiles must be well defined; it appears in the ES formula. Suppose that thicknesses of two targets are known to be the same. Suppose that each target is bombarded with a collimated beam of alpha particles for one hour. Suppose the number of particles detected at 30 degrees, for a metallic target is 1000. Suppose the same is done for the dielectric target and the number of particles detected at 30 degrees is 2000, under otherwise identical conditions. That would mean the cross section for the dielectric target is twice as large as for the metallic target. It would also mean that the coulomb barrier in the dielectric environment is four times lower than in the metallic environment.

6) Yes I know that gedanken experiments are much easier than real experiments. In reality the two targets would probably have slightly different thicknesses. A correction would have to be made, to account for this. Another correction should be made to account for the presence of barium atoms and oxygens atoms in the dielectric target. These atoms would also be scattering alpha particles. To avoid a serious error (an illusion of the coulomb barrier lowering) , I would place thin layers of Ba and O atoms (in one form or another) on the metallic target, matching the mg/cm2 of Ba and O in the dielectric target. Similar considerations would be necessary for experiments based on nuclear reactions, rather than on scattering. Yes, the devil is in the details.


Relevant references can be foud in this apparently unpublished (2006?) manuscript:

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