Ionic debye screening in dense liquid plasmas observed for Li+p,d reactions with liquid Li target

J.Kasagi, H.Yonemura, Y.Toriyabe,
A.Nakagawa, T.Sugawara, WANG Tie-shan
Thick target yields of α particles emitted in the 6Li(d,α)4He and 7Li(p,α)4He reactions were measured for Li target in the solid and liquid phase.
Observed reaction rates for the liquid Li are always larger than those for the solid.
This suggests yhat the stopping power of hydrogen ion in the liquid Li metal might be smaller than in the solid . Using the empirically obtained stopping power for the liquid Li, we have deduced the screening potentials of the Li+p and Li+d reactions in both phases.
The deduced screening potential for the liquid Li is about 500 eV larger than for the solid.
This difference is attributed to the effect of liquefied Li+ ions.
It is concluded that the ionic screening is much stronger than the electronic screening in a low-temperature dense plasmas.
Key Words: low energy nuclear reaction; Li+p and Li+d reaction inn liquid Li; liquid metal Li screening energy.

CLC number:
O571.4        Document code: A

1. Introduction
Low energy nuclear reactions play an important role in nuclear synthesis and energy prooduction in stars, where thermal nuclear reactions take place in various plasma conditions.
In order to simulate such process, reaction rates should be known from the nuclear reaction experiments in a laboratory.
The progress of accelerators made it possible to measure nuclear cross sections for variety of nuclear reactions.
However, the reaction rate depends on the environments very strongly. For example, it has been well known thar the screening by electrons enhances the nuclear cros section very much, even in the laboratory experiment where a target nucleus is usually in atom or molecule.
Thus, the nuclear reactions in various conditions should be explored more, in order to estimate the reaction rates in stars, although it is impossible to prepare for very high density plasmas, at present.
We have developed measurements of low-energy nuclear reactions in metal environments [1], where target nuclei are surrounded by conduction elecrons, i.e., terget nuclei in degenerated electron plasmas.
The screening potentials of the D+D and Li+D reactions in such conditions were found out to be very large [2-4]: about 600eV for D+D reaction in PdO Host, for example. Subsequently, we have tried to prepare another condition of the environment for low-energy nuclear reactions.
In the present work, we report on nuclear reactions in liquid Li metal plasmas, for the first time, where Li+ ions are moving freely in a conduction electron sea, and much highter density (ρ≈10^22 ions/cm^3) can be realized than in laboratory gas plasmas.

2. Plasma properties of liquid Li
One of the quantities which characterizes plasma is the Wigner-Seits radius, aws=(3/4πn)^1/3:n is the number density of particles.
The radius is 0.17nm for both the Li+ ions and the electrons calculated with nLi=ne≈4.6X10^22 eelectrons/cm^3.
The so-called plasma-parameter, L=h/(2π MkT)^1/2 /aws, where M is the mass of particles, is estimated to be 0.1 for the Li+ ions and 15 for the electrons.
The particles with L<<1 can be considered classic ones, while those with L>>1 can be considered quantum ones.
Therefore, the liquid Li may be regarded as plasma consisting of classical Li+ ions and quantum electrons.
It should be noticed that the number density of particles is much larger than that of gas plasma in laboratory. Thus, the liquid metal plasma in laboratory can realize similar plasma conditions in the core of Jupiter with slighly lower temperature and density.
The present work aims at obtaining the screening potential of the Li+p and Li+d reactions in liquid Li.
Since the target Li is surrounded by the conduction electrons in addition to the bound electrons, the screening potential due to both electrons is estimated to be Ue=3e^2X(1/^2λbe+1/λ^2ce)^1/2, where λbe(ce) is a screening lenght due to the bound (conduction) electrons.
They are simply estimated to be 24pm from the adiabatic approximation and 61pm from the Thomas-Fermi approximation for the bound and conduction electrons, respectively.
Thus, the screening potential of 194eV is expected froom the electrons.
For the solid Li case, the screening effect is provided only by these electrons, i.e., the screening potential Usol=194eV is predicted.
For the liquid Li, in addition to the electrons, the effect of classical Li+ ion gas should be considered. In this case, a screening lenght can be estimated by the Deybe model which gives λLi=6.7pm at T=520K; much shorter than those originated from quantum electrons.
Thus the screening potential of the Li+p(d) reaction in the liquid Li  is estimated to be Uliq=673eV; almost 500eV differnce may be expected between the solid and the liquid target.
One of the interesting questions is whether the screening due to positive ions can work effectively or not. Since the mass of ions is much lager than that of electrons, positive ions cannot respond quickly to change, and, hence, the ionic screening might be reduced very much.

3. Experimental procedure
The experiments were performed by using proton and deuteron beams obtained from a low-energy ion generator at Laboratory of Nuclear Science at Tohoku University.
Natural Li (92.4%7Li, 7.6%6Li) and enriched 6Li were used for 7Li+p and 6Li+d reactions, respectively.
A technique to generate the liquid Li metal target has been developed. A lump of natural Li or enriched 6Li metal was placed horizontally on a small saucer which can be heated up to 500°C in a vacuum chamber.
The temperature of the surface of the Li target was monitored directly by a radiation thermometer. The melting point of the Li metal is about 180°C; a phase change was easily known by watching the temperature.
A beam was injected from the upper part of the chamber, with its angle of 30° with respect to the vertical line.
Alpha particles emitted in the 6Li(d,α)4He and 7Li(p,α)4He reactions were measured with a Si detector of 300µm in thickness.
A 5µm thick Al foil covered the detector surface to prevent electrons and scattered beam particles from hitting the detector directly.
Thick target yields of α particles from the 7Li(p,α)4He and 6Li(d,α)4He reactions were measured for the solid (T≈60°C) and the liquid (T≈250°C) Li target as a function of bombarding energy between 25 and 70keV by 2.5keV steps.
The beam current was measured from the target, on which a permanent dipole magnet was placed to suppress secondary electron emissions. Its intensity was adjusted for each bombarding energy so as to keep the input beam power constant.

4. Results and discussion
Observed excitation functions show clear difference for the liquid and the solid target. It turned out that the reaction rates for the liquid Li are always larger than those for the solid one in both the 7Li(p,α)4He and 6Li(d,α)4He and 6Li(d,α)4He reactions. The thick target yield at the bombarding energy Eb described as
Here, pLi is the number density of Li, dE/dx is the stopping power of Li metal, and σ(E) is the cross section of the 7Li(p,α)4He and 6Li(d,α)4He reaction. The enhancement due to the screening potential Us is expected only at very low bombarding energies. Thus, larger reaction rates for the liquid target observed for Ep,d>40keV are considered mainly due to the reduction of the stopping power in the liquid phase.
In the following preliminary analysis, the density of Li is taken from Ref.[5] and the stopping power for the solid Li is from Ref.[6]. For the cross sections, astrophysical S-factor is taken from Ref.[7] for the 7Li(p,α)4He reaction and from Ref.[8]  6Li(d,α)4He reacion.
Ratios of the reaction rates in the liquid target to the solid are shown in Fig.1 as a function of bombarding energy per nucleon (E/u). The data plotted with solid squares correspond to the 7Li(p,α)4He reaction for Ep>35keV, and solid circles to the 6Li(d,α)4He reaction for Ed>40keV. As seen in the figure, the ratio becomes larger and larger as the E/u increases.
This surprises us very much, but the phenomena were easily reproduced in the continuous measurement of the yield versus temperature. In such measurements, the yield is suddenly decreased when the target phase is changed from the liquid to the solid.

Fig.1 Ratio of the reaction rates in the liquid to solid phase as a function of E/u. Data plotted with solid squares are from the 7Li(p,α)4He reaction and those with solid circles from the 6Li(d,α)4He reaction.

In Fig.1, the two data sets are smoothly connected as if described by a function of E/u or velocity of the hydrogen. This indicates that the stopping power of hydrogen ion in the liquid Li metal might be smaller than that in the solid one. In order to compare the screening potential for both in the liquid and in the solid phase, the stopping power in the liquid Li metal is indispensable. It is, then, deduced empirically so as to reproduce the data in Fig.1.
The stopping power for the liquid target used in the following analysis is (dE/dx)liq=F(E/u)X(dE/dx)sol; the function F is a quadratic function of E/u and is determined to reproduce the solid curve in Fig.1. The origin of the reduction of the stopping power in the liquid is not known at present. However, we try to reduce the screening potential in the liquid target as well as in the solif target.
We try to deduce the screening potentials of the Li+p and Li+d reactions in the liquid and solid phase.
The thick target yields of α particles measured in the 6Li+d reaction are shown in Fig.2; the left part for the solid Li and the right part for the liquid Li. In the upper part, the thick target yields normalized at 70keV are plotted as a functionjof the bombarded energy.
In the lower part, the enhancement factor which is the experimental yield divided by that calculated by Eq. (1) with Us=0 is plotted.

Fig.2 Thick Target yield of a particles emitted in the 7Li(d,α)4He reaction for the solid and liquid target. In the upper part, the data normalized to the yield at 70keV are plotted. In the lower part, the esperimental yields divided by the yield calculated without screening energy are plotted.

It is clear that the reaction rates are more strongly enhanced with the decrease of the bombarding energy, as can be seen in the lower part of Fig.2.
Also noticed is the fact that much larger enhancement is observed in the liquid target. The screening potential Us of the Li+d reaction is deduced by fitting the calculated yields to the experimental ones.
The deduced values are Usol=(350±50)eV and Uliq=(900±50)eV, respectively for the solid Li and the liquid Li. The difference of the screening energies is about 550eV.
For the 7Li+p reaction, similar results of the screening potential have been obtained.
In this case, however, the data only for Ep<45keV are analyzed, because of large uncertainties of the stopping power for highter energy region.
The screening energies from the 7Li+p reaction are Usol=(360±100)eV and Uliq=(1000±200)eV, respectively for the solid Li and the liquid Li. Again, very large difference between solid and liquid is obtained.
As already discussed, the simple plasma picture gives the screening energies, Usol=194eV and Uliq=673eV, respectively, for the solid and thr liquid Li metal. The experimental ones deduced in the present analysis gives slightly larger values, Usol=(350±50)eV and Uliq=(900±50)eV.
Although the simple plasma picture does not explain well the screening energy for each phase, the difference between the solid and the liquid is well explained. Therefore, we can conclude that the ionic screening mechanism affects the reaction rate very much in the liquid Li metal.

5. Summary
We have investigated the 7Li+p and 6Li+d reactions for bombarding energies between 25 and 70keW with liquid Li target, for the first time.
The effects of the solid-liquid phase transition are clearly seen in the reaction rates. The reaction yield in the liquid phase is always larger than in the solid phase. This observation suggests that the stopping power in the liquid Li is smaller than that in the solid one.
Using the data of the yield ratio between the liquid and the solid for Eb>40keV, we have made an empirical correction to the stopping power of the liquid Li.
Screening potentials for the Li+p,d reaction are successfully obtained for the liquid Li as well as the solid one. It turns out that the liquid Li provides much larger sreening potential than the solid: the difference is about 500eV in the present preliminary analysis. This difference is very well explained by a simple plasma picture of the solid and the liquid Li metal. It can be concluded that the ionic screening in much stronger than the elecronic screening in a low-temperature dense plasmas.

[1] Kasagi J, Prog Theor Phys, 2004, 154 (Supp): 365.
[2] Yuki H, J.Kasagi, Lipson A G, etal. JETP Lett, 1998, 68: 823.
[3] Kasagi J, Yuki H, Baba T, et al. J Phys Soc Jpn, 2002, 71: 2881.
[4] Kasagi J, Yuki H, Baba T, et al. J Phys Soc Jpn, 2004, 73: 608.
[5] Shimizu Y, Mizuno A, Masaki T et al., Phys Chem Phys, 2002, 4: 4431.
[6] Ziegler J F, Biersack J P, code SRIM,
[7] Engstler S, Raimann G, Angulo C, et al., Z. Phys, 1992, A342: 471.
[8] Lattuada M, Pizzone R G, Typel S, et al. Astro J, 2001, 562: 1076.

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9 comments to Ionic debye screening in dense liquid plasmas observed for Li+p,d reactions with liquid Li target

  • You should take part in a contest for one of the best weblogs on the internet. I will highly recommend this website!

  • Andrea Rossi

    OK, Dr Billi, I’m gonna do it: lavolale, lavolale! (Never mind: this is a joke between Dr Billi and me).
    Anyway, good suggestion, I will go through it.

  • Enrico Billi

    Could be interesting to setup an experiment like this one, may be send Protons on the Nickel surfaces already loaded with hydrogen and heated up to different temperatures. If the theory of the virtual neutron is correct, may be the detector could see deuterons and g-rays or neutrinos come out from the Nickel sourface not only protons.

  • When I read a really good post I usually do a few things:1.Forward it to all the close it in all my best social sharing sites.3.Be sure to visit the same blog where I first read the article.After reading this post I am seriously concidering going ahead and doing all of the above.

  • Hey, this is a tremendously helpful post! Funny, I came over just to make sure I hadn’t missed anything and I come across a really worthwhile post :)

  • Andrea Rossi

    I am still studyind the physical phenomena which occur in the reactor, anyway your suggestion is interesting.
    Warmest REGARDS,

  • Enrico Billi

    If the proton interact with electrons with Electromagnetic field and behaves more like a quasiproton or became a neutron throught weak interactions, your reactor should be called an electroweak reactor.
    Enrico Billi

  • Andrea Rossi

    I agree,

  • Enrico Billi

    It is interesting to see how much the Enhancement Factor increse so much in the liquid fase for energies below 40KeV

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