Laboratory of Nuclear Science,

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Laboratory of Nuclear Science, Low energy Li+p,d reactions in liquid plasmas and the effect of liquefied Li+ ions on the screening potential J. Kasagi H. Yonemura, Y. Toriyabe, Nakagawa, T. Sugawara Laboratory of Nuclear Science, Tohoku University

Sapporo: very nice city to discuss on Origin and Evolution of Star

Stars where nuclear reactions occur in various dense plasmas Sun; rm ~102 g/cm3, T ~107 K, Jupiter; rm ~ 2 – 5 g/cm3, T~103 K White dwarfs; rm ~107 – 1010 g/cm3, T~107 – 109 K Brown dwarfs; rm~102 – 103 g/cm3, T~ (2 - 3)×106 K Rate of nuclear reactions is an essential element for evolution of stars. Nuclear reaction rates are modified by the environments very much: for example, screening effects Laboratory experiments on nuclear reaction in dense plasmas should be explored more. Low-energy reactions in various conditions have been studied at LNS: 6Li(d,a)4He, 7Li(p,a)4He: solid/liquid metal target, Ei < 80 keV Screening, especially on ionic screening

Naive picture of screening in plasmas re, ri r0 r e- + Plasma ion Free electron Z e- + Plasma ion Free electron re ri Dr- = Dre, Dr+= Dri ; polarized charge e0 → e0(1+ce+ci), c: susceptibility Simplest approximation f(r) = (1/4pe0)・Ze/r ・exp(-r/D), D: screening length 1/D2 = 1/De2 + 1/Di2; both – and + charge Screening by electrons and ions Z Why we can say that liquid metal is a kind of plasma. We have almost freely moving ions and electrons together in condensed state, which in whole is electrically neutral. In this figure, I just illustrate such a condition. For the liquid Lithium case, the density of positive ions is about 10 to 22 per cubic cm, and so is negative electrons. Highly dense condition can be realized,. This is very important to simulate the nuclea reaction in stellar conditions. One of the quantity which characterize a plasma is the Wigner-Seitz radius. They are this order. From this, we can calculate so-called quantum parameter: De Blogie length divided by the Wigner-Seitz radius. We can say that the Li ion is a classical particle but the electron is a quantum particle. And, also the electro-coupling is not week, rather strong for both components of plasma, for liquid metal. Thus, we can regard the liquid Li as a strongly coupled plasma with classical positive ions and quantum negative electrons. Question: Is ionic screening reduced? electronic cloud can adjust quickly speeds of ions are not so fast

Liquid metal: a laboratory for dense plasma experiments Ion-electron system: Li+ + e- nLi~1022/cm3 ne ~1022/cm3 Solid metal Li Liquid metal Li e- Li3+ e- Li3+ Free Li+ Free T>180oC free Li+ ions turn on ionic screening electronic screening only Dre≠0, Dri = 0 screening by electrons and ions Dre≠0, Dri≠0 Quantum electron plasma Plasma with classical Li+ and quantum e-

Screening energy for Li+p,d reaction Naive assumption; classical Li+ and quantum e gas Screening energy for Li+p,d electrons: bound electrons: Ube = 180 eV conduction electrons: degenerated Fermi gas-Thomas-Fermi Uce=e2[4e2m/(h/2)2(3/・ne)1/3]1/2 ~25 eV; no dependence on T and r U(eV) ULi: Classical Li+ gas ×3 Ube: Bound electrons Ions: classical gas, Debye screening ULi=3e2(4e2nLi/kT)1/2 ~690 eV at 200oC T dependence, strong r dependence Uce: Degenerated e- gas Solid to Liquid phase transition Usol~190 eV → Uliq~710 eV DU~520 eV difference is expected!! Ion/electron density n (1022/cm3)

Liquid Li metal target experimental setup liquid Li target thermometer scraper liquid Li target Si Det Θ=125° slit 5mΦ D+ beam magnet Target sourcer cooling system heater

deuteron accumulation: solid : < 3% of Li liquid : < 0.2% charged particles from the 6Li + d reaction d(d,p)t 7Li(d,α)n4He 6Li(d,α)4He 6Li(d,p)7Li Liquid Solid Experiment target: enriched 6Li natLi beam:  E = 25~80keV  I = 4~12μA target temperature:  solid : ~40℃  liquid : 220~250℃ deuteron accumulation: solid : < 3% of Li liquid : < 0.2%

Phase transition of Li metal target y yield of Li+D reaction Ed=80keV Ed=90keV Ed=100keV solid liquid target temperature Yield of p d(d,p)t liquid solid First, let me show how the situation is changing at around the melting point, which is 190 degrees in Celsious. This graph shows temperature measured by the radiation thermometer as a function of time for increasing the target temperature. Solid-liquid phase change is easily seen, here, because the temperature stays constant for a while. This can be seen also in reaction yields of the D+D reaction shown in the lower figure. You can see dramatic drop of the yield; more than one order of magnitude change between solid and liquid. For the D+D reaction, the target deuteron is the implanted one and Li behaves as a host. For the solid phase, Li cannot move freely: this makes the deuteron density at the surface very large. On the other hand, in the liquid phase Li can move almost freely, and implanted deuterons can diffuse very quickly resulting in very small deuteron density at the surface; then, yield of the D+D reaction drops very much. Right three figures shows that the yield of the Li+D reaction also depends on the phase of Li. I show, here, alpha particle yield as a function of time for bombarding energies of 80 keV, 90 keV and 100 keV. The time when the Li is melted or solidified is shown by red and blue lines. Of course, the change between solid and liquid is not so dramatic as for the D+D reaction. However, change of the Li density is very small in this case. Some other things should be changed. Y(p) rapidly decrease rd in liquid << rd in solid fluidity of deuteron increase sudden jump of yield Y(liquid) > Y(solid) but rliq ~0.99 rsol

Y(liquid)/Y(solid) vs Einc 6Li(d,a) 7Li(p,a) Y(liquid) > Y(solid) As Einc decreases ratio decreases at higher energies ratio increases at low energy Thick target yield For low energies effect of screening! For high energies due to dE/dx?

Y(liquid)/Y(solid) vs E/mass For higher incident energies, Y(liquid)/Y(solid) ∝f(E/m) i.e., depends only on projectile velocity 7Li(p,a) strongly suggests Y(liquid)/Y(solid) ∝ {dE/dx(liquid)}/{dE/dx(solid)} 6Li(d,a) solid smaller for liquid dE/dx(v)liquid = C(v)×dE/dx(v)solid C(v): empirical correction factor Ion energy/A (keV/amu)

Screening energy for 6Li(d,a)4He reaction Obtained screening energy Usol = 350 ±40 eV for Solid Li (cf. 380±250 eV for LiF) Uliq = 860 ±50 eV for Liquid Li DU = 510 eV Usol = 350 eV Uliq = 860 eV Screening; strongly enhanced in Liquid → contribution of Li+ ions; very large

Screening energy for 7Li(d,a)4He reaction Usol = 1580 ±100 eV Uliq = 2050 ±100 eV ??? From 6Li+d Usol = 350 ±40 eV Uliq = 860 ±50 eV dE/dx for Ep > 40 keV ?? using only data below 45 keV Usol = 360 ±100 eV for Solid Li Uliq = 1000 ±200 eV for Liquid Li Usol = 1580 eV Uliq = 2050 eV U = 360 eV U = 1000 eV Consistent with the 6Li+d results! Large effect of free Li+ ions!! Screening in liquid phase is more than two times stronger in solid phase.

Screening energy due to Li+ ions Present results Usol = 350 eV Uliq = 860 eV Dsol = 12.3 pm Dliq = 5.0 pm DLi = 5.5 pm, i.e., ULi = 782 eV simple prediction ULi = 690 eV Screening due to Li+: more than two times larger than electrons consistent with a prediction of a simple model No reduction of ionic screening in plasmas

Summary Low-energy 6,7Li+d,p reactions below Einc = 80 keV with liquid Li target were investigated for the first time: effects of the solid-liquid phase transition are clearly seen in the reaction rates. dE/dx of p and d in the liquid Li is smaller than in the solid: the difference becomes larger as the bombarding energy increases. Screening energy for the Li+p,d reaction were successfully obtained: Uliq ~860 eV, which is more than two times larger than Usol. contribution of Li+ ions to the screening is deduced; ULi~780 eV which is consistent with a naïve prediction based on a liquid plasma. the ionic screening is much stronger than the electronic screening in a low-temperature dense plasmas. T-dependence and r-dependence of ULi will be studied: various target conditions should be developed, such as a cavitation.