Low Energy Li+ and D Reactions in Liquid Plasmas: Effect of Liquefied Li+ Ions on Screening Potential

1. 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

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

3. 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

4. re, ri Plasma Plasma re r0 e- e- ri e- e- + + + + + + + + + + + + + + e- e- + r + e- e- Z + + e- e- e- e- e- e- e- e- e- + + e- + + + + Z Free electron Free electron Plasma ion Plasma ion Naive picture of screening in plasmas 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 Question: Is ionic screening reduced? electronic cloud can adjust quickly speeds of ions are not so fast

5. e- e- e- Li3+ Li3+ e- e- e- e- e- e- e- e- e- e- Li3+ Li3+ e- Free Li+ e- e- e- e- e- e- e- e- Li3+ Li3+ Li3+ Li3+ Li3+ Li3+ e- e- e- e- e- e- e- e- e- e- Free e- e- Li3+ Li3+ e- e- e- e- e- e- e- e- e- e- e- e- Li3+ Li3+ e- e- e- e- Li3+ Li3+ e- e- e- e- e- e- 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 T>180oC free Li+ ions turn on ionic screening screening by electrons and ions Dre≠0, Dri≠0 electronic screening only Dre≠0, Dri = 0 Plasma with classical Li+ and quantum e- Quantum electron plasma

6. Screeningenergy 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)

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

8. 6Li(d,p)7Li 6Li(d,α)4He d(d,p)t Liquid 7Li(d,α)n4He Solid charged particles from the 6Li + d reaction 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%

9. yield of Li+D reaction target temperature solid y Ed=80keV liquid solid liquid solid liquid Ed=90keV Yield of p d(d,p)t solid Ed=100keV solid liquid liquid Phase transition of Li metal target 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

10. 6Li(d,a) 7Li(p,a) Y(liquid)/Y(solid) vs Einc 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?

11. 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)

12. 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

13. 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.

14. 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

15. 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.