1. 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

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. 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

5. 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-

6. 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)

7. 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

8. 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%

9. Phase transition of Li metal targety
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

10. 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?

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.