Electron screening: can metals simulate plasmas?
Marialuisa Aliotta
School of Physics - University of Edinburgh
International Workshop XXXIV on Gross Properties of Nuclei and Nuclear Excitations
Hirschegg, Kleinwalsertal, Austria, January 15 - 21, 2006
electron screening
d(d,p)t reaction in deuterated materials
experimental results and interpretation
testing the model
overview of final results
in the lab and in stellar plasmas interaction is affected by presence of electrons
Rn Rt
Cou
lom
b po
tent
ial
Ec
0
E
bare
screenedE + Ue
Ratomic
Electron screening
(E) = exp(-2) S(E) E1 assumption: 2 ~ Z1Z2(/E)½ bare nuclei
Energy gain = SCREENING POTENTIAL Ue typically tiny amount (~ 10-100 eV)
corrections typically negligible
except for ultra-low energies
E0
bare S(E)
S(E)
high-energy dataextrapolation
screened S(E)
fit to measuredlow-energy data
Ue
Screening potential: experimental approach
typically, experimental investigations Ue in excess of theoretical limit !
flab(E) =Sscreen(E)
Sbare(E)~ exp(Ue/E)
ideally one would use a plasma to investigate screening effects in plasmas
can we use metals instead?
100 kV accelerator – Ruhr-Universität Bochum
Si
Ni foil
aperture8 mm f
x/y wobbling units
D+ ion beam MxD target
Cu pipe-200 V
SiLN2-cooled
turbo pump = 130°P = 2x10-8 mbar
Experimental procedure
Kr sputtering at E = 35 keV (remove ~ 200 mono-layers)
D implantation (at Ed ~ 5-30 keV until saturation)
stoichiometry MxD attained
target preparation
experimental run and data analysis
thin-target yield differential thick-target yields determine cross section
determine solubility y = 1/x weighted average cross section S-factor
fit low-energy data to determine Ue
)σ(E)(Eαεθ),Y(E eff1
deffd
)(Exε)(Eε)(Eε dMdDdeff thick-target yield curve
d(d,p)t
t p
Anomalous behaviour of Ue in deuterated metals
F. Raiola et al.: Phys. Lett. B547 (2002) 193
F. Raiola et al.: Eur. Phys. J A19 (2004) 283
compared to D2 gas target
(Ue 30 eV)
anomalous enhancements observed for
some materials but not for others
WHY?
factor ~ 20 higher
factor ~ 25 higher
comparable to gas target case
comparable to gas target case
CuUe = 470 eV
PtUe = 670 eV
HfUe < 30 eV
NdUe < 30 eV
FEATURES:
elements in same group show similar Ue values
exceptions: group 13 (B = insulator) and group 14 (C, Si, Ge = semiconductors)
large effect ~ 300 eV metals with low “H solubility” (1/x) metallic character retained during implantation with D
small effect ~ 30 eV metals with large “H solubility”metallic character lost during implantation with D
Results overview
F.
Ra
iola
et
al.:
Eu
r. P
hys
. J
A1
9 (
20
04
) 2
83
55 samplesin total
group 4
similarly for all elements of groups 3 & 4 and Lanthanides
Temperature dependence of H solubility
solubility y drops to a few percent
increase in screening potential Ue
Ti – group 4
at room temperature
metals of group 3 and 4 and lanthanides all have HIGH hydrogen solubility y=1/x
solubility decreases with temperature repeat measurements at T = 200 oC
enhancement clearly linked to properties of the metallic environment
overview of final results
A possible classical explanation?
neff = number of quasi-free electrons/atom (typically 1)
a = atomic density (typically 6x1028 m-3)
[m]ρn
T69
ρne
kTεR
aeffaeff2
0D
for T ~ 300 K RD ~ 1/10 Ra
TEMPERATURE DEPENDENCE
CHARGE DEPENDENCE
A SIMPLE MODEL:
following Debye’s plasma theory:
“free” electrons in metals cluster around deuterons in lattice at radius
Ue,D Z1Z2e2/RD Ue,D ~ 300 eV
T
1(T)UD
CRITICAL TESTS:
)1Z(Z tt DU
Temperature dependence of Ue
need elements with almost constant solubility at all T
examples: Pt and Co
range of T = 20 – 200 oC
group 10
T
ρy(T)(T)(1n2.09x10(T)U aeff11
D
T
1(T)UD
Target-charge dependence of Ue
Debye radius scales inversely with nuclear charge Zt of target atoms
in insulators: neff = 0 UD = 0
in H2 gas target: UA = 300±160 eV
in Li metal: neff(Li) = 0.8±0.2 UD = 820±100 eV
expect: Ue = UA + UD = 1120±260 eV
7Li(p,a)4He
in PdLix alloy: neff(Pd) = 6.3±1.2 UD = 2800±280 eV (for x < few percent)
expect: Ue = UA + UD = 3100±440 eV
expect: Ue = UA + UD = 300±160 eV
)1Z(Z tt DUexpect increased effect in screening potential with Zt
example
Results
Ue = 1280±60 eV
Ue = 3790±330 eV
Ue,A = 185±150 eV
similar results observed for
6Li(p,) (Zt = 3)
9Be(p,)6Li and 9Be(p,d)8Be (Zt = 4)
50V(p,n)50Cr (Zt = 23)
176Lu(p,n)176Hf (Zt=71)
J. Cruz et al. Phys Lett B 624 (2005) 181
J. C
ruz
et
al.
Ph
ys L
ett
B 6
24
(2
00
5)
18
1
D. Zahnow et al. Z. Phys. A359 (1997)211
C. Rolfs, (2005) private communication
C. Rolfs, (2005) private communication
Summary
enhanced electron screening in metals explained using Debye model
temperature dependence of Ue verified
target-charge dependence of Ue verified
need for improved theory
another crucial prediction of Debye model:
a metallic environment should alter the half-lives of radioactive decay?
measurements currently in progress at Bochum…
F.Raiola1, J.Cruz2, G.Gyürky3, Z.Fülöp3, S.Zeng4, M.Aliotta5, H.W.Becker1, B.Burchard1, C.Broggini6, A.Di Leva1, A.D’Onofrio7, M.Fonseca2, L.Gang4, L.Gialanella8, G.Imbriani8,
A.P.Jesus2, M.Junker9, K.U.Kettner10, B.Limata8, H.Luis2, J.P. Ribeiro2, V.Roca8, C. Rolfs1, M.Romano8, D. Schürmann1, E.Somorijai3, F.Strieder1, F. Terrasi7
1 Institut für Physik mit Ionenstrhalen, Ruhr-Universität Bochum, Germany2 Centro de Fisica Nuclear, Universidade de Lisboa, Portugal
3 Atomki, Debrecen, Hungary4 China Institute of Atomic Energy, Beijing, P.R.China
5 School of Physics, University of Edinburgh, UK6 INFN, Sezione di Padova, Padova, Italy
7 Dipartimento di Scienze Ambientali, Seconda Università di Napoli, Caserta, Italy8 Dipartimento di Scienze Fisiche, Università Federico II and INFN, Napoli, Italy
9 Laboratori Nazionali del Gran Sasso dell’INFN, Assergi, Italy10 Fachhochschule Bielefeld, Germany
the collaboration
My special thanks to Francesco Raiola and João Cruz for much of the material presented
investigate 6,7Li(p,a) reactions in different materials to test Zt dependence of UD
at room temperature
metals of group 3 and 4 and lanthanides all have HIGH hydrogen solubility y=1/x
in general, hydrogen solubility decreases with temperature
modified setup to investigate effects of temperature dependence
target
MACORCu plate
MACORgraphite
MACOR
thermosensor
diamond
diamondheater
Temperature dependence of H solubility
previous studies of 9Be(p,)6Li and 9Be(p,d)8Be reactions
[D. Zahnow et al. Z. Phys. A359 (1997)211]
on metallic Be targets led to Ue = 900±50 eV, not understood at that time
with neff(Be) = 0.21±0.04
T = 293 K
Zt = 4
UD = 870±80 eV
UA = 240 eV
Ue = UA + UD = 1110±80 eV
consistent with observation and further supporting Zt scaling of Debye model
Additional remarks
Zt scaling recently verified also for Zt=23 [50V(p,n)50Cr] and Zt=71 [176Lu(p,n)176Hf]
(Rolfs, private communication)