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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
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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
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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?
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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
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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
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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
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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
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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
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enhancement clearly linked to properties of the metallic environment
overview of final results
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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
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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
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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
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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
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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…
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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
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investigate 6,7Li(p,a) reactions in different materials to test Zt dependence of UD
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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
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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)