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)