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 , 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 RnRn RtRt Coulomb potential EcEc 0 E bare screened E + U e R atomic Electron screening  (E) = exp(-2  ) S(E) assumption: 2  ~ Z 1 Z 2 (  /E) ½ bare nuclei Energy gain = SCREENING POTENTIAL U e typically tiny amount (~ eV)  corrections typically negligible  except for ultra-low energies

E 0 bare S(E) S(E) high-energy data extrapolation screened S(E) fit to measured low-energy data  Ue Ue Screening potential: experimental approach typically, experimental investigationsU e in excess of theoretical limit ! f lab (E) = S screen (E) S bare (E) ~ exp(  U e /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 aperture 8 mm f x/y wobbling units D + ion beam M x D target Cu pipe -200 V Si LN 2 -cooled turbo pump  = 130° P = 2x10 -8 mbar

Experimental procedure  Kr sputtering at E = 35 keV (remove ~ 200 mono-layers)  D implantation (at E d ~ 5-30 keV until saturation)  stoichiometry M x D 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 U e thick-target yield curve d(d,p)t t p

Anomalous behaviour of U e in deuterated metals F. Raiola et al.: Phys. Lett. B547 (2002) 193 F. Raiola et al.: Eur. Phys. J A19 (2004) 283 compared to D 2 gas target (U e  30 eV) anomalous enhancements observed for some materials but not for others WHY? factor ~ 20 higher factor ~ 25 higher comparable to gas target case Cu U e = 470 eV Pt U e = 670 eV Hf U e < 30 eV Nd U e < 30 eV

FEATURES:  elements in same group show similar U e 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. Raiola et al.: Eur. Phys. J A19 (2004) samples in 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 U e 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 o C

enhancement clearly linked to properties of the metallic environment overview of final results

A possible classical explanation? n eff = number of quasi-free electrons/atom (typically 1)  a = atomic density (typically 6x10 28 m -3 ) for T ~ 300 K  R D ~ 1/10 R a TEMPERATURE DEPENDENCE CHARGE DEPENDENCE A SIMPLE MODEL: following Debye’s plasma theory: “free” electrons in metals cluster around deuterons in lattice at radius U e,D  Z 1 Z 2 e 2 /R D  U e,D ~ 300 eV CRITICAL TESTS:

Temperature dependence of U e need elements with almost constant solubility at all T examples: Pt and Co range of T = 20 – 200 o C group 10

Target-charge dependence of U e Debye radius scales inversely with nuclear charge Z t of target atoms in insulators: n eff = 0  U D = 0 in H 2 gas target:  U A = 300±160 eV in Li metal: n eff (Li) = 0.8±0.2  U D = 820±100 eV expect:U e = U A + U D = 1120±260 eV 7 Li(p,a) 4 He in PdLi x alloy: n eff (Pd) = 6.3±1.2  U D = 2800±280 eV (for x < few percent) expect:U e = U A + U D = 3100±440 eV expect:U e = U A + U D = 300±160 eV expect increased effect in screening potential with Z t example

Results U e = 1280±60 eV U e = 3790±330 eV U e,A = 185±150 eV similar results observed for 6 Li(p,  ) (Z t = 3) 9 Be(p,  ) 6 Li and 9 Be(p,d) 8 Be (Z t = 4) 50 V(p,n) 50 Cr (Z t = 23) 176 Lu(p,n) 176 Hf (Z t =71) J. Cruz et al. Phys Lett B 624 (2005) 181 D. Zahnow et al. Z. Phys. A359 (1997)211 C. Rolfs, (2005) private communication

Summary  enhanced electron screening in metals explained using Debye model  temperature dependence of U e verified  target-charge dependence of U e 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.Raiola 1, J.Cruz 2, G.Gyürky 3, Z.Fülöp 3, S.Zeng 4, M.Aliotta 5, H.W.Becker 1, B.Burchard 1, C.Broggini 6, A.Di Leva 1, A.D’Onofrio 7, M.Fonseca 2, L.Gang 4, L.Gialanella 8, G.Imbriani 8, A.P.Jesus 2, M.Junker 9, K.U.Kettner 10, B.Limata 8, H.Luis 2, J.P. Ribeiro 2, V.Roca 8, C. Rolfs 1, M.Romano 8, D. Schürmann 1, E.Somorijai 3, F.Strieder 1, F. Terrasi 7 1 Institut für Physik mit Ionenstrhalen, Ruhr-Universität Bochum, Germany 2 Centro de Fisica Nuclear, Universidade de Lisboa, Portugal 3 Atomki, Debrecen, Hungary 4 China Institute of Atomic Energy, Beijing, P.R.China 5 School of Physics, University of Edinburgh, UK 6 INFN, Sezione di Padova, Padova, Italy 7 Dipartimento di Scienze Ambientali, Seconda Università di Napoli, Caserta, Italy 8 Dipartimento di Scienze Fisiche, Università Federico II and INFN, Napoli, Italy 9 Laboratori Nazionali del Gran Sasso dell’INFN, Assergi, Italy 10 Fachhochschule Bielefeld, Germany the collaboration My special thanks to Francesco Raiola and João Cruz for much of the material presented

investigate 6,7 Li(p,a) reactions in different materials to test Z t dependence of U D

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 MACOR Cu plate MACOR graphite MACOR thermosensor diamond heater Temperature dependence of H solubility

previous studies of 9 Be(p,  ) 6 Li and 9 Be(p,d) 8 Be reactions [D. Zahnow et al. Z. Phys. A359 (1997)211] on metallic Be targets led to U e = 900±50 eV, not understood at that time with n eff (Be) = 0.21±0.04 T = 293 K Z t = 4 U D = 870±80 eV U A = 240 eV U e = U A + U D = 1110±80 eV consistent with observation and further supporting Z t scaling of Debye model Additional remarks Z t scaling recently verified also for Z t =23 [ 50 V(p,n) 50 Cr] and Z t =71 [ 176 Lu(p,n) 176 Hf] (Rolfs, private communication)