K. Czerski Institute of Physics, University of Szczecin

Euratom Workshop Szczecin, 23.03.2006

Deuteron Fusion Reactions inMetallic Environments

V(r)

-50 MeV

r

V(r)

-50 MeV

r

Electron Screening in Nuclear Reactions

V(r) = exp (- r /a ) Z1 Z2 e 2

r

Z1 Z2 e 2

r≈ - Ue

R a

screening energy

Ue =Z1 Z2 e 2

a

E

E

E

EEP GG exp)(

s-wave penetration factor

P(E) P(E+Ue)

Experimental Set-Up

200 kV accelerator

TU Berlin

d d +

+

Similar results:J. Kasagi et al., J.Phys.Soc.Jap. 71 (2002) 2281F. Raiola et al., Eur.Phys.J. A13 (2002) 337

gas target

K. Czerski et al., Europhys. Lett. 54 (2001) 449metal targets

d + d 3He + n

d + d 3H + p

Ue = 25±5 eVU.Greife et al., Z.Phys. A351 (1995) 107

Enhanced Electron Screening Effect I

E

U

E

E

E

UEEF eGe

bare

scr

2

1exp

)(

)()(

F(E

)

enhancement factor :

in metallic environments

Ue screening energy

εc(q)

Dielectric Function Theory

v= c= 1 r

e2

self-consistent charge formfactor

z number of bound electronskTF Thomas-Fermi wave number

valence-electron dielectric function

P(q) Lindhard RPA polarizabilityG(q) local field correction

core-electron dielectric function from f-sum rule

qdrqiqqq

qer

r

erV

cv

32

2

3

2

)exp()()(

))((4

)2(

1)()(

)/(1)( 222TFkqzqzq

)()()(1

)()(1)(

qPqGqv

qPqvqv

K. Czerski et al., Europhys. Lett. 68 (2004) 363

Enhanced Electron Screening Effect II

0,0 0,4 0,8 1,2 1,6 2,0

0,0

0,4

0,8

1,2

PdD

(r)

Deuteron-Deuteron Distance (10-10m)

screening function with LFC exponential screening function screening function without LFC

0 20 40 60 80 100

0

50

100

150

200

250

300 exp

theo

polarization

cohesion

Scr

eeni

ng E

nerg

y (

eV)

Atomic Number

Li Be Al Zr Pd Ta

C

D-D Potentialdielectric-function theory

Results

K. Czerski et al., Europhys. Lett. 68 (2004) 363

Comparison of Experimental Results

Proposal I

Experimental:new measurements under ultra-high vacuum conditionslooking for the target material and temperature dependence

Theoretical:improvement of the dielectric-function theorypolarization of deuterons within the crystal lattice

Collaboration

University of Szczecin: Prof. K. Czerski, Prof. A. Bechler, Ż. Wyrwał-Artyszuk

Technical University of Berlin: Prof. P. Heide, Prof. G. von Oppen, Dr. A. Huke

Humboldt University of Berlin: Prof. H. Winter, Dr. M. Busch

cos1 22Pa

d

dtot

Angular Distribution

d + d 3He + n d + d 3H + p

Taa2

Energy Spectra

Suppression of Neutron Channel

16 transition matrix elementss, p und d waves

channel spin S = 0,1,2

experimental results can be explained

if

S = 0

Polarisation von Deuteronen ?

A. Huke, K. Czerski, accepted Eur. Phys. J. A

Proposal II

Experimental:direct measurement of the neutron channelenergy and target material dependence of the effect

Theoretical:search for a theoretical explanation of the deuteron polarization within the crystal lattice

Collaboration

University of Szczecin: Prof. K. Czerski, Prof. R. Fedaruk, Prof. J. Stelmach

Technical University of Berlin: Prof. P. Heide, Dr. A. Huke, L. Martin

Humboldt University of Berlin: Prof. H. Winter, Dr. M. Busch