![Page 1: K. Czerski Institute of Physics, University of Szczecin Euratom Workshop Szczecin, 23.03.2006 Deuteron Fusion Reactions in Metallic Environments](https://reader036.vdocuments.mx/reader036/viewer/2022062321/56649ec05503460f94bcc11c/html5/thumbnails/1.jpg)
K. Czerski Institute of Physics, University of Szczecin
Euratom Workshop Szczecin, 23.03.2006
Deuteron Fusion Reactions inMetallic Environments
![Page 2: K. Czerski Institute of Physics, University of Szczecin Euratom Workshop Szczecin, 23.03.2006 Deuteron Fusion Reactions in Metallic Environments](https://reader036.vdocuments.mx/reader036/viewer/2022062321/56649ec05503460f94bcc11c/html5/thumbnails/2.jpg)
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)
![Page 3: K. Czerski Institute of Physics, University of Szczecin Euratom Workshop Szczecin, 23.03.2006 Deuteron Fusion Reactions in Metallic Environments](https://reader036.vdocuments.mx/reader036/viewer/2022062321/56649ec05503460f94bcc11c/html5/thumbnails/3.jpg)
Experimental Set-Up
200 kV accelerator
TU Berlin
d d +
+
![Page 4: K. Czerski Institute of Physics, University of Szczecin Euratom Workshop Szczecin, 23.03.2006 Deuteron Fusion Reactions in Metallic Environments](https://reader036.vdocuments.mx/reader036/viewer/2022062321/56649ec05503460f94bcc11c/html5/thumbnails/4.jpg)
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
![Page 5: K. Czerski Institute of Physics, University of Szczecin Euratom Workshop Szczecin, 23.03.2006 Deuteron Fusion Reactions in Metallic Environments](https://reader036.vdocuments.mx/reader036/viewer/2022062321/56649ec05503460f94bcc11c/html5/thumbnails/5.jpg)
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
![Page 6: K. Czerski Institute of Physics, University of Szczecin Euratom Workshop Szczecin, 23.03.2006 Deuteron Fusion Reactions in Metallic Environments](https://reader036.vdocuments.mx/reader036/viewer/2022062321/56649ec05503460f94bcc11c/html5/thumbnails/6.jpg)
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
![Page 7: K. Czerski Institute of Physics, University of Szczecin Euratom Workshop Szczecin, 23.03.2006 Deuteron Fusion Reactions in Metallic Environments](https://reader036.vdocuments.mx/reader036/viewer/2022062321/56649ec05503460f94bcc11c/html5/thumbnails/7.jpg)
Comparison of Experimental Results
![Page 8: K. Czerski Institute of Physics, University of Szczecin Euratom Workshop Szczecin, 23.03.2006 Deuteron Fusion Reactions in Metallic Environments](https://reader036.vdocuments.mx/reader036/viewer/2022062321/56649ec05503460f94bcc11c/html5/thumbnails/8.jpg)
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
![Page 9: K. Czerski Institute of Physics, University of Szczecin Euratom Workshop Szczecin, 23.03.2006 Deuteron Fusion Reactions in Metallic Environments](https://reader036.vdocuments.mx/reader036/viewer/2022062321/56649ec05503460f94bcc11c/html5/thumbnails/9.jpg)
cos1 22Pa
d
dtot
Angular Distribution
d + d 3He + n d + d 3H + p
Taa2
![Page 10: K. Czerski Institute of Physics, University of Szczecin Euratom Workshop Szczecin, 23.03.2006 Deuteron Fusion Reactions in Metallic Environments](https://reader036.vdocuments.mx/reader036/viewer/2022062321/56649ec05503460f94bcc11c/html5/thumbnails/10.jpg)
Energy Spectra
![Page 11: K. Czerski Institute of Physics, University of Szczecin Euratom Workshop Szczecin, 23.03.2006 Deuteron Fusion Reactions in Metallic Environments](https://reader036.vdocuments.mx/reader036/viewer/2022062321/56649ec05503460f94bcc11c/html5/thumbnails/11.jpg)
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
![Page 12: K. Czerski Institute of Physics, University of Szczecin Euratom Workshop Szczecin, 23.03.2006 Deuteron Fusion Reactions in Metallic Environments](https://reader036.vdocuments.mx/reader036/viewer/2022062321/56649ec05503460f94bcc11c/html5/thumbnails/12.jpg)
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