1Multiple Resonance Scattering

T.ToimelaVaasa Polytechnic

(Vaasa University of Applied Sciences)tuomo.toimela@puv.fi

2Assumptions:

Consider nano-size cluster of Pd atoms Deuterons absorbed into the Pd cluster can

move quasi-freely within the cluster Quantum many-body theory Collective reaction of the deuterons in the

Pd cluster, with two deuterons fusingtogether and other carrying the energy andmomentum

3Assumptions (contd)

Fermi Golden Rule Nuclear interaction potential

Elastic interaction potential

)(4

)(2

rr am

H

kk,k

4

kk,4

)(

D2D

D2

c

cH

k

k

4Fusion rate H2

2

if

))-E(ED

),qG()(

pdV

)(m

a=

ffi

N

ll

N

N-

i =iiN

NN

rel

pk ()2()()c(4

21

04

421

1

)1(2

21

13

3

0

22

22

1),( 2

i

mq

qG

5Dominant diagram

6Multiple resonance scattering

Momenta of the virtual and final state particles:

7MRS transition rate

UQ

N

D NUQ

Vkmc

QNVma /

1

03

22

02

223

4(const.))0(

const)(

mk

U D2

22

8Implications:

He-4 (ground state) is the overwhelminglydominant fusion channel

The energy is transferred to heat by the largenumber of final state particles

Only soft, secondary radiation No p-p fusion (the energy released too small) Transmutation reactions, if the released energy

large enough (rate depending on the energy Q, thenuclear charge Z and the cluster volume V)

9Transmutation example 1

Consider transmutation of Ba (Iwamura et al.)

MeV68.3SmD6Ba

MeV69.0SmD6Ba

MeV70.0SmD6Ba

MeV71.0SmD6Ba

MeV71.6SmD6Ba

MeV73.1SmD6Ba

MeV71.3SmD6Ba

1502138

1492137

1482136

1472135

1462134

1442132

1422130

10

Example 1 (contd):

The lighter isotopes of Ba have larger reactionenergy and consequently larger transition rate

Hence, they are consumed more rapidly, althoughtthe dominant channel for them is not known:

fissionBa

MeV50.1NdD4Ba

MeV71.6SmD6Ba

134

1422134

1462134

11

Transmutation example 2:

The enhancement of the transition rate bythe MRS formalism does not require anyparticle to penetrate the nucleus

Hence spontaneous fission possible Moreover, the decay rate of unstable nuclei

can be enhanced by MRS (without highenergy particles) = Reifensweiler effect

12

Example 2 (contd)

MeV2.26HeYb

MeV2.51HeHfW

4172

4176180

MeV2.08HeYb

MeV1.77HeHfW

4174

4178182

13

Conclusions

Anomalies in hydrogen/deuterium loaded metalscan be understood by the MRS-formalism in theframework of the quantum many-body theory

Reaction rates depend very sensitively on thereleased energy

Also enhancement of the rate for spontaneousfission or decay rate of radionuclides