Comparison of Rotating Finite Range Model

and Thomas-Fermi Fission barriersK. Mahata

Nuclear Physics Division

Bhabha Atomic Research Centre

Mumbai –400 085, INDIA

Plan of the talk

Introduction

Fission barrier models

Compound nucleus formation and decay

Statistical model of CN decay

Discrepancy in fold distribution measurement

Inconsistency in fold distribution and cross-section

Summary an conclusion

En

erg

y

Bf

Fission barrier which inhibit fission results from near cancellation of surface and Coulomb energy.

Single particle effects

Angular momentum dependence

Compound nucleus formation

Competition between the fission and the particle evaporation channel

saddle point shape determine the angular distribution of fission fragments.

Introduction

Rotating Liquid Drop Model (1974):

Potential energies and equilibrium configuration of a rotating uniformly charged incompressible fluid with sharp boundary.

Bf required to reduce by a factor varying between 0.5 to 0.9

extracted eff were found to be larger.

Rotating Finite Range Model (1986):

Finite range effects in the nuclear surface energy

Finite surface diffuseness effects in the Coulomb energy and effective moment of inertia.

Thomas-Fermi Model (1996):

Effective two-body interaction were adjusted to fit shell-corrected masses, diffuseness of nuclear surface and depth of optical model potential

Fission barrier model

Angular momentum dependence

27

14)0(

)0()(22 2/

J

f

Jff

MeVB

eBJB J

Thomas-Fermi fissionbarrier falls faster than RFRM fission barrier

TargetP

CN

ER Saddle

FF FF

Scission

Compound nucleus formation and decay

n p

J()

E*

Fu

s(J)

(J) xn

Fission

Statistical Model for the decay of compound nucleus

All possibilities for decay are equally likely

Governed and T.

dEJE

jET

hdEsjEJER

sj

sjS

SJ

SJl ii

flfii

i

i

|| || ),(

),()(

1),,;,(

Def.

E*

Important input

Bf

af/an

48Ca + 142Nd 190Hg 80Se + 110Pd

B. Djerroud et al., PRC 61, 024607 (2000)

Discrepancy in fold distribution

Enhancement of the high-spin population for the more symmetric system, brought in by the coupling to inelastic channels.

No enhancement was observed.

Fold distribution cont…

ER-fission data not availableAvailable for 40Ar + 148Sm 188Hg (similar to 48Ca + 142Nd)ER data for 86Kr + 104Ru 190Hg(similar to 80Se + 110Pd)

What happens to ER-fission cross-section

Reisdorf et al., NPA444 (1985) 154 Reisdorf et al., NPA438 (1985) 212

Entry Spin distribution

Sensitivity of the fission and the ER excitation function

Use of Thomas-Fermi fission barriers produces good agreement

RFRM fission barrier has to be reduced by a factor 0.85

Inclusion of –3 MeV shell correction in Thomas-Fermi fission barriers produces large discrepancy

ER-fission data and fold distribution data are not consistent

The accuracy of fission barrier height can be checked by comparing the measured fission and ER cross-sections with the statistical model predictions.

Effort should be put to parameterize Thomas-Fermi barrier

Summary & Conclusion