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Canadian Journal of Physics

Penetrability Calculations Through a Double-Hump Barrier in Nuclear Fission

J.N. Leboeuf, Rajni Sharma

Published Feb 15, 1973• 12 citations
Publisher

Abstract

The penetrability through double-hump barrier in nuclear fission processes is calculated in the JWKB approximation based on Fröman's F-matrix formalism. Particular attention is paid to coinciding classical turning points where other methods break down. A qualitative discussion of results is also included.
DOI
10.1139/p73-058

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Physics of Particles and Nuclei•Oct 1, 1976•1 citation
In the first part, calculated lifetimes for spontaneous fission from the ground and from the isomer state are presented. The agreement reached with experiments correponds to the crude approximations done, but is better than expected. The calculations are based on the shell correction approach for the potential energy and on the cranking model for the collective mass. In the second part we discuss the behaviour of the so-called least action trajectories: there are two of them, one for symmetric and one for asymmetric shapes. The systematic behaviour of the dynamic barriers and of the peak-to-peak ratio of the fission fragment mass distribution and their correlation with the experimental in formation support this point of view.
Quantum-mechanical tunneling theory in more than one dimension is reviewed. Several systems from nuclear and molecular science are considered specifically, such as, alpha decay of spheroidal nuclei, spontaneous fission, and reactive collinear collisions of hydrogen atoms with hydrogen molecules. The ranges of validity of various approximations that reduce to one-dimensional path integrals or Froeman-Nosov matrices are examined, testing where possible against fully quantum-mechanical coupled-channel solutions. The classical-equations-of-motion methods using complex variables (uniform semiclassical approximation) are explored for nonseparable fission-like model systems. Effects of variable valley widths, curving valleys, and of variable inertial tensors are delineated.