Statistical Theory of Neutron-Induced Nuclear Fission and of Heavy-Ion Fusion

TL;DR

This paper develops a statistical framework for neutron-induced nuclear fission and heavy-ion fusion using random-matrix theory, providing analytical expressions for reaction probabilities based on compound nucleus models.

Contribution

It introduces a novel statistical approach connecting compound nucleus theory with barrier penetration, yielding explicit formulas for fission and fusion probabilities.

Findings

Derived closed-form analytical expressions for reaction probabilities.

Partially calculated using existing compound-nucleus theory.

Probabilities linked to barrier passage can be determined experimentally or theoretically.

Abstract

For both reactions we use an approach similar to that of compound-nucleus reaction theory. For neutron-induced fission, we describe the compound system generated by absorption of the neutron and the nuclear system near the scission point as two statistically independent systems governed by random-matrix theory. The systems are connected either by a barrier penetration factor or by a set of transition states above the barrier. Each system is coupled to a different set of channels. An analogous model is used for heavy-ion fusion. Assuming that (seen from the entrance channel) the system on the other side of the barrier is in the regime of strongly overlapping resonances, we obtain for fixed spin and parity closed-form analytical expressions for the total probability for fission and for fusion. Parts of these expressions can be calculated reliably within existing compound-nucleus reaction theory. The remaining parts are the probabilities for passage through or over the barrier. These may be determined theoretically from the liquid-drop model or experimentally from total fission or fusion cross sections.