Equilibrium statistical treatment of angular momenta associated with collective modes in fission and heavy-ion reactions

Abstract

The angular momentum effects in deep inelastic processes and fission have been studied in the limit of statistical equilibrium. The model consists of two touching liquid drop spheres. Angular momentum fractionation has been found to occur along the mass asymmetry coordinate. If neutron competition is included (i.e., in compound nucleus formation and fission), the fractionation occurs only to a slight degree, while extensive fractionation is predicted if no neutron competition occurs (i.e., in "fusion-fission" without compound nucleus formation). Thermal fluctuations in the angular momentum are predicted to occur due to degrees of freedom which can bear angular momentum such as wriggling, tilting, bending, and twisting. The coupling of relative motion to one of the wriggling modes, leading to fluctuations between orbital and intrinsic angular momentum, is considered first. Next the effect of the excitation of all the collective modes on the fragment spin is treated. General expressions for the first and second moments of the fragment spins are derived as a function of total angular momentum and the limiting behavior at large and small total angular momentum is examined. Furthermore, the effect of collective mode excitation on the fragment spin alignment is explored and is discussed in light of recent experiments. The relevance of the present study to the measured first and second moments of the y-ray multiplicities as well as to sequential fission angular distributions is illustrated by applying the results of the theory to a well studied heavy-ion reaction.NUCLEAR REACTIONS Studied angular momentum fractionation along mass asymmetry mode. Investigated effect of collective rotational modes on fragment spins. Equilibrium statistical treatment.

Angular momentum misalignment in deep inelastic processes and angular distribution of sequentially emitted particles and gamma rays

“…2~5 Furthermore, additional angular momentum can be generated in the two nuclei by the excitation of angular-momentumbearing modes of the intermediate complex. 6 Several determinations of the magnitude of the transferred angular momentum have been performed, mostly by measuring the associated gamma ray multiplicities, both as a function of the Q value and of the exit channel mass asymmetry. 2 -5 There is, in general, an increase of the transferred angular momentum with increasing Q value.…”

The influence of fluctuations on the correlation between exit-channel kinetic energy and entrance-channel angular momentum for heavy ion collisions

“…Let us consider the simple analytical case of two equal touching spheres with one wriggling mode [5] coupled to the orbital motion.…”

“…In this paper we shall discuss two sources of fluctuations relevant to this problem: a) the coupling of orbital motion to a thermally excited wriggling mode [5] and b) the effect of random shape fluctuations at scission [6][7][8].…”

Fragment spin correlations in damped nuclear reactions

“…-4-In order to judge the significance of the calculated results, we also consider the statistical model developed by Moretto [5]. The statistical model idealizes the dinuclear reaction complex as two rigid spheres (with moments of inertia JA = t mAR 2 and .../ 8 = t mBR 2 ) in statistical equilibrium at a given separation R. The associated temperature T ·is related to the dissipated energy Q by Q = ai with a= (A+B)/{8 MeV).…”