Information-theoretic analysis of energy disposal in heavy-ion transfer reactions

Abstract

Heavy-ion transfer reactions to highly excited states are examined in terms of surprisal analysis-a constrained statistical approach motivated by information-theoretic considerations. The practical use of the procedure is discussed and illustrated by application to the available data from a variety of reactions. The experimentally measured energy spectra for multinucleon transfer are found to be well described by a distribution of maximal entropy subject to constraints. These constraints are shown to imply that the distribution of single nucleon occupation numbers in the heavy residual nucleus is fully relaxed but that the two-particle (and higher) correlation functions are not. For few-nucleon transfers the energy spectra contain a second, smaller, component which is more strongly damped. The dynamical origin of the constraints is discussed in terms of sum rules derived from models for the transfer process. A simple model for grazing collisions which includes the effects of tangential friction (with the same damping constant for all exit channels) provides a qualitative and a quantitative account of the variation of the optimal $Q$ value with the number of transferred nucleons.NUCLEAR REACTIONS Heavy ions, $^{232}\mathrm{Th}$($^{16}\mathrm{O}$,$X$), $X=^{17,16,15}\mathrm{N}, ^{15,14,13,12}\mathrm{C}, ^{13,12,11}\mathrm{B}, ^{10}\mathrm{Be}$, $E=105$ MeV. $^{96}\mathrm{Mo}$($^{14}\mathrm{N}$,$X$), $X=^{15}\mathrm{O}, ^{13}\mathrm{C}, ^{10}\mathrm{B}, ^{9}\mathrm{Be}, ^{7}\mathrm{Li}$, $E=97$ MeV. $^{A}\mathrm{Mo}(^{14}\mathrm{N},X)$, $X=^{13}\mathrm{C}, ^{12}\mathrm{B}$, $A=100, 98,97,96,95,94,92$, $E=97$ MeV. $^{53}\mathrm{Cr}$($^{14}\mathrm{N}$,$X$), $X=^{13}\mathrm{C}, ^{11}\mathrm{B}, ^{9}\mathrm{Be}$, $E=90$ MeV. $^{232}\mathrm{Th}$($^{15}\mathrm{N}$,$X$), $X=^{14,12}\mathrm{C}, ^{13,11}\mathrm{B}, ^{10}\mathrm{Be}, ^{9}\mathrm{Li}$, $E=145$ MeV. $^{232}\mathrm{Th}$($^{22}\mathrm{Ne}$,$X$), $X=^{26}\mathrm{Na}, ^{19,18}\mathrm{O}, ^{17}\mathrm{N}, ^{16,15}\mathrm{C}$, $E=174$ MeV. $^{197}\mathrm{Au}$($^{16}\mathrm{O}$,$X$), $X=^{15}\mathrm{N}, ^{11}\mathrm{B}, ^{9}\mathrm{Be}$, $E=218 \mathrm{and} 250$ MeV. Ni($^{16}\mathrm{O}$, $^{12}\mathrm{C}$)Zn, $E=96$ MeV Energy and nucleon occupation numbers in the ejectiles. Models for optimal Q values. Tangential friction.