Branching ratios in heavy ion reactions: Constrained phase space approach

Abstract

Branching ratios in heavy ion reactions can be quantitatively predicted using the procedure of maximal entropy subject to the constraints that determine the energy distribution. Including the two constraints required to quantitatively determine the energy distribution accounts very well for the branching fractions for all the reactions examined. The branching ratio amongst two ejectiles is given as the ratio of two nuclear partition functions. Including only the single dominant constraint on the energy distribution provides a near quantitative description of the branching ratios. In this latter case, the branching fractions can be computed directly from the optimal $Q$ value. The exact procedure for doing so is described. An approximation to the order of magnitude of the branching fraction into a given exit channel is $\mathrm{ln}P=\ensuremath{\beta}({Q}_{\mathrm{gg}}\ensuremath{-}〈Q〉)$, where $\ensuremath{\beta}$ is the temperature of the residual nucleus, ${Q}_{\mathrm{gg}}$ is the ground-state to ground-state $Q$ value, and $〈Q〉$ is the mean value. In general, both $\ensuremath{\beta}$ and $〈Q〉$ differ for different exit channels, less so, however, within a given family of isotopes.NUCLEAR REACTIONS Heavy ions, $^{232}\mathrm{Th}(^{16}\mathrm{O}, X)$, $X=^{9,10}\mathrm{Be}, ^{11\ensuremath{-}13}\mathrm{B}, ^{12\ensuremath{-}15}\mathrm{C}, ^{15\ensuremath{-}17}\mathrm{N}, ^{18,19}\mathrm{O}$, $E=105$ MeV at $\ensuremath{\theta}=70\ifmmode^\circ\else\textdegree\fi{}$, $X=^{10}\mathrm{Be}, ^{11}\mathrm{B}, ^{12\ensuremath{-}14}\mathrm{C}, ^{15}\mathrm{N}$, $E=105$ MeV at $\ensuremath{\theta}=50\ifmmode^\circ\else\textdegree\fi{}, 60\ifmmode^\circ\else\textdegree\fi{}$, $E=125$ MeV at $\ensuremath{\theta}=50\ifmmode^\circ\else\textdegree\fi{}, 60\ifmmode^\circ\else\textdegree\fi{}$. $^{232}\mathrm{Th}(^{15}\mathrm{N}, X)$, $X=^{9,10}\mathrm{Be}, ^{11\ensuremath{-}13}\mathrm{B}, ^{12\ensuremath{-}15}\mathrm{C}$, $E=86$ MeV at $\ensuremath{\theta}=60\ifmmode^\circ\else\textdegree\fi{}$, $X=^{9\ensuremath{-}11}\mathrm{Be}, ^{11\ensuremath{-}13}\mathrm{B}, ^{12\ensuremath{-}15}\mathrm{C}$, $E=95$ MeV at $\ensuremath{\theta}=70\ifmmode^\circ\else\textdegree\fi{}$. $^{181}\mathrm{Ta}(^{35}\mathrm{Cl}, X)$, $X=^{30,31}\mathrm{Si}, ^{31\ensuremath{-}33}\mathrm{P}, ^{33\ensuremath{-}35}\mathrm{S}, ^{36,37}\mathrm{Cl}$, $E=205$ MeV at $\ensuremath{\theta}=70\ifmmode^\circ\else\textdegree\fi{}$. $^{53}\mathrm{Cr}(^{14}\mathrm{N}, X)$, $X=^{6,7}\mathrm{Li}, ^{7,9,10}\mathrm{Be}, ^{10\ensuremath{-}12}\mathrm{B}, ^{12,13}\mathrm{C}$, $E=90$ MeV at $\ensuremath{\theta}=16\ifmmode^\circ\else\textdegree\fi{}$. Branching fractions and energy distribution of ejectiles. Maximal entropy subject to constraints. Nuclear partition functions.