Nucleon Tunneling inN14+N14Reactions

Abstract

The tunneling process is considered as a partial explanation of observations by Reynolds and Zucker on the reactions ${\mathrm{N}}^{14}$(${\mathrm{N}}^{14}$,${\mathrm{N}}^{13}$)${\mathrm{N}}^{15}$ and ${\mathrm{N}}^{14}$(${\mathrm{N}}^{14}$,${\mathrm{C}}^{13}$)${\mathrm{O}}^{15}$. The theory of reactions of this type is first formulated in reasonably general terms, employing a classical mechanics treatment of the motion of the colliding nuclei and of the reaction products. The starting point is a set of adiabatic (fixed centers of mass of heavy aggregates) wave functions, which is transformed to a related system of functions insuring a better initial convergence of the iteration procedure. The anisotropy of transfer inherent in the $p$-nucleon eigenfunctions is taken into account but finally eliminated by the consideration of extreme $j-j$ coupling shell structure eigen-function assignments, as well as the spin and statistics of the nuclei. The effect of antisymmetrizing the wave function with respect to neutrons and protons in the incomplete shells is worked out. The relation of the angular distribution problem presented by the case of dominant Coulomb effects to a popular form of stripping theory is discussed, with the conclusion that the classical dynamics approximation to the motion of the colliding nuclei is adequate. The dependence of the total cross section on energy and of the differential cross section on angle, when compared with experiment, indicates the presence of another reaction mechanism participating especially at the lower energies.