N14(N14,N13)N15Reaction at Low Energies and the Elastic Scattering ofN14byN14

The molecular-viewpoint form of nucleon tunneling theory is used in the two-level approximation and with neglect of the dynamic reaction terms for a partial-wave analysis allowing the inclusion of the effects of wave function absorption through the use of an imaginary part of the potential. The equations are used in an analysis of improved measurements of the differential and total cross sections of the reaction ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$(${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$,${}_{}{}^{13}{}_{}{}^{}\mathrm{N}$)${}_{}{}^{15}{}_{}{}^{}\mathrm{N}$, with special attention to laboratory energies $E_l\le 16$ MeV which are below the Coulomb barrier. At the lowest energies, the analysis involves only the Coulomb interaction between the heavy particles. Fits to data are improved at the higher energies through the introduction of optical potentials. The principal function of these in the present work is to modify the wave function at distances larger than those corresponding to definite contact between ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ and ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$. The transfer function $\beta \mathrm{}\left(R\right)\mathrm{}$ is cut off at small values of the internuclear distance $R$ to avoid the inclusion of unrealistic contributions to neutron transfer when the two nuclei are no longer distinct. The potential has been adjusted for best fits to neutron-transfer data. The long distance tail of the potentials tried was made to agree, regarding relative values at different distances, with that calculated by McIntosh, Rawitscher, and Park in their work on the elastic scattering of ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ by ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$, and depends therefore on nucleon-nucleus scattering information. The potentials were adjusted to represent the elastic-scattering ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ + ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ data simultaneously with neutron-transfer data. These combined requirements are met best by potentials referred to as 2 and 3 in the text. The reduced width of the transferred neutron obtained from transfer data depends on the potential only weakly. The same reduced width from elastic-scattering information is sensitive to the choice of potential. The best agreement of the elastic-scattering and neutron-transfer reduced widths is obtained for potential 3, the disagreement being less than by a factor 2. The combined uncertainty of the two ways of arriving at the reduced width is believed to be large and to make the discrepancy insignificant. The combined treatment of neutron transfer and of elastic scattering is self-consistent in the sense described. The neutron transfer reduced width is slightly smaller than the single-particle reduced width calculated with the nucleon-nucleus potential employed in obtaining the proportionality constant of the long-distance nucleus-nucleus potential tail.