(d,Li6) Reactions in Light Elements and Distorted-Wave Born Approximation Calculations

Differential cross sections for ($d$, ${\mathrm{Li}}^6$) reactions have been measured for ${\mathrm{C}}^{13}$, ${\mathrm{O}}^{17}$, ${\mathrm{O}}^{18}$, and ${\mathrm{F}}^{19}$ targets in addition to those reported previously for ${\mathrm{C}}^{12}$, ${\mathrm{O}}^{16}$, and ${\mathrm{F}}^{19}$.${\mathrm{Li}}^6$ particles were identified by using time-of-flight analysis in conjunction with energy analysis. ($d$, ${\mathrm{Li}}^6$) reactions for all six targets, investigated at incident deuteron energies near 15 MeV, have large total cross sections (4.2 to 0.6 mb). The angular distributions are diffraction-like, and show forward peaking and minor sensitivity to energy changes of a few hundred keV. A theoretical interpretation of the ($d$, ${\mathrm{Li}}^6$) reactions is given in terms of a simple direct four-nucleon transfer mechanism. Most calculations are made in the zero-range distorted-wave Born approximation (DWBA). The reaction form factor is calculated in the alpha transfer limit; i.e., an $\alpha$-cluster (with predictable quantum numbers) is assumed to exist in the target at the instant of the reaction and to be transferred as a whole. The cluster wave function is generated in a Saxon well of a depth determined by the $\alpha$ separation energy. Best-fit optical-model parameters for 15-MeV deuterons were used to generate the incident deuteron waves. All ${\mathrm{Li}}^6$ distorted waves were based on an optical-model fit to the ${\mathrm{C}}^{12}$(${\mathrm{Li}}^7$, ${\mathrm{Li}}^7$)${\mathrm{C}}^{12}$ scattering at 7 MeV. No adjustable parameters were used. In spite of these restrictions and the simplicity of the model, good agreement between data and calculations is observed for ${\mathrm{C}}^{12}$, ${\mathrm{C}}^{13}$, ${\mathrm{O}}^{16}$, ${\mathrm{O}}^{17}$, and ${\mathrm{O}}^{18}$. Agreement for ${\mathrm{F}}^{19}(d, {\mathrm{Li}}^6){\mathrm{N}}^{15}$ could be obtained only by parameter adjustments. The normalization of the DWBA predictions also appears to be in general agreement with the absolute magnitude for these reactions, and tentative spectroscopic factors for the...