Direct-Capture Model for the ${\mathrm{He}}^3(\alpha , \gamma ){\mathrm{Be}}^7$ and $\mathrm{T}(\alpha , \gamma ){\mathrm{Li}}^7$ Reactions

Using the ${\mathrm{He}}^3$+${\mathrm{He}}^4$ scattering phase shifts, the cross section for the ${\mathrm{He}}^3(\alpha , \gamma ){\mathrm{Be}}^7$ reaction is calculated on the basis of a ${\mathrm{He}}^3$+${\mathrm{He}}^4$ model for the ground state and first excited state of ${\mathrm{Be}}^7$. Capture of particles from the $S$, $P$, $D$, and $F$ partial waves by means of $E1\mathrm{}$, $M1\mathrm{}$, and $E2\mathrm{}$ transitions is considered. The results are in excellent agreement with the experimental data presented in the preceding paper and indicate that the reaction proceeds chiefly by means of $E1\mathrm{}$ capture from the $S$ and $D$ waves. It is a surprising consequence that the $D$ wave contributes an appreciable fraction of the total capture cross section for alpha-particle energies as low as 1 MeV. Using the same values for the reduced widths of the final states that were determined for the ${\mathrm{He}}^3(\alpha , \gamma ){\mathrm{Be}}^7$ reaction, similar calculations have also yielded excellent agreement with the experimental data for both the branching ratio and the total cross section of the mirror reaction $\mathrm{T}(\alpha , \gamma ){\mathrm{Li}}^7$.