The radiative capture reaction ${}_{}{}^3{}_{}{}^{}\mathrm{He}(\alpha ,\gamma ){}_{}{}^7{}_{}{}^{}\mathrm{Be}$ at low energies has been analyzed on the basis of the direct capture model in order to provide a theoretical estimate of the stellar reaction rate. The scattering wave functions of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ by $\alpha$ and the bound state wave functions of ${}_{}{}^7{}_{}{}^{}\mathrm{Be}$ were constructed by the empirical model, the phenomenological Woods-Saxon potential model, and the orthogonality condition model; these models account for the measured elastic scattering and excitation energies of the low-lying states of ${}_{}{}^7{}_{}{}^{}\mathrm{Be}$. The total cross section factors $S\left(E_{\mathrm{c}.\mathrm{m}.\mathrm{}}\right)$ of the $E1\mathrm{}$, $M1\mathrm{}$, and $E2\mathrm{}$ capture from the $l=0\mathrm{}-3$ partial waves clearly show a rising behavior as the incident energy goes lower, which agrees with the experimental data. The negative scattering phase shifts, which can be associated with the presence of almost energy-independent inner oscillations in the relative wave function between ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ and $\alpha$ due to the Pauli exclusion principle, seem to be responsible for this behavior.

NUCLEAR REACTIONS ${}_{}{}^3{}_{}{}^{}\mathrm{He}(\alpha ,\gamma ){}_{}{}^7{}_{}{}^{}\mathrm{Be}$ at low energies; direct capture model analysis; othogonality condition model; calculated $\sigma \mathrm{}\left(E\right)\mathrm{}$, $S\left(E\right)\mathrm{}$, and branching ratios.

• Received 25 August 1980

DOI:https://doi.org/10.1103/PhysRevC.23.33