Radiative capture reactionHe3(α,γ)Be7at low energies

Abstract

The radiative capture reaction $^{3}\mathrm{He}(\ensuremath{\alpha},\ensuremath{\gamma})^{7}\mathrm{Be}$ 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 $\ensuremath{\alpha}$ 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 $S({E}_{\mathrm{c}.\mathrm{m}.})$ of the $E1$, $M1$, and $E2$ capture from the $l=0\ensuremath{-}3$ 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 $\ensuremath{\alpha}$ due to the Pauli exclusion principle, seem to be responsible for this behavior.NUCLEAR REACTIONS $^{3}\mathrm{He}(\ensuremath{\alpha},\ensuremath{\gamma})^{7}\mathrm{Be}$ at low energies; direct capture model analysis; othogonality condition model; calculated $\ensuremath{\sigma}(E)$, $S(E)$, and branching ratios.