Microscopic description of the ${}^2\mathrm{H}(\alpha ,\gamma ){}^6\mathrm{Li}$ radiative capture reaction

The ${}^2\mathrm{H}(\alpha ,\gamma ){}^6\mathrm{Li}$ radiative capture responsible for the ${}^6\mathrm{Li}$ production during the big-bang nucleosynthesis is comprehensively studied within a microscopic approach. The approach implements microscopically clustering aspects of nuclear structure and dynamics in an oscillator-basis representation. The total astrophysical $S$ factor of the reaction is calculated. All allowed partial electric quadrupole and magnetic dipole transitions between the ${}^4\mathrm{He}+{}^2\mathrm{H}$ continuum and the ${}^6\mathrm{Li}$ ground state are considered in the standard long-wavelength limit. Isospin-forbidden electric dipole transitions are taken into account in two ways. The first method is based on the expression for the electric dipole operator at the leading order of the long-wavelength approximation with the usage of the exact-mass prescription. In the second method, this operator is written at the first order beyond the leading-order approximation. Contributions of the transitions are compared to each other. The ${}^4\mathrm{He}+{}^2\mathrm{H}$ nuclear phase shifts for the initial channels of the considered reaction are computed. Important properties of the ${}^6\mathrm{Li}$ nucleus, such as the breakup threshold, the asymptotic normalization constants, and the electric quadrupole moment are also described. Deformation effects and their manifestations in ${}^6\mathrm{Li}$ are discussed. The obtained results are shown to be in good agreement with a large set of experimental data.

Figure 1

The $1^{+}$ $S$-wave nuclear phase shift for the ${}^4\mathrm{He}+{}^2\mathrm{H}$ elastic scattering.

Figure 2

The $0^{\text{–}}$ $P$-wave nuclear phase shift for the ${}^4\mathrm{He}+{}^2\mathrm{H}$ elastic scattering.

Figure 3

The $1^{\text{–}}$ $P$-wave nuclear phase shift for the ${}^4\mathrm{He}+{}^2\mathrm{H}$ elastic scattering.

Figure 4

The $2^{\text{–}}$ $P$-wave nuclear phase shift for the ${}^4\mathrm{He}+{}^2\mathrm{H}$ elastic scattering.

Figure 5

The $1^{+}$ $D$-wave nuclear phase shift for the ${}^4\mathrm{He}+{}^2\mathrm{H}$ elastic scattering.

Figure 6

The $2^{+}$ $D$-wave nuclear phase shift for the ${}^4\mathrm{He}+{}^2\mathrm{H}$ elastic scattering.

Figure 7

The $3^{+}$ $D$-wave nuclear phase shift for the ${}^4\mathrm{He}+{}^2\mathrm{H}$ elastic scattering.

Figure 8

The total astrophysical $S$ factor for the ${}^2\mathrm{H}(\alpha ,\gamma ){}^6\mathrm{Li}$ reaction with the $\mathrm{E}1$ transitions described by using the PEM.

Figure 9

The total astrophysical $S$ factor for the ${}^2\mathrm{H}(\alpha ,\gamma ){}^6\mathrm{Li}$ reaction with the $\mathrm{E}1$ transitions at the FOLWA.

Figure 10

The ${}^2\mathrm{H}(\alpha ,\gamma ){}^6\mathrm{Li}$ astrophysical $S$ factors for the total $\mathrm{E}1$, $\mathrm{E}2$, and $\mathrm{M}1$ captures calculated by using the $\mathrm{PHN}$-I potential.

Figure 11

Predictions from the present paper for the ${}^2\mathrm{H}(\alpha ,\gamma ){}^6\mathrm{Li}$ total astrophysical $S$ factor calculated with the $\mathrm{E}1$-PEM (dashed-dot line) and $\mathrm{E}1$-FOLWA (full line) contributions compared to the results of the previous works [20, 22, 33].

Figure 12

Comparison of the $\mathrm{E}1$ and $\mathrm{E}2$ contributions to the energy dependence of the ${}^2\mathrm{H}(\alpha ,\gamma ){}^6\mathrm{Li}$ total astrophysical $S$ factor obtained in the different works.