Description of the proton and neutron radiative capture reactions in the Gamow shell model

We formulate the Gamow shell model (GSM) in coupled-channel (CC) representation for the description of proton/neutron radiative capture reactions and present the first application of this new formalism for the calculation of cross sections in mirror reactions ${}^7\mathrm{Be}(p,\gamma ){}^8\mathrm{B}$ and ${}^7\mathrm{Li}{(n,\gamma )}^8\mathrm{Li}$. The GSM-CC formalism is applied to a translationally invariant Hamiltonian with an effective finite-range two-body interaction. Reactions channels are built by GSM wave functions for the ground state $3/2^{-}$ and the first excited state $1/2^{-}$ of ${}^7\mathrm{Be}$/${}^7\mathrm{Li}$ and the proton/neutron wave function expanded in different partial waves.

Figure 1

Plot of the E1 astrophysical factor for the ${}^7\text{Be}(p,\gamma ){}^8\text{B}$ reaction. The solid line represents the exact, fully antisymmetrized calculation with both the ground state $J^{\pi }=3/2_1^{-}$ and the first excited state $J^{\pi }=1/2_1^{-}$ of the ${}^7\text{Be}$ target included. The dashed line shows results of the calculations if the first excited state of ${}^7\text{Be}$ is omitted. For more details, see the description in the text.

Figure 2

The same as in Fig. 1 but for the $M1$ transitions. The two peaks correspond to the $1_1^{+}$ and $3_1^{+}$ resonances of ${}^8\text{B}$.

Figure 3

The same as in Fig. 1 but for the $E2$ transitions. The two peaks correspond to the $1_1^{+}$ and $1_2^{+}$ resonances of ${}^8\text{B}$.

Figure 4

Plot of the total astrophysical factor for the ${}^7\text{Be}(p,\gamma ){}^8\text{B}$ reaction. Data are taken from Refs. [22, 26]. The solid line represents the exact, fully antisymmetrized calculation including both the ground state $J^{\pi }=3/2_1^{-}$ and the first excited state $J^{\pi }=1/2_1^{-}$ of the ${}^7\text{Be}$ target. Calculations neglecting the first excited state of the target are shown with the dashed line. For more details see the description in the text.

Figure 5

Plot of the $E1$ astrophysical factor for the ${}^7\text{Be}(p,\gamma ){}^8\text{B}$ reaction. The solid line represents the exact, fully antisymmetrized calculation. The calculations in the long-wavelength approximation are represented by the dashed and dotted lines in the fully antisymmetrized and non-antisymmetrized cases, respectively. For more details, see the description in the text.

Figure 6

The same as in Fig. 5 but for the $M1$ transitions. The two peaks correspond to the $1_1^{+}$ and $3_1^{+}$ resonances of ${}^8\text{B}$.

Figure 7

The same as in Fig. 1 but for the ${}^7\text{Li}(n,\gamma ){}^8\text{Li}$ reaction. For more details, see the description in the text.

Figure 8

The same as in Fig. 1 but for $M1$ transitions in the ${}^7\text{Li}(n,\gamma ){}^8\text{Li}$ reaction. The peak corresponds to the $3_1^{+}$ resonance in ${}^8\text{Li}$.

Figure 9

The same as in Fig. 8 but for the $E2$ transitions. The two peaks correspond to the $3_1^{+}$ and $1_2^{+}$ resonances of ${}^8\text{Li}$.

Figure 10

Plot of the total cross section for the ${}^7\text{Li}(n,\gamma ){}^8\text{Li}$ reaction. Data are taken from Ref. [62]. The solid line represents the exact, fully antisymmetrized calculation. Calculations in the long-wavelength approximation are represented by the dashed and dotted lines in the antisymmetrized and non-antisymmetrized cases, respectively. For more details see the description in the text.

Figure 11

The same as in Fig. 5 but for the ${}^7\text{Li}(n,\gamma ){}^8\text{Li}$ reaction. For more details, see the description in the text.

Figure 12

The same as in Fig. 11 but for the $M1$ transitions. The peak corresponds to the $3_1^{+}$ resonance in ${}^8\text{Li}$.