Low-energy ${}^7\mathrm{Li}(n,\gamma ){}^8\mathrm{Li}$ and ${}^7\mathrm{Be}(p,\gamma ){}^8\mathrm{B}$ radiative capture reactions within the Skyrme Hartree-Fock approach

The electromagnetic dipole transitions in ${}^7\mathrm{Be}(p,\gamma ){}^8\mathrm{B}$ and ${}^7\mathrm{Li}(n,\gamma ){}^8\mathrm{Li}$ reactions at the keV-energy region were analyzed simultaneously within the Skyrme Hartree-Fock potential model. The Skyrme Hartree-Fock calculation is adopted as a microscopic approach to obtain consistently the single-particle bound and scattering states in the calculation of the radial overlap function within the potential model. All nonresonant and resonant electromagnetic dipole transitions are taken into account. The electric dipole transitions are successfully described with the slightest adjustment. The resonant magnetic dipole transitions at 633 keV and 2184 keV of the ${}^7\mathrm{Be}(p,\gamma ){}^8\mathrm{B}$ reaction, and the one at 222 keV of ${}^7\mathrm{Li}(n,\gamma ){}^8\mathrm{Li}$ are also analyzed. The astrophysical ${\mathcal{S}}_{17}\left(0\right)$ factor of the ${}^7\mathrm{Be}(p,\gamma ){}^8\mathrm{B}$ reaction is found to be 22.3 eV b.

Figure 1

Level schemes of ${}^8\mathrm{Li}$ (a) and ${}^8\mathrm{B}$ (b). All low-lying resonances are caused by the $M1$ transitions to the ground states ($2^{+}$) of ${}^8\mathrm{Li}$ and ${}^8\mathrm{B}$. The blue dotted lines are the reaction thresholds. The arrows are bound-to-bound $M1$ transitions. The black dashed arrows are the transitions above the threshold. The dotted arrow is the subthreshold $M1$ transition.

Figure 2

The total $E1$ transition (solid line) caused by $s$ (dashed line) and $d$ waves (dotted line) in the partial-wave analysis. $S_F=1.0$. The experimental data were taken from Refs. [8, 28, 29, 30].

Figure 3

The $E1$ transitions caused by $s$ and $d$ waves in the partial-wave analysis. The experimental data were taken from Refs. [31, 32, 33, 34, 35, 36, 37, 38, 39].

Figure 4

The relevance of ${\mathcal{S}}_{17}$ factor of ${}^7\mathrm{Be}(p,\gamma ){}^8\mathrm{Be}$ at low energy. The calculation using ${\mathcal{N}}_b=0.70$ gives ${\mathcal{S}}_{17}\left(0\right)=22.3$ eV b. While the value of 21.2 eV b is given by calculation with ${\mathcal{N}}_b=1.00$. The experimental data are from JUN10 [39] (circle), SCH06 [38] (cross), BAB03 [37] (square), STR01 [36] (triangle), HAM98 [35] (diamond), FIL83 [33] (pentagram), and KAV69 [31] (octagram).

Figure 5

All transitions are considered. The dashed line is the contribution of the $E1$ transition as shown in Fig. 3. The dotted and dash-dotted lines are of the $M1$ transitions. The solid line shows our final result. The experimental data were taken from Refs. [31, 32, 33, 34, 35, 36, 37, 38, 39].

Figure 6

The calculation for the ${}^7\mathrm{Li}(n,\gamma ){}^8\mathrm{Li}$ radiative-capture reaction. All electromagnetic transitions are in consideration. The values of $S_F$ are adjusted to reproduce the data of Ref. [28] ($S_F=0.17$) or Ref. [29] ($S_F=0.05$).

Figure 7

The partial analysis for the three $M1$ resonances. In (a), (b), and (c), the contributions by the spin-orbit partners with all channel spin are shown. (d), (e), and (f) illustrate the contribution of different channel spins.