Constraints on the ${}^7\mathrm{Be}(p,\gamma ){}^8\mathrm{B}$ radiative capture rate from charge symmetry

Cross sections for the dipole radiative capture reactions ${}^7\mathrm{Li}(n,\gamma ){}^8\mathrm{Li}$ and ${}^7\mathrm{Be}(p,\gamma ){}^8\mathrm{B}$ are calculated in a two-body model, which is based on a Woods-Saxon parametrization of the nuclear interaction. The well depth is adjusted for each reaction channel so that the measured separation energies and $s$-wave scattering lengths are reproduced. The calculations are repeated for a wide range of the radius and the diffuseness of the interaction. The predicted $S$ factor for the radiative proton capture on ${}^7\mathrm{Be}$ falls within a surprisingly narrow range of values when the model is calibrated to reproduce measurements of the mirror reaction ${}^7\mathrm{Li}(n,\gamma ){}^8\mathrm{Li}$. The simplified model used here is consistent with the shell model approach for proton capture on ${}^7\mathrm{Be}$ but it gives a significantly smaller cross section for neutron capture on ${}^7\mathrm{Li}$.

Figure 1

Cross sections for radiative neutron capture on ${}^7\mathrm{Li}$ to the $2^{+}$ ground state ${}^8\mathrm{Li}$ (upper curves and data) and to the $1^{+}$ excited state (lower curves). The data are from Refs. 14, 15. The dashed curves show the $1∕\sqrt{E_n}$ extrapolation of the thermal neutron cross sections [9]. The solid curves are the calculated cross sections discussed in the text.

Figure 2

The normalization factor defined in Eq. (2) for the radiative neutron capture on ${}^7\mathrm{Li}$ is shown as a function of the nuclear radius parameter $r_0$ for three choices of the diffuseness $a$.

Figure 3

$S$ factor for the radiative proton capture on ${}^7\mathrm{Be}$ as function of the c.m. energy. The data are from Ref. 2. The solid curves show the separate contributions from $s$ and $d$ waves, and the sum. The potential parameters are $r_0=1.3$ and $a=0.58\mathrm{fm}$, and the spectroscopic factor is 1. The dashed curves were obtained for a $d$-wave well depth set equal to zero (lower dashed curves) or $V(s_{1∕2},2^{-})$ (upper dashed curves).

Figure 4

$S$ factor for radiative proton capture on ${}^7\mathrm{Be}$ at zero energy, calculated as a function of the radius parameter $r_0$ for three values of the diffuseness $a$. The spectroscopic factor was set equal to 1.

Figure 5

Correlation between the normalization factor $N_{nc}$ for neutron capture on ${}^7\mathrm{Li}$ and the effective $S$ factor, $N_{nc}\times S_{17}\left(0\right)$, for proton capture on ${}^7\mathrm{Be}$ obtained for three values of the diffuseness.