Influence of protons on the capture of electrons by ${}^7\mathrm{Be}$ in the Sun

The capture of electrons by the nucleus ${}^7\mathrm{Be}$ from the three-body initial state $p+e^{-}+$${}^7\mathrm{Be}$ in the continuum is studied. On the basis of the expansion of the three-body continuum wave function in the small parameter $\epsilon \approx (m_e/m_p){}^{1/2}$ [$m_e$ ($m_p$) is the electron (proton) mass], the role of the protons on the electron capture is considered. The results are compared with the traditional treatment of the electron capture by the nucleus ${}^7\mathrm{Be}$. For stars with density and temperature like in the center of the Sun the studied mechanism can make a non-negligible contribution to the capture rate.

Figure 1

The Jacobi coordinates for the $p+e^{-}{+}^7$Be system.

Figure 2

The dependence of the mean value $\langle \varsigma (R_0,T)\rangle$ on the temperature $T$ and the value of the mean distance $R_0$. Solid line, $R_0=0.1\times {10}^4$ fm; dashed line, $R_0=0.25\times {10}^4$ fm; dotted line, $R_0=0.5\times {10}^4$ fm; dashed and dotted line, $R_0=1.0\times {10}^4$ fm; dashed and double dotted line, $R_0=1.5\times {10}^4$ fm.

Figure 3

The dependence of the mean value $\langle \varsigma (R_0,T)\rangle$ on the values of the mean distance $R_0$. Solid curve, $\mathit{kT}=1.161$ keV, $\beta =1/7$, and $Z=5$; dashed and dotted curve, $\mathit{kT}=1.161$ keV, $\beta =4/7$, and $Z=6$; dashed curve, $\mathit{kT}=1.5$ keV, $\beta =1/7$, and $Z=5$. The dashed and dotted curve corresponds to analogous calculations for the nuclei ${}^4\mathrm{He}$.

Figure 4

The dependence of the mean value $\langle \varsigma (R_0,T)\rangle$ on the temperature $T$ and the value of the mean distance $R_0$. Solid line, $R_0=3.25\times {10}^4$ fm; dashed line, $R_0=2.75\times {10}^4$ fm; dashed and dotted line, $R_0=3.75\times {10}^4$ fm.