Isotopic trends in capture reactions with radioactive and stable potassium beams

The isotopic dependence of the capture cross section is analyzed in the reactions ${}^{37,39,41,43,45,46,47}\text{K}+{}^{124}\text{Sn},{}^{208}\text{Pb}$ with stable and radioactive beams. A comparison between the reactions ${}^{46}\text{K}+{}^{124}\text{Sn},{}^{208}\text{Pb}$ and ${}^{48}\text{Ca}+{}^{124}\text{Sn},{}^{208}\text{Pb}$ is performed. The sub-barrier capture cross sections are larger in the reactions with a stable beam at fixed $E_{\mathrm{c}.\mathrm{m}.}\text{−}{V}_b$.

Figure 1

Calculated dependence of capture cross section ${\sigma }_{\mathrm{cap}}$ on $E_{\mathrm{c}.\mathrm{m}.}-V_b$ for the indicated reactions ${}^A\text{K}+{}^{208}\text{Pb}$.

Figure 2

Calculated dependence of capture cross section ${\sigma }_{\mathrm{cap}}$ on $A$ for the reactions ${}^A\text{K}+{}^{208}\text{Pb}$ at fixed bombarding energies $E_{\mathrm{c}.\mathrm{m}.}=V_b+5$ MeV (triangles), $V_b$ (squares), $V_b-5$ MeV (circles).

Figure 3

Calculated dependence of capture cross section $\sigma$ on $E_{\mathrm{c}.\mathrm{m}.}$ for the reactions ${}^{46}\text{K}+{}^{208}\text{Pb}$ (solid line) and ${}^{48}\text{Ca}+{}^{208}\text{Pb}$ (dashed line). Experimental data (symbols) for the ${}^{48}\text{Ca}+{}^{208}\text{Pb}$ reaction are from Refs. [17, 18, 19].

Figure 4

Calculated dependencies of $F\left(x\right)=\frac{2E_{\mathrm{c}.\mathrm{m}.}}{\hslash {\omega }_b{R}_b^2}\sigma$ on $x=\frac{E_{\mathrm{c}.\mathrm{m}.}-V_b}{\hslash {\omega }_b}$ for the reactions ${}^{46}\text{K}+{}^{208}\text{Pb}$ (solid line) and ${}^{48}\text{Ca}+{}^{208}\text{Pb}$ (dashed line).

Figure 5

The same as in Fig. 1, but for the indicated reactions ${}^A\text{K}+{}^{124}\text{Sn}$.

Figure 6

The same as in Fig. 2, but for the indicated reactions ${}^A\text{K}+{}^{124}\text{Sn}$.

Figure 7

Calculated dependence of capture cross section ${\sigma }_{\mathrm{cap}}$ on $E_{\mathrm{c}.\mathrm{m}.}-V_b$ for the indicated reactions ${}^{46}\text{K}+{}^{124}\text{Sn}$ (solid line) and ${}^{48}\text{Ca}+{}^{124}\text{Sn}$ (dashed line).