Single-charge-exchange reactions and the neutron density at the surface of the nucleus

In this paper, we study the charge-exchange reaction to the isobaric analog state using two types of transition densities. One transition density is equal to the difference of the total neutron density minus the total proton density and the other one is the density of the excess neutrons only. We show that for projectiles that do not probe the interior of the nucleus but mostly the surface of this nucleus, distinct differences in the cross section arise when two types of transition densities are employed. We demonstrate this by considering the (${}^3\mathrm{He},t$) reaction.

Figure 1

${\rho }_n\left(r\right)-{\rho }_p\left(r\right), {\rho }_{n\left(\mathrm{exc}\right)}\left(r\right)$, and $\delta \rho \left(r\right)$ of the ${}^{90}\mathrm{Zr}$ nucleus obtained from the HF-BCS calculation using the BSk17 version of the Skyrme interaction.

Figure 2

The same as in Fig. 1, but for the ${}^{120}\mathrm{Sn}$ nucleus.

Figure 3

The same as in Fig. 1, but for the ${}^{208}\mathrm{Pb}$ nucleus.

Figure 4

Differential cross section of the ${}^{208}\mathrm{Pb}({}^3\mathrm{He},t)$ reaction to the IAS at $E_{\mathrm{lab}}=420\mathrm{MeV}$, given by the DWBA calculation using the SCX form factors obtained with the ${\rho }_n\left(r\right)-{\rho }_p\left(r\right)$ (dashed curve) and the ${\rho }_{n\left(\mathrm{exc}\right)}\left(r\right)$ (solid curve). The experimental data were taken from Ref. [7].

Figure 5

The same as in Fig. 4, but for ${}^{90}\mathrm{Zr}$ target.

Figure 6

The same as in Fig. 4, but for ${}^{58}\mathrm{Ni}$ target.

Figure 7

Differential cross sections of the ${}^{120}\mathrm{Sn}(p,n)$ IAS reaction at $E_{\mathrm{lab}}=170\mathrm{MeV}$, given by the DWBA calculation using the SCX form factors obtained with ${\rho }_n\left(r\right)-{\rho }_p\left(r\right)$ (dashed curve) and the ${\rho }_{n\left(\mathrm{exc}\right)}\left(r\right)$ (solid curve).