Enhancement factor for two-neutron transfer reactions with a schematic coupled-channels model

Probabilities for heavy-ion two-neutron transfer reactions $P_{2\mathrm{n}}$ are often discussed in comparison with the square of the corresponding probabilities for the one-neutron transfer process ${\left(P_{1\mathrm{n}}\right)}^2$, implicitly assuming that ${\left(P_{1\mathrm{n}}\right)}^2$ provides the probability of two-neutron transfer reactions in the absence of the pairing correlation. We use a schematic coupled-channels model, in which the transfers are treated as effective inelastic channels, and demonstrate that this model leads to $P_{2\mathrm{n}}={\left(P_{1\mathrm{n}}\right)}^2/4$, rather than $P_{2\mathrm{n}}={\left(P_{1\mathrm{n}}\right)}^2$, in the pure sequential limit. We argue that a simple model with spin-up and spin-down neutrons in a single-particle orbital also leads to the same conclusion.

Figure 1

The transfer probabilities, defined as the ratio of the transfer cross sections to the Rutherford cross sections, for the ${}^{40}\mathrm{Ca} + {}^{96}\mathrm{Zr}$ reaction. These probabilities are plotted as a function of the distance of the closest approach $D$ of the classical Rutherford trajectory. The dotted and the solid lines denote the one- and two-neutron transfer probabilities, respectively, while the dashed line is a quarter of the square of the one-neutron transfer probability. The experimental data are taken from Ref. [12].

Figure 2

A schematic model for the two-neutron transfer process of spin-up and spin-down neutrons. $P$ and $T$ denote the projectile and the target nuclei, respectively.