Local α-removal strength in the mean-field approximation

Background: The & alpha; cluster is a prominent feature, not only in light nuclei but also in heavy nuclei. To study the & alpha;-particle formation in the mean-field calculation, the localization function has been extensively utilized. However, the localization function does not guarantee the proximity of four different nucleons which is required by the & alpha;-particle formation. A simple indicator of the proximity is desired. Recently, experimental measurement of the quasifree & alpha;-knockout reaction for Sn isotopes reveals the cross sections with a monotonic decrease with increasing neutron number. [Science 371, 260 (2021)]. This is interpreted as evidence of the surface & alpha; formation. Purpose: We propose a simple and comprehensible quantity to assess the proximity of four nucleons with different spins and isospins. Using this, we examine the recent measurement of & alpha;-knockout cross sections in Sn isotopes. Methods: The local & alpha;-removal strength is proposed to quantify the possibility to form an & alpha; particle at a specific location inside the nucleus. In addition, it provides the strength of ground and excited states in the residual nuclei after the removal of the & alpha; particle. To make the calculation feasible, we introduce several approximations, such as point-& alpha;, mean-field, and no rearrangement approximations. We use the Hartree-Fock-plus-BCS method for the mean-field calculation for Sn isotopes. We also propose another measure, the local & alpha; probability, which should provide a better correlation with the & alpha;-knockout cross sections. Results: The calculation of the local & alpha;-removal strength is extremely easy in the mean-field model with no rearrangement. For even-even Sn isotopes, the local & alpha;-removal strengths to the ground state of residual nuclei are almost universal in the nuclear surface region. In contrast, the local & alpha; probability produces strong neutron number dependence consistent with the experiment. Conclusions: The local & alpha;-removal strength and the local & alpha; probability are easily calculable in the mean-field models. Recent experimental data for Sn isotopes may be explained by a simple model without explicit consideration of & alpha; correlation.