${\varvec{\alpha }}$ clustering and neutron-skin thickness of carbon isotopes

Abstract

The interplay between the formation of neutron skin and $\alpha$ cluster at the dilute surface of neutron-rich nuclei is one of the interesting subjects in the study of neutron-rich nuclei and nuclear clustering. A theoretical model has predicted that the growth of neutron skin will prevent the $\alpha$ clustering at nuclear surface. Quite recently, this theoretical perspective, the suppression of $\alpha$ clustering by the neutron-skin formation, was firstly confirmed experimentally in Sn isotopes as the reduction of the $(p,p\alpha )$ reaction cross section. Motivated by the novel discovery, in this work, we have investigated the relationship between the neutron-skin thickness and $\alpha$ clustering in C isotopes. Based on the analysis by the antisymmetrized molecular dynamics, we show that the $\alpha$ spectroscopic factor at nuclear exterior decreases in neutron-rich C isotopes, and the clustering suppression looks correlated with the growth of the neutron-skin thickness.

Appendix A: Coulomb interaction

To reduce the computational cost, the Coulomb interaction is approximated by a sum of seven Gaussians as

$$\begin{aligned} \frac{1}{r} \simeq \sum _{n=1}^7 c_n\sqrt{\bar{\nu }} \exp (-\frac{\bar{\nu }r^2}{\gamma _n^2}),\quad \bar{\nu } = (\nu _x\nu _y\nu _z)^{1/3}, \end{aligned}$$

(A.1)

where the dimensionless parameters $c_n$ and $\gamma _n$ are listed in Table 2. The parameters are determined to yield approximate values of the Coulomb interaction when the matrix elements of Eq. (A.1) are calculated from the nucleon Gaussian wave packets.

Table 2 The dimensionless parameters for an approximate expression of the Coulomb interaction