Probing resonances in deformed nuclei by using the complex-scaled Green's function method

Resonance plays a key role in the formation of many physical phenomena. The complex-scaled Green's function method provides a powerful tool for exploring resonance. In this paper, we combine this method with the theory describing deformed nuclei with the formalism presented. Taking ${}^{45}\text{S}$ as an example, we elaborate numerical details and demonstrate how to determine the resonance parameters. The results are compared with those obtained by the complex scaling method and the coupled-channel method and satisfactory agreement is obtained. In particular, the present scheme focuses on the advantages of the complex scaling method and the Green's function method and is more suitable for the exploration of resonance.

Figure 1

A demonstrating example for the continuum level density. The projection of the peak on the horizontal axis corresponds to the resonance energy. The width of the peak at a half height corresponds to the resonance width.

Figure 2

The eigenvalues of $H_{\theta }$ for the state $5/2^{+}$, where the complex rotation angle $\theta =8^{\circ }$, the deformation ${\beta }_2=0.2$, and the size of basis $N=60$.

Figure 3

The level densities in the CGF calculations, where the black solid line, red dashed line, and blue doted line represent respectively the density of states ${\rho }_{\theta }^N\left(E\right)$, the density of continuum states ${\rho }_{\theta }^{0N}\left(E\right)$, and the continuum level density $\mathrm{\Delta }\rho \left(E\right)$ for the state $5/2^{+}$. The other parameters are the same as those in Fig. 2.

Figure 4

The continuum level density for several different complex rotation angles.

Figure 5

The continuum level density for several different quadruple deformations ${\beta }_2$.

Figure 6

The continuum level density in several different deformations for the state 7/2[413].

Figure 7

The neutron single-particle levels in ${}^{45}\text{S}$ as a function of the quadruple deformation ${\beta }_2$. Every level is labeled with the asymptotic quantum numbers $\mathrm{\Omega }\left[N{n}_z\mathrm{\Lambda }\right]$.