Quasiparticle and quasihole states of nuclei around ${}^{56}\mathrm{Ni}$

The single-particle spectral function of ${}^{56}\mathrm{Ni}$ has been computed within the framework of self-consistent Green's functions theory. The Faddeev random phase approximation method and the $G$ matrix technique are used to account for the effects of long- and short-range physics on the spectral distribution. Large-scale calculations have been performed in spaces including up to ten oscillator shells. The chiral ${\mathrm{N}}^3\mathrm{LO}$ interaction is used together with a monopole correction that accounts for eventual missing three-nucleon forces. The single-particle energies associated with nucleon transfer to valence $1p0f$ orbits are found to be almost converged with respect to both the size of the model space and the oscillator frequency. The results support that ${}^{56}\mathrm{Ni}$ is a good doubly magic nucleus. The absolute spectroscopic factors to the valence states on $A=55,57$ are also obtained. For the transition between the ground states of ${}^{57}\mathrm{Ni}$ and ${}^{56}\mathrm{Ni}$, the calculations nicely agree with heavy-ion knockout experiments.

Figure 1

Diagrammatic equations for the polarization (top) and the two-particle (bottom) propagators in the RPA approach. Dashed lines are matrix elements of the effective nucleon-nucleon interaction, Eq. (8). The solid lines represent the independent-particle model propagator $g^{\mathrm{IPM}}(\omega )$, which is employed instead of the fully dressed one. See the text for details.

Figure 2

Example of one of the diagrams that are summed to all orders by means of the Faddeev random phase approximation Eqs. (12) (left). The corresponding contribution to the self-energy, obtained upon insertion into Eq. (3), is also shown (right).

Figure 3

Dependence of neutron spectroscopic factors (given as a fraction of the independent-particle model value) for the $1p_{3/2}$ and the $0f_{7/2}$ valence orbits with respect to the ph gap $\Delta E_{\mathrm{ph}}$. For each model space, different points correspond to different choices of ${\kappa }_M$ in the range 0.4–0.7 MeV.

Figure 4

Dependence of the neutron $1p_{3/2}$ particle energy and the $0f_{7/2}$ hole energy with respect to the oscillator frequency and the size of the model space.

Figure 5

Dependence of neutron single-particle energies on the oscillator frequency. The energies plotted here are the poles of $g(\omega )$ corresponding to the valence $1p0f$ orbits. Calculations were performed for $N_{max}=9$ and $l⩽7$.

Figure 6

Spectral strengths for one-neutron transfer on ${}^{56}\mathrm{Ni}$ obtained from the self-consistent single-particle propagator $g(\omega )$. Poles above (below) the Fermi energy, $E_F$, correspond to transition to eigenstates of ${}^{57}\mathrm{Ni}$ (${}^{55}\mathrm{Ni}$). The respective spectroscopic factors are given as a fraction of the independent-particle model value. The quasiparticle poles corresponding to the valence orbits of the $1p0f$ shell are indicated by arrows. A logarithmic scale was chosen to put in stronger evidence the distribution of the fragmented strength. Results are for $\hslash \Omega =10$ MeV, $N_{max}=9$, and ${\kappa }_M=0.57$ MeV.