Collectivity-induced quenching of signatures for shell closures

Mass differences are an often used as signature and measure for shell closure. Using the angular-momentum projected generator coordinate method and the Skyrme interaction SLy4, we analyze the modification of mass differences due to static deformation and dynamic fluctuations around the mean-field ground state.

Figure 1

Top: Single-particle spectra of the protons for the chain of Sn $(Z=50)$ isotopes and $-1/2$ times the two-proton separation energy for the $Z=50$ and $Z=52$ isotopic chains (see text). Solid (dotted) lines denote single-particle levels of positive (negative) parity. Bottom: Comparison of the gaps between $-S_{2p}(Z=50,N)/2$ and $-S_{2p}(Z=52,N)/2$ obtained at three levels of approximation with the experimental data. A linear trend equal to $(N-82)\hspace{1em}[S_{2p}(Z=50,N=50)-S_{2p}(Z=50,N=82)]/2$ using the spherical mean-field $S_{2p}$ values has been subtracted from all $-S_{2p}(Z,N)/2$, such that the distance between the curves for a given $N$ is unchanged. In particular, the plotted values at $N=82$ are not affected, and the plotted spherical mean-field values for $(Z=50,N=50)$ and $(Z=50,N=82)$ are identical.

Figure 2

Same as Fig. 1 but for neutrons. In the lower panel, a global descending trend $(N-50)[S_{2n}(Z=28,N=50)-S_{2n}(Z=50,N=50)]/2$ using the spherical mean-field $S_{2n}$ values has been subtracted from all $-S_{2n}(Z,N)/2$. The overall reduction of the distance between $S_{2n}(Z,N=50)$ and $S_{2n}(Z,N=52)$ when approaching $Z=28$ is clearly visible.

Figure 3

Two proton-separation energy $S_{2p}$ for even-even nuclei. Lines connect nuclei in isotonic chains.

Figure 4

Two-neutron separation energy $S_{2n}$ for even-even nuclei. Lines connect nuclei in isotopic chains.