Nucleonic shells and nuclear masses

The binding energy of an isotope is a sensitive indicator of the underlying shell structure as it reflects the net energy content of a nucleus. Since magic nuclei are significantly lighter, or more bound, compared to their neighbors, the presence of nucleonic shell structure makes an imprint on nuclear masses. In this work, using a carefully designed binding-energy indicator, we catalog the appearance of spherical and deformed shell and subshell closures throughout the nuclear landscape. After presenting experimental evidence for shell and subshell closures as seen through the lens of nuclear masses, we study the ability of global nuclear mass models to predict local binding-energy variations related to shell effects.

Figure 1

Experimental values and model predictions of $\mathrm{\Delta }{e}_n$ across zirconium isotopes. Extrapolated values from experimental data are marked with stars. Strong peaks appear for the deformed gap at $N=40$, the magic gap at $N=50$, and the spherical gap at $N=56$. See text for details.

Figure 2

Experimental values of the dimensionless splitting $\mathrm{\Delta }{\tilde{e}}_p$ Eq. (12) throughout the nuclear landscape. The nuclei for which the expression (8) involves binding energies extrapolated from systematic trends in [30] are marked by circles. Shell closures corresponding to the bands of locally elevated values of $\mathrm{\Delta }{\tilde{e}}_p$ are clearly seen.

Figure 3

Similar to Fig. 2 but for $\mathrm{\Delta }{\tilde{e}}_n$. The nuclei with negative values of $\mathrm{\Delta }{\tilde{e}}_n$ are marked by an asterisk.

Figure 4

Similar as in Fig. 2 but for the mass model UNEDF1. The range of experimental data is marked by a solid black line.

Figure 5

Similar as in Fig. 3 but for the mass model UNEDF1. The range of experimental data is marked by a solid black line and asterisks denote negative values.

Figure 6

Similar as in Fig. 2 but for experimental values of the dimensionless single-particle splitting ${\tilde{\delta }}_{2p}$.

Figure 7

Similar as in Fig. 3 but for experimental values of the dimensionless single-particle splitting ${\tilde{\delta }}_{2n}$.

Figure 8

Sample screenshot of the Bayesian Mass Explorer web interface in a configuration similar to what was used for the present investigation. The configuration and quantity of interest for each plot is accessed through the tab functionality on the left and additional data series can be added to the isotopic chains in the sidebar. The current view can be saved and shared using the “Share View” button on the right sidebar. Vector graphics in the PDF format can also be exported through the web interface for easy integration into documents.