Nuclear Pairing Gap: How Low Can It Go?

The pairing gap for ${}^{53}\mathrm{Ca}$ obtained from new experimental data on the masses of ${}^{52–54}\mathrm{Ca}$ has the smallest value yet observed. This is explained in the framework of the nuclear shell model with schematic and realistic Hamiltonians as being due to shell gaps around the low-$j$ orbital $1p_{1/2}$. Minima in the pairing gaps for all nuclei are shown and discussed.

Figure 1

The bottom panel shows the ground-state energies for the calcium isotopes obtained from the $pf$ shell-model calculation with the GX1A Hamiltonian relative to ${}^{40}\mathrm{Ca}$ with filled circles for even $N$ and open circles for odd $N$, all connected by a line. The crosses are the experimental data. The top panel shows the one-neutron separation energies for GX1A and experiment.

Figure 2

$D_n$ and $E_x(2^{+})$ for the calcium isotopes as a function of neutron number. $D$ values are shown by the filled circles for even $N$ and open circles for odd $N$, all connected by a line. The $E_x(2^{+})$ values are shown by the crosses.

Figure 3

$D_n$ and $E_x(2^{+})$ obtained with the SDI interaction as a function of the shell gap between the $0f_{7/2}$ orbital and the degenerate ($0f_{5/2}$, $1p_{3/2}$, $1p_{1/2}$) set of orbitals. The second panel from the top also shows the results for $D_n$ (thin lines) obtained when the shell gap is infinite. The results for the MSDI interaction are shown in the top panel.

Figure 4

$D_n$ and $E_x(2^{+})$ obtained with the SDI interaction as a function of the shell gaps below and above the $1p_{1/2}$ orbital. The dip is at $N=33$.

Figure 5

$D_n$ for the calcium isotopes from experiment (points connected by a line) compared with those obtained with the DZ31 mass model [10] and the HFB-21 Skyrme energy functional [11] (green lines).

Figure 6

Experimental values of $D_{no}$ for all nuclei with even $Z$. Values are plotted as a function of the number of neutrons ($N>Z$) and connected by lines for a given $Z$ value. The value for ${}^{53}\mathrm{Ca}$ is shown by the red dot. They are compared to theoretical values for all nuclei with the same range of $N$ and $Z$ given by the experimental data in the top panel. The vertical lines show the locations of the magic numbers 20, 28, 50, 82, and 126.

Figure 7

Experimental values of $D_{po}$ for all nuclei with even $N$. Values are plotted as a function of the number of protons ($N>Z$) and connected by lines for a given $N$ value. The vertical lines show the locations of the magic numbers 20, 28, 50, and 82.