Evolution of Shell Structure in Neutron-Rich Calcium Isotopes

We employ interactions from chiral effective field theory and compute the binding energies and low-lying excitations of calcium isotopes with the coupled-cluster method. Effects of three-nucleon forces are included phenomenologically as in-medium two-nucleon interactions, and the coupling to the particle continuum is taken into account using a Berggren basis. The computed ground-state energies and the low-lying $J^{\pi }=2^{+}$ states for the isotopes ${}^{42,48,50,52}\mathrm{Ca}$ are in good agreement with data, and we predict the excitation energy of the first $J^{\pi }=2^{+}$ state in ${}^{54}\mathrm{Ca}$ at 1.9 MeV, displaying only a weak subshell closure. In the odd-mass nuclei ${}^{53,55,61}\mathrm{Ca}$ we find that the positive parity states deviate strongly from the naive shell model.

Figure 1

Ground-state energy of the calcium isotopes as a function of the mass number $A$. Black circles: experimental data; red squares: theoretical results including the effects of three-nucleon forces; blue diamonds: predictions from chiral $NN$ forces alone. The experimental results for ${}^{51,52}\mathrm{Ca}$ are from Ref. [36].

Figure 2

(Excitation energies of $J^{\pi }=2^{+}$ states in the isotopes ${}^{42,48,50,52,54,56}\mathrm{Ca}$ (experiment: black circles, theory: red squares).

Figure 3

Theoretical excitation spectra of ${}^{52–56}\mathrm{Ca}$ compared to available data. The continuum is indicated as a gray area.

Figure 4

Theoretical excitation spectra of ${}^{50,54,56}\mathrm{Ti}$ compared to data.