Data-driven configuration-interaction Hamiltonian extrapolation to ${}^{60}\mathrm{Ca}$

Following the many successful implementations of effective universal configuration-interaction Hamiltonians, we endeavored to produce a universal $fp$ shell interaction tailored for the calcium isotopes, which we call UFP-CA. Starting from a state-of-the-art in-medium similarity renormalization group (IMSRG) interaction, linear combinations of Hamiltonian parameters that define the natural basis of the parameter space are constrained by the latest experimental data for the neutron-rich calcium isotopes. We show that this data-driven method for improving the Hamiltonian provides an excellent description of the known binding energies and spectra for the calcium isotopes within the $fp$ model space. This together with comparisons to results from energy-density functional models leads us to conclude that ${}^{60}\mathrm{Ca}$ is doubly magic at a similar level to ${}^{68}\mathrm{Ni}$. Several predictions are presented for unobserved low-lying excited states in ${}^{55-59}\mathrm{Ca}$ that will be accessible to future experiments.

Figure 1

Theoretical level schemes for neutron-rich calcium isotopes with $A>45$ calculated using UFP-CA. Experimental excitation energies included in the fit are marked in green. Positive-parity states are shown in red, and negative-parity states are shown in blue. Each of these lines represents a level predicted to exist by the theory. Theoretical one- and two-neutron separation energies are shown as the purple and black lines, respectively.

Figure 2

Root-mean-square (rms) deviations plotted against varied LC. The black circles show the energy rms deviation between theory and experiment for the well-known levels included in the fit. The black crosses show the parameter rms deviation from the starting interaction. The average and maximum $\mathrm{\Delta }p$ are denoted by the purple triangles and points. The singular values are plotted on a log scale in the inset.

Figure 3

A comparison of the TBME between UFP-CA and the initial IMSRG interaction is shown in panel (a). The ESPE discussed in the text are shown for GPFX1A (b), UFP-CA (c), and a Skyrme interaction (d). The red crosses show the IMSRG values at $N=28$. The $0f_{5/2}$ ($⊲$) and $0g_{9/2}$ ($⊳$) are shown for the SKM* (green) and UNEDF0 (blue) EDF functionals.

Figure 4

Experimental and calculated $S_{2n}$ for the calcium isotopes. See text for a description of the bottom panel.