New “USD” Hamiltonians for thesdshell

Abstract

We derive new Hamiltonians for the sd shell, USDA and USDB, based on a renormalized G matrix with linear combinations of two-body matrix elements adjusted to fit a complete set of data for experimental binding energies and excitation energies for the sd-shell nuclei. These Hamiltonians provide a new level of precision for realistic sd-shell wave functions for applications to nuclear structure and nuclear astrophysics.

In-medium similarity renormalization group for closed and open-shell nuclei

“…The USDB interaction is optimized to simultaneously describe more than 600 excited states in sd-shell nuclei [8], hence it is not surprising that the USDB spectra agree very well with experiment. We observe the most notable deviation for the second 0 + and the 3 + state in 22 O, which are nearly degenerate and whose ordering is inverted compared to experiment.…”

“…Then, the Hamiltonian is re-normal ordered with respect to the 16 O core that is assumed by the Shell model calculation. As shown in figure 17, this procedure essentially eliminates the difference between the IMSRG+SM and MR-IMSRG (2) In figure 18, we show the effect of the TNO on the low-lying excitation spectra of 22−24 O and the neutron separation energies , the A-dependent CCEI approach of [190] (e max = 12, E 3max = 14, ω = 20 MeV), and the phenomenological USDB interaction [8] to experimental data [193]. The dashed lines represent the neutron separation energies.…”

“…Ground-state rotational bands of 20 Ne and 24 Mg, based on the N N + 3N (400) interaction at λ = 1.88 fm −1 . We compare results for effective interactions derived by IMSRG valence-space decoupling (e max = 14, E 3max = 14, ω = 20 MeV (dashed lines) and 24 MeV (solid lines)), the A-independent CCEI interaction [194] (e max = 12, E 3max = 14, ω = 20 MeV), and the phenomenological USDB interaction [8] to experimental data [189,193]. The dashed lines represent the neutron separation energies.…”

“…We note that the former depends on the mass number A of the target nucleus through a scaling of the two-body matrix elements [8]. In the latter, interactions for specific target masses were constructed for use in the oxygen isotopes, starting from the same Hamiltonian that we used for the IMSRG+SM here.…”

“…The traditional nuclear configuration interaction (CI) approach (see, e.g., [6,7]) uses phenomenological interactions that are highly optimized, e.g., to sd-shell data [8], and treats only the dynamics of valence nucleons on top of an inert core in fully microscopic fashion. Finally, nuclear Density Functional Theory (DFT) takes a global perspective, and aims for a microscopic description of the entire nuclear chart based on energy density functionals (EDFs) that are optimized to data [9][10][11][12].…”