Microscopic mass formulas

Neutrino-driven wind simulations and nucleosynthesis of heavy elements

“…Their impact on the abundances have been studied (see e.g., [47,10,79,80]) by using different theoretical mass models (e.g., FRDM [81], ETFSI [82], Duflo & Zuker [83], HFB-x [84,85]). Beta decay rates [86] control the speed of the r-process and during decay to stability become specially important due to the delayed neutron emission.…”

Occupation-number-based energy functional for nuclear masses

“…The construction of our occupation-number-based functional is guided by semiclassical scaling arguments that guarantee nuclear saturation [33,34], and isospin symmetry (with the exception of the Coulomb interaction). In the harmonic oscillator basis, a nucleus of A nucleons has about A 1/3 occupied shells below the Fermi level, and about A 2/3 nucleons are in the highest energetic, completely filled shell.…”

“…The simple arguments based on filling the major shells of the spherical harmonic oscillator yield incorrect shell closures. As a remedy, we follow Duflo and Zuker [33] and consider shells where the high-j intruder orbital of the shell p + 1 enters the shell p. Since a single j orbital of the shell p holds on the order of p nucleons-while a major shell holds about p 2 nucleons-our scaling arguments are unchanged. In the modified shell-model, the resulting shell closures have occupation numbers 2, 6, 14, 28, 50, 82, 126, 184, ....…”

“…(18). The two-body term I 2B is motivated by the monopole Hamiltonian in the mass formula by Duflo and Zuker [33]. Here, the fermionic nature in the proton-proton and neutron-neutron interaction is evident as we have terms as n p (n p − 1) (and not simply n 2 p ).…”

“…Obtaining the occupations from an optimization is in contrast to the mass formula [33], where occupations are fixed and input by hand. We refer to the optimization of the coefficients c as the upper-level optimization problem.…”