Thermal quasiparticle random-phase approximation calculations of stellar electron capture rates with the Skyrme effective interaction

Abstract

A microscopic thermodynamically consistent approach is applied to compute electron capture (EC) rates and cross sections on nuclei in hot stellar environments. The cross section calculations are based on the Donnelly-Walecka multipole expansion method for treatment of semi-leptonic processes in nuclei. To take into account thermal effects, we express the electron capture cross section in terms of temperature-and momentum-dependent spectral functions for respective multipole chargechanging operators. The spectral functions are computed by employing the self-consistent thermal quasiparticle random-phase approximation (TQRPA) with the Skyrme effective interaction. Three different Skyrme parametrizations (SkM * , SGII and SLy4) are used to investigate thermal effects on EC for 56 Fe and 78 Ni. For 56 Fe, the impact of thermally unblocked Gamow-Teller GT+ transitions on EC is discussed and the results are compared with those from shell-model calculations. In particular, it is shown that for some temperature and density regimes the TQRPA rates exceed the shell-model rates due to violation of the Brink-Axel hypothesis within the TQRPA. For neutron-rich 78 Ni, the full momentum-dependence of multipole transition operators is considered and it is found that not only thermally unblocked allowed 1 + transitions but also thermally unblocked first-forbidden 1 − and 2 − transitions favor EC. PACS numbers: 26.50.+x, 23.40.-s 21.60.Jz, 24.10.Pa, charge, longitudinal, transverse electric, and transverse magnetic multipole operators: σ J CL (E, T ) = (1 + a cos Θ)S MJ MJ + (1 + a cos Θ − 2b sin 2 Θ)S LJ LJ + E q (1 + a cos Θ) + c 2Re{S MJ LJ } (8) and σ J T (E, T ) = (1−a cos Θ+b sin 2 Θ) S T mag J T mag J +S T el J T el J

Unblocking of stellar electron capture for neutron-rich N=50 nuclei at finite temperature

“…(1) is impossible with current nuclear models. As was shown in [35], within a statistical description the thermalaveraged cross section can be expressed through the temperature-dependent spectral functions for the various momentum-dependent multipole operators derived in [36,37].…”

A modified Brink-Axel hypothesis for astrophysical Gamow-Teller transitions

“…Such schematic calculations, however, tend to have significantly different strength functions even from random phase approximation calculations using realistic shell-model forces [47]. Related thermal QRPA calculations using Skyrme interactions [48][49][50] can also reach highly excited transitions, but may underestimate the total rates due to missing correlations [51]. (In ground state proton-neutron RPA calculations, fragmentation of the Fermi surface due to breaking of axial symmetry can also increase Gamow-Teller strength; furthermore, at least in the lower pf -shell, breaking of rotational symmetries has a stronger effect than breaking particle number in spherical proton-neutron QRPA calculations [52].…”

“…The problem with this approach is the computational burden to reach higher energies. For example, for 49 Cr, which has an M -scheme dimension of only 6 million basis states, the first 100 levels only gets one to 5.5 MeV in excitation energy, and the first 500 levels, which requires about 7000 iterations using thick-restart Lanczos [66], only gets one to 8.28 MeV in excitation energy. While for many astrophysical calculation these initial excitation energies may be sufficient, they also require heroic computational efforts.…”

Stellar electron capture rates based on finite temperature relativistic quasiparticle random-phase approximation

“…Thermal evolution of GT + strengths was presented for 54,56 Fe and 76,78,80 Ge. Recently, the thermal QRPA (TQRPA) approach was used to calculate the electron capture rates for N=50 nuclei and 56 Fe [23,24]. It was shown that thermal excitations can take significant contribution from the GT + strength to electron capture rates.…”