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Register a new userSensitivity of stellar electron-capture rates to parent neutron number: A case study on a continuous chain of twenty Vanadium isotopes
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Gamow-Teller (GT) strength distributions (B(GT)) in electron-capture (EC) daughters stemming from the parent ground state are computed with the shell-model in the full pf-shell space, with quasi-particle random-phase approximation (QRPA) in the formalism of Krumlinde and Moller and with an Approximate Method (AM) for assigning an effective B(GT). These are compared to data available from decay and charge-exchange (CE) experiments across titanium isotopes in the pf-shell from A=43 to A=62, the largest set available for any chain of isotopes in the pf-shell. The present study is the first to examine B(GT) and the associated EC rates across a particular chain of isotopes with the purpose of examining rate sensitivities as neutron number increases. EC rates are also computed for a wide variety of stellar electron densities and temperatures providing concise estimates of the relative size of rate sensitivities for particular astrophysical scenarios. This work underscores the astrophysical motivation for CE experiments in inverse kinematics for nuclei away from stability at the luminosities of future Radioactive Ion Beam Facilities.
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This paper presents a systematic evaluation of the ability of theoretical models to reproduce experimental Gamow-Teller transition strength distributions measured via (n,p)-type charge-exchange reactions at intermediate beam energies. The focus is on transitions from stable nuclei in the pf shell (45<A<64). The impact of deviations between experimental and theoretical Gamow-Teller strength distributions on derived stellar electron-capture rates at densities and temperatures of relevance for Type Ia and Type II supernovae is investigated. The theoretical models included in the study are based on the shell-model, using the KB3G and GXPF1a interactions, and quasiparticle random-phase approximation (QRPA) using ground-state deformation parameters and masses from the finite-range droplet model.
Radiative capture reactions play a crucial role in stellar nucleosynthesis but have proved challenging to determine experimentally. In particular, the large uncertainty ($sim$100%) in the measured rate of the $^{12}$C$(alpha,gamma)^{16}$O reaction is the largest source of uncertainty in any stellar evolution model. With development of new high current energy-recovery linear accelerators (ERLs) and high density gas targets, measurement of the $^{16}$O$(e,e^prime alpha)^{12}$C reaction close to threshold using detailed balance opens up a new approach to determine the $^{12}$C$(alpha,gamma)^{16}$O reaction rate with significantly increased precision ($<$20%). We present the formalism to relate photo- and electro-disintegration reactions and consider the design of an optimal experiment to deliver increased precision. Once the new ERLs come online, an experiment to validate the new approach we propose should be carried out. This new approach has broad applicability to radiative capture reactions in astrophysics.
The electron capture process plays an important role in the evolution of the core collapse of a massive star that precedes the supernova explosion. In this study, the electron capture on nuclei in stellar environment is described in the relativistic energy density functional framework, including both the finite temperature and nuclear pairing effects. Relevant nuclear transitions $J^pi = 0^pm, 1^pm, 2^pm$ are calculated using the finite temperature proton-neutron quasiparticle random phase approximation with the density-dependent meson-exchange effective interaction DD-ME2. The pairing and temperature effects are investigated in the Gamow-Teller transition strength as well as the electron capture cross sections and rates for ${}^{44}$Ti and ${}^{56}$Fe in stellar environment. It is found that the pairing correlations establish an additional unblocking mechanism similar to the finite temperature effects, that can allow otherwise blocked single-particle transitions. Inclusion of pairing correlations at finite temperature can significantly alter the electron capture cross sections, even up to a factor of two for ${}^{44}$Ti, while for the same nucleus electron capture rates can increase by more than one order of magnitude. We conclude that for the complete description of electron capture on nuclei both pairing and temperature effects must be taken into account.
We propose a new model to calculate stellar electron capture rates for neutron-rich nuclei. These nuclei are encountered in the core-collapse of a massive star. Using the Shell Model Monte Carlo approach, we first calculate the finite temperature occupation numbers in the parent nucleus. We then use these occupation numbers as a starting point for calculations using the random phase approximation. Using the RPA approach, we calculate electron capture rates including both allowed and forbidden transitions. Such a hybrid model is particularly useful for nuclei with proton numbers Z<40 and neutron numbers N>40, where allowed Gamow-Teller transitions are only possible due to configuration mixing by the residual interaction and by thermal unblocking of $pf$-shell single-particle states. Using the even germanium isotopes Ge-68 to Ge-76 as examples, we demonstrate that the configuration mixing is strong enough to unblock the Gamow-Teller transitions at all temperatures relevant to core-collapse supernovae.
Total radiative thermal neutron-capture $gamma$-ray cross sections for the $^{182,183,184,186}$W isotopes were measured using guided neutron beams from the Budapest Research Reactor to induce prompt and delayed $gamma$ rays from elemental and isotopically-enriched tungsten targets. These cross sections were determined from the sum of measured $gamma$-ray cross sections feeding the ground state from low-lying levels below a cutoff energy, E$_{rm crit}$, where the level scheme is completely known, and continuum $gamma$ rays from levels above E$_{rm crit}$, calculated using the Monte Carlo statistical-decay code DICEBOX. The new cross sections determined in this work for the tungsten nuclides are: $sigma_{0}(^{182}{rm W}) = 20.5(14)$ b and $sigma_{11/2^{+}}(^{183}{rm W}^{m}, 5.2 {rm s}) = 0.177(18)$ b; $sigma_{0}(^{183}{rm W}) = 9.37(38)$ b and $sigma_{5^{-}}(^{184}{rm W}^{m}, 8.33 mu{rm s}) = 0.0247(55)$ b; $sigma_{0}(^{184}{rm W}) = 1.43(10)$ b and $sigma_{11/2^{+}}(^{185}{rm W}^{m}, 1.67 {rm min}) = 0.0062(16)$ b; and, $sigma_{0}(^{186}{rm W}) = 33.33(62)$ b and $sigma_{9/2^{+}}(^{187}{rm W}^{m}, 1.38 mu{rm s}) = 0.400(16)$ b. These results are consistent with earlier measurements in the literature. The $^{186}$W cross section was also independently confirmed from an activation measurement, following the decay of $^{187}$W, yielding values for $sigma_{0}(^{186}{rm W})$ that are consistent with our prompt $gamma$-ray measurement. The cross-section measurements were found to be insensitive to choice of level density or photon strength model, and only weakly dependent on E$_{rm crit}$. Total radiative-capture widths calculated with DICEBOX showed much greater model dependence, however, the recommended values could be reproduced with selected model choices. The decay schemes for all tungsten isotopes were improved in these analyses.
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