Neutrinoless ββ\beta\beta decay nuclear matrix elements in an isotopic chain

We analyze nuclear matrix elements (NME) of neutrinoless double beta decay calculated for the Cadmium isotopes. Energy density functional methods including beyond mean field effects such as symmetry restoration and shape mixing are used. Strong shell effects are found associated to the underlying nuclear structure of the initial and final nuclei. Furthermore, we show that NME for two-neutrino double beta decay evaluated in the closure approximation, $M^{2\nu}_{\mathrm{cl}}$, display a constant proportionality with respect to the Gamow-Teller part of the neutrinoless NME, $M^{0\nu}_{\mathrm{GT}}$. This opens the possibility of determining the $M^{0\nu}_{\mathrm{GT}}$ matrix elements from $\beta^{\mp}$ Gamow-Teller strength functions. Finally, the interconnected role of deformation, pairing, configuration mixing and shell effects in the NMEs is discussed

Systematic study of infrared energy corrections in truncated oscillator spaces

We study the convergence properties of nuclear binding energies and two-neutron separation energies obtained with self-consistent mean-field calculations based on the Hartree-Fock-Bogolyubov (HFB) method with Gogny-type effective interactions. Owing to lack of convergence in a truncated working basis, we employ and benchmark one of the recently proposed infrared energy correction techniques to extrapolate our results to the limit of an infinite model space. We also discuss its applicability to global calculations of nuclear masses.Comment: 12 pages, 12 figure

Sensitivity study of explosive nucleosynthesis in type Ia supernovae: Modification of individual thermonuclear reaction rates

Background: Type Ia supernovae contribute significantly to the nucleosynthesis of many Fe-group and intermediate-mass elements. However, the robustness of nucleosynthesis obtained via models of this class of explosions has not been studied in depth until now. Purpose: We explore the sensitivity of the nucleosynthesis resulting from thermonuclear explosions of massive white dwarfs with respect to uncertainties in nuclear reaction rates. We put particular emphasis on indentifying the individual reactions rates that most strongly affect the isotopic products of these supernovae. Method: We have adopted a standard one-dimensional delayed detonation model of the explosion of a Chandrasekhar-mass white dwarf and have postprocessed the thermodynamic trajectories of every mass shellwith a nucleosynthetic code to obtain the chemical composition of the ejected matter. We have considered increases (decreases) by a factor of 10 on the rates of 1196 nuclear reactions (simultaneously with their inverse reactions), repeating the nucleosynthesis calculations after modification of each reaction rate pair. We have computed as well hydrodynamic models for different rates of the fusion reactions of 12C and of 16O. From the calculations we have selected the reactions that have the largest impact on the supernova yields, and we have computed again the nucleosynthesis using two or three alternative prescriptions for their rates, taken from the JINA REACLIB database. For the three reactions with the largest sensitivity we have analyzed as well the temperature ranges where a modification of their rates has the strongest effect on nucleosynthesis. Results: The nucleosynthesis resulting from the type Ia supernova models is quite robust with respect to variations of nuclear reaction rates,with the exception of the reaction of fusion of two 12C nuclei. The energy of the explosion changes by less than ∼4% when the rates of the reactions 12C + 12C or 16O + 16O are multiplied by a factor of ×10 or ×0.1. The changes in the nucleosynthesis owing to the modification of the rates of these fusion reactions are also quite modest; for instance, no species with a mass fraction larger than 0.02 experiences a variation of its yield larger than a factor of 2. We provide the sensitivity of the yields of the most abundant species with respect to the rates of the most intense reactions with protons, neutrons, and α. In general, the yields of Fe-group nuclei are more robust than the yields of intermediate-mass elements. Among the species with yields larger than 10−8M , 35S has the largest sensitivity to the nuclear reaction rates. It is remarkable that the reactions involving elements with Z > 22 have a tiny influence on the supernova nucleosynthesis. Among the charged-particle reactions, the most influential on supernova nucleosynthesis are 30Si + p 31P + γ , 20Ne + α 24Mg + γ , and 24Mg + α 27Al + p. The temperatures at which a modification of their rate has a larger impact are in the range 2 T 4 GK.Postprint (published version

Energy density functional study of nuclear matrix elements for neutrinoless ββ\beta\beta decay

We present an extensive study of nuclear matrix elements (NME) for the neutrinoless double beta decay of the nuclei $^{48}$Ca, $^{76}$Ge, $^{82}$Se, $^{96}$Zr, $^{100}$Mo, $^{116}$Cd, $^{124}$Sn, $^{128}$Te, $^{130}$Te, $^{136}$Xe, and $^{150}$Nd based on state-of-the-art energy density functional methods using the Gogny D1S functional. Beyond mean-field effects are included within the generating coordinate method with particle number and angular momentum projection for both initial and final ground states. We obtain a rather constant value for the NME's around 4.7 with the exception of $^{48}$Ca and $^{150}$Nd, where smaller values are found. We analyze the role of deformation and pairing in the evaluation of the NME and present detailed results for the decay of $^{150}$Nd.Comment: accepted in Phys. Rev. Let

Shell Model Applications in Nuclear Astrophysics

In recent years, shell model studies have significantly contributed in improving the nuclear input, required in simulations of the dynamics of astrophysical objects and their associated nucleosynthesis. This review highlights a few examples such as electron capture rates and neutrino-nucleus cross sections, important for the evolution and nucleosynthesis of supernovae. For simulations of rapid neutron-capture (r-process) nucleosynthesis, shell model studies have contributed to an improved understanding of half lives of neutron-rich nuclei with magic neutron numbers and of the nuclear level densities and γ-strength functions that are both relevant for neutron capture rates

On the nuclear robustness of the r process in neutron-star mergers

We have performed r-process calculations for matter ejected dynamically in neutron star mergers based on a complete set of trajectories from a three-dimensional relativistic smoothed particle hydrodynamic simulation. Our calculations consider an extended nuclear network, including spontaneous, $\beta$- and neutron-induced fission and adopting fission yield distributions from the ABLA code. We have studied the sensitivity of the r-process abundances to nuclear masses by using different models. Most of the trajectories, corresponding to 90% of the ejected mass, follow a relatively slow expansion allowing for all neutrons to be captured. The resulting abundances are very similar to each other and reproduce the general features of the observed r-process abundance (the second and third peaks, the rare-earth peak and the lead peak) for all mass models as they are mainly determined by the fission yields. We find distinct differences in the abundance yields at and just above the third peak, which can be traced back to different predictions of neutron separation energies for r-process nuclei around neutron number $N=130$. The remaining trajectories, which contribute 10% by mass to the total integrated abundances, follow such a fast expansion that the r process does not use all the neutrons. This also leads to a larger variation of abundances among trajectories as fission does not dominate the r-process dynamics. The total integrated abundances are dominated by contributions from the slow abundances and hence reproduce the general features of the observed r-process abundances. We find that at timescales of weeks relevant for kilonova light curve calculations, the abundance of actinides is larger than the one of lanthanides. Hence actinides can be even more important than lanthanides to determine the photon opacities under kilonova conditions. (Abridged)Comment: 17 pages, 7 figures, resubmitted to PRC addressing referee comment

Testing the importance of collective correlations in neutrinoless ββ decay

We investigate the extent to which theories of collective motion can capture the physics that determines the nuclear matrix elements governing neutrinoless double-β decay. To that end we calculate the matrix elements for a series of isotopes in the full pf shell, omitting no spin-orbit partners. With the inclusion of isoscalar pairing, a separable collective Hamiltonian that is derived from the shell model effective interaction reproduces the full shell-model matrix elements with good accuracy. A version of the generator coordinate method that includes the isoscalar pairing amplitude as a coordinate also reproduces the shell model results well, an encouraging result for theories of collective motion, which can include more single-particle orbitals than the shell model. We briefly examine heavier nuclei relevant for experimental double-β decay searches, in which shell-model calculations with all spin-orbit partners are not feasible; our estimates suggest that isoscalar pairing also plays a significant role in these nuclei, though one we are less able to quantify precisely.This work was supported in part by an International Research Fellowship from the Japan Society for the Progress of Science (JSPS), and JSPS KAKENHI Grant No. 26·04323, by the Deutsche Forschungsgemeinschaft through Contract No. SFB 634, by the Helmholtz Association through the Helmholtz Alliance Program, Contract No. HA216/EMMI “Extremes of Density and Temperature: Cosmic Matter in the Laboratory”, by the European Research Council under Grant No. 307986 STRONGINT, by the U.S. Department of Energy through Contract No. DE-FG02-97ER41019, and by the Spanish MINECO under Programa Ramón y Cajal 11420 and FIS-2014-53434-

Impact of pions on binary neutron star mergers

We study the impact of pions in simulations of neutron star mergers and explore the impact on gravitational-wave observables. We model charged and neutral pions as a non-interacting Boson gas with a chosen, constant effective mass. We add the contributions of pions, which can occur as a condensate or as a thermal population, to existing temperature and composition dependent equations of state. Compared to the models without pions, the presence of a pion condensate decreases the characteristic properties of cold, non-rotating neutron stars such as the maximum mass, the radius and the tidal deformability. We conduct relativistic hydrodynamical simulations of neutron star mergers for these modified equations of state models and compare to the original models, which ignore pions. Generally, the inclusion of pions leads to a softening of the equation of state, which is more pronounced for smaller effective pion masses. We find a shift of the dominant postmerger gravitational-wave frequency by up to 150~Hz to higher frequencies and a reduction of the threshold binary mass for prompt black-hole formation by up to 0.07~$M_\odot$. We evaluate empirical relations between the threshold mass or the dominant postmerger gravitational-wave frequency and stellar parameters of nonrotating neutron stars. These relations are constructed to extract these stellar properties from merger observations and are built based on large sets of equation of state models which do not include pions. Comparing to our calculations with pions, we find that these empirical relations remain valid to good accuracy, which justifies their use although they neglect a possible impact of pions. We also address the mass ejection by neutron star mergers and observe a moderate enhancement of the ejecta mass by a few ten per cent. (abridged)Comment: 27 pages, 24 figures, accepted for publication in Phys. Rev.