Weak decay processes in pre-supernova core evolution within the gross theory

The beta decay and electron capture rates are of fundamental importance in the evolution of massive stars in a pre-supernova core. The beta decay process gives its contribution by emitting electrons in the plasma of the stellar core, thereby increasing pressure, which in turn increases the temperature. From the other side, the electron capture removes free electrons from the plasma of the star core contributing to the reduction of pressure and temperature. In this work we calculate the beta decay and electron capture rates in stellar conditions for 63 nuclei of relevance in the pre-supernova stage, employing Gross Theory as the nuclear model. We use the abundances calculated with the Saha equations in the hypothesis of nuclear statistical equilibrium to evaluate the time derivative of the fraction of electrons. Our results are compared with other evaluations available in the literature. They have shown to be one order less or equal than the calculated within other models. Our results indicate that these differences may influence the evolution of the star in the later stages of pre-supernova. © 2014. The American Astronomical Society. All rights reserved..Fil: Ferreira, R. C.. Universidade Estadual Do Sudoeste Da Bahía; BrasilFil: Dimarco, A. J.. Universidade Estadual de Santa Cruz, Bahía, Brasil; BrasilFil: Samana, Arturo Rodolfo. Universidade Estadual de Santa Cruz, Bahía, Brasil; BrasilFil: Barbero, César Alberto. Universidad Nacional de La Plata. Facultad de Ciencias Exactas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentin

QRAP: A numerical code for projected (Q)uasiparticle (RA)ndom (P)hase approximation

A computer code for quasiparticle random phase approximation – QRPA and projected quasiparticle random phase approximation – PQRPA models of nuclear structure is explained in details. The residual interaction is approximated by a simple δ -force. An important application of the code consists in evaluating nuclear matrix elements involved in neutrino–nucleus reactions. As an example, cross sections for 56 Fe and 12 C are calculated and the code output is explained. The application to other nuclei and the description of other nuclear and weak decay processes are also discussed.Program summary Title of program: QRAP ( Q uasiparticle RA ndom P hase approximation) Computers: The code has been created on a PC, but also runs on UNIX or LINUX machines Operating systems: WINDOWS or UNIX Program language used: Fortran-77 Memory required to execute with typical data: 16 Mbytes of RAM memory and 2 MB of hard disk space No. of lines in distributed program, including test data, etc.: ∼ 8000 No. of bytes in distributed program, including test data, etc.: ∼ 256 kB Distribution format: tar.gz Nature of physical problem: The program calculates neutrino– and antineutrino–nucleus cross sections as a function of the incident neutrino energy, and muon capture rates, using the QRPA or PQRPA as nuclear structure models. Method of solution: The QRPA, or PQRPA, equations are solved in a self-consistent way for even–even nuclei. The nuclear matrix elements for the neutrino–nucleus interaction are treated as the beta inverse reaction of odd–odd nuclei as function of the transfer momentum. Typical running time: ≈ 5 min on a 3 GHz processor for Data set 1.Instituto de Física La Plat

Neutrino-nucleus reactions and muon capture in <SUP>12</SUP>C

The neutrino-nucleus cross section and the muon-capture rate are discussed within a simple formalism that facilitates nuclear structure calculations. The corresponding formulas depend on only four types of nuclear matrix elements currently used in nuclear β decay. We have also considered nonlocality effects arising from the velocity-dependent terms in the hadronic current. We show that for both observables in ¹²C the higher order relativistic corrections are of the order of ∼5% only and therefore do not play a significant role. As a nuclear model framework we use the projected quasiparticle random-phase approximation and show that the number projection plays a crucial role in removing the degeneracy between the proton-neutron two-quasiparticle states at the level of the mean field. Comparison is done with both the experimental data and the previous shell model calculations. The possible consequences of the present study on the determination of the νμ → νe neutrino oscillation probability are briefly addressed.Facultad de Ciencias ExactasInstituto de Física La PlataFacultad de Ciencias Astronómicas y Geofísica

Neutrino and antineutrino charge-exchange reactions on ¹²C

We extend the formalism of weak interaction processes, obtaining newexpressions for the transition rates, which greatly facilitate numerical calculations, for both neutrino- nucleus reactions and muon capture. Explicit violation of the conserved vector current hypothesis by the Coulomb field, as well as development of a sum-rule approach for inclusive cross sections, has been worked out. We have done a thorough study of exclusive (ground-state) properties of ¹²B and ¹²N within the projected quasiparticle random phase approximation (PQRPA). Good agreement with experimental data achieved in this way put into evidence the limitations of the standard RPA and QRPA models, which come from the inability of the RPA to open the p3/2 shell and from the nonconservation of the number of particles in the QRPA. The inclusive neutrino/antineutrino (ν/ṽ) reactions ¹²C(ν, e⁻)¹²N and ¹²C(ṽ, e⁺)¹²B are calculated within both the PQRPA and the relativistic QRPA. It is found that (i) the magnitudes of the resulting cross sections are close to the sum-rule limit at low energy, but significantly smaller than this limit at high energies, for both ν and ṽ; (ii) they increase steadily when the size of the configuration space is augmented, particularly for ν/ṽ energies >200 MeV ; and (iii) they converge for sufficiently large configuration space and final-state spin. The quasi-elastic ¹²C(ν, μ⁻)¹²N cross section recently measured in the MiniBooNE experiment is briefly discussed. We study the decomposition of the inclusive cross section based on the degree of forbiddenness of different multipoles. A few words are dedicated to the ν/ṽ-¹²C charge-exchange reactions related to astrophysical applications.Facultad de Ciencias ExactasInstituto de Física La Plat

Quasiparticle-rotor model description of carbon isotopes

In this work we perform quasiparticle-rotor coupling model calculations within the usual BCS and the projected BCS for the carbon isotopes 15C, 17C and 19C using 13C as the building block. Owing to the pairing correlation, we find that 13C as well as the cores of the other isotopes, namely 14C, 16C and 18C acquire strong and varied deformations. The deformation parameter is large and negative for 12C, very small (or zero) for 14C and large and positive for 16C and 18C. This finding casts a doubt about the purity of the supposed simple one-neutron halo nature of 19C.Instituto de Física La PlataFacultad de Ciencias Astronómicas y Geofísica

Nuclear structure model for double-charge-exchange processes

A new model, based on the BCS approach, is especially designed to describe nuclear phenomena (A, Z) → (A, Z ± 2) of double-charge exchange (DCE). Although it was proposed and applied in the particle-hole limit, by one of the authors [Krmpotić, Fizika B 14, 139 (2005)], it has not yet been applied within the BCS mean-field framework, nor has its ability to describe DCE processes been thoroughly explored. It is a natural extension of the pn-QRPA model, developed by Halbleib and Sorensen [Nucl. Phys. A 98, 542 (1967)] to describe the single β decays (A, Z) → (A, Z ± 1), to the DCE processes. As such, it exhibits several advantages over the pn-QRPA model when used in the evaluation of the double beta decay (DBD) rates. For instance, (i) the extreme sensitivity of the nuclear matrix elements (NMEs) on the model parametrization does not occur; (ii) it allows us to study the NMEs, not only for the ground state in daughter nuclei, as the pn-QRPA model does, but also for all final 0⁺ and 2⁺ states, accounting at the same time for their excitation energies and the corresponding DBD Q values; (iii) together with the DBD-NMEs it also provides the energy spectra of Fermi and Gamow-Teller DCE transition strengths, as well as the locations of the corresponding resonances and their sum rules; (iv) the latter are relevant for both the DBD and the DCE reactions, since the underlying nuclear structure is the same; this correlation does not exist within the pn-QRPA model. As an example, detailed numerical calculations are presented for the (A, Z) → (A, Z + 2) process in ⁴⁸Ca → ⁴⁸Ti and the (A, Z) → (A, Z − 2) process in ⁹⁶Ru → ⁹⁶Mo, involving all final 0⁺ states and 2⁺ states.Facultad de Ciencias ExactasInstituto de Física La Plat

Weak decay processes in pre-supernova core evolution within the gross theory

The beta decay and electron capture rates are of fundamental importance in the evolution of massive stars in a pre-supernova core. The beta decay process gives its contribution by emitting electrons in the plasma of the stellar core, thereby increasing pressure, which in turn increases the temperature. From the other side, the electron capture removes free electrons from the plasma of the star core contributing to the reduction of pressure and temperature. In this work we calculate the beta decay and electron capture rates in stellar conditions for 63 nuclei of relevance in the pre-supernova stage, employing Gross Theory as the nuclear model. We use the abundances calculated with the Saha equations in the hypothesis of nuclear statistical equilibrium to evaluate the time derivative of the fraction of electrons. Our results are compared with other evaluations available in the literature. They have shown to be one order less or equal than the calculated within other models. Our results indicate that these differences may influence the evolution of the star in the later stages of pre-supernova.Facultad de Ciencias ExactasInstituto de Física La Plat

Effects of Antineutrino mass on β⁻-Decay Rates Calculated Within the Gross Theory of Beta Decay

We analyze the effect of the antineutrino mass over the β⁻-decay rates calculated within the scheme of the Gross Theory of Beta Decay (GTBD). We give a non-null value to the mass of the antineutrino participating in β⁻-decay, (A,Z) → (A,Z+1) + e⁻ + ͞νₑ, which is usually neglected because we know it is small compared with electron mass. We have slightly modified the GTDB by inserting the antineutrino mass in the formalism. We have adopted a Gaussian energy distribution function with the axial-vector weak coupling constant gA = 1, as well as a new set of the adjustable parameter σN related to the standard deviation for the Gamow-Teller resonance, updated experimental mass defects, and also an improved approximation for the Fermi function. Our sample consists of a set of 94 nuclei of interest in the pre-supernova phase, which have experimental data in terrestrial conditions available in the Letter of Nuclide. We have compared the calculation without the inclusion of the antineutrino mass with that adopting a really overestimated value of 50 keV for it to illustrate the effect on the decay rates. We have shown that they are improved only by approximately one per thousand in this case. We conclude that the effect of the antineutrino mass on decay rates is not relevant.Facultad de Ciencias ExactasInstituto de Física La Plat

Computer code for double beta decay QRPA based calculations

The computer code developed by our group some years ago for the evaluation of nuclear matrix elements, within the QRPA and PQRPA nuclear structure models, involved in neutrino-nucleus reactions, muon capture and β± processes, is extended to include also the nuclear double beta decay.Facultad de Ciencias ExactasInstituto de Física La Plat

Dispersión neutrino-núcleo y estructura nuclear

Facultad de Ciencias Exacta