General behavior of double beta decay amplitudes in the quasiparticle random phase approximation

Simple formulas for the 0+ → 0+ double beta decay matrix elements, as a function of the particle-particle strength gpp, have been designed within the quasiparticle random phase approximation. The 2v amplitude is a bilinear function of gpp, and all 0v moments behave as ratios of a linear function and the square root of another linear function of gpp. It is suggested that these results are of general validity and that any modifications of the nuclear Hamiltonian or the configuration space cannot lead to a different functional dependence.Facultad de Ciencias Exacta

Asymmetry parameter for the nonmesonic decay of Λ5He

We report the preliminary result of an exact calculation of the asymmetry parameter, aΛ, in the nonmesonic hypernuclear decay, based on a one-meson-exchange (OME) model. For the case of Λ 5He and including one-pion-exchange only, the result is shown not to differ considerably from the one obtained with the approximate formula widely used in the literature. In particular, the sign of aΛ remains negative, in disagreement with its most recent experimental determination. Whether these facts remain true for heavier hypernuclei and in a more complete OME model is still under investigation.Facultad de Ciencias Exacta

Nonmesonic weak decay dynamics from proton spectra of Λ-hypernuclei

A novel comparison between the data and the theory is proposed for the nonmesonic (NM) weak decay of hypernuclei. Instead of confronting the primary decay rates, as is usually done, we focus our attention on the effective decay rates that are straightforwardly related with the number of emitted particles. Proton kinetic energy spectra of 5∧Be, 11 ∧ B, 12∧C, 13∧C, 15∧N, and 16∧O , measured by FINUDA, are evaluated theoretically. The independent particle shell model (IPSM) is used as the nuclear structure framework, while the dynamics is described by the one-meson-exchange (OME) potential. Only for the , and hypernuclei it is possible to make a comparison with the data, since for the rest there is no published experimental information on number of produced hypernuclei. Considering solely the one-nucleon-induced (1N-NM) decay channel, the theory reproduces correctly the shapes of all three spectra at medium and high energies (Ep ≳ 40 MeV). Yet, it greatly overestimates their magnitudes, as well as the corresponding transition rates when the full OME (π + K + η + ρ + ω + K*) model is used. The agreement is much improved when only the π + K mesons with soft dipole cutoff parameters participate in the decay process. We find that the IPSM is a fair first-order approximation to disentangle the dynamics of the 1N-NM decay, the knowledge of which is indispensable to inquire about the baryon–baryon strangeness–flipping interaction. It is shown that the IPSM provides very useful insights regarding the determination the 2N-NM decay rate. In a new analysis of the FINUDA data, we derive two results for this quantity with one of them close to that obtained previously.Instituto de Física La Plat

Decaimiento beta doble: nuevo formalismo

Se estudia la legitimidad de los métodos consistentes en promediar las soluciones asociadas a los estados iniciales y finales dentro de la aproximación de fases al azar para cuasipartículas (QRPA), para el decaimiento beta doble. Se desarrolla un nuevo método, que trabaja con una única ecuación de QRPA para el núcleo intermedio, en el cual las correlaciones de estado fundamental para las transiciones β⁻ son las β⁺ y viceversa. Los resultados numéricos coinciden en las distintas formulaciones, lo que avala los procedimientos de promedio conocidos, a la vez que exhibe la mayor simplicidad operativa del método propuesto, que en el caso del modo de dos neutrinos permite sustituir el proceso de diagonalización por una inversión de matriz. La comparación con los datos experimentales muestra un excelenteFacultad de Ciencias Exacta

Kinetic energy sum spectra in nonmesonic weak decay of hypernuclei

We evaluate the coincidence spectra in the nonmesonic weak decay (NMWD) \Lambda N\go nN of $\Lambda$ hypernuclei $^{4}_\Lambda$He, $^{5}_\Lambda$He, $^{12}_\Lambda$C, $^{16}_\Lambda$O, and $^{28}_\Lambda$Si, as a function of the sum of kinetic energies $E_{nN}=E_n+E_N$ for $N=n,p$. The strangeness-changing transition potential is described by the one-meson-exchange model, with commonly used parameterization. Two versions of the Independent-Particle Shell Model (IPSM) are employed to account for the nuclear structure of the final residual nuclei. They are: (a) IPSM-a, where no correlation, except for the Pauli principle, is taken into account, and (b) IPSM-b, where the highly excited hole states are considered to be quasi-stationary and are described by Breit-Wigner distributions, whose widths are estimated from the experimental data. All $np$ and $nn$ spectra exhibit a series of peaks in the energy interval 110 MeV $<E_{nN}<170$ MeV, one for each occupied shell-model state. The IPSM-a could be a pretty fair approximation for the light $^{4}_\Lambda$He and $^{5}_\Lambda$He hypernuclei. For the remaining, heavier, hypernuclei it is very important, however, to take into account the spreading in strength of the deep-hole states, and bring into play the IPSM-b approach. Notwithstanding the nuclear model that is employed the results depend only very weakly on the details of the dynamics involved in the decay process proper. We propose that the IPSM is the appropriate lowest-order approximation for the theoretical calculations of the of kinetic energy sum spectra in the NMWD. It is in comparison to this picture that one should appraise the effects of the final state interactions and of the two-nucleon-induced decay mode.Comment: v1: 20 pages, 3 figures, 1 table, submitted for publication; v2: minor corrections, improved figures, published versio

On some properties of the Surface Delta Interaction

A method is discussed for solving the RPA equations without discarding any term in the case of separable interactions. It is specialized to the SDI for both spherical and deformed nuclei and applied in two simple examples.Facultad de Ciencias Exacta

Asymmetry parameter for the nonmesonic decay of Λ5He

We report the preliminary result of an exact calculation of the asymmetry parameter, aΛ, in the nonmesonic hypernuclear decay, based on a one-meson-exchange (OME) model. For the case of Λ 5He and including one-pion-exchange only, the result is shown not to differ considerably from the one obtained with the approximate formula widely used in the literature. In particular, the sign of aΛ remains negative, in disagreement with its most recent experimental determination. Whether these facts remain true for heavier hypernuclei and in a more complete OME model is still under investigation.Facultad de Ciencias Exacta

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