Calculation of the beta decay of Pd. Quasiparticle random phase approximation results

Single beta decay transitions in ^114–120Pd are calculated. Theoreticalβ⁺ and β⁻ strength distributions, for transitions to 1⁺ states in the nuclei ^114–120Ag and ^114–120Rh, are obtained in the framework of the quasiparticle random phase approximation (QRPA). The effective two-body interaction which is used in the calculations is constructed from the Bonn one-boson-exchange potential (OBEP). Particle-hole and particle-particle like channels of the two-body force are included in the definition of the QRPA matrix equations. Effects associated with the particle number violation of the quasiparticle mean field are accounted for by using a particle-number-projected version of the QRPA formalism. Theoretical strength distributions for the β⁻ and β⁺ braches are shown and compared with data.     

Renormalized proton- neutron QRPA and double beta decay of 82Se to excited states in 82Kr

We apply the self-consistent renormalized proton-neutron QRPA (RQRPA) method to calculate the two-neutrino double beta (2νββ) decay matrix elements associated with the ground-state and excited-state transitions of the ⁸²Se → ⁸²Kr decay. The RQRPA method is an extension of the pnQRPA method and promotes the Pauli exclusion principle violated by the pnQRPA ground state and yields more stable nuclear matrix elements with increasing strength of the proton-neutron interaction. In the present work the RQRPA wave functions are also used to evaluate 2νββ-decay rates to excited final states. The resulting theoretical half lives are compared with the new stringent experimental limits obtained by using a HPGe detector and external sources of enriched selenium.     

β-衰变中容许跃迁和禁戒跃迁的衰变规律

在考虑容许跃迁和禁戒跃迁的基础上, 对远离β稳定线附近原子核的β^-衰变寿命进行了系统的研究, 发现对于远离β稳定线的原子核的β^-衰变寿命, 其容许跃迁和禁戒跃迁寿命(T_1/2)与母核的质子数和中子数之间存在指数规律. 利用这个规律, 计算了β^-衰变中的容许跃迁和禁戒跃迁(包括一级禁戒跃迁和二级禁戒跃迁)的衰变寿命, 理论计算结果与实验值符合得很好. 在此基础上, 对于一些核素的β^-衰变寿命进行预言, 这对于核物理和天体物理中β^-衰变研究具有重要意义.     

Isospin symmetry breaking in double-beta-decay processes

The nuclear structure physics of double-beta-decay transitions is reviewed starting from the consideration of the isospin symmetry breaking in the nuclear many body problem. The difficulties found in the use of the QRPA and related approximations, in dealing with the calculation of nuclear double-beta-decay observables, are understood in terms of the mixing between isospin collective and intrinsic variables and in terms of isospin breaking approximations.     

Self-consistent random phase approximation within the O(5) model and Fermi transitions

Self-consistent quasiparticle random phase approximation (SCQRPA) is considered in application to the Fermi transitions within the O(5) model. It is demonstrated that SCQRPA improves on renormalized QRPA (RQRPA), a method that has recently become rather popular in this context. The analytical form of the SCQRPA vacuum is used to evaluate all the matrix elements. The SCQRPA results show a general trend similar to the exact solutions. The necessity to change the single particle basis beyond the transition point, and to include the proton-proton and neutron-neutron channels in the QRPA operator, in addition to the proton-neutron one, is pointed out.     

A comparative study of double beta decay by shell model and quasiparticle RPA

Nuclear matrix elements of the two-neutrino and neutrinolessββ decays of⁴⁸Ca(0 _g.s. ⁺ )→⁴⁸Ti(0 _g.s. ⁺ ) are calculated by shell model and QRPA. The two-neutrino matrix elementM _GT ^2v is rather reliably evaluated in the QRPA approach by a careful fit of the particle-particle interaction strength in the 1⁺ channel, which governs the spinisospin ground-state correlations. The shell-model value ofM _GT ^2v depends not only on the 1⁺ interaction but largely on the pairing and quadrupole interactions. Concerning the neutrinoless-mode nuclear matrix elements, the shell model gives generally smaller values than the QRPA. A detailed analysis indicates that the discrepancies originate mainly from the truncation of shell-model configurations (fp-space). The QRPA calculation in a larger model space well takes into account transitions from/to single-particle orbits far from the Fermi surface, and those transitions give rise to sizable contributions because of large momentum transfers due to the exchange of a virtual neutrino.     

The quasiparticle rpa as a model for gamow-teller ß-decay

The validity of the quasiparticle random-phase approximation is studied by comparing it with full shell-model calculations in the sd-shell. Phenomenological interactions relevant for the sd-shell have been applied, and Gamow-Teller ß⁺ strengths are calculated. It is found that in the QRPA, the ß⁺ strength is a factor of two higher than the shell-model result. The shell-model results are less sensitive to the particle-particle interaction strength than the QRPA. With u, v factors from the shell-model wavefunctions, the ß⁺ strength in the QRPA reproduces the shell-model result. This suggests that the QRPA does not contain enough ground-state correlations.     

Self-consistent approach to β-decay and delayed multi-neutron emission

The beta-decay half-lives and delayed multi- neutron emission branchings for the nuclei near the new neutron shell N = 34 are treated within self-consistent Density Functional + Continuum QRPA model (DF + CQRPA). A comparison with the recent self-consistent calculations from relativistic QRPA and standard (semi-microscopic) FRDM is performed.     

Looking for an Optimal Ground State Within Quasiparticle Random Phase Approximation

A new ansatz for the correlated ground state of the many-nucleon system is proposed which results in obtaining a modified Quasiparticle Random Phase Approximation (QRPA). An additional degree of freedom is introduced which allows to determine variationally the ground state simultaneously with solving the QRPA equations. This new approach, QRPA with an optimal ground state, is studied within the proton-neutron Lipkin model. New solutions have been found, in the range of the interaction strength where the standard QRPA formalism does not work. A relation between one of them and the solution obtained within a semi-classical approach is established. A detailed study of the expectation value of the quasiparticle number operator in the ground state and the transition amplitude for the two-neutrino double beta Fermi decay, is also presented.     

Ikeda sum rule,self-consistency and double-beta decay in the renormalized quasiparticle random phase approximation

The effect of the inclusion of ground-state correlations into the QRPA equation of motion for the two-neutrino double-beta (ββ_2ν) decay is carefully analyzed. The resulting model, called renormalized QRPA (RQRPA), does not collapse near the physical value of the nuclear force strength in the particle-particle channel, as happens with the ordinary QRPA. Still, the ββ_2ν transition amplitude is only slightly less sensitive on this parameter in the RQRPA than that in the plain QRPA. It is argued that this fact reveals once more than the characteristic behavior of the ββ_2ν transition amplitude within the QRPA is not an artifact of the model, but a consequence of the partial restoration of the spin-isospin SU(4) symmetry. It is shown that the price paid for bypassing the collapse in the RQRPA is the violation of the Ikeda sum rule.     

Two possible improvements for pnQRPA: Application to the 2νββ decay

Two distinct many body procedures, aiming at improving the QRPA formalism for proton-neutron dipole excitations are succintly described. These are the boson expansion for bi-fermion operators and the full selfconsistent QRPA. Applications for the 2νββ process are presented. Presented by A.A. Raduta at the Workshop on calculation of double-beta-decay matrix elements (MEDEX’97), Prague, May 27–31, 1997.     

The Skyrme-TQRPA calculations of electron capture on hot nuclei in pre-supernova environment

We combine the thermal QRPA approach with the Skyrme energy density functional theory (Skyrme–TQRPA) for modelling the process of electron capture on nuclei in supernova environment. For a sample nucleus, ⁵⁶Fe, the Skyrme–TQRPA approach is applied to analyze thermal effects on the strength function of GT₊ transitions which dominate electron capture at E _e ≤ 30 MeV. Several Skyrme interactions are used in order to verify the sensitivity of the obtained results to the Skyrme force parameters. Finite-temperature cross sections are calculated and the results are comparedwith those of the other model calculations.     

Effects of ground-state correlations on 2νββ decay rates and limitations of the QRPA approach

Half-lives of the 2νββ decay are calculated in the proton-neutron QRPA for⁷⁶Ge,⁸²Se,¹⁰⁰Mo,^128,130Te,¹³⁶Xe and¹⁵⁰Nd. The strength of the particle-particle interaction, which plays a decisive role for a reliable evaluation of the half-lives, is determined from a QRPA calculation of singleβ ⁺ decays. The 2ν decay rates calculated with the interaction strength fitted in this way are strongly suppressed and found to be consistent with the existing experimental data. Effects of the ground-state correlations on the suppression are investigated. On the other hand, the present calculation indicates limitations of the QRPA approach.     

Spin and orbital contributions to collective M1 transitions in 46,48Ti

Low- and high-lying K^π = 1⁺ states and M1 transitions in ^46,48Ti are studied. The model hamiltonian is treated in the quasi-particle particle random phase approximation (QRPA) with an exact restoration of its rotational invariance. A considerable spin contribution to the transition matrix elements is found for the low-energy (about 4 MeV) strong M1 transition (the orbital contribution being 30–70% of the spin one), although the microscopic structure of this state in ⁴⁶Ti is typical for an orbital isovector excitation. The calculated energies and B(M1) values are in good agreement with the experimental data. The results are compared to the estimates of the isovector scissor model.     

Neutron-proton pairing

The two topics discussed here are the treatment of neutron-proton pairing and the problem of phase transitions in systems of neutrons and protons. The conclusions are based on exact calculations, possible in simplified situations, and the exact results are compared with the BCS treatment. QRPA, and many of its modifications, which are the most popular approaches to double beta decay, involve the quasiparticle transformation as a decisive first step. It is therefore imperative to understand its strengths and limitations. Presented at Workshop on calculation of double-beta-decay matrix elements (MEDEX’97), Prague, May 27–31, 1997. The work reported here is based on Refs. 3, 4, and 5. The credit for it belongs to my collaborators, in particular to Osvaldo Civitarese, Jonathan Engel, and Stuart Pittel. This work was supported by the U.S. Department of Energy under Grant. No. DE-FG03-88ER-40397.     

Non-collapsing QRPA for neutrinoless double beta decay

The standard quasiparticle random phase approximation(QRPA) is widely used to describe the neutrinoless double beta decay process. Although it has been quite successful in many cases of interest, it has some shortcomings. The most important one is that its solutions collapse for physical values of the particle-particle strength. We shall show that modifications can be done which can extend the validity of this standard QRPA beyond the point of collapse. Such modifications are: The introduction of proton-neutron pairing, the inclusion of the Pauli principle and the extension of the Hilbert space. If all these modifications are introduced into the standard QRPA then the collapse does not occur for physical values of the particle-particle strengths. Thus, one might be able to extract more accurate values on the effective neutrino mass by using the best available experimental limits on the half life of neutrinoless double beta decay. Presented by G. Pantis at the Workshop on calculation of double-beta-decay matrix elements (MEDEX’97), Prague, May 27–31, 1997.     

Quasiparticle shell-model calculation within multi-phonon subspace and SU(6) boson model

The hamiltonian with quadrupole interaction is diagonalized within the multi-phonon subspace for the cases of ⁷⁴Se, ¹¹⁴Cd and ¹²⁶Xe. The results are compared with those of the SU(6) boson model based on the Tamm-Dancoff phonon and the applicability of the boson model is discussed. As a by-product, the applicability of the quasiparticle random-phase approximation (QRPA) is investigated. It is shown that the SU(6) boson model is much better than the QRPA. The contribution from non-collective phonon degrees of freedom to the many-phonon high-spin states is also discussed.