Quasiparticle Random Phase Approximation Approach Research Articles

Isoscalar pairing interaction for the quasiparticle random-phase approximation approach to double- β and β decays

We have proposed in a series of previous articles a method to determine the effective axial-vector current coupling and the strength of the isoscalar proton-neutron pairing interaction for calculating the nuclear matrix elements of the neutrinoless double-$\ensuremath{\beta}$ ($0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$) decay by the quasiparticle random-phase approximation (QRPA). The combination of these two parameters has had an uncertainty in the QRPA approach, but now this uncertainty is removed by introducing a mathematical identity derived under the closure approximation to the nuclear matrix element of the $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ decay. In this article, we apply our method to the $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ decays of $^{136}\mathrm{Xe}$ and $^{130}\mathrm{Te}$ and show the nuclear matrix elements and reduced half-lives. Our calculation is tested first by a self-check method using the two-neutrino double-$\ensuremath{\beta}$ decay, and this test ensures the application of our method to $^{136}\mathrm{Xe}$. It turns out, however, that our method is not successful in $^{130}\mathrm{Te}$. Further tests are made for our calculation, and satisfactory results are obtained for $^{136}\mathrm{Xe}$.

Giant dipole resonance parameters from photoabsorption cross-sections * * Supported by the IAEA Coordinated Research Project F41032 (20466), the National Natural Science Foundation of China (U1432247, 11775013, 11305270, 11465005, U1630143), and the Science Challenge Project (TZ2018001) and the Key Laboratory fund key projects (6142A080201)

The structural effect is believed to have no influence on the decay properties of medium and heavy-mass nuclei at excitation energies above the pairing gap. These properties can be described by statistical properties using so-called photon strength functions for different multipolarities, and directly related to the photoabsorption cross-section ( ). is dominated by the electric giant dipole resonance at energy MeV. In this study, we construct two kinds of systematic giant dipole resonance parameters by fitting the experimental photoabsorption cross-sections. One is based on the microscopic relativistic quasiparticle random phase approximation approach, whereas the other is estimated by the phenomenological models within the Lorentzian representation. Both of them are demonstrated ot efficiently describe the experimental photoabsorption cross-sections available for medium to heavy-mass nuclei, and they can obtain more reliable predictions for the unknown nuclear system.

Examination of the consistency of the quasiparticle random-phase approximation approach to double- β decay of Ca48

The nuclear matrix elements (NMEs) of the neutrinoless and two-neutrino double-$\beta$ decays of $^{48}$Ca are calculated by the quasiparticle random-phase approximation (QRPA) with emphasis on the consistency examinations of this calculation method. The main new examination points are the consistency of two ways to treat the intermediate-state energies in the two-neutrino double-$\beta$ NME and comparison with the experimental charge-exchange strength functions obtained from $^{48}$Ca$(p,n)$ and $^{48}$Ti$(n,p)$ reactions. No decisive problem preventing the QRPA approach is found. The obtained neutrinoless double-$\beta$ NME adjusted by the ratio of the effective and bare axial-vector current couplings is lowest in those calculated by several groups and close to one of the QRPA values obtained by another group.

Self-consistent relativistic quasiparticle random-phase approximation and its applications to charge-exchange excitations

The self-consistent quasiparticle random-phase approximation (QRPA) approach is formulated in the canonical single-nucleon basis of the relativistic Hatree-Fock-Bogoliubov (RHFB) theory. This approach is applied to study the isobaric analog states (IAS) and Gamov-Teller resonances (GTR) by taking Sn isotopes as examples. It is found that self-consistent treatment of the particle-particle residual interaction is essential to concentrate the IAS in a single peak for open-shell nuclei and the Coulomb exchange term is very important to predict the IAS energies. For the GTR, the isovector pairing can increase the calculated GTR energy, while the isoscalar pairing has an important influence on the low-lying tail of the GT transition. Furthermore, the QRPA approach is employed to predict nuclear $\beta$-decay half-lives. With an isospin-dependent pairing interaction in the isoscalar channel, the RHFB+QRPA approach almost completely reproduces the experimental $\beta$-decay half-lives for nuclei up to the Sn isotopes with half-lives smaller than one second. Large discrepancies are found for the Ni, Zn, and Ge isotopes with neutron number smaller than $50$, as well as the Sn isotopes with neutron number smaller than $82$. The potential reasons for these discrepancies are discussed in detail.

Nuclear β-decay half-lives in the relativistic point-coupling model

The self-consistent proton–neutron quasiparticle random phase approximation approach is employed to calculate β-decay half-lives of neutron-rich even–even nuclei with . A newly proposed nonlinear point-coupling effective interaction PC-PK1 is used in the calculations. It is found that the isoscalar proton–neutron pairing interaction can significantly reduce β-decay half-lives. With an isospin-dependent isoscalar proton–neutron pairing strength, our results well reproduce the experimental β-decay half-lives, although the pairing strength is not adjusted using the half-lives calculated in this study.

Impact of phonon coupling on the photon strength function

The pygmy dipole resonance and photon strength function in stable and unstable Ni and Sn isotopes are calculated within the microscopic self-consistent version of the extended theory of finite Fermi systems, which, in addition to the standard quasiparticle random-phase approximation approach, includes phonon coupling effects. The Skyrme force SLy4 is used. A pygmy dipole resonance in $^{72}\mathrm{Ni}$ is predicted at the mean energy of 12.4 MeV exhausting 25.7% of the total energy-weighted sum rule. The microscopically obtained photon $E1$ strength functions are compared with available experimental data and used to calculate nuclear reaction properties. Average radiative widths and radiative neutron capture cross sections have been calculated taking phonon coupling into account as well as uncertainties caused by various microscopic level density models. In all three quantities considered, the contribution of phonon coupling turned out to be significant and is found necessary to explain available experimental data.

Description of the2ννββdecay within a fully renormalized proton-neutron quasiparticle random-phase approximation approach with a restored gauge symmetry

A many body Hamiltonian involving the mean field for a projected spherical single particle basis, the pairing interactions for alike nucleons and the dipole-dipole proton-neutron interactions in the particle-hole ($ph$) and particle-particle ($pp$) channels is treated by the projected gauge fully renormalized proton-neutron quasiparticle random phase approximation (PGFRpnQRPA) approach. The resulting wave functions and energies for the mother and the daughter nuclei are used to calculate the $2\nu\beta\beta$ decay rate and the process half life. For illustration, the formalism is applied for the decay $^{100}$Mo$ \to$ $^{100}$Ru. The results are in good agreement with the corresponding experimental data. The Ikeda sum rule ($ISR$) is obeyed. The gauge projection makes the $pp$ interaction inefficient.

Gamow-Teller strength distributions in Xe isotopes

The energy distributions of the Gamow-Teller (GT) strength are studied for even-even Xe isotopes with mass numbers from 124 to 142. A self-consistent microscopic formalism is used to generate the single-particle basis, using a deformed Skyrme Hartree-Fock mean field with pairing correlations in the BCS approximation. The GT transitions are obtained within a quasiparticle random phase approximation approach using a residual spin-isospin interaction in the particle-hole (ph) and particle-particle (pp) channels. We then discuss the pairing BCS treatment and the determination of the ph and pp residual interaction coupling constants. We study the GT${}^{+}$ and GT${}^{\ensuremath{-}}$ strength distributions for the equilibrium nuclear shapes, which comprise essential information for studies of charge-exchange reactions and double-\ensuremath{\beta} processes involving these isotopes.

Quasiparticle random-phase approximation with an optimal groundstate

A new quasiparticle random-phase approximation approach (QRPA) is presented.The corresponding ground state is variationally determined and exhibits aminimum energy. New solutions for the ground state, some withspontaneously broken symmetry, of a solvable Hamiltonian are found. Anon-iterative procedure to solve the nonlinear QRPA equations is used andthus all possible solutions are found. These are compared with the exactresults as well as with the solutions provided by other approaches.

Doubleβdecay to excited states of several medium-heavy nuclei within the renormalized quasiparticle random phase approximation

The renormalized proton-neutron quasiparticle random phase approximation approach has been used to study double \ensuremath{\beta} decay matrix elements and associated transition half-lives for neutrino-accompanied double \ensuremath{\beta} decay to the first excited ${2}^{+}$ state for five medium-heavy parent nuclei ${}^{76}$Ge, ${}^{82}$Se, ${}^{96}$Zr, ${}^{100}$Mo, and ${}^{116}$Cd. The results of these calculations are compared with the normal approach and experiments where available. The dependence on the size of the single particle basis is also discussed.

Theoretical and experimental investigation of the double beta processes in 106Cd

The double beta decay of 106 Cd to the ground and excited states of 106 Pd is investigated both theoretically and experimentally. The quasiparticle random-phase approximation approach is used for the two-neutrino decay mode calculations. Estimations show that detections of β + EC decays to the ground state and 0 1 + excited state and ECEC(0 + å 0 1 + ) transition could be detected with today low-background techniques. Using a HPGe detector and an external source of natural cadmium, new stringent limits on β + β + (0 ν + 2 ν ), β + EC(0 ν + 2 ν ) and ECEC(0 ν + 2 ν ) decays into the ground and excited states are derived.

Investigation of the decay of to excited states in

The two-neutrino mode of double beta decay of is investigated both theoretically and experimentally. The calculations, using the quasiparticle random phase approximation approach, show that for the detection of transitions to the two first excited states in the daughter nuclide will be possible in the very near future. On the experimental side, new, most stringent limits on half-lives for the double beta decay of to excited states in have been obtained with a `well-type' germanium detector. They range between and years (90% CL).

Description of orbital and spin excitations within a projected spherical single-particle basis

Orbital and spin excitations in even Sm isotopes have been studied microscopically in a quasiparticle random phase approximation approach formulated in the laboratory frame using a projected spherical single-particle basis which reproduces the Nilsson level scheme to a good approximation. The orbital magnetic dipole excitations are found to fall below 4 MeV with a summed strength which follows closely the observed deformation quadratic law. The M1 spin strength is found to be strongly fragmented over a range of 4 to 10 MeV and, in the case of the well deformed 154Sm isotope, distributed so as to reproduce the double hump pattern observed experimentally.

The neutrinoless double beta decay of 76Ge, 82Se, 86Kr, 114Cd, 128, 130Te and 134, 136Xe in the framework of a relativistic quark confinement model

The half-life of the 0 + → 0 + neutrinoless double beta decay is calculated for 76Ge, 82Se, 86Kr, 114Cd, 128, 130Te and 134, 136Xe and the upper limit for the effective neutrino mass of 3.0 eV is deduced from available experimental data. In addition, the contribution of the right-handed charged weak currents to the effective weak hamiltonian is estimated. The relevant parameters attain the values |〈 Λ〉| < 4.1 × 10 −6 and |〈 ν〉| < 6.6 × 10 −8. The nucleonic weak current is treated starting from the current quark level and evaluating the quark current using relativistic quark wave functions obtained from a Dirac equation with a harmonic confinement potential. The nuclear matrix elements of the thus obtained effective weak operators are evaluated using the proton-neutron quasi-particle random phase approximation approach avoiding the use of closure and the accompanying singular neutrino potentials. The dependence of the decay half-life on the recoil effects and the p-wave contribution is analyzed. Detailed presentation of the theory is pursued.