Standard Quasiparticle Random-phase Approximation Research Articles

Neutrino reactions onLa138andTa180via charged and neutral currents by the quasiparticle random-phase approximation

Cosmological origins of the two heaviest odd-odd nuclei, $^{138}$La and $^{180}$Ta, are believed to be closely related to the neutrino-process. We investigate in detail neutrino-induced reactions on the nuclei. Charged current (CC) reactions, $^{138}$Ba$ (\nu_e, e^{-}) ^{138}$La and $^{180}$Hf$ (\nu_e, e^{-}) ^{180}$Ta, are calculated by the standard Quasi-particle Random Phase Approximation (QRPA) with neutron-proton pairing as well as neutron-neutron, proton-proton pairing correlations. For neutral current (NC) reactions, $^{139}$La$ (\nu \nu^{'}) ^{139}${La}$^*$ and $^{181}$Ta$ (\nu, \nu^{'}) ^{181}$Ta$^*$, we generate ground and excited states of odd-even target nuclei, $^{139}$La and $^{181}$Ta, by operating one quasi-particle to even-even nuclei, $^{138}$Ba and $^{180}$Hf, which are assumed as the BCS ground state. Numerical results for CC reactions are shown to be consistent with recent semi-empirical data deduced from the Gamow-Teller strength distributions measured in the ($^{3}$He, t) reaction. Results for NC reactions are estimated to be smaller by a factor about 4 $\sim$ 5 rather than those by CC reactions. Finally, cross sections weighted by the incident neutrino flux in the core collapsing supernova are presented for further applications to the network calculations for relevant nuclear abundances.

Investigations of proton-neutron correlations close to the drip line

Proton-neutron correlations in nuclei above the $Z=50$ shell closure are investigated with the aim of understanding the behavior of the $2$${}^{+}$ and $4$${}^{+}$ states in Te and Xe isotopes, which remain at a rather constant energy as one approaches the shell closure at $N=50$. Our calculations reveal that standard quasiparticle random phase approximation calculations, involving a quadrupole-quadrupole (QQ) interaction with constant strengths, cannot explain this feature. It is found that to reproduce the experimental data within this model one has to include a variable proton-neutron interaction. It turns out that an increased proton-neutron QQ interaction increases the collectivity (i.e., $B(E2)$ values) when approaching the $N=50$ region, whereas an increased proton-neutron pairing interaction decreases the collectivity. We thus conclude that the ratio between the $B(E2)$ value and ${2}^{+}$ energy is a ``fingerprint'' of proton-neutron collectivity and it should be determined in future experiments concerning light Te isotopes. Based on this criterion, we conclude that the available experimental data indicate an enhanced proton-neutron pairing interaction by approaching doubly magic $Z=N=20$ and $Z=N=28$ regions.

Pygmy dipole resonance in nuclei

A brief survey of the state of the modern microscopic theory of the so-called pygmy dipole resonance in nuclei is given—in particular, some unresolved problems are listed. It is emphasized that, in order to explain the pygmy dipole resonance, it is necessary but not sufficient to take into account the coupling of single-particle degrees of freedom to photon degrees of freedom. The results of the calculations performed for the first time for the isovector pygmy dipole resonance and the isovector electric giant dipole resonance in 124Sn within a self-consistent approach involving, in addition to the standard quasiparticle random-phase approximation, a single-particle continuum and quasiparticle-phonon coupling of single-particle degrees of freedom to phonon degrees of freedom are presented. The results are found to be in satisfactory agreement with experimental data. The calculation of the isoscalar strength function in the energy region of the pygmy dipole resonance revealed that the nuclear-structure mechanism does not provide the isoscalar-strength suppression observed at energies in excess of 7 MeV in (α, α′γ) reactions; therefore, this suppression may stem from the reaction mechanism.

Two-neutrino doubleβdecay within fully renormalized quasiparticle random-phase approximation: Effect of the restoration of the Ikeda sum rule

The recently proposed fully renormalized quasiparticle random-phase approximation (QRPA), which fulfills the Ikeda sum rule exactly, is applied to the two-neutrino double $\ensuremath{\beta}$ decay of $^{76}\mathrm{Ge}$, $^{82}\mathrm{Se}$, $^{100}\mathrm{Mo}$, $^{116}\mathrm{Cd}$, $^{128}\mathrm{Te}$, and $^{130}\mathrm{Xe}$. The results obtained are compared with those of other approaches, standard QRPA and self-consistent QRPA. The similarities and the differences among the methods are discussed. The influence of the restoration of the Ikeda sum rule on the $2\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$-decay amplitude is analyzed.

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.

Quasiparticle random phase approximation with inclusion of the Pauli exclusion principle

Limitations of the quasiparticle random phase approximation (QRPA) are studied within an exactly solvable model, with a two body interaction of Fermi type. A special attention is paid to the violation of the Pauli exclusion principle (PEP) in solving the QRPA equation. A comparison of the exact solution, obtained by the diagonalization of a schematic nuclear Hamiltonian and those obtained within the standard QRPA, the renormalized QRPA, the QRPA with pertubative treatment of the PEP, and the QRPA with exact consideration of the PEP, is presented. The agreement quality is judged in terms of the quasiparticle number operator matrix elements in the ground state and in the first excited states, of the $\ensuremath{\beta}$ transition amplitudes, of the Ikeda sum rule, and of the nuclear matrix element for the double $\ensuremath{\beta}$ decay. We have found that by restoring the PEP, the QRPA solutions are considerably stabilized and a better agreement with the exact solution is obtained.

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.

Quasiparticle random-phase approximation andβ-decay physics: Higher-order approximations in a boson formalism

The quasiparticle random-phase approximation (QRPA) is reviewed and higher-order approximations are discussed with reference to {beta}-decay physics. The approach is fully developed in a boson formalism. Working within a schematic model, we first illustrate a fermion-boson mapping procedure and apply it to construct boson images of the fermion Hamiltonian at different levels of approximation. The quality of these images is tested through a comparison between approximate and exact spectra. Standard QRPA equations are derived in correspondence with the quasi-boson limit of the first-order boson Hamiltonian. The use of higher-order Hamiltonians is seen to improve considerably the stability of the approximate solutions. The mapping procedure is also applied to Fermi {beta} operators: exact and approximate transition amplitudes are discussed together with the Ikeda sum rule. The range of applicabilty of the QRPA formalism is analyzed. {copyright} {ital 1997} {ital The American Physical Society}

Single- and double-beta decay Fermi transitions in an exactly solvable model

An exactly solvable model suitable for the description of single- and double-beta decay processes of the Fermi type is introduced. The model is equivalent to the exact shell-model treatment of protons and neutrons in a single-$j$ shell. Exact eigenvalues and eigenvectors are compared to those corresponding to the Hamiltonian in the quasiparticle basis (qp) and with the results of both the standard quasiparticle random phase approximation (QRPA) and the renormalized one (RQRPA). The role of the scattering term of the quasiparticle Hamiltonian is analyzed. The presence of an exact eigenstate with zero energy is shown to be related to the collapse of the QRPA. The RQRPA and the qp solutions do not include this zero-energy eigenvalue in their spectra, probably due to spurious correlations. The meaning of this result in terms of symmetries is presented.