Particle-hole Interaction Research Articles

β -decay properties of neutron-rich rare-earth isotopes

In this paper, beta-decay properties of even-even neutron-rich isotopes in the rare-earth mass region are studied within a microscopic theoretical approach based on a proton-neutron quasiparticle random-phase approximation. The underlying mean field is constructed selfconsistently from a deformed Hartree-Fock calculation with Skyrme interactions and pairing correlations to which particle-hole and particle-particle residual interactions are added. Nuclei in this mass region participate in the astrophysical rapid neutron capture process and are directly involved in the generation of the rare-earth peak in the isotopic abundance pattern centered at A=160. The energy distributions of the Gamow-Teller strength as well as the beta-decay half-lives and the beta-delayed neutron-emission probabilities are discussed and compared with the available experimental information and with calculations based on different approaches.

Medium polarization and pairing in asymmetric nuclear matter

The many-body theory of asymmetric nuclear matter is developed beyond the Brueckner–Hartree–Fock approximation to incorporate the medium polarization effects. The extension is performed within the Babu–Brown induced interaction theory. After deriving the particle–hole interaction in the form of Landau–Migdal parameters, the effects of the induced component on the symmetry energy are investigated along with the screening of 1S0 proton–proton and 3PF2 neutron–neutron pairing, which are relevant for the neutron-star cooling. The crossover from repulsive (screening) to attractive (anti-screening) interaction going from pure neutron matter to symmetric nuclear matter is discussed.

Random matrix analysis of the monopole strength distribution in 208Pb

We study statistical properties of the $0^+$ spectrum of $^{208}$Pb in the energy region $E_x\leq20$ MeV. We use the Skyrme interaction SLy4 as our model Hamiltonian to create a single-particle spectrum and to analyze excited states. The finite-rank separable approximation for the particle-hole interaction enables us to perform the calculations in large configuration spaces. We show that while the position of the monopole resonance centroid is determined by one phonon excitations of $0^+$, the phonon-phonon coupling is crucial for the description of a strength distribution of the $0^+$ spectrum. In fact, this coupling has an impact on the spectral rigidity $\Delta_3(L)$ which is shifted towards the random matrix limit of the Gaussian orthogonal ensembles.

Nongeneric dispersion of excitons in the bulk ofWSe2

We combine electron energy-loss spectroscopy (EELS) and density functional theory (DFT) calculations to study the dispersion and effective mass of excitons in the bulk of ${\mathrm{WSe}}_{2}$. Our EELS data suggest substantial deviations from the generic quadratic momentum dependence along the $\mathrm{\ensuremath{\Gamma}}K$ direction. From the DFT-derived Kohn-Sham states we deduce the EELS response without the inclusion of particle-hole attraction to study the possible role of the single-particle band structure on the exciton behavior. Based on this analysis we argue in favor of a strongly momentum dependent particle-hole interaction in ${\mathrm{WSe}}_{2}$ and other group-VI-transition-metal dichalcogenides.

Atomic-scale electronic structure of the cuprate d-symmetry form factor density wave state

Extensive research into high temperature superconducting cuprates is now focused upon identifying the relationship between the classic 'pseudogap' phenomenon$^{1,2}$ and the more recently investigated density wave state$^{3-13}$. This state always exhibits wave vector $Q$ parallel to the planar Cu-O-Cu bonds$^{4-13}$ along with a predominantly $d$-symmetry form factor$^{14-17}$ (dFF-DW). Finding its microscopic mechanism has now become a key objective$^{18-30}$ of this field. To accomplish this, one must identify the momentum-space ($k$-space) states contributing to the dFF-DW spectral weight, determine their particle-hole phase relationship about the Fermi energy, establish whether they exhibit a characteristic energy gap, and understand the evolution of all these phenomena throughout the phase diagram. Here we use energy-resolved sublattice visualization$^{14}$ of electronic structure and show that the characteristic energy of the dFF-DW modulations is actually the 'pseudogap' energy $\Delta_{1}$. Moreover, we demonstrate that the dFF-DW modulations at $E=-\Delta_{1}$ (filled states) occur with relative phase $\pi$ compared to those at $E=\Delta_{1}$ (empty states). Finally, we show that the dFF-DW $Q$ corresponds directly to scattering between the 'hot frontier' regions of $k$-space beyond which Bogoliubov quasiparticles cease to exist$^{31,32,33}$. These data demonstrate that the dFF-DW state is consistent with particle-hole interactions focused at the pseudogap energy scale and between the four pairs of 'hot frontier' regions in $k$-space where the pseudogap opens.

Interweaving of elementary modes of excitation in superfluid nuclei through particle-vibration coupling: Quantitative account of the variety of nuclear structure observables

A complete characterization of the structure of nuclei can be obtained by combining information arising from inelastic scattering, Coulomb excitation and $\gamma-$decay, together with one- and two-particle transfer reactions. In this way it is possible to probe the single-particle and collective components of the nuclear many-body wavefunction resulting from their mutual coupling and diagonalising the low-energy Hamiltonian. We address the question of how accurately such a description can account for experimental observations. It is concluded that renormalizing empirically and on equal footing bare single-particle and collective motion in terms of self-energy (mass) and vertex corrections (screening), as well as particle-hole and pairing interactions through particle-vibration coupling allows theory to provide an overall, quantitative account of the data.

Effect of complex configurations on the description of properties of 132Sn beta decay

Gamow–Teller transitions in the beta decay of the 132Sn neutron-rich nucleus was described microscopically. The coupling of one- and two-phonon components of the wave functions was taken into account on the basis of Skyrme interactions featuring various contributions of the tensor component. A separable approximation of the particle—hole interaction made it possible tohole interaction perform calculations in a large configuration space. It was shown that an increase in the strength of the neutron—proton tensor interaction led to an increase in the energy of Gamow—Teller transitions. In addition, a decrease in the 132Sn half-life with respect to beta decay was obtained.

Structure of the two-neutrino double-βdecay matrix elements within perturbation theory

The two-neutrino double-$\ensuremath{\beta}$ Gamow-Teller and Fermi transitions are studied within an exactly solvable model, which allows a violation of both spin-isospin SU(4) and isospin SU(2) symmetries, and is expressed with generators of the SO(8) group. It is found that this model reproduces the main features of realistic calculation within the quasiparticle random-phase approximation with isospin symmetry restoration concerning the dependence of the two-neutrino double-$\ensuremath{\beta}$ decay matrix elements on isovector and isoscalar particle-particle interactions. By using perturbation theory an explicit dependence of the two-neutrino double-$\ensuremath{\beta}$ decay matrix elements on the like-nucleon pairing, particle-particle $T=0$ and $T=1$, and particle-hole proton-neutron interactions is obtained. It is found that double-$\ensuremath{\beta}$ decay matrix elements do not depend on the mean field part of Hamiltonian and that they are governed by a weak violation of both SU(2) and SU(4) symmetries by the particle-particle interaction of Hamiltonian. It is pointed out that there is a dominance of two-neutrino double-$\ensuremath{\beta}$ decay transition through a single state of intermediate nucleus. The energy position of this state relative to energies of initial and final ground states is given by a combination of strengths of residual interactions. Further, energy-weighted Fermi and Gamow-Teller sum rules connecting $\mathrm{\ensuremath{\Delta}}Z=2$ nuclei are discussed. It is proposed that these sum rules can be used to study the residual interactions of the nuclear Hamiltonian, which are relevant for charge-changing nuclear transitions.

Sensitivity ofβ-decay rates to the radial dependence of the nucleon effective mass

We analyze the sensitivity of $\ensuremath{\beta}$-decay rates in $^{78}\mathrm{Ni}$ and $^{100,132}\mathrm{Sn}$ to a correction term in Skyrme energy-density functionals (EDFs) which modifies the radial shape of the nucleon effective mass. This correction is added on top of several Skyrme parametrizations which are selected from their effective mass properties and predictions about the stability properties of $^{132}\mathrm{Sn}$. The impact of the correction on high-energy collective modes is shown to be moderate. From the comparison of the effects induced by the surface-peaked effective mass in the three doubly magic nuclei, it is found that $^{132}\mathrm{Sn}$ is largely impacted by the correction, while $^{78}\mathrm{Ni}$ and $^{100}\mathrm{Sn}$ are only moderately affected. We conclude that $\ensuremath{\beta}$-decay rates in these nuclei can be used as a test of different parts of the nuclear EDF: $^{78}\mathrm{Ni}$ and $^{100}\mathrm{Sn}$ are mostly sensitive to the particle-hole interaction through the $B(\text{GT})$ values, while $^{132}\mathrm{Sn}$ is sensitive to the radial shape of the effective mass. Possible improvements of these different parts could therefore be better constrained in the future.

Effects of Phonon--Phonon Coupling on Properties of Pygmy Resonance in $^{132}$Sn

Starting from an effective Skyrme interaction, we study the effects of phonon–phonon coupling on the low-energy spectrum of the 1− states in 132Sn. The calculations are performed within a finite rank separable approximation for the particle-hole interaction. The inclusion of two-phonon configurations brings a sizeable contribution to the low-lying strength. Comparison with available experimental data shows a reasonable agreement for the low-energy E1 strength distribution.

Crossing of large multiquasiparticle magnetic-rotation bands inBi198

High-spin states in the doubly-odd $^{198}$Bi nucleus have been studied by using the $^{185,187}$Re($^{16}$O, xn) reactions at the beam energy of 112.5 MeV. $\gamma-\gamma$ coincidence were measured by using the INGA array with 15 Compton suppressed clover HPGe detectors. The observed levels have been assigned definite spin-parity. The high spin structure is grouped into three bands (B1, B2 and B3), of which two (B1 and B2) exhibit the properties of magnetic rotation (MR). Tilted axis cranking calculations were carried out to explain the MR bands having large multi-quasiparticle configurations. The calculated results explain the bands B1 and B2 very nicely, confirming the shears mechanism and suggest a crossing of two MR bands in both the cases. The crossing is from 6-qp to 8-qp in band B1 and from 4-qp to 6-qp in band B2, a very rare finding. A semiclassical model has also been used to obtain the particle-hole interaction strengths for the bands B1 and B2, below the band crossing.

Collective modes in a superfluid neutron gas within the quasiparticle random-phase approximation

We study collective excitations in a superfluid neutron gas at zero temperature within the quasiparticle random phase approximation. The particle-hole residual interaction is obtained from a Skyrme functional, while a separable interaction is used in the pairing channel which gives a realistic density dependence of the pairing gap. In accordance with the Goldstone theorem, we find an ungapped collective mode (analogous to the Bogoliubov-Anderson mode). At low momentum, its dispersion relation is approximately linear and its slope coincides with the hydrodynamic speed of sound calculated with the Skyrme equation of state. The response functions are compared with those obtained within the Landau approximation. We also compute the contribution of the collective mode to the specific heat of the neutron gas, which is relevant for the thermodynamic properties of the inner crust of neutron stars.

β-decay half-lives including first-forbidden contributions for neutron-rich Zn isotopes in the extended QRPA with neutron-proton pairing

The β decays of neutron-rich Zn isotopes are investigated within the extended quasiparticle random-phase approximation, where neutron-neutron, proton-proton, and neutron-proton pairing correlations are considered in the similar manner. The Brückner G-matrix obtained with the charge-dependent Bonn nucleon-nucleon force is used for the residual particle-particle and particle-hole interactions in addition to the pairing interactions. Contributions from both allowed Gamow-Teller and first-forbidden transitions are considered, and β-decay half-lives together with β-delayed neutron emission probabilities are calculated. The calculated results are found to agree well with the available experimental data.

β-decay rates of neutron-rich Kr and Sr isotopes in the deformed QRPA with realistic interactions

Deformed quasiparticle random phase approximation with realistic nucleon–nucleon interactions is employed to investigate β-decay half-lives and β-delayed neutron emission probabilities of neutron-rich Kr and Sr isotopes. The residual particle–particle and particle-hole interactions are obtained in terms of the Brückner G-matrix with the charge-dependent Bonn nucleon–nucleon force. Both allowed Gamow–Teller and first-forbidden transitions are taken into account. The available experimental half-lives are well reproduced with a factor of about three. Predictions on β-decay properties are made for more neutron-rich isotopes, which could be useful for future experiments.

Description of the simplest photonuclear reactions within the particle-hole dispersive optical model

A recently developed particle-hole dispersive optical model is applied to describe the cross sections of photoabsorption, $\text{direct}+\text{semidirect}$ photoneutron and inverse reactions accompanied by excitation of the isovector giant dipole and quadrupole resonances in medium--heavy-mass spherical nuclei. The model is an extension of the standard and nonstandard versions of the continuum-random-phase approximation by including the spreading effect in a phenomenological way. It contains the following ingredients: the Landau--Migdal particle-hole interaction and a phenomenological mean field consistent with this interaction, isovector velocity-dependent forces taken in the simplest form and the imaginary part of an effective single-particle optical-model potential determining the corresponding dispersive part. All the model parameters are taken from the other data and from the description of photoabsorption, while the $\text{direct}+\text{semidirect}$ photoneutron and inverse reactions are described without the use of specific adjustable parameters. Calculation results obtained for a few neutron-closed-shell nuclei are compared with the corresponding experimental data.

β-decay rates of neutron-rich Zr and Mo isotopes in the deformed quasiparticle random-phase approximation with realistic interactions

The ${\ensuremath{\beta}}^{\ensuremath{-}}\mathrm{-decay}$ rates of neutron-rich Zr and Mo isotopes are investigated within the deformed quasiparticle random-phase approximation with realistic nucleon-nucleon interactions. Axially symmetric deformations are considered in the calculations from a mean-field description of a quasiparticle picture and of both particle-hole and particle-particle excitations. The Br\"uckner $G$ matrix obtained with charge-dependent Bonn nucleon-nucleon forces is employed for residual particle-particle and particle-hole interactions. Contributions from both allowed Gammow-Teller and first-forbidden transitions are calculated and the sensitivity of the calculated results to the particle-particle strength is discussed. The calculated $\ensuremath{\beta}$-decay half-lives show a good agreement with the available experimental data. Moreover, predictions of $\ensuremath{\beta}$-decay half-lives are made for some extremely neutron-rich isotopes, which could be useful for future experiments.

Landau–Migdal vs. Skyrme

The magnitude and density-dependence of the non-spin dependent Landau-Migdal parameters are derived from Skyrme energy functionals and compared with the phenomenological ones. We perform RPA calculations with various approximations for the Landau-Migdal particle-hole interaction and compare them with the results obtained with the full Skyrme interaction. For the first time the next to leading order in the Landau-Migdal approach is considered in nuclear structure calculations.

β-decay rates of r-process waiting-point nuclei in the extended quasiparticle random-phase approximation

The β− decays of the r-process waiting-point nuclei at the neutron magic numbers N = 50 and N = 82 are investigated within the extended quasiparticle random-phase approximation (QRPA), where neutron–neutron, proton–proton and neutron–proton (np) pairing correlations are considered in the specialized Hartree–Fock–Bogoliubov (HFB) calculation. The Brückner G-matrix obtained with the charge-dependent Bonn nucleon–nucleon force is used for the residual particle–particle and particle–hole interaction in addition to the pairing interaction. It is found that the np pairing interaction plays an important role in reducing the calculated β−-decay half-lives. The calculations with np pairing show good agreement with the available experimental data including the decay half-lives of Ni isotopes, which are usually overestimated in the self-consistent proton–neutron QRPA calculations.

Nuclear charge-exchange excitations in localized covariant density functional theory

The recent progress in the studies of nuclear charge-exchange excitations with localized covariant density functional theory is briefly presented, by taking the fine structure of spin-dipole excitations in 16O as an example. It is shown that the constraints introduced by the Fock terms of the relativistic Hartree-Fock scheme into the particle-hole residual interactions are straightforward and robust.

Large-amplitude pairing fluctuations in atomic nuclei

Pairing fluctuations are self-consistently incorporated on the same footing as the quadrupole deformations in present state-of-the-art calculations including particle-number and angular-momentum conservation as well as configuration mixing. The approach is complemented by the use of the finite-range density-dependent Gogny force which, with a unique source for the particle-hole and particle-particle interactions, guarantees a self-consistent interplay in both channels. We have applied our formalism to study the role of the pairing degree of freedom in the description of the most relevant observables like spectra, transition probabilities, separation energies, etc. We find that the inclusion of pairing fluctuations mostly affects the description of excited states, depending on the excitation energy and the angular momentum. $E0$ transition probabilities experience rather big changes while $E2$'s are less affected. Genuine pairing vibrations are thoroughly studied with the conclusion that deformations strongly inhibits their existence. These studies have been performed for a selection of nuclei: spherical, deformed, and with different degrees of collectivity.