Two-body Residual Interaction Research Articles

Finite-temperature linear response theory based on relativistic Hartree Bogoliubov model with point-coupling interaction

The finite-temperature linear response theory based on the finite-temperature relativistic Hartree-Bogoliubov (FT-RHB) model is developed in the charge-exchange channel to study the temperature evolution of spin-isospin excitations. Calculations are performed self-consistently with relativistic point-coupling interactions DD-PC1 and DD-PCX. In the charge-exchange channel, the pairing interaction can be split into isovector ($T = 1$) and isoscalar ($T = 0$) parts. For the isovector component, the same separable form of the Gogny D1S pairing interaction is used both for the ground-state calculation as well as for the residual interaction, while the strength of the isoscalar pairing in the residual interaction is determined by comparison with experimental data on Gamow-Teller resonance (GTR) and Isobaric analog resonance (IAR) centroid energy differences in even-even tin isotopes. The temperature effects are introduced by treating Bogoliubov quasiparticles within a grand-canonical ensemble. Thus, unlike the conventional formulation of the quasiparticle random-phase approximation (QRPA) based on the Bardeen-Cooper-Schrieffer (BCS) basis, our model is formulated within the Hartree-Fock-Bogoliubov (HFB) quasiparticle basis. Implementing a relativistic point-coupling interaction and a separable pairing force allows for the reduction of complicated two-body residual interaction matrix elements, which considerably decreases the dimension of the problem in the coordinate space. The main advantage of this method is to avoid the diagonalization of a large QRPA matrix, especially at finite temperature where the size of configuration space is significantly increased. The implementation of the linear response code is used to study the temperature evolution of IAR, GTR, and spin-dipole resonance (SDR) in even-even tin isotopes in the temperature range $T = 0 - 1.5$ MeV.

Spectral fluctuations and thermalization in the f5p-shell space

Chaos against thermalization, which was earlier investigated in the sd-shell space, is examined in the f5p-shell space. The two-body residual interaction of f5pvh with realistic single-particle energies have been utilized for carrying out f5p-shell space calculations. The present study demonstrates that the spectral fluctuations computed with realistic single-particle energies are in accordance with the Gaussian orthogonal ensemble of random matrices. Besides, the equilibrium heating is extremely related with the progress of many-body quantum chaos. Moreover, the single-particle entropy of individual states in the mean field basis is dissimilar to the thermodynamic entropy determined from the level density. The present results, which are a check of the ideas of many-body quantum chaos in a different version of the nuclear shell model applied to another part of the periodic table, are fully confirming what was formerly achieved in the sd-shell space and in this way exhibit their generality.

Nuclear response to supernova neutrino spectra

In current probes searching for rare event processes, appropriate nuclear targets are employed (in the COBRA double-beta decay detector the CdZnTe semiconductor is used). In this work the response of such detectors to various low-energy neutrino spectra is explored starting from state-by-state calculations of the neutrino-nucleus reactions cross sections obtained by using the quasi particle random phase approximation (QRPA) based on realistic two-body residual interactions. As a concrete example, we examine the response of 64Zn isotope to low energy supernova neutrinos.

Multifractal spectrum and spectral behavior of calcium and titanium isotopes based on nuclear shell model

We investigate the effect of valence space nucleons on the multifractal analysis (MFA) and spectral analysis of calcium and titanium isotopes. The multifractality of wavefunctions is characterized by its associated singularity spectrum f(α) and generalized dimension Dq. The random matrix theory (RMT) has been employed in the study of properties of the distribution of energy levels. In particular, we find that the number of nucleons and two-body residual interactions particularly affect the singularity and energy level spectra.

Shell-model interactions from chiral effective field theory

We construct valence-space Hamiltonians for use in shell-model calculations, where the residual two-body interaction is based on symmetry principles and the low-momentum expansion from chiral effective field theory. In addition to the usual free-space contact interactions, we also include novel center-of-mass--dependent operators that arise due to the Galilean invariance breaking by in-medium effects. We fitted the low-energy constants to 441 ground- and excited-state energies in the sd shell and obtained a root-mean-square derivation of 1.8 MeV at leading order and of 0.5 MeV at next-to-leading order, with natural low-energy constants in all cases. The developed chiral shell-model interactions enable order-by-order uncertainty estimates and show promising predictions for neutron-rich isotopes beyond the fitted data set.

Medium-induced change of the optical response of metal clusters in rare-gas matrices

Interaction with the surrounding medium modifies the optical response of embedded metal clusters. For clusters from about ten to a few hundreds of silver atoms, embedded in rare-gas matrices, we study the environment effect within the matrix random phase approximation with exact exchange (RPAE) quantum approach, which has proved successful for free silver clusters. The polarizable surrounding medium screens the residual two-body RPAE interaction, adds a polarization term to the one-body potential, and shifts the vacuum energy of the active delocalized valence electrons. Within this model, we calculate the dipole oscillator strength distribution for Ag clusters embedded in helium droplets, neon, argon, krypton, and xenon matrices. The main contribution to the dipole surface plasmon red shift originates from the rare-gas polarization screening of the two-body interaction. The large size limit of the dipole surface plasmon agrees well with the classical prediction.

Odd-even staggering of binding energy for nuclei in thesdshell

In this paper we study odd-even staggering phenomena of binding energy in the framework of the nuclear shell model for nuclei in the $sd$ shell. We decompose the USDB effective interaction into the monopole interaction and multipole (residual) interactions. We extract the empirical proton-neutron interaction, the Wigner energy, and the one-neutron separation energy using calculated binding energies. The monopole interaction, which represents the spherical mean field, provides contributions to the empirical proton-neutron interaction, the symmetry energy, and the Wigner energy. It does not induce odd-even staggering of the empirical proton-neutron interaction or the one-neutron separation energy. Isovector monopole and quadrupole pairing interactions and isoscalar spin-1 pairing interactions play a key role in reproducing an additional binding energy in both even-even and odd-odd nuclei. The Wigner energy coefficients are sensitive to residual two-body interactions. The nuclear shell structure has a strong influence on the evolution of the one-neutron separation energy, but not on empirical proton-neutron interactions. The so-called three-point formula is a good probe of the shell structure.

Electron-capture and beta-decay modes with realistic nuclear structure calculations

In this work, we concentrate on the e-capture and β-decay processes in isotopes that are important for searching the explosive nucleosynthesis in massive stars. To this aim, we improved our codes which use compact analytical expressions for the required reduced matrix elements of all basic multipole operators (isospin repre- sentation). The ground state of the nuclear isotopes chosen, is constructed in the context of the BCS method while their excited states are calculated by solving the QRPA equations, using as residual two-body interactions that of the Bonn C-D one-meson exchange potential. We focus on the role of the charged Gamow-Teller and Fermi transitions in Fe group nuclei that are the main constituents of the core in presupernovae formation.

Theory of the unusual high-temperature anisotropic resistivity of underdoped iron arsenide superconductors: Evidence for an orbital nematic order

Recent finding of an unusual in-plane resistivity anisotropy in the underdoped 122 family at high temperature ($T$) suggests an orbital nematic (ON) order, posing a challenge to extant theories. The sign of the anisotropy contradicts expectations from weakly correlated as well as pure spin-only nematic views. Here, we show how such an ON order with accompanying structural distortion arises from residual, intersite, and interorbital two-body interactions in an incoherent ``bad metal'' close to Mottness. Enhancement of orbital-selective incoherence is shown to be necessary for understanding transport anisotropy. Our results suggest that ON order, with subsequent antiferromagnetic order, might be the primary competitor to superconductivity in Fe arsenides.

The nuclear response of terrestrial detectors to low-energy neutrino spectra

In current probes searching for rare–event processes, appropriate nuclear targets are employed. In this work the response of such detectors to various low-energy neutrino spectra is explored starting from state-by-state calculations of the neutrino-nucleus reactions cross sections obtained by using the quasi particle random phase approximation (QRPA) based on realistic two-body residual interactions.

Rotation and shape changes inTb151andPb196: Probes of nuclear structure and tunneling process in warm nuclei. I. Experimental analysis

The {gamma} decay associated with the warm rotation of the superdeformed nuclei {sup 151}Tb and {sup 196}Pb has been measured with the Euroball IV array. Several experimental quantities are presented, putting strong constraints on the decay dynamics in the superdeformed well. The data are successfully reproduced using a Monte Carlo simulation of the {gamma} decay based on microscopically calculated energy levels, E2 decay probabilities, collective mass parameters, and potential energy barriers between the wells associated with normal and super deformation. This allows one to test the basic ingredients of the physical process, such as the strength of the two-body residual interaction and the potential barriers as a function of spin and excitation energy. We also show that the data probe the E1 strength function, indicating an enhancement around 1-2 MeV {gamma} rays, which might be related to octupole vibrations.

NUCLEAR STRUCTURE ADDRESSED AT GSI/RISING

Nuclear structure spectroscopy studies at GSI recently gained increased momentum within a broad international community with the installation of the Rare Isotopes Spectroscopic INvestigation at GSI (RISING) project. A wide range of physical phenomena has been addressed by high-resolution in-beam γ-ray spectroscopy experiments with radioactive beams. Relativistic radioactive beams are implanted and their subsequent γ and β decay is investigated. Within this "stopped beam campaign" germanium detectors were arranged in a close geometry around the passive stopper or an array of DSSSD detectors. The exceptionally high γ-ray efficiency of that configuration made it possible to identify decays of excited or ground states of nuclei which have not been observed before. The results discussed here include the astrophysically relevant shell structure of N =82 isotones, N = Z nuclei around 54 Ni , and proton drip-line nuclei below 100 Sn . The experimental data are compared to the results of large scale shell-model calculations using various sets of realistic residual two-body interaction.

TO WHAT EXTENT DOES THE SELF-CONSISTENT MEAN-FIELD EXIST?

A non-convergent difficulty near level-repulsive region is discussed within the self-consistent mean-field theory. It is shown by numerical and analytic studies that the mean-field is not realized in the many-fermion system when quantum fluctuations coming from two-body residual interaction and quadrupole deformation are larger than an energy difference between two avoided crossing orbits. An analytic condition indicating a limitation of the mean-field concept is derived for the first time.

Applicability of self-consistent mean-field theory

Within the constrained Hartree-Fock (CHF) theory, an analytic condition is derived to estimate whether a concept of the self-consistent mean field is realized in the level repulsive region. The derived condition states that an iterative calculation of the CHF equation does not converge when the quantum fluctuations coming from two-body residual interaction and quadrupole deformation become larger than a single-particle energy difference between two avoided crossing orbits. By means of numerical calculation, it is shown that the analytic condition works well for a realistic case.

Evolution of the $\pi g_{9/2} \nu h_{11/2}^{2}$ multiplet in the neutron-rich 49 In isotopes: Evidence for the gradual filling of the neutron sub-shell

High-spin states from the three-quasiparticle (3qp) configuration $\pi$ g $_{9/2}\nu$ h11/2 2 in the neutron-rich 49In isotopes have been studied in the framework of shell model calculation. The two-body residual interactions needed for such calculations have been extracted from the level schemes of neighbouring nuclei. In particular, the evolution of the proton-neutron $\pi g_{9/2}\nu h_{11/2}$ interaction has been analyzed as a function of the neutron number. When the gradual filling of the $\nu h_{11/2}$ sub-shell is taken into account, the results of the 3qp configuration calculations are found to be very close to the experimental positive-parity yrast states located above 2 MeV excitation energy in $^{113\mbox{--}121}$ In. Moreover, several long-lived isomeric states with positive parity are predicted in 123,125,127In.

Violation and persistence of the K-quantum number in warm rotating nuclei

The validity of the K-quantum number in rapidly rotating warm nuclei is investigated as a function of thermal excitation energy U and angular momentum I, for the rare-earth nucleus 163Er. The quantal eigenstates are described with a shell model which combines a cranked Nilsson mean-field and a residual two-body interaction, together with a term which takes into account the angular momentum carried by the K-quantum number in an approximate way. K-mixing is produced by the interplay of the Coriolis interaction and the residual interaction; it is weak in the region of the discrete rotational bands ( U≲1 MeV), but it gradually increases until the limit of complete violation of the K-quantum number is approached around U∼2–2.5 MeV. The calculated matrix elements between bands having different K-quantum numbers decrease exponentially as a function of Δ K, in qualitative agreement with recent data.

Gamow shell model description of weakly bound nuclei and unbound nuclear states

We present a study of weakly bound, neutron-rich nuclei using the nuclear shell model employing the complex Berggren ensemble representing bound single-particle states, unbound Gamow states, and the nonresonant continuum. In the proposed Gamow shell model, the Hamiltonian consists of a one-body finite depth (Woods-Saxon) potential and a residual two-body interaction. We discuss the basic ingredients of the Gamow shell model. The formalism is illustrated by calculations involving several valence neutrons outside the double-magic core: ${}^{6--10}\mathrm{He}$ and ${}^{18--22}\mathrm{O}.$

Symmetry violations in nuclear Hamiltonians and their consequences for electroweak decays

We discuss the results of the treatment of nuclear Hamiltonians in terms of collective and intrinsic variables. The BRST method is adapted to identify spurious and physical sectors of the wave functions and operators. Counterterms are added to the Hamiltonian to enforce the symmetries broken by the single-particle field and/or by the residual two-body interactions. We focus on the study of Fermi and Gamow-Teller transitions, with reference to the nuclear double-beta-decay processes, and on the study of vector operators (λπ = 1−) with reference to (μ, e−) conversion processes. We address the following aspects of the problem: (a) Isospin symmetry and the calculation of 0+ and 1+ states; sensitivity of the Fermi and Gamow-Teller response in double-beta-decay processes; (b) Restoration of the translational and Galilean invariance of the nuclear Hamiltonians and the calculation of Iπ = 1− states; sensitivity of the nuclear response to the spurious center-of-mass motion and μ-electron lepton-flavor-violation processes.

Relativistic random-phase approximation with density-dependent meson-nucleon couplings

The matrix equations of the relativistic random-phase approximation (RRPA) are derived for an effective Lagrangian characterized by density-dependent meson-nucleon vertex functions. The explicit density dependence of the meson-nucleon couplings introduces rearrangement terms in the residual two-body interaction, that are essential for a quantitative description of excited states. Illustrative calculations of the isoscalar monopole, isovector dipole and isoscalar quadrupole response of $^{208}$Pb, are performed in the fully self-consistent RRPA framework, based on effective interactions with a phenomenological density dependence adjusted to nuclear matter and ground-state properties of spherical nuclei. The comparison of the RRPA results on multipole giant resonances with experimental data constrains the parameters that characterize the isoscalar and isovector channel of the density-dependent effective interactions.

Separable random phase approximation for self-consistent nuclear models

Self-consistent factorization of two-body residual interaction is proposed for arbitrary density- and current-dependent energy functionals. Following this procedure, a separable RPA (SRPA) method is constructed. SRPA considerably simplifies the calculations and demonstrates quick convergence to exact results. The method is tested for SkI3 and SkM* forces.