Realistic Effective Interaction Research Articles

Tetrahedral symmetry in Zr nuclei: calculations of low-energy excitations with Gogny interaction

We report on the results of the calculations of the low energy excitation patterns for three Zirconium isotopes, viz 80Zr40, 96Zr56 and 110Zr70, reported by other authors to be doubly-magic tetrahedral nuclei (with tetrahedral magic numbers Z = 40 and N = 40, 56 and 70). We employ the realistic Gogny effective interactions using three variants of their parametrization and the particle-number, parity and the angular-momentum projection techniques. We confirm quantitatively that the resulting spectra directly follow the pattern expected from the group theory considerations for the tetrahedral symmetric quantum objects. We also find out that, for all the nuclei studied, the correlation energy obtained after the angular momentum projection is very large for the tetrahedral deformation as well as other octupole deformations. The lowering of the energies of the resulting configurations is considerable, i.e. by about 10 MeV or even more, once again confirming the significance of the angular-momentum projections techniques in the mean-field nuclear structure calculations.

Two-neutron transfer in Sn isotopes beyond theN=82shell closure

We have performed microscopic distorted-wave Born approximation calculations of differential cross sections for the two reactions $^{136}\mathrm{Sn}(p,t)^{134}\mathrm{Sn}$ and $^{134}\mathrm{Sn}(t,p)^{136}\mathrm{Sn}$, which are within reach of near-future experiments with radioactive ion beams. We have described the initial and final nuclear states in terms of the shell model, employing a realistic low-momentum two-body effective interaction derived from the CD-Bonn nucleon-nucleon potential that has already proved quite successful in describing the available low-energy spectrum of $^{134}\mathrm{Sn}$. We discuss the main features of the predicted cross sections for the population of the low-lying yrast states in the two nuclei considered.

Identification of a millisecond isomeric state in [formula omitted] via the detection of internal conversion and Compton electrons

The decay of an isomeric state in the neutron-rich nucleus 129Cd has been observed via the detection of internal conversion and Compton electrons providing first experimental information on excited states in this nucleus. The isomer was populated in the projectile fission of a 238U beam at the Radioactive Isotope Beam Factory at RIKEN. From the measured yields of γ-rays and internal conversion electrons, a multipolarity of E3 was tentatively assigned to the isomeric transition. A half-life of T1/2=3.6(2) ms was determined for the new state which was assigned a spin of (21/2+), based on a comparison to shell model calculations performed using state-of-the-art realistic effective interactions.

Yrast 6⁺ seniority isomers of (136,138)Sn.

Delayed γ-ray cascades, originating from the decay of (6⁺) isomeric states, in the very neutron-rich, semimagic isotopes (136,138)Sn have been observed following the projectile fission of a ²³⁸U beam at RIBF, RIKEN. The wave functions of these isomeric states are proposed to be predominantly a fully aligned pair of f(7/2) neutrons. Shell-model calculations, performed using a realistic effective interaction, reproduce well the energies of the excited states of these nuclei and the measured transition rates, with the exception of the B(E2;6⁺→4⁺) rate of ¹³⁶Sn, which deviates from a simple seniority scheme. Empirically reducing the νf(7/2)(2) orbit matrix elements produces a 4₁⁺ state with almost equal seniority 2 and 4 components, correctly reproducing the experimental B(E2;6⁺→4⁺) rate of ¹³⁶Sn. These data provide a key benchmark for shell-model interactions far from stability.

Spin and orbitalgfactors with a surfaceδinteraction

Using an attractive surface delta interaction we obtain wave functions for two protons (or proton holes) in the ${f}_{5/2}$ and ${p}_{3/2}$ shells. We take the single-particle energies to be degenerate. We obtain the remarkable result that the $g$ factors of the lowest ${2}^{+}$ and the lowest ${4}^{+}$ states are equal to 1. We find that only the orbital part of the $g$ factors contributes---the spin part cancels out. Shell-model calculations are also performed for these same $g$ factors in a larger model space and with realistic effective interactions.

Realistic shell-model calculations and exotic nuclei

This paper presents a short overview of the shell-model approach with realistic effective interactions to the study of exotic nuclei. We first give a sketch of the current state of the art of the theoretical framework of this approach, focusing on the main ingredients and most relevant recent advances. Then, we present some selected results for neutron-rich nuclei in various mass regions, namely oxygen isotopes, N = 40 isotones, and nuclei around 132Sn, to show the merit as well as the limits of these calculations.

From nucleon-nucleon interaction matrix elements in momentum space to an operator representation

Starting from the matrix elements of the nucleon-nucleon interaction in momentum space we present a method to derive an operator representation with a minimal set of operators that is required to provide an optimal description of the partial waves with low angular momentum. As a first application we use this method to obtain an operator representation for the Argonne potential transformed by means of the unitary correlation operator method and discuss the necessity of including momentum-dependent operators. The resulting operator representation leads to the same results as the original momentum space matrix elements when applied to the two-nucleon system and various light nuclei. For applications in fermionic and antisymmetrized molecular dynamics, where an operator representation of a soft but realistic effective interaction is indispensable, a simplified version using a reduced set of operators is given.

Neutron-rich $^{208}$Pb nucleus with delta excitation under compression

The spherical Hartree-Fock approximation is applied to a no-core shell model with a realistic effective baryon-baryon interaction. The ground state properties of a heavy spherical neutron-rich doubly magic 208Pb nucleus under compression are investigated. It is found that the nucleus becomes more bound with the occurrence of Delta resonances. The creation of Delta increases as the compression is continuous. There is a considerable reduction in the compressibility when the Delta degree of freedom is activated. It is found that the Delta particle is the basic component of the 208Pb nucleus besides nucleons at the ground state without any compression. When the nucleus is compressed to about 4.31 times the ordinary density, the Delta component is sharply increased to about 14.4% of all baryons in the system. It is found that there is a radial density distribution for Delta at the ground state of 208Pb nucleus without any compression. The single particle energy levels are calculated and their behaviors are examined under compression too. A good agreement was obtained between the results of the effective Hamiltonian and the phenomenological shell model for the low lying single-particle spectra.

Behavior of odd-even mass staggering around132Sn

We have performed shell-model calculations of binding energies of nuclei around ${}^{132}$Sn. The main aim of our study has been to find out if the behavior of odd-even staggering across $N=82$ is explainable in terms of the shell model. In our calculations, we have employed realistic low-momentum two-body effective interactions derived from the charge-dependent Bonn nucleon-nucleon potential that have already proved quite successful in describing the spectroscopic properties of nuclei in the ${}^{132}$Sn region. Comparison shows that our results fully explain the trend of the experimental staggering.

Recoil-corrected continuum shell model calculations for11B(p,n)11C,11B(p,p′)11B*,12C(e,e′x)

Background: The recoil-corrected continuum shell model provides coupled-channels solutions for bound and unbound wave functions from realistic effective interactions. The wave functions are antisymmetric and contain no spurious components because the calculations are performed in the center-of-mass system.Purpose: This model has now been extended to include 1$\ensuremath{\hbar}\ensuremath{\omega}$ excitations in the structure of $p$-shell target (residual) nuclei, hence allowing 0$s$-shell knockout processes. Several reactions involving the ${}^{12}$C compound system are investigated to demonstrate the utility of the model.Methods: The states of ${}^{11}$B and ${}^{11}$C are constructed in the nonspurious 0$\ensuremath{\hbar}\ensuremath{\omega}$ plus 1$\ensuremath{\hbar}\ensuremath{\omega}$ model space. An interaction, fitted to Cohen and Kurath (8-16) plus Reid soft core $g$-matrix elements, is employed. One nucleon is coupled to these states to create a basis for the bound and scattering states for ${}^{12}$C.Results: Calculated elastic and inelastic cross sections agree well with available data. The calculated transverse response at high momentum transfer is lower than that extracted from data. Although significant, meson exchange currents are not sufficient to give agreement with data. Likewise inclusion of 0$s$-shell knockout is not sufficient to provide agreement. The high-energy octupole resonance appears at low momentum transfer and an energy of 106/${A}^{1/3}$.Conclusions: The model should provide meaningful predictions for states near the proton drip line via the ($p$,$n$) reaction. Coupled-channels solutions are necessary for describing ${}^{12}$C($e$,${e}^{\ensuremath{'}}x$) at low momentum transfer. Lack of strength at low energy and momentum transfer in optical model calculations of ${}^{12}$C($e$,${e}^{\ensuremath{'}}x$) is at least partly attributable to the omission of giant resonances. Data for (${\ensuremath{\pi}}^{+}$,${\ensuremath{\pi}}^{+\ensuremath{'}}p$)/(${\ensuremath{\pi}}^{\ensuremath{-}}$,${\ensuremath{\pi}}^{\ensuremath{-}\ensuremath{'}}p$) could verify this conclusion. Lack of strength in the transverse response may be attributable to recoil terms which are omitted in most calculations.

Constrained-Path Quantum Monte Carlo Approach for the Nuclear Shell Model

A new quantum MonteCarlo approach is proposed to investigate low-lying states of nuclei within the shell model. The formalism relies on a variational symmetry-restored wave function to guide the underlying Brownian motion. Sign or phase problems that usually plague quantum MonteCarlo fermionic simulations are controlled by constraining stochastic paths through a fixed-node-like approximation. Exploratory results in the sd and pf valence spaces with realistic effective interactions are presented. They prove the ability of the scheme to yield nearly exact yrast spectroscopies for both even- and odd-mass nuclei.

Probing the quenching of [formula omitted] by single and double beta decays

Ground-state-to-ground-state two-neutrino double beta (2νββ) decays and single beta (EC and β−) decays are studied for the A=100 (100Mo100Tc100Ru), A=116 (116Cd116In116Sn) and A=128 (128Te128I128Xe) nuclear systems by using the proton–neutron quasiparticle random-phase approximation exploiting realistic effective interactions in very large single-particle bases. The aim of this exercise is to see if both the single-beta and double-beta decay observables related to the ground states of the initial, intermediate and final nuclei participant in the decays can be described simultaneously by changing the value of the axial-vector coupling constant gA. In spite of the very different responses to single and 2νββ decays of the considered nuclear systems, the obtained results point consistently to a quenched effective value of gA that is (slightly) different for the single and 2νββ decays.

Effect of spin-spin interactions on nucleon-nucleus scattering

In this thesis we investigate the interactions between nucleons, which have spin-1/2, and nuclei, which may also have intrinsic spin. The dependence of the nucleon-nucleon interaction on the relative orientations of the spin of the two particles is well known and suggests a similar dependence may be present in the interactions of nucleons with nuclei. The effect of the spin of the nucleus on the nucleon-nucleus potential has been the subject of much theoretical and experimental interest. Previous work has found that in many cases spin-spin interactions cannot be ignored, especially for high spin exotic nuclei such as those likely to be produced in the next generation of radioactive beam facilities. In this work a model has been developed for determining spin-spin terms in the nucleon-nucleus optical potential. These terms are constructed by folding a realistic effective nucleon-nucleon interaction, which includes both direct and exchange parts, over the nuclear wavefunction. The target is assumed, for our purposes, to have a simple two valence-particle structure, with the total spins of the two valence nucleons coupling to give the total spin of the nucleus. The resulting spin-spin tensors are evaluated within Distorted Wave Born Approximation to obtain the spin-spin amplitudes. This general model has been used for the specific calculation of the elastic scattering of protons by 10B, for which relevant experimental data exist. New spin-spin interactions that have higher order couplings of the target and projectile spins are included. In addition, where previous work on spin-spin interactions has only included exchange corrections for the central parts of the nucleon-nucleon interaction, we have included the non-local exchange contribution from the tensor parts of the nucleon-nucleon interaction. The effect of these spin-spin interactions on observables sensitive to the spin polarisation of the incident beam, specifically the polarisation transfer coefficient -DNN, has been investigated. We have found that the spin-spin interactions derived from this model have a significant effect on DNN when used to examine the elastic scattering of protons from 10B. The calculation of DNN has also been shown to be particularly sensitive to the parameters of the model used to describe the nuclear structure.

Evolution of single-particle states beyond132Sn

We have performed shell-model calculations for the two one valence-neutron isotones $^{135}$Te and $^{137}$Xe and the two one valence-proton isotopes $^{135,137}$Sb. The main aim of our study has been to investigate the evolution of single-particle states with increasing nucleon number. To this end, we have focused attention on the spectroscopic factors and the effective single-particle energies. In our calculations, we have employed a realistic low-momentum two-body effective interaction derived from the CD-Bonn nucleon-nucleon potential that has already proved quite successful in describing the spectroscopic properties of nuclei in the $^{132}$Sn region. Comparison shows that our results reproduce very well the available experimental data. This gives confidence in the evolution of the single-particle states 4 figures predicted by the present study.

Exotic structure and decay of medium mass nuclei near the drip lines

Nuclei at or near the N=Z line are of particular interest as micro-laboratory for fundamental effects. The simulation of many astrophysical objects requires the knowledge of properties and decay rates of nuclei near the drip lines. The structure and dynamics of proton-rich A70 nuclei and neutron-rich A100 nuclei are influenced by shape coexistence and mixing. A realistic description of shape coexistence phenomena requires beyond-mean-field approaches. Results concerning the self-consistent description of exotic phenomena including anomalies in mirror energy differences of proton-rich nuclei, triple shape coexistence in neutron-rich N=58 Sr and Zr isotopes as well as Gamow-Teller β-decay strength distributions, half-lives, and β- delayed neutron emission probabilities of neutron-rich nuclei in the A100 mass region obtained in the frame of the complex Excited Vampir model using realistic effective interactions in large model spaces are presented.

Shell-model study of single-neutron strength fragmentation in137Xe

We have performed shell-model calculations for the nucleus $^{137}$Xe, which was recently studied experimentally using the $^{136}$Xe($d,p$) reaction in inverse kinematics. The main aim of our study has been to investigate the single-neutron properties of the observed states, focusing attention on the spectroscopic factors. We have employed a realistic low-momentum two-body effective interaction derived from the CD-Bonn nucleon-nucleon potential that has already proved quite successful in describing the spectroscopic properties of nuclei in the $^{132}$Sn region. Comparison shows that our calculations reproduce very well the experimental excitation energies and yield spectroscopic factors that come close to those extracted from the data.

Shape evolution and Gamow-Tellerβ-decay of neutron-rich A∼100 nuclei within beyond-mean-field approach

Neutron-rich nuclei in the A∼100 mass region manifest drastic changes in some isotopic chains and sudden variations of particular nuclear properties with increasing spin and excitation energy. Our recent investigations represent an attempt to the self-consistent description of exotic phenomena in neutron-rich A∼100 nuclei within the complex Excited Vampir model using a realistic effective interaction in a large model space. Triple shape coexistence and shape evolution in the N=58 Sr and Zr isotopes as well as Gamow-Teller β-decay of 102,104Tc nuclei are discussed.

Clusters and halos in light nuclei

The fermionic molecular dynamics approach uses Gaussian wave packets as single-particle basis states. Many-body basis states are Slater determinants projected on parity, angular momentum and total linear momentum. The wave-packet basis is very flexible – FMD contains harmonic oscillator shell model and Brink-type cluster states as special cases. The parameters of the wave packets are obtained by variation. A realistic effective interaction derived from the Argonne V18 interaction by means of the unitary correlation operator method is employed. We discuss the fully microscopic calculation of the 3He(α, γ)7Be capture reaction within the FMD approach. The model space contains frozen cluster configurations at large distances and polarized configurations in the interaction region. The polarized configurations are essential for a successful description of the 7Be bound state properties and for the S- and D-wave scattering states. The calculated cross section agrees well with recent measurements regarding both the absolute normalization and the energy dependence. We also discuss the structure of the cluster states, including the famous Hoyle state, in 12C. From the two-body densities we conclude that the Hoyle state has a spatially extended triangular α-cluster structure, whereas the third 0+ state features a chain-like obtuse triangle structure. We also calculate the NħΩ decomposition of our wave functions to illuminate the challenges of no-core shell model calculations for these cluster states.

Regular–chaos transition of the energy spectrum and electromagnetic transition intensities in 44V nucleus using the framework of the nuclear shell model

Abstract The spectral fluctuations and the statistics of electromagnetic transition intensities and electromagnetic moments in 44 V nucleus are studied by the framework of the interacting shell model, using the FPD 6 as a realistic effective interaction in the isospin formalism for 4 particles move in the fp -model space with a 40 Ca core. To look for a regular–chaos transition in 44 V nucleus, we perform shell model calculations using various interaction strengths β to the off-diagonal matrix elements of the FPD 6. The nearest-neighbors level spacing distribution P ( s ) and the distribution of electromagnetic transition intensities [such as, B ( M 1 ) and B ( E 2 ) transitions] are found to have a regular dynamic at β = 0 , a chaotic dynamic at β ⩾ 0.3 and an intermediate situation at 0 β 0.3 . For the Δ 3 statistic we have found a regular dynamic at β = 0 , a chaotic dynamic at β ⩾ 0.4 and an intermediate situation at 0 β 0.4 . It is also found that the statistics of the squares of M 1 and E 2 moments, which are consistent with a Porter–Thomas distribution, have no dependence on the interaction strength β .

High resolution spectroscopy of112Sn through the114Sn(p,t)112Sn reaction

The ${}^{114}$Sn($p$,$t$)${}^{112}$Sn reaction has been investigated in a high resolution experiment at incident proton energy of 22 MeV. Angular distributions for 28 transitions to levels of ${}^{112}$Sn up to the excitation energy of 3.624 MeV have been measured. The spin and parity identification has been carried out by means of a distorted-wave Born approximation (DWBA) analysis, performed by using conventional Woods-Saxon potentials. A shell-model study of ${}^{112}$Sn nucleus has been performed using a realistic two-body effective interaction derived from the CD-Bonn nucleon-nucleon potential. The energy spectra have been calculated and compared with the experimental ones, while the theoretical two-nucleon spectroscopic amplitudes, evaluated in a truncated seniority space, have been used in the microscopic DWBA calculation of the cross-section angular distributions.