Realistic Effective Interaction Research Articles

Large-scale shell-model study of two-neutrino double beta decay of 82Se, 94Zr, 108Cd, 124Sn, 128Te, 130Te, 136Xe, and 150Nd

Large-scale shell-model calculations have been performed for the study of two-neutrino double-beta (2νββ) decay in 82Se, 94Zr, 108Cd, 124Sn, 128Te, 130Te, 136Xe, and 150Nd. We have employed JUN45 interaction to calculate the nuclear matrix element (NME) for 2νββ decay in 82Se. In the case of 94Zr, the glekpn effective interaction is used. For 108Cd, we have used a realistic effective interaction derived through the G-matrix approach. In the case of 124Sn, 128,130Te and 136Xe, the sn100pn effective interaction is employed. For 150Nd, we have used KHHE effective interaction based on holes in a 208Pb core. We have extracted the half-lives of these nuclei for the 2νββ decay with the help of calculated NME. Our results are consistent with the available experimental half-lives. The variation of cumulative 2νββ NME with respect to the excitation energy of the intermediate 1+ states is also shown, and in all cases, it is ensured that their values are almost saturated. In the present work we have calculated more intermediate 1+ states as much as possible in comparison to results available in the literature.

Analysis of α + 16O elastic scattering in the semi-microscopical dispersive optical model

We study the elastic scattering cross sections of the α +16O system at 49.5, 69.5, and 80.7 MeV using the optical potentials calculated in the framework of the semi-microscopical dispersive optical model. In this model, the optical potential contains an energy-independent part calculated in the double folding model with a realistic effective nucleon-nucleon interaction, as well as an energy-dependent dynamic polarization potential, the parameters of which are adjusted to the data. The parameters of the real and imaginary parts of the dynamic polarization potential are connected by the dispersion relations.

Systematic shell-model study of 98−130Cd isotopes and 8+ isomeric states

We present systematic shell-model studies of even-even 98−130Cd isotopes using a realistic effective shell-model interaction derived from the G-matrix approach with an inert core 88Sr. Our calculated low-lying excited energy spectra and electromagnetic properties are compared with the experimental data. On the basis of recently available experimental data, we predict spins and parities corresponding to unconfirmed states. We also discuss the properties of 8+ isomeric states in 98−104,130Cd isotopes.

Entanglement and seniority

Background: In quantum mechanics, entanglement is the most striking phenomenon which has no counterpart in classical systems. Although different approaches have already been developed to study correlations in the case of indistinguishable particles, the exploration of the so-called mode entanglement is still in its initial stage in nuclear physics.Purpose: We aim to study mode entanglement in the seniority model, derive analytic formulas for the one-body reduced density matrix of states with seniority $\ensuremath{\nu}=0,\phantom{\rule{0.16em}{0ex}}1,\phantom{\rule{0.16em}{0ex}}2$, and 3, and also determine the particle number dependence of the one-body reduced density matrix for arbitrary seniority. In addition, we compare the predictions of the seniority model with the results of the shell model to gain insight into the structure and correlations of the ground and lowest yrast states.Methods: In the seniority model the analytic results are calculated using the quasispin formalism. The numerical shell model calculations are carried out in the standard shell model framework using an inert core. The applied realistic effective interactions are derived earlier using the $G$-matrix formalism. The density matrix renormalization group method is also applied in order to directly calculate the mode entropies.Results: In the seniority model simple analytical expressions are given for the mode entropies. The peculiar behavior of the half-filled shells and the seniority-zero states is revealed. Numerical results are presented for the lightest stable calcium isotopes and for $^{94}\mathrm{Ru}$ nucleus.Conclusions: For $^{94}\mathrm{Ru}$, the seniority model accounts for the $0{g}_{9/2}$ mode entropies, but seniority mixing is important for certain yrast states. Interaction induced quantum fluctuations decrease the occupation of the $0{f}_{5/2}$, $1{p}_{3/2}$, and $1{p}_{1/2}$ shells, and result in non-negligible mode entropies on these shells, too, clearly outside the scope of the simple ${(0{g}_{9/2})}^{4}$ seniority model. The $0{f}_{7/2}$ shell based seniority model is more accurate for the $\mathrm{Ca}$ isotopes, but seniority mixing is substantial for some $^{44}\mathrm{Ca}$ yrast states, too. Mode and one-body entanglement entropies are useful tools to investigate the structure of quantum correlations in nuclei.

Large-scale shell-model calculations of nuclear Schiff moments of Xe129 and Hg199

The theoretical uncertainty in the nuclear Schiff moment is an obstacle to set constraints on $ CP $ violation beyond the standard model from experimental upper bounds on atomic electric dipole moments. We perform large-scale shell-model calculations of the $^{129}$Xe and $^{199}$Hg nuclei with realistic effective interactions. To estimate the Schiff moments caused by the $ P $, $ T $-odd $ \pi NN $ interaction perturbatively, we employ the one-particle one-hole approximation to the intermediate states. The Schiff moments of $^{129}$Xe and $^{199}$Hg are reduced due to the configuration mixing by $ \sim 10 \% $ from the evaluation of the independent particle model. On the other hand, the reduction is more significant in mean-field based calculations and shell-model calculations with a drastic truncation. In order to resolve the discrepancy in the Schiff moment of $^{199}$Hg among several nuclear models, we survey low-energy nuclear structure. The large-scale shell-model calculations reveal that the Schiff moment of $^{199}$Hg is considerably quenched in the second $ \frac{ 1 }{ 2 }^- $ state.

Analysis of strong refractive effect within 11Li projectile structure

In the context of the double folding optical model, the strong refractive effect for elastic scattering of 11Li + 12C and 11Li + 28Si systems at incident energies of 29, 50, and 60 MeV/n is studied. Real folded potentials are generated based on a variety of nucleon-nucleon interactions with the suggested density distributions for the halo structure of 11Li nuclei. The rearrangement term (RT) of the extended realistic density dependent CDM3Y6 effective interaction is considered. The imaginary potential was taken in the traditional standard Woods-Saxon form. Satisfactory results for the calculated potentials are obtained, with a slight effect of the RT in CDM3Y6 potential. Successful reproduction with a normalization factor close to one for the observed angular distributions of the elastic scattering differential cross section has been achieved using the derived potentials. The obtained reaction cross-section is studied as a guide by extrapolating our calculations and previous results.

Realistic shell model and nuclei around 132Sn

This contribution reports on a shell-model study of nuclei in the 132Sn region employing a realistic effective interaction derived from the CD-Bonn nucleon-nucleon potential renormalized through the use of the Vlow−k approach. We shall focus on some selected results for nuclei with a few valence particles and/or holes with respect to 132Sn, namely Sn isotopes with N > 82 and 130Te, which have, in part, been discussed in previous papers. Results are compared with experiments, and predictions that may provide guidance to future experiments are also discussed. It is the aim of this contribution to underline the importance of studying 132Sn neighbours to acquire a deep understanding of nuclear structure, that may be very useful also in other physics fields, and to show that the realistic shell model is a very effective tool to conduct these studies.

Study of the Shell Evolution Effect on the Nuclei around the 78Ni Core Structure

Study of the Shell Evolution Effect on the Nuclei around the 78Ni Core Structure

The structure of neutron-rich calcium isotopes studied by the shell model with realistic effective interactions * * Supported by National Natural Science Foundation of China (U1732138, 11605054,11505056, 11305108, 11790325, 11847315)

We study the structure of neutron-rich calcium isotopes in the shell model with realistic interactions. The CD-Bonn and Kuo-Brown (KB) interactions are used. As these interactions do not include the three-body force, their direct use leads to poor results. We tested whether the adjustment of the single particle energies (SPEs) would be sufficient to include the three-body correlations empirically. It turns out that the CD-Bonn interaction, after the adjustment of SPEs, gives good agreement with the experimental data for the energies and spectroscopy. For the KB interaction, both the SPEs and monopole terms require adjustments. Thus, the monopole problem is less serious for modern realistic interactions which include perturbations up to the third order. We also tested the effect of the non-central force on the shell structure. It is found that the effect of the tensor force in the CD-Bonn interaction is weaker than in the KB interaction.

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

Properties of medium mass nuclei near the drip lines are not only relevant for nuclear structure, but are of high interest in nuclear astrophysics and in several applications, in particular nuclear technology. Shape coexistence effects play an essential role in the structure and dynamics of proton-rich A∼70 nuclei and neutron-rich A∼100 nuclei. Results concerning a self-consistent description of exotic phenomena including Gamow-Teller β-decay of proton-rich nuclei, triple shape coexistence and shape evolution in the N=58 Sr and Zr isotopes as well as Gamow-Teller β-decay strength distributions and structure properties of neutron- rich nuclei relevant for reactor decay heat obtained in the frame of the complex Excited Vampir model using realistic effective interactions in large model spaces will be presented.

The effect of short range correlation on the inelastic C2 and C4 form factors of 18O nucleus

The effect of short range correlations on the inelastic Coulomb form factors for excited +2 states (1.982, 3.919, 5.250 and 8.210MeV) and +4 states (3.553, 7.114, 8.960 and 10.310 MeV) in O18 is analyzed. This effect (which depends on the correlation parameterβ) is inserted into the ground state charge density distribution through the Jastrow type correlation function. The single particle harmonic oscillator wave function is used with an oscillator size parameter .b The parameters β and b are adjusted for each excited state separately so as to reproduce the experimental root mean square charge radius of .18O The nucleusO18 is considered as an inert core of C12 with two protons and four neutrons distributed over 212521211sdp−− active orbits. The total transition charge density comes from both the model space and core polarization transition charge densities. The realistic effective interaction of Reehal–Wildenthal (REWIL) is used for this model space. It is found that the introduction of the effect of short range correlations is necessary for obtaining a remarkable improvement for the calculated inelastic Coulomb form factors and considered as an essential for explanation the data amazingly throughout the whole range of considered momentum transfer.

Millisecond 23/2+ isomers in the N=79 isotones Xe133 and Ba135

Detailed information on isomeric states in A ≈ 135 nuclei is exploited to benchmark shell-model calculations in the region northwest of doubly-magic nucleus 132Sn. The N = 79 isotones 133Xe and 135Ba are studied after multinucleon transfer (MNT) in the 136Xe + 208Pb reaction employing the high-resolution Advanced GAmma Tracking Array (AGATA) coupled to the magnetic spectrometer PRISMA at the Laboratori Nazionali di Legnaro, Italy and in a pulsed-beam experiment at the FN tandem accelerator of the University of Cologne, Germany utilizing a 9Be+130Te fusion-evaporation reaction at a beam energy of 40 MeV. Isomeric states are identified via delayed γ-ray spectroscopy. Hitherto tentative excitation energy, spin, and parity assignments of the 2107-keV Jπ = 23/2+ isomer in 133Xe are confirmed and a half-life of T1/2 = 8.64(13) ms is measured. The 2388-keV state in 135Ba is identified as a Jπ = 23/2+ isomer with a half-life of 1.06(4) ms. The new results show a smooth onset of isomeric Jπ = 23/2+ states along the N = 79 isotones and close a gap in the high-spin systematics towards the recently investigated Jπ = 23/2+ isomer in 139Nd. The resulting systematics of M2 reduced transition probabilities is discussed within the framework of the nuclear shell model. Latest large-scale shell-model calculations employing the SN100PN, GCN50:82, SN100-KTH, and a realistic effective interaction reproduce the experimental findings generally well and give insight into the structure of the isomers.

High-spin structure in the transitional nucleus Xe131 : Competitive neutron and proton alignment in the vicinity of the N=82 shell closure

The transitional nucleus 131Xe is investigated after multinucleon transfer (MNT) in the 136Xe+208Pb and 136Xe+238U reactions employing the high-resolution Advanced GAmma Tracking Array (AGATA) coupled to the magnetic spectrometer PRISMA at the Laboratori Nazionali di Legnaro, Italy and as an elusive reaction product in the fusion-evaporation reaction 124Sn(11B,p3n) 131Xe employing the HORUS γ-ray array coupled to a double-sided silicon strip detector (DSSSD) at the University of Cologne, Germany. The level scheme of 131Xe is extended to 5 MeV. A pronounced backbending is observed at ~ω ≈ 0.4 MeV along the negative-parity one-quasiparticle νh11/2(α = −1/2) band. The results are compared to the high-spin systematics of the Z = 54 isotopes and the N = 77 isotones. Large-scale shell-model calculations (LSSM) employing the PQM130, SN100PN, GCN50:82, SN100-KTH and a realistic effective interaction reproduce the experimental findings and provide guidance to elucidate the structure of the high-spin states. Further calculations in 129−132Xe provide insight into the changing nuclear structure along the Xe chain towards the N = 82 shell closure. Proton occupancy in the π 0h11/2 orbital is found to be decisive for the description of the observed backbending phenomenon.

Realistic Gamow shell model for resonance and continuum in atomic nuclei

The Gamow shell model can describe resonance and continuum for atomic nuclei. The model is established in the complex-moment (complex-k) plane of the Berggren coordinates in which bound, resonant and continuum states are treated on equal footing self-consistently. In the present work, the realistic nuclear force, CD Bonn, has been used. We have developed the full -box folded-diagram method to derive the realistic effective interaction in the model space which is nondegenerate and contains resonance and continuum channels. The CD-Bonn potential is renormalized using the Vlow-k method. With choosing 16O as the inert core, we have applied the Gamow shell model to oxygen isotopes.

Observation of a γ-decaying millisecond isomeric state in 128Cd80

A new high-spin isomer in the neutron-rich nucleus 128Cd was populated in the projectile fission of a 238U beam at the Radioactive Isotope Beam Factory at RIKEN. A half-life of T1/2=6.3(8) ms was measured for the new state which was tentatively assigned a spin/parity of (15−). The experimental results are compared to shell model calculations performed using state-of-the-art realistic effective interactions and to the neighbouring nucleus 129Cd. In the present experiment no evidence was found for the decay of a 18+E6 spin-trap isomer, based on the complete alignment of the two-neutron and two-proton holes in the 0h11/2 and the 0g9/2 orbit, respectively, which is predicted to exist by the shell model.

Spectral Fluctuations in A=32 Nuclei Using the Framework of the Nuclear Shell Model

Chaotic properties of nuclear energy spectra in A=32 nuclei are investigated via the framework of the nuclear shell model. The energies (the main object of this investigation) are calculated through accomplishing shell model calculations employing the OXBASH computer code with the realistic effective interaction of W in the isospin formalism. The A=32 nuclei are supposed to have an inert 16O core with 16 nucleons move in the 1d5/2, 2s1/2 and 1d3/2 orbitals. For full hamiltonian calculations, the spectral fluctuations (i.e., the nearest neighbor level spacing distributions P(S) and the Δ3 statistics) are well characterized by the Gaussian orthogonal ensemble of random matrices. Besides, they show no dependency on the spin J and isospin T. For unperturbed hamiltonian calculations, we find a regular behavior for the distribution of P(S) and an intermediate behavior between the GOE and the Poisson limits for the Δ3 statistics.

Nucleon-pair states of even-even Sn isotopes based on realistic effective interactions

In this paper we study yrast states of $^{128,126,124}\mathrm{Sn}$ and $^{104,106,108}\mathrm{Sn}$ by using the monopole-optimized realistic interactions in terms of both the shell model (SM) and the nucleon-pair approximation (NPA). For yrast states of $^{128,126}\mathrm{Sn}$ and $^{104,106}\mathrm{Sn}$, we calculate the overlaps between the wave functions obtained in the full SM space and those obtained in the truncated NPA space, and find that most of these overlaps are very close to 1. Very interestingly, for most of these states with positive parity and even spin or with negative parity and odd spin, the SM wave function is found to be well represented by one nucleon-pair basis state, viz., a simple picture of ``nucleon-pair states'' (nucleon-pair configuration without mixings) emerges. In $^{128,126}\mathrm{Sn}$, the positive-parity (or negative-parity) yrast states with spin $J>10$ (or $J>7$) are found to be well described by breaking one or two $S$ pairs in the ${10}_{1}^{+}$ (or ${7}_{1}^{\ensuremath{-}}$) state, i.e., the yrast state of seniority-two, spin-maximum, and positive-parity (or negative-parity), into non-$S$ pair(s). Similar regularity is also pointed out for $^{104,106}\mathrm{Sn}$. The evolution of $E2$ transition rates between low-lying states in $^{128,126,124}\mathrm{Sn}$ is discussed in terms of the seniority scheme.

Pairing properties of realistic effective interactions

We investigate the pairing properties of an effective shell-model interaction defined within a model space outside 132 Sn and derived by means of perturbation theory from the CD-Bonn free nucleon-nucleon potential. It turns out that the neutron pairing component of the effective interaction is significantly weaker than the proton one, which accounts for the large pairing gap difference observed in the two-valence identical particle nuclei 134 Sn and 134 Te. The role of the contribution arising from one particle-one hole excitations in determining the pairing force is discussed and its microscopic structure is also analyzed in terms of the multipole decomposition.

Stellar weak interaction rates and shape coexistence for 68Se and 72Kr waiting points

Beyond-mean-field results on stellar beta-decay and continuum electron capture rates for the rp-process waiting point nuclei 68Se and 72Kr at densities ρYe = 104−107 mol/cm3 and temperatures T = 108−1010 K are presented. The structure of the even-even parent and odd-odd daughter nuclei dominated by shape coexistence and mixing is self-consistently described within the complex Excited Vampir model using realistic effective interactions in rather large model spaces. The influence of the shape mixing in the structure of the low-lying parent states as well as in the independently calculated daughter states on the stellar weak interaction rates is discussed.

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.