Shell-model Investigation Research Articles

Analyzing the Nuclear Structure of 13O-13B and 13N-13C Mirror Nuclei

In the context of the shell model, electromagnetic transitions were used to analyze the nuclear structure of a mirror nucleus with the same mass number, A = 13. The shell model investigation was performed by calculating the root mean square (rms) for the proton, neutron, matter and charge radii, occupancies, the excitation energies, as well as electromagnetic moments, using the elements of a body density matrix of the PSDMOD two-body effective interactions carried out in the psdpn-shell model space. The present results adopted the harmonic oscillator's single particle eigen functions and Hartree-Fock approximation. In addition, the effect of core polarization was added using the effective charge and effective g factors to calculate electromagnetic moments. To acquire a fair analysis of the information, the core polarization has to be present. The outcomes were compared with experimental data

Shell Model Investigation of Some p and sd-Shell Nuclei with Harmonic Oscillator and Skyrme Interactions

In this study, the longitudinal charge and form factors for the nuclei 9Be and 28Si lying in the p and sd shells are studied by employing the Harmonic Oscillator potential (HO) and Skyrme effective interaction (Sk35−Skzs∗). The C0 and C2 from factors calculated for the ground state 3/2-, the 5/2- (2.429 MeV) and 7/2- (6.380 MeV) for 9Be, while the ground state 0+ and 2+ (1.779 MeV) state for 28Si nucleus. Calculations of microscopic perturbations that involve intermediate one-particle, one-hole excitation from the core and MS orbits into all upper orbits with excitations are utilized to generate the effective charges necessary to account for the “core polarization effect”. The shell model calculations are utilized on the extended model space to include all 1s, 1p, 2s–1d, 2p‑1f orbits with truncation. Bohr-Mottelson collective model and Tassie model with properly estimated effective neutron and proton charges are taken into account to consider the effect of the core contribution. The estimated form factors were compared with the measured available data and they were in good agreement for most of the studied states. A conclusion can be drawn that truncation is very good choice to study the longitudinal form factors.
 
 The choice of Harmonic Oscillator potential (HO) and Skyrme effective interaction (Sk35−Skzs∗) is adequate for form estimation of longitudinal form factors.
 The estimation of the effective charges based on microscopic perturbations that involve intermediate one-particle, one-hole excitation from the core and MS orbits into all upper orbits with excitations is adequate.
 The truncation proves to be very successful to perform the study.

Nuclear structure aspects of the heaviest N∼Z nuclei south of 100Sn

Ever-lasting interest in the structure of 100Sn and neighbouring nuclei is still well justified by the fact that it is the heaviest doubly-magic nucleus with N=Z. State-of-the-art experimental techniques involving stable and radioactive beam facilities have enabled access to these exotic nuclei. In particular, the analysis of experimental data obtained in two DESPEC experiments at GSI Darmstadt extends the information on the shell structure and its evolution towards N = Z = 50, and allows the study of seniority conservation and proton-neutron interaction in the g9/2 orbit. Several theoretical approaches for shell-model investigations are discussed and their predictive power assessed. The calculated systematics of the reduced transition probabilities for high- to medium-spin states in N∼Z isotopes with active g9/2 orbit is presented for the first time.

New shell-model investigation of the lead-208 mass region: Spectroscopic properties and collectivity

Within the large-scale shell-model framework, an investigation of even-even nuclei in the vicinity of the $^{208}\mathrm{Pb}$ closed core is reported in the present work. The calculations of the low-lying state energies and the electromagnetic transitions of the Pb, Po, Rn, Ra, and Th nuclei with $126\ensuremath{\le}N\ensuremath{\le}134$ are performed using a new effective interaction H208 derived from CD-Bonn nucleon-nucleon potential, through the ${V}_{\mathrm{low}\text{\ensuremath{-}}k}$ procedure. A special focus is devoted to the degree of the collectivity, where a transitional region from spherical nuclear shape to weakly collective behavior is revealed.

Modelling nuclei far from stability with a multichannel approach

Recently, new high-precision data reconfirmed the existence of narrow resonances in the p+14O cross section, first predicted by the multi-channel algebraic scattering (MCAS) theory of light-mass, low-energy scattering and later found by other experimental means. Prompted by this and a decade of extension to the method, we have updated the original MCAS study.Additionally, we use MCAS to interpret the low-energy spectrum of 19 F, which has an interesting structure that appears to stem from clusterisation, and we compare the results of several types. As only early, small-basis shell model investigations of this spectrum exist, we also perform a complete (0 + 2)ħω calculation.MCAS is well suited to these studies, having the advantage of accounting for the Pauli principle between the nucleons of the clusters, and so spurious states of the compound nucleus are removed.

Perturbative Approach to Effective Shell-Model Hamiltonians and Operators

The aim of this work is to present an overview of the derivation of the effective shell-model Hamiltonian and decay operators within many-body perturbation theory, and to show the results of selected shell-model studies based on their utilisation. More precisely, we report some technical details that are needed by non-experts to approach the derivation of shell-model Hamiltonians and operators starting from realistic nuclear potentials, in order to provide some guidance to shell-model calculations where the single-particle energies, two-body matrix elements of the residual interaction, effective charges and decay matrix elements, are all obtained without resorting to empirical adjustments. On the above grounds, we will present results of studies of double-beta decay of heavy-mass nuclei where shell-model ingredients are derived from theory, so to assess the reliability of such a way to shell-model investigations. Attention will be also focussed on the relevant aspects that are connected to the behavior of the perturbative expansion, whose knowledge is needed to establish limits and perspectives of this approach to nuclear structure calculations.

Recent shell-model investigation and its possible role in nuclear structure data study

Up to now, the nuclear shell model is rarely used in the nuclear data study because of several reasons. First, medium and heavy mass nuclei far from the shell-model cores, normally doubly magic nuclei, require a huge amount of calculation resource even in a limited shell-model space. Second, large deformation is difficult to be described in the limited model space, which is based on spherical symmetry. Third, high precision evaluation of nuclear structure data challenges the ability of the shell model. Even so, it is worth starting preliminary nuclear data investigations based on the shell model. With the present computational ability, it is possible to investigate 1000 or more nuclei in the framework of the shell model, which should be helpful for nuclear data study. In the present work, some recent shell-model investigations are briefly introduced. Based on these works, a simple nuclear force is suggested to be used in the systematic nuclear structure data study. The south-west region of 132Sn is taken as an example to show the ability of such a simple nuclear force.

New shell-model investigation of the 208Pb mass region

In the present contribution, a new investigation of the heavy mass region beyond 208Pb closed core is performed within the shell-model framework. Making use of a new effective interaction H208 derived from CD-Bonn nucleon–nucleon potential through the procedure, the low-lying state energies, the electromagnetic transitions, and the binding energies of Z = 82 isotopes and N = 126 isotones are calculated, providing a complete description of their wave functions components. Our calculations are widely discussed and compared to KHBW theoretical results and to the experimental data.

Nuclear-Structure Physics with MINIBALL at HIE-ISOLDE

The MINIBALL spectrometer utilizes successfully a variety of post-accelerated radioactive ion beams provided by the new HIE-ISOLDE accelerator at CERN. In-beam γ-ray spectroscopy after Coulomb excitation (CE) or transfer reactions is performed with optimized setups of ancillary detectors for particle detection. The physics program covers a wide range of shell model investigations. Exotic heavy ion beams will enable unique studies of collective properties up to the actinide region. First data taking with HIE-ISOLDE beams started recently. The higher energies and intensities of the new post-accelerator provides a promising perspective for a new generation of MINIBALL experiments. Intriguing first results were obtained by employing beams of 74,76,78Zn, 110,132Sn, 144Xe with beam energies in the range of 4.0 - 5.5 MeV/u for CE experiments at ‘safe’ energies. In all cases first results for various B(Eλ) values for these isotopes were obtained.

Shell-model investigation of odd-mass nuclei in the 132Sn region

New shell-model calculations are performed in the mass region around 132Sn robust core, where the low-lying states energies and the magnetic dipole moments of even-odd (135,137Te, 137,l39Xe, 139,141Ba, 141,143Ce), and odd-even (135Sb, 135,137I, 135,139Cs, 139,141La) nuclei are obtained with the N3LOP effective interaction. The position of 5/2+ state in 135Sb is discussed with the variation of the proton gap between 0g7/2 and 1d5/2 orbits.

Impact of off-diagonal cross-shell interaction on 14C**Supported by National Natural Science Foundation of China (11305272), Special Program for Applied Research on Super Computation of the NSFC Guangdong Joint Fund (the second phase), the Guangdong Natural Science Foundation (2014A030313217), the Pearl River S&T Nova Program of Guangzhou (201506010060), the Tip-top Scientific and Technical Innovative Youth Talents of Guangdong special support program

A shell-model investigation is performed to show the impact on the structure of 14C from the off-diagonal cross-shell interaction, 〈pp|V|sdsd〉, which represents the mixing between the 0 and 2ħω configurations in the psd model space. The observed levels of the positive states in 14C can be nicely described in 0–4ħω or a larger model space through the well defined Hamiltonians, YSOX and WBP, with a reduction of the strength of the 〈pp|V|sdsd〉 interaction in the latter. The observed B(GT) values for 14C can be generally described by YSOX, while WBP and their modifications of the 〈pp|V|sdsd〉 interaction fail for some values. Further investigation shows the effect of such interactions on the configuration mixing and occupancy. The present work shows examples of how the off-diagonal cross-shell interaction strongly drives the nuclear structure.

Shell-model investigation of spectroscopic properties and collectivity in the nuclei beyond Sn132

The recent shell-model results of even-even chains of nuclei: $^{134,136,138}\mathrm{Te},^{136,138,140}\mathrm{Xe},^{138,140,142}\mathrm{Ba},^{140,142,144}\mathrm{Ce}$, and $^{142,144,146}\mathrm{Nd}$ are explored in this manuscript. The low-lying states energies, E2 and M1 transitions, are investigated using the $same$ effective interaction based on the realistic effective field theory potential N3LO. Significant quadrupole correlations appear in the $N=86$ isotonic chain, with the signature of nonaxial $\ensuremath{\gamma}\phantom{\rule{0.28em}{0ex}}\mathrm{band}$. This class of collectivity is interpreted within the SU(3) symmetries scheme and confirmed by constrained Hartree-Fock shell-model calculations.

Shell Model Studies of Competing Mechanisms to the Neutrinoless Double-Beta Decay in 124Sn, 130Te, and 136Xe

Neutrinoless double-beta decay is a predicted beyond Standard Model process that could clarify some of the not yet known neutrino properties, such as the mass scale, the mass hierarchy, and its nature as a Dirac or Majorana fermion. Should this transition be observed, there are still challenges in understanding the underlying contributing mechanisms. We perform a detailed shell model investigation of several beyond Standard Model mechanisms that consider the existence of right-handed currents. Our analysis presents different venues that can be used to identify the dominant mechanisms for nuclei of experimental interest in the mass A~130 region (124Sn, 130Te, and 136Xe). It requires accurate knowledge of nine nuclear matrix elements that we calculate in addition to the associated energy-dependent phase space factors.

Theoretical approaches to many-body perturbation theory and the challenges

A brief review of the history of many-body perturbation theory (MBPT) and its applications in nuclear physics is given. Problems regarding its application to nuclear-structure calculations are discussed and analysed. It is concluded that the usefulness of nuclear MBPT in terms of an expansion in the nuclear reaction matrix G for the calculation of effective interactions in shell-model investigations is severely challenged and restricted by the problems and uncertainties connected with this approach. New methods based on unitary transformation approaches have proven to be more accurate and reliable, particularly for light nuclei.

In-beam study and structure of the N = 82 nucleus 141Pr

High-spin states in 141Pr have been studied in the reactions 139La(α, 2n)141Pr and 140Ce(d, n)141Pr. Using in-beam spectroscopic methods energies, intensities, excitation functions, γγ coincidences, time and angular distributions and the linear polarization of γ-rays as well as conversion electron spectra were measured. Positive- and negative-parity states of 141Pr have been established for spin values up to J = 272 and Ex < 4750 keV including 19 news lvels. For three levels ns-lifetimes were determined. The experimental data on positive-parity states are in remarkable agreement with shell-model predictions. In the case of positive-parity states no evidence for particle-core coupling is found. The shell-model investigation suggests, however, that the negative-parity states in 141Pr as well as in 143Pm can be explained by particle-core coupling.

A shell-model investigation of the binding energies of some exotic isotopes of sodium and magnesium

Standard shell-model calculations of the binding energies of the neutron-rich isotopes of sodium and magnesium are in strong disagreement with the experimental values near N=20. The authors show that the discrepancy can be explained by allowing neutron excitations from the d3/2 shell into the f7/2 shell.

Continuum shell-model investigation of the photoexcited giant dipole resonance in the non-magic nucleus 13C

Abstract The influence of 3p-2h configurations on the properties of the giant dipole resonance (GDR) in 13 C has been investigated. An extended formulation of the continuum shell model has been used to analyse the photoabsorption process. The results are compared with experimental data and earlier calculations. The 3p-2h configurations are found to be important for the higher excitation energies in the GDR. The particle widths estimated in a R -matrix formulation are discussed in the light of the present results.

Shell-model calculations in the sd shell. IX. Masses, spectra and beta decays of the mass-24 nuclei

For pt.VIII see ibid., vol.3, no.7, p.919 (1977). The authors present the results of a shell-model investigation of the masses, spectra, Coulomb energies and beta decays of the mass-24 nuclei. They have used the effective interaction of Chung and Wildenthal together with an empirically-determined Coulomb interaction. The ab initio use of a reasonably good Coulomb interaction reveals the presence of quite large errors in the calculated energies of certain states and hence of serious imperfections in the nuclear effective interaction. The calculated Coulomb energy differences in the mass-24 system have been used to improve the empirical Coulomb matrix elements.

Shell model investigation of the Raman scattering in the ordered and disordered phases of NH4Br

We describe a formalism for the Raman scattering from orientationally disordered solids, in particular for the ammonium halides. The electronic polarizability is treated in a shell model. Applying the theory to the ordered phase of NH4Br we analyze the extreme scattering anisotropy of the 56 cm−1 band observed by Wang and Wright. This allows us to determine the temperature dependence of the order parameter and to deduce a potential for the orientation dependent interaction of the Br shell with neighboring H atoms. With the use of this potential predictions can be made for all the polarizability coefficients which enter numerical calculations of the Raman scattering intensity in the disordered phase. These calculations are in good agreement with experiment and show that one does not have to assume short range order among the NH4+ ions to explain the appearance of sharp bands in the Raman spectra of the disordered phase.

Shell model investigation of RaE beta-decay

Starting from Yamada's assumption of accidental cancellation of matrix elements, the shape correction factor and the electron polarization for RaE beta-decay are investigated. The phenomenologically acceptable range of the two relevant parameters is determined to be −1.6 ⪅ i∫ r/∫ σ × r ⪅ −0.8 and 2.2 ⪅ 1/ ζ∫ α/ i∫ r ⪅ 3.1. The first of these ratios, designated A, is investigated theoretically by calculating the necessary shell-model matrix elements using both zero-order and then first-order wave functions for RaE. The results obtained for A with first-order wave functions, which arise from the breaking up of the rigid core of RaE, are seen to resolve the longstanding disagreement between theory and experiment. The same first-order wave functions are also used to calculate the magnetic moment of RaE and agreement with the experimental value is obtained.