Shell-model Study Research Articles

Large-scale shell-model study of the Sn isotopes

We summarize the results of an extensive study of the structure of the Sn isotopes using a large shell-model space and effective interactions evaluated from realistic two-nucleon potentials. For a fuller account, see ref. [1].

Large-scale shell-model study of the Sn isotopes

We summarize the results of an extensive study of the structure of the Sn isotopes using a large shell-model space and effective interactions evaluated from realistic two-nucleon potentials. For a fuller account, see ref. [1].

Shell model structure of43Sand44Sre-examined

We report on a shell model study of ${}^{43}S$ and ${}^{44}S$. Quadrupole rotational invariants proposed by Kumar about 40 years ago allow us to estimate axial and triaxial deformation parameters from shell model calculations. Present results, showing the large impact of the triaxial degree of freedom on the low-lying structure of studied sulfur isotopes, resolve several inconsistencies in previous interpretations of experimental data. In ${}^{43}S$ the prolate ground-state band coexists with a triaxial band built on the 7/2${}_{1}^{\ensuremath{-}}$ isomer and an excited prolate structure built on the ${K}^{\ensuremath{\pi}}$ = 5/2${}^{\ensuremath{-}}$ deformed orbit originating from the $\ensuremath{\nu}{f}_{7/2}$ shell. In ${}^{44}S$ coexistence of two deformed bands built on mixed 0${}_{1,2}^{+}$ states is reported as well as a pseudo-$\ensuremath{\gamma}$-band and an excited triaxial structure for which a particle-hole neutron excitation couples to proton collectivity. Present results are in good global agreement with recent antisymmetrized molecular dynamics and beyond-mean-field calculations.

Shell-model study of the 4th- and 6th-forbiddenβ-decay branches ofCa48

Shell-model study of the 4th- and 6th-forbidden<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>β</mml:mi></mml:math>-decay branches of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi mathvariant="normal">Ca</mml:mi><mml:mprescripts /><mml:none /><mml:mrow><mml:mn>48</mml:mn></mml:mrow></mml:mmultiscripts></mml:math>

Multi-shell effective interactions

Background: Effective interactions, either derived from microscopic theories or based on fitting selected properties of nuclei in specific mass regions, are widely used inputs to shell-model studies of nuclei. The commonly used unperturbed basis functions are given by the harmonic oscillator. Until recently, most shell-model calculations have been confined to a single oscillator shell like the $sd$ shell or the $pf$ shell. Recent interest in nuclei away from the stability line requires, however, larger shell-model spaces. Because the derivation of microscopic effective interactions has been limited to degenerate models spaces, there are both conceptual and practical limits to present shell-model calculations that utilize such interactions.Purpose: The aim of this work is to present a novel microscopic method to calculate effective nucleon-nucleon interactions for the nuclear shell model. Its main difference from existing theories is that it can be applied not only to degenerate model spaces but also to nondegenerate model spaces. This has important consequences, in particular for intershell matrix elements of effective interactions.Methods: The formalism is presented in the form of a many-body perturbation theory based on the recently developed extended Kuo-Krenciglowa method. Our method enables us to microscopically construct effective interactions not only in one oscillator shell but also for several oscillator shells.Results: We present numerical results using effective interactions within (i) a single oscillator shell (a so-called degenerate model space) like the $sd$ shell or the $pf$ shell and (ii) two major shells (nondegenerate model space) like the $sd{f}_{7}{p}_{3}$ shell or the $pf{g}_{9}$ shell. We also present energy levels of several nuclei that have two valence nucleons on top of a given closed-shell core.Conclusions: Our results show that the present method works excellently in shell-model spaces that comprise several oscillator shells, as well as in a single oscillator shell. We show, in particular, that the microscopic intershell interactions are much more attractive than has been expected by degenerate perturbation theory. The consequences for shell-model studies are discussed.

Projected shell model study of quasiparticle structure of arsenic isotopes

Odd-mass isotopic chain of 67–79As has been studied within the context of the projected shell model. Deformed single-particle states generated by the standard Nilsson potential are used to calculate various nuclear structure properties like yrast spectra, rotational frequencies and reduced transition probabilities. The study of band structures of these As nuclei based on the band diagrams indicates the presence of multi-quasiparticle structure in the high spin realm of these nuclei. Rotational alignment phenomenon has also been studied in terms of band crossing which is understood to occur due to the rotational alignment of g9/2 neutron pair. We also have compared the results of the present calculations with the available experimental as well as the other theoretical data and an overall good agreement has been achieved between the two.

Spherical coupled-cluster theory for open-shell nuclei

A microscopic description of nuclei is important to understand the nuclear shell-model from fundamental principles. This is difficult to achieve for more than the lightest nuclei without an effective approximation scheme. The purpose of this paper is to define and evaluate an approximation scheme that can be used to study nuclei that are described as two particles attached to a closed (sub-)shell nucleus. The equation-of-motion coupled-cluster formalism has been used to obtain ground and excited state energies. This method is based on the diagonalization of a non-Hermitian matrix obtained from a similarity transformation of the many-body nuclear Hamiltonian. A chiral interaction at the next-to-next-to-next-to leading order using a cutoff at 500 MeV was used. The ground state energies of ${}^6$Li and ${}^6$He were in good agreement with a no-core shell-model calculation using the same interaction. Several excited states were also produced with overall good agreement. Only the $J^\pi=3^+$ excited state in ${}^6$Li showed a sizable deviation. The ground state energies of ${}^{18}$O, ${}^{18}$F and ${}^{18}$Ne were converged, but underbound compared to experiment. Moreover, the calculated spectra were converged and comparable to both experiment and shell-model studies in this region. Some excited states in ${}^{18}$O were high or missing in the spectrum. It was also shown that the wave function for both ground and excited states separates into an intrinsic part and a Gaussian for the center-of-mass coordinate. Spurious center-of-mass excitations are clearly identified.

Ab initio and shell model studies of structural, thermoelastic and vibrational properties of SnO2 under pressure

The pressure dependences of the structural, thermoelastic and vibrational properties of SnO2 in its rutile phase are studied, as well as the pressure-induced transition to a CaCl2-type phase. These studies have been performed by means of ab initio (AI) density functional theory calculations using the localized basis code SIESTA. The results are employed to develop a shell model (SM) for application in future studies of nanostructured SnO2. A good agreement of the SM results for the pressure dependences of the above properties with the ones obtained from present and previous AI calculations as well as from experiments is achieved. The transition is characterized by a rotation of the Sn-centered oxygen octahedra around the tetragonal axis through the Sn. This rotation breaks the tetragonal symmetry of the lattice and an orthorhombic distortion appears above the critical pressure Pc. A zone-center phonon of B1g symmetry in the rutile phase involves such rotation and softens on approaching Pc. It becomes an Ag mode which stabilizes with increasing pressure in the CaCl2 phase. This behavior, together with the softening of the shear modulus (C11−C12)/2 related to the orthorhombic distortion, allows a precise determination of a value for Pc. An additional determination is provided by the splitting of the basal plane lattice parameters. Both the AI and the experimentally observed softening of the B1g mode are incomplete, indicating a small discontinuity at the transition. However, all results show continuous changes in volume and lattice parameters, indicating a second-order transition. All these results indicate that there should be sufficient confidence for the future employment of the shell model.

A shell model study of the high spin states of 88Y

Experiments were carried out at the Wright Nuclear Structure Laboratory at Yale University using the 21MV ESTU Tandem Van de Graaff accelerator with the purpose of studying 88Y. A beam of 18O impinged at laboratory energies of 60, 65 and 70 MeV on a 600 μg/cm2 74Ge target with a thick (10mg/cm2) 197Au backing. This experiment was performed with the specific aim of accessing medium spin states of the nucleus of interest. A second experiment was undertaken to populate the nucleus of interest in higher spin states by impinging the same 18O beam on a thin 62 μg/cm2 76Ge target with a 20 μg/cm2 carbon backing at a laboratory beam energy of 90 MeV. Gamma rays emitted following the decay of excited states in 88Y and other nuclei populated in the reactions were measured using the YRAST ball detector array, consisting of 10 Compton suppressed HPGe clover detectors. In conjunction with the experimental study presented here, nuclear shell model calculations using a truncated valence space have also been performed in an attempt to describe the single-particle make-up of the states observed. Preliminary results from these experiments and theoretical calculations are presented.

Shell and cluster structure in atomic nuclei

The shell and cluster structure of the atomic nucleus, as well as their interrelation (the SU(3) connection) is discussed. Some recent results indicating the importance of the shell-like clusterization are reviewed. Special attention is paid to the aspects of symmetries and phases. The important role of the SU(3) connection in the no-core shell model studies is mentioned.

Shell model description of Ge isotopes

A shell model study of the low energy region of the spectra in Ge isotopes for 38 ≤ N ≤ 50 is presented, analyzing the excitation energies, quadrupole moments, B(E2) values and occupation numbers. The theoretical results have been compared with the available experimental data. The shell model calculations have been performed employing three different effective interactions and valence spaces. We have used two effective shell model interactions, JUN45 and jj44b, for the valence space f5/2 pg9/2 without truncation. To include the proton subshell f7/2 in valence space we have employed the fpg effective interaction due to Sorlin et al., with 48Ca as a core and a truncation in the number of excited particles.

Shell model study on the astrophysical neutron capture of 8Li

The astrophysical important neutron capture of 8Li is investigated by combining the shell model and potential model. Three effective interactions, SFO, PSDMK2 and PSDWBP are used to calculate the spectroscopic factors and reaction widths. For the resonant capture from 8Li to the first continuum state of 9Li , the three effective interactions give similar neutron partial widths, and they are well compared with the experimental results. However, the calculated photon widths are over 5 times less than the previous estimate. This will make the substantial difference that, at high temperature, the direct capture mechanism still dominates. The calculated capture rates generally agree well with the experimental data. The uncertainty of calculated cross-sections and capture rates mainly results from the different prediction of spectroscopic factors for the three effective interactions. The total neutron capture rates in our calculations are less than 4300 cm3 mole−1 s−1 for T9 < 5 which confirms that the main reaction flow will proceed through the reaction 8Li (α, n) 11B in the stellar environments.

Shell-model study of boron, carbon, nitrogen, and oxygen isotopes with a monopole-based universal interaction

We study boron, carbon, nitrogen, and oxygen isotopes with a newly constructed shell-model Hamiltonian developed from a monopole-based universal interaction (${V}_{MU}$). The present Hamiltonian can reproduce well the ground-state energies, energy levels, electric quadrupole properties, and spin properties of these nuclei in full $psd$ model space including $(0\ensuremath{-}3)\ensuremath{\hbar}\ensuremath{\omega}$ excitations. Especially, it correctly describes the drip lines of carbon and oxygen isotopes and the spins of the ground states of ${}^{10}$B and ${}^{18}$N while some former interactions such as WBP and WBT fail. We point out that the inclusion of $2\ensuremath{\hbar}\ensuremath{\omega}$ excitations is important in reproducing some of these properties. In the present $(0+2)\ensuremath{\hbar}\ensuremath{\omega}$ calculations small but constant $E2$ effective charges appear to work quite well. As the inclusion of the $2\ensuremath{\hbar}\ensuremath{\omega}$ model space makes a rather minor change, this seems to be related to the smallness of the ${}^{4}$He core. Similarly, the spin $g$ factors are very close to free values. The applicability of tensor and spin-orbit forces in free space, which are taken in the present Hamiltonian, is examined in shell-model calculations.

Projected shell model study for neutron-rich, odd-odd Mn isotopes

Odd-odd nuclei are good candidates for probing possible structure changes away from the valley of stability. By using the projected shell model in which deformed Nilsson single-particle states are taken to build the model basis, we study band properties in odd-odd Mn ($Z=25$) isotopes with neutron number $N=33,35$, and 37. With the help of model analysis, we interpret the low-lying positive-parity states in these nuclei in terms of their intrinsic structures. Our study on high-spin negative-parity states explores the important role of the neutron ${g}_{9/2}$ orbit in this mass region.

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.

Projected shell model study of yrast bands in even-even 100–118Pd isotopes

The projected shell model (PSM) study of 100–118Pd nuclei is carried out. The reliability of the ground-state wave functions is checked by reproducing yrast spectra and electromagnetic properties. The results of calculations indicate that the observed deformation systematics in 100–118Pd isotopes depends on the increase of occupation probability of (1h 11/2 ν ) orbit and the deformation producing tendency of n-p interaction operating between Spin Orbit Partner (SOP) orbits (d 5/2)π−(d 3/2) ν and (g 9/2)π−(g 7/2) ν . Beside this, the results on band diagrams show that the yrast spectra in Pd isotopes do not arise from a single intrinsic state only but also from multi-quasiparticle states.

A MICROSCOPIC PERSPECTIVE ON STRUCTURE OF YRAST BANDS IN 100-112Ru ISOTOPES

The projected shell model (PSM) study of 100 - 112 Ru nuclei is carried out. The reliability of the ground state wave functions is checked by reproducing yrast spectra and electromagnetic properties. The results of calculations indicate that the observed deformation systematics in 100 - 112 Ru isotopes depends on the increase of occupation probability of (1h11/2)ν orbit and the deformation producing tendency of n–p interaction operating between spin orbit partner (SOP) orbits (d5/2)π-(d3/2)ν and (g9/2)π-(g7/2)ν. Besides this, the results on band diagrams show that the yrast spectra in Ru isotopes do not arise from a single intrinsic state only but also from multi-quasiparticle states.

Triaxial projected shell model study of chiral rotation in odd–odd nuclei

Chiral rotation observed in 128Cs is studied using the newly developed microscopic triaxial projected shell model (TPSM) approach. The observed energy levels and the electromagnetic transition probabilities of the nearly degenerate chiral dipole bands in this isotope are well reproduced by the present model. This demonstrates the broad applicability of the TPSM approach, based on a schematic interaction and angular-momentum projection technique, to explain a variety of low- and high-spin phenomena in triaxial rotating nuclei.

Extended application of the DMRG methodology to nuclei in the 1f – 2p shell

In this paper, we present systematic results of the J-DMRG method (an angular-momentum-conserving version of the Density Matrix Renormalization Group) in truncated shell-model calculations of nuclei in the 1f – 2p shell. In contrast to earlier studies, these calculations consider both even-even and odd-mass nuclei. Comparison of the results of these calculations with those of exact shell-model treatments of the same nuclei shows that the method converges smoothly to the exact results in all cases and furthermore that the fraction of the full shell-model space required to obtain accurate agreement with the exact results decreases rapidly as the size of the full space grows. This latter result bodes well for the future applicability of the method to even larger nuclei with even larger shell-model spaces as is the ultimate goal of our development of this approach to large-scale shell model studies.

Renormalization persistency of the tensor force in nuclei

In this work we analyze the tensor-force component of effective interactions appropriate for nuclear shell-model studies, with particular emphasis on the monopole term of the interactions. Standard nucleon-nucleon ($NN$) interactions such as AV8' and $\ensuremath{\chi}$N${}^{3}$LO are tailored to shell-model studies by employing ${V}_{\mathrm{low}k}$ techniques to handle the short-range repulsion of the $NN$ interactions and by applying many-body perturbation theory to incorporate in-medium effects. We show, via numerical studies of effective interactions for the $sd$ and the $pf$ shells, that the tensor-force contribution to the monopole term of the effective interaction is barely changed by these renormalization procedures, resulting in almost the same monopole term as the one of the bare $NN$ interactions. We propose to call this feature renormalization persistency of the tensor force, as it is a remarkable property of the renormalization and should have many interesting consequences in nuclear systems. For higher multipole terms, this feature is maintained to a somewhat smaller extent. We present general intuitive explanations for the renormalization persistency of the tensor force as well as analyses of core-polarization terms in perturbation theory. The central force does not exhibit a similar renormalization persistency.