Study of neutron-rich Mo isotopes by the projected shell model approach

The projected shell model (PSM) calculations have been performed for the neutron-rich even–even ^102?110Mo and odd—even ^103?109Mo isotopes. The present calculation reproduces the available experimental data on the yrast bands. In case of even–even nuclei, the structure of yrast bands is analysed and electromagnetic quantities are compared with the available experimental data. The g-factors have been predicted for high spin states. For the odd-neutron nuclei, the structures of yrast positive- and negative-parity bands are analysed and found to be in reasonable agreement with the experiments for ^103?107Mo. The disagreement of the calculated and observed plots for energy staggering quantity clearly establishes the occurrence of sizable triaxiality in ^103,105Mo and also predicts a decrease in the quantum of triaxiality with increasing neutron number and angular momentum for odd mass neutron-rich Mo isotopes.     

Self-consistency in the projected shell model

The projected shell model is a shell-model theory built up over a deformed BCS mean field. Ground state and excited bands in even-even nuclei are obtained through diagonalization of a pairing plus quadrupole Hamiltonian in an angular momentum projected 0-, 2-, and 4-quasiparticle basis. The residual quadrupole-quadrupole interaction strength is fixed self-consistently with the deformed mean field and the pairing constants are the same used in constructing the quasiparticle basis. Taking ¹⁶⁰Dy as an example, we calculate low-lying states and compare them with experimental data. We exhibit the effect of changing the residual interaction strengths on the spectra. It is clearly seen that there are many J^π = 0⁺, 1⁺, 4⁺ bandheads whose energies can only be reproduced using the self-consistent strengths. It is thus concluded that the projected shell model is a model with essentially no free parameters. The predicted energy of the 2⁺ bandhead lies however in nearly twice the experimental value.     

Evolution of shell structure in neutron-rich calcium isotopes

We employ interactions from chiral effective field theory and compute the binding energies and low-lying excitations of calcium isotopes with the coupled-cluster method. Effects of three-nucleon forces are included phenomenologically as in-medium two-nucleon interactions, and the coupling to the particle continuum is taken into account using a Berggren basis. The computed ground-state energies and the low-lying J^{π}=2^{+} states for the isotopes ^{42,48,50,52}Ca are in good agreement with data, and we predict the excitation energy of the first J^{π}=2^{+} state in ^{54}Ca at 1.9?MeV, displaying only a weak subshell closure. In the odd-mass nuclei ^{53,55,61}Ca we find that the positive parity states deviate strongly from the naive shell model.     

Rotational structure of the odd-proton nuclide 171Tm:A projected shell model study

Deformed odd-mass nuclei are ideal examples where the interplay between single-particle and collective degrees of freedom can be studied. Inspired by the recent experimental high-spin data in the odd-proton nuclide 171 Tm, we perform projected shell model(PSM) calculations to investigate structure of the ground band and other bands based on isomeric states. In addi- tion to the usual quadrupole-quadrupole force in the Hamiltonian, we employ the hexadecapole-hexadecapole(HH) interac- tion, in a self-consistent way with the hexadecapole deformation of the deformed basis. It is found that the known experi- mental data can be well described by the PSM calculation. The effect of the HH force on the quasiparticle isomeric states is discussed.     

Gamow shell model description of neutron-rich nuclei

This work presents the first continuum shell-model study of weakly bound neutron-rich nuclei involving multiconfiguration mixing. For the single-particle basis, the complex-energy Berggren ensemble representing the bound single-particle states, narrow resonances, and the nonresonant continuum background is taken. Our shell-model Hamiltonian consists of a one-body finite potential and a zero-range residual two-body interaction. It is demonstrated that the residual interaction coupling to the particle continuum is important; in some cases, it can give rise to the binding of a nucleus.     

Structure of high spin state in proton-rich ~(74,76,78)Kr isotopes:A projected shell model description

The N≈Z nuclei in the mass A~80 region has been researched because of an abundance of nuclear structure phenomena.The projected shell model(PSM)was adopted to investigate the structure of high spin state in proton-rich 74,76,78Kr isotopes including yrast spectra,moment of inertia,electric quadrupole transitions and the behavior of single particle.The calculated results are in good agreement with available data and the shape coexistence in low-spin is also discussed.     

The structure of neutron-rich calcium isotopes studied by the shell model with realistic effective interactions

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.     

Disturbance of the shell structure of neutron-rich nuclei in the oxygen-magnesium region

The effects related to nuclear deformation and their influence on the shell structure and nuclear properties have been investigated. Calculations were performed within the self-consistent theory of finite Fermi systems. The possibility of existence of strongly deformed nuclei at the neutron drip line and behind it, such as ²⁸O, ³⁹Na, and ^41–43Na, is discussed.     

Tensor force effect on proton shell structure in neutron-rich Ca isotopes

In the framework of the Skyrme-Hartree-Fock approach with 36 sets of the TI J parameterizations,the tensor force effect on the evolution of the single-proton states in the calcium isotopes is systematically investigated.It is shown that the single-proton states with higher angular momenta are influenced significantly by the tensor force and the trend in the evolution of somesingle-particle energy differences with the mass number of the isotopes depends sensitively on a parameter βT associated with the intensity of the tensor force.To understand this phenomenon,we analyze the spin-orbit potentials and the radial wave functions of relevant single-proton orbits in detail.In addition,it is found that some TI J interactions could cause the 2s1/21d3/2 energy level inversion in 48Ca.     

A note on the structure of the 1518 keV isomeric state in174Yb

Studies of the decay of¹⁷⁴Tm and^174m Lu show that, in both cases, a level at 1517.6±0.8 keV in¹⁷⁴Yb is populated, which decays to the 4⁺, 6⁺ and 8⁺ members of the g.s. rotational band.     

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.     

Study of neutron-rich nuclei with an m -scheme cluster-orbital shell model approach

We propose an m -scheme approach of the cluster-orbital shell model (COSM) formalism. In order to take into account the contribution of the unbound states, the radial wave function is treated as the super position of the Gaussian functions with different width parameters. We apply the m -scheme COSM to oxygen isotopes. Energies and r.m.s. radii of oxygen isotopes are studied.     

On the projected spectra from a deformed correlated intrinsic state

It is argued that the residual interaction being relatively of long range, should produce Random Phase Approximation (RPA) type of correlations in the Hartree-Fock (HF) intrinsic state. A model is described to take these correlations inti account in the intrinsic state. A comparison of the projected spectra from this state with the exact shell model diagonalization for a model problem bears out this point. An application of the model is distinguishing two almost degenerate HF solutions for the 2s-1d shell nuclei is mentioned.     

The oscillator shell model with the state dependent frequencies

The frequencies of the oscillator potential are suggested to bs dependent on the state quantum numbers. They may play a role of variational parameters. This procedure is applied in the shell model calculation for light nuclei.On leave fromFaculty of Physics, Hanoi University, Vietnam.The author would like to thank Prof. I. Úlehla for his encouraging interest in this work.     

On the influence of shell structure in dissipative collisions

A kinematically complete study of the symmetric systems ¹⁴⁴Sm+¹⁴⁴Sm and ¹⁵⁴Sn+¹⁵⁴Sm has been performed at energies 30% in excess of the interaction barrier. They have been chosen because of their different internal structure: ¹⁴⁴Sm has a closed N = 82 neutron shell and a spherical ground-state configuration; ¹⁵⁴Sm with ten neutrons outside this shell is strongly deformed. The observed gross features of both reactions like energy, angular and total mass or element distributions are very similar; the ratio of the mass variances as function of the total kinetic energy loss indicates the number of exchanged nucleons to be comparable in all stages of the reactions. At small energy losses, however, the element distributions of the ¹⁴⁴Sm + ¹⁴⁴Sm reaction are considerably broader, pointing at an enhanced proton transfer at the cost of the number of exchanged neutrons in this system. This observation is attributed to the influence of the closed shell which seems to block the transfer of neutrons at low excitation energies. These results can be explained quantitatively by the different gradients of the shell-corrected potential energy surfaces of the two systems.