Moments of Inertia, Magnetic Dipole Moments, and Electric Quadrupole Moments of the Lithium Isotopes

The single-particle Schrödinger fluid model is designed mainly to calculate the moments of inertia of the axially symmetric deformed nuclei by assuming that each nucleon in the nucleus is moving in a single-particle potential which is deformed with time t, through its parametric dependence on a classical shape variable α(t). Also, the Nilsson model is designed for the calculations of the single-particle energy levels, the magnetic dipole moments, and the electric quadrupole moments of axially symmetric deformed nuclei by assuming that all the nucleons are moving in the field of an anisotropic oscillator potential. On the other hand, the nuclear superfluidity model is designed for the calculations of the nuclear moments of inertia and the electric quadrupole moments of deformed nuclei which have no axes of symmetry by assuming that the nucleons are moving in a quadruple deformed potential. Furthermore, the cranked Nilsson model is designed for the calculations of the total nuclear energy and the quadrupole moments of deformed nuclei which have no axes of symmetry by modifying the Nilsson potential to include second and fourth order oscillations. Accordingly, to investigate whether the six p-shell isotopes 6Li, 7Li, 8Li, 9Li, 10Li, and 11Li have axes of symmetry or not, we applied the four mentioned models to each nucleus by calculating their moments of inertia, their magnetic dipole moments, and their electric quadrupole moments by varying the deformation parameter β and the non-axiality parameter γ in wide ranges of values for this reason. Hence for the assumption that these isotopes are deformed and have axes of symmetry, we applied the single-particle Schrödinger fluid model and the Nilsson model. On the other hand, for the assumption that these isotopes are deformed and have no axes of symmetry, we applied the cranked Nilsson model and the nuclear super fluidity model. As a result of our calculations, we can conclude that the nucleus 6Li may be assumed to be deformed and has an axis of symmetry.

Finite-field calculation of electric quadrupole moments of^2P3/2,^2D3/2,5/2,and^2F5/2,7/2 states for Yb^+ion

Electric quadrupole moments of low-lying excited states of Yb^+are calculated by relativistic coupled-cluster theory with perturbations from external fields.The field-dependent energy differentiation provides accurate values of the electric quadrupole moments of^2P3/2,^2D3/2,5/2,and^2F5/2,7/2 states which agree well with experimental values.The important role of the electronic correlation to the electric quadrupole moments is investigated.Our calculations indicate the early dispute of the electric quadrupole moment of the Yb^+(2F7/2)state for which the measured and theoretical values have a large discrepancy.These electric quadrupole moment values can help us to determine the electric quadrupole shifts in start-of-the-art experiments of the Yb+ion.

Corrections to atomic ground state energy due to interaction between atomic electric quadrupole and optical field

We study the ground state energy of an atom interacting with an oscillating optical field with electric dipole and quadrupole coupling.Under the rotating wave approximation,we derive the effective atomic Hamiltonians of the dipole/quadrupole coupling term within the perturbation theory up to the second order.Based on the effective Hamiltonians,we analyze the atomic ground-state energy corrections of these two processes in detail.As an application,we find that for alkali-like atoms,the energy correction from the quadrupole coupling is negligible small in comparison with that from the dipole coupling,which justifies the so-called dipole approximation used in literatures.Some special cases where the quadrupole interaction may have considerable energy corrections are also discussed.Our results would be beneficial for the study of atom–light interaction beyond dipole approximation.

Theoretical study of the hyperfine interaction constants, Landé g-factors, and electric quadrupole moments for the low-lying states of the 61Niq+(q=11,12,14,and 15) ions

Highly charged nickel ions have been suggested as candidates for the ultra-precise optical clock, meanwhile the relevant experiment has been carried out. In the framework of the multiconfiguration Dirac–Hartree–Fock(MCDHF)method, we calculated the hyperfine interaction constants, the Landég-factors, and the electric quadrupole moments for the low-lying states in the 61Ni11+,61Ni12+,61Ni14+, and61Ni15+ ions. These states are clock states of the selected clock transitions in highly charged nickel ions(see Fig. 1). Based on discussing the effects of the electron correlations, the Breit interaction, and quantum electrodynamics(QED) effect on these physical quantities, reasonable uncertainties were obtained for our calculated results. In addition, the electric quadrupole frequency shifts and the Zeeman frequency shifts of the clock transitions concerned were analyzed.

Calculations of electric quadrupole moments and charge radii for high-K isomers

Configuration-constrained potential-energy-surface calculations are performed to investigate high-K isomers in97Y,130Ba,176Yb,177Lu,and178Hf that were observed to have increased electric quadrupole moments but decreased charge radii relative to the states on which they are built.Taking into account the efects of deformation change and unpaired protons,our calculations can reproduce the enhancement of electric quadrupole moments for the isomers in97Y,130Ba,176Yb,177Lu and the Kπ=8 isomer in178Hf,and can reproduce the reduction of charge radii for the Kπ=27/2 isomer in97Y and the Kπ=16+isomer in178Hf.

Systematic description of nuclear electric quadrupole moments

The nuclear electric quadrupole moment （NQM） is one of the fundamental bulk properties of the nucleus with which nuclear deformations can be investigated. The number of measured NQMs is significantly less than that of known masses, and there is still no global NQM formula for all bound nuclei. In this paper, we propose an analytical formula, which includes the shell corrections and which is the function of the charge number, mass number, spin, charge radius, and nuclear deformation, for calculating the NQMs of all bound nuclei. Our calculated NQMs of 524 nuclei in their ground states are reasonable compared to the experimental data based on the nuclear deformation parameters derived from the Weizsacker-Skyrme （WS） nuclear mass models. Smaller rms deviations between the calculated NQMs and experimental data indicate that the deformation parameters predicted from the WS mass models are reasonable. In addition, 161 unmeasured NQMs with known spins are also predicted with the proposed formula.

Quantum phase for an electric quadrupole moment in noncommutative quantum mechanics

We study the noncoInmutative nonrelativistic quantum dynamics of a neutral particle, which possesses an electric qaudrupole moment, in the presence of an external magnetic field. First, by intro ducing a shift for the magnetic field, we give the Schrodinger equations in the presence of an external magnetic field both on a noncommutative space and a noncomlnutative phase space, respectively. Then by solving the SchrSdinger equations both on a noneommutative space and a noncommutative phase space, we obtain quantum phases of the electric quadrupole moment, respectively. Wc demonstrate that these phases are geometric and dispersive.

Systematics of 2_(1)^(+)States in N=82 Even-even Isotones

In this paper,we study the systematics of the 2_(1)^(+)states in the N=82 even-even isotones with proton numbers between 52 and 72.We calculate the level energies of the 0_(1)^(+),2_(1)^(+)states and the electric quadrupole reduced transition probabilities B(E2;2_(1)^(+)→0_(1)^(+)),in the framework of the nuclear shell model with a monopole-and multipole-optimized realistic interaction.Our calculations yield good agreement with the experimental data and show a 2.5 MeV gap at Z=64 subshell closure in^(146)Gd.We predict that the B(E2;2_(1)^(+)→0_(1)^(+))value for^(146)Gd is close to those for^(142)Nd and^(144)Sm,and the values increase rapidly from^(148)Dy to^(152)Yb.

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.

Systematic study of the product((E(2_2^+)/E(2_1^+)) * B(E2)↑) through the asymmetric rotor model

A systematic study of the product（（E（22^＋）/E（21^＋））＊B（E2）↑） is carried out in the major shell space Z=50-82,N=82-126 within the framework of the asymmetric rotor model where the asymmetry parameter γ0reflects change in the nuclear structure.A systematic study of the product（（E（2^＋）/E（2^＋））＊B（E2）↑） with neutron number N is also discussed.The product（（E（22^＋）/E（21^＋））＊B（E2）↑） provides a direct correlation with the asymmetry parameter γ0.The effect of subshells is visible in Ba-Gd nuclei with N 〉 82,but not in Hf-Pt nuclei with N 〉 104.We study,for the first time,the dependency of the product（（E（22^＋）/E（21^＋））＊B（E2）↑） on the asymmetry parameterγ0.