Mean field and beyond in nuclei far from stability lines

We calculate, for the first time, the state-dependent pairing gap of a finite nucleus (¹²⁰Sn) diagonalizing the bare nucleon-nucleon potential (Argonne v₁₄) in a Hartree-Fock basis. The resulting gap accounts for about half of the experimental gap. Going beyond the mean field in the particle-particle channel, the combined effect of the bare nucleon-nucleon potential and of the induced pairing interaction arising from the exchange of low-lying surface vibrations between nucleons moving in time reversal states close to the Fermi energy accounts for the experimental gap. Examples for light, halo nuclei are also reported. The more studied effects of the particle-vibration coupling in the particle-hole channel are discussed for the low-lying quadrupole vibration in ¹²⁰Sn and the giant dipole resonance in the unstable oxygen isotopes and ¹³²Sn.     

Orbital dependent nucleonic pairing in the lightest known isotopes of tin

By studying the (109)Xe→(105)Te→(101)Sn superallowed α-decay chain, we observe low-lying states in (101)Sn, the one-neutron system outside doubly magic (100)Sn. We find that the spins of the ground state (J=7/2) and first excited state (J=5/2) in (101)Sn are reversed with respect to the traditional level ordering postulated for (103)Sn and the heavier tin isotopes. Through simple arguments and state-of-the-art shell-model calculations we explain this unexpected switch in terms of a transition from the single-particle regime to the collective mode in which orbital-dependent pairing correlations dominate.     

Effects of phonon-phonon coupling on low-lying states in neutron-rich Sn isotopes

Starting from an effective Skyrme interaction we present a method to take into account the coupling between one- and two-phonon terms in the wave functions of excited states. The approach is a development of a finite rank separable approximation for the quasiparticle RPA calculations proposed in our previous work. The influence of the phonon-phonon coupling on energies and transition probabilities for the low-lying quadrupole and octupole states in the neutron-rich Sn isotopes is studied.     

Electromagnetic properties of neutron-rich Ge isotopes

The electric quadrupole moment Q and the magnetic momentp(or the g factor) of low-lying states in even-even nuclei ~(72-80)Ge and odd-mass nuclei ~(75-79) Ge are studied in the framework of the nucleon pair approximation(NPA) of the shell model,assuming the monopole and quadrupole pairing plus quadrupole-quadrupole interaction.HA H.Our calculations reproduce well the experimental values of Q(2_1~+) and g(2_1~+) for ~(72,74,76) Ge,as well as the yrast energy levels of these isotopes.The structure of the 2_1~+ states and the contributions of the proton and neutron components in Q(2_1~+) and g(2_1~+) are discussed in the SD-pair truncated shell-model subspace.The overall trend of Q(2_1~+) and g(2_1~+)as a function of the mass number A,as well as their signs,are found to originate essentially from the proton contribution.The negative value of Q(2_1~+) in ~(72,74)Ge is suggested to be due to the enhanced quadrupole-quadrupole correlation and configuration mixing.     

Pairing isomers

The formalism for quadrupole pairing forces acting simultaneously with monopole pairing and quadrupole particle-hole forces has been worked out in the framework of BCS and RPA. The low-lying 0⁺ states are studied. Expressions for E0 and E2 transition probabilities as well as spectroscopic amplitudes for (t, p) and (p, t) reactions are given. The formalism is applied to the actinide region and it is shown that the low-lying 0⁺ states strongly populated in (p, t) but not in (t, p) reactions can be explained as pairing isomers having an appreciably smaller value of the pairing gap Δ than the ground state. This phenomenon is similar to the phenomenon of gapless superconductivity in solid state physics, i.e. the pairing isomers are formed because of the inhomogeneity of oblate and prolate levels in the vicinity of the Fermi surface.     

Pygmy and Giant Dipole Resonances in Proton-Rich Nuclei ~(17,18)Ne

The pygmy and giant dipole resonances in proton-rich nuclei~(17,18)Ne are investigated with a fully self-consistent approach. The properties of ground states are calculated in the Skyrme Hartree-Fock with the Bardeen-CooperSchrieffer approximation to take into account the pairing correlation. The quasiparticle random phase approximation(QRPA) method is used to explore the properties of excited dipole states. In the calculations the SLy5 Skyrme interaction is employed. In addition to the giant dipole resonances, pygmy dipole resonances(PDR) are found to be located in the energy region below 10 MeV in both 17,18 Ne. The strength and transition density show that the low-lying states are typical PDR states. However, analyzing the QRPA amplitudes of proton and neutron 2 quasiparticle(2 qp) configurations for a given low-lying state in ~(17,18)Ne, we find that the PDR state is less collective, more like a single 2 qp excitation.     

Self-Consistent Calculations of the Quadrupole Moments of the Lowest 3<Superscript>–</Superscript> States in Sn and Pb Isotopes

self-consistent approach to anharmonic effects based on the quantum many-body theory is for the first time used to calculate the quadrupole moments of the lowest 3^– states in Sn and Pb isotopes, including the ¹⁰⁰Sn, ¹³²Sn, and ²⁰⁸Pb doubly magic ones. The consistency between the mean nuclear field and the effective interaction is maintained using the energy-density-functional method with known parameters of the Fayans functional. Thereby, the quadrupole moments of the lowest 3^– states of isotopes with nucleon pairing are reliably predicted, and the existing data for the ²⁰⁸Pb isotope are reproduced. It has been shown that the new three-quasiparticle correlations are responsible for slightly more than half of the observed effect and the remaining part is due to the quadrupole polarizability of the nucleus.     

Electromagnetic transition properties and isospin excitation in the cross-conjugate nuclei 44Ti and 52Fe

The interacting boson model with isospin (IBM-3) is applied to study the band structure and electromagnetic transition properties of the low-lying states in the cross-conjugate nuclei 44Ti and S2Fe. The isospin excitation states with T=0, 1 and 2 are identified and compared with available data. The E2 and M1 matrix elements for the low-lying states have been investigated. According to this study, the 2+3 state is the lowest mixed symmetry state in the cross-conjugate nuclei 44Ti and 52Fe. The excitation energy of the second 0+2 and 2+2 states with T=0 in the nucleus 52Fe are identified. The agreement between the model calculations and data is reasonably good.     

Effect of time-odd fields on odd-even mass differences of semi-magic nuclei

The effect of time-odd fields of Skyrme interaction on neutron odd-even mass differences is studied in the framework of axially deformed Skyrme Hartree-Fock(DSHF)+BCS model. To this end, we take into account both the time-even and time-odd fields to calculate the one-neutron and two-neutron separation energies and pairing gaps of semi-magic Ca, Ni, and Sn isotopic chains. In the calculations, a surface-type pairing interaction(IS pairing) and an isospin dependent contact pairing interaction(IS+IV pairing)are adopted on top of Skyrme interactions SLy4, SLy6 and Sk M*, respectively. We find that the time-odd fields have in general small effects on pairing gaps, but achieve better agreement with experimental data using SLy4 and Sly6 interactions, respectively.It is also shown that the calculations with IS+IV pairing reproduce the one-neutron separation energies of Sn isotopes better than those with the IS pairing interaction when the contributions of the time-odd fields are included.     

奇质量核的超越平均场玻色子费米子模型描述(英文)

对近年发展起来的一个基于核密度泛函理论和粒子核心耦合方案来计算中重质量奇A核谱性质的理论方法进行了评述。该方法首先在平均场层面通过选择合适的能量密度泛函和对力结构来自洽求解偶偶核心的势能曲面、球单粒子能级和奇粒子占有率,进一步将得到的结果作为微观输入来建立相互作用玻色子费米子模型哈密顿量,其中三个与粒子核心耦合强度相关的参数需要通过拟合一些特定奇质量核低激发谱数据来最终确定。通过对轴形变奇质量Eu同位素的低激发能谱和电磁跃迁几率的系统研究来说明该模型方法的有效性。另外,还讨论了该方法在描述轴形变奇质量核形状相变以及描述丰中子奇质量Ba同位素中八极关联方面的应用。A recently developed method for calculating spectroscopic properties of medium-mass and heavy atomic nuclei with an odd number of nucleons is reviewed, that is based on the framework of nuclear energy density functional theory and the particle-core coupling scheme. The deformation energy surface of the eveneven core, as well as the spherical single-particle energies and occupation probabilities of the odd particle(s), are obtained by a self-consistent mean-field calculation with the choice of the energy density functional and pairing properties. These quantities are then used as a microscopic input to build the interacting bosonfermion Hamiltonian. Only three strength parameters for the particle-core coupling are specifically adjusted to selected data for the low-lying states of a particular odd-mass nucleus. The method is illustrated in a systematic study of low-energy excitation spectra and electromagnetic transition rates of axially-deformed odd-mass Eu isotopes. Recent applications of the method, to the calculations of the signatures of shapes phase transitions in axially-deformed odd-mass nuclei, octupole correlations in neutron-rich odd-mass Ba isotopes, are discussed.     

Collective bands in doubly even Sn nuclei

Starting from a simplified picture treating proton two-particle two-hole excitations coupled with spherical quadrupole vibrations, in interaction with the low-lying quadrupole vibrational states in the doubly even Sn nuclei, we are able to account for a regular ΔJ = 2 band structure on top of excited J^π = 0⁺ states. We compare in some detail results for ¹¹⁶Sn concering energy spectra and E2 transition rates.     

Proton-neutron sdg boson model and spherical-deformed phase transition

The spherical-deformed phase transition in nuclei is described in terms of the proton-neutron sdg interacting boson model. The sdg hamiltonian is introduced to model the pairing+quadrupole interaction. The phase transition is reproduced in this framework as a function of the boson number in the Sm isotopes, while all parameters in the hamiltonian are kept constant at values reasonable from the shell-model point of view. The sd IBM is derived from this model through the renormalization of g-boson effects.     

The (18O,16O) reaction on even tin isotopes

The two-neutron transfer reaction^ASn(¹⁸O,¹⁶O)^A+2Sn has been measured for the isotopes A=112, 116, 118, 120, 122 and 124 at bombarding energies of 57 and 60 MeV together with the elastic scattering. Angular distributions have been analysed for the transitions to the ground state and to the first excited 2⁺ state. The observed ground state transition is strongly enhanced. The theoretical DWBA analysis is performed with a finite range 2n-transfer form factor including recoil correction. The calculated cross section reproduces the observed systematic change over all isotopes. The absolute cross sections are normalized by a factor of 4.7 and 7.5, depending on the two different sets of 2n-wave functions used in the analysis. The results confirm the prediction of the pairing model that the transition strengths of a neutron pair between the ground states of even tin isotopes are the same.     

156Gd基态SU(3)→O(6)相变的一种微观理解

γ射线能量自旋曲线指认156Gd核基态具有SU(3)和O(6)两种对称性。 基于微观sdIBM-max方案和单粒子能量实验值, 用两组核子之间的对作用、 四极对作用、 四极 四极作用的等效强度参数, 都很好地再现了这两种能谱及其演化过程。 计算结果揭示出对基态相变的一种新理解: SU(3)的基准态是低激发 低有序态, 而O(6)基准态则是高激发 高有序的, 它们有临界区6+1—8+1态; 当核退耦到临界区时, 高有序基准态释放多余的有序结构能, 导致低有序基准态重组, 实现减速旋转驱动高有序核向着低有序核过渡的量子相变。最后用156Gd核的势能曲面作了直观说明。 The γ ray energy over spin curves identifies that there are the SU(3) and O(6) symmetries in the ground states of the 156Gd nucleus; by means of the microscopic sdIBM max approach and signal particle experimental energies the spectra of those two symmetries and their transient process are successfully reproduced through two parameters of nucleon nucleon effective interaction with pairing plus quadrupole pairing plus quadrupole quadrupole forces. The calculated results reveal a new way to recognize ground states quantum phase transition, in which the basic state of the SU(3) symmetry is a low lying and low ordered state, while one of the O(6) are a high lying and high ordered state, their critical region is between 6+1—8+1 states, the high ordered basic state releases spare ordered structure energy, reducing rotation speed, thus causing the restructure of low ordered basic state and accomplishing the quantum phase transition from the high ordered phase into the low ordered phase, the shape phase transition takes place along the yrast line of nucleus when it de excited to the critical region. Because the structural phase transition takes place by no obvious charge of boson structure constants in the critical region it is a benignancy and calm transition with respect to its macroscopic behave. The potential energy surface of 156Gd nucleus has been illustrated to visualize.     

Behavior of shell effects with the excitation energy in atomic nuclei

We study the behavior of shell effects, like pairing correlations and shape deformations, with the excitation energy in atomic nuclei. The analysis is carried out with the finite temperature Hartree-Fock-Bogoliubov method and a finite range density dependent force. For the first time, properties associated with the octupole and hexadecupole deformation and with the superdeformation as a function of the excitation energy are studied. Calculations for the well quadrupole deformed 164Er and 162Dy, superdeformed 152Dy, octupole deformed 224Ra, and spherical 118Sn nuclei are shown. We find, in particular, the level density of superdeformed states to be 4 orders of magnitude smaller than for normal deformed ones.     

Systematics of the first 2+ excitation with the Gogny interaction

We report the first comprehensive calculations of 2(+) excitations with a microscopic theory applicable to over 90% of the known nuclei. The theory uses a quantal collective Hamiltonian in five dimensions. The only parameters in theory are those of the finite-range, density-dependent Gogny D1S interaction. The following properties of the lowest 2(+) excitations are calculated: excitation energy, reduced transition probability, and spectroscopic quadrupole moment. We find that the theory is very reliable to classify the nuclei by shape. For deformed nuclei, average excitation energies and transition quadrupole moments are within 5% of the experimental values, and the dispersion about the averages are roughly 20% and 10%, respectively. Including all nuclei in the performance evaluation, the average transition quadrupole moment is 11% too high and the average energy is 13% too high.     

Coexistence of Prolate and Oblate Shapes in ~(98)Sr Nuclei Using IBM2

The properties of the low-lying states and the shape coexistence in Sr are investigated within the framework of the proton-neutron interacting boson model(IBM2).By considering the relative energy of the d proton boson to be different from that of the neutron boson,it is found that the calculated energy levels and the B(E2)transition strengths agree with the experimental data perfectly.Particularly,the second 0~+ state,which is associated with the shape coexistence phenomenon and has the lowest energy E(0_2~+) among all known even-even nuclei,is reproduced very well.The behavior of the calculated quadrupole shape invariants is consistent with the experimental results.