Spectra and electromagnetic transitions of ^(98–104)Zr in the interacting boson model

The low-lying energy levels and electromagnetic transitions of even-even nuclei ^98Zr, ^100Zr, ^102Zr,^104Zr are studied within the framework of the interacting boson model. The Hamiltonian matrix elements and some of their states have been respectively analyzed and determined with respect to the current nuclear experimental data. The B（E2） of electromagnetic transitions have also been calculated and the wave function structures also analyzed. The results show good agreement with the available experimental data. The present study shows that these series of nuclei are in the transition from U（5） to SU（3）, namely from vibration to rotation.

Spectral fluctuations in the interacting boson model

The energy dependence of the spectral fluctuations in the interacting boson model(IBM)and its connections to the mean-field structures are analyzed by adopting two statistical measures:the nearest neighbor level spacing distribution P(S)measuring the chaoticity(regularity)in energy spectra and the Δ_(3)(L)statistics of Dyson and Metha measuring the spectral rigidity.Specifically,the statistical results as functions of the energy cutoff are determined for different dynamical scenarios,including the U(5)-SU(3)and SU(3)-O(6)transitions as well as those near the AW arc of regularity.We observe that most of the changes in spectral fluctuations are triggered near the stationary points of the classical potential,particularly for cases in the deformed region of the IBM phase diagram.Thus,the results justify the stationary point effects from the perspective of statistics.In addition,the approximate degeneracies in the 2^(+)spectrum on the AW arc is also revealed from the statistical calculations.

A nucleon-pair and boson coexistent description of nuclei

We study a mixture of s-bosons and like-nucleon pairs with the standard pairing interaction outside an inert core. Competition between the nucleon-pairs and s-bosons is investigated in this scenario. The robustness of the BCS-BEC coexistence and crossover phenomena are examined through an analysis of pf-shell nuclei with realistic single-particle energies, in which two configurations with Pauli blocking of nucleon-pair orbits due to the formation of the s-bosons is taken into account. When the nucleon-pair orbits are considered to be independent of the s-bosons, the BCS-BEC crossover becomes smooth, with the number of the s-bosons noticeably more than that of the nucleon-pairs near the half-shell point, a feature that is demonstrated in the pf-shell for several values of the standard pairing interaction strength. As a further test of the robustness of the BCS-BEC coexistence and crossover phenomena in nuclei, results are given for B（E2; 01^＋→21^＋） values of even-even ^102-130 Sn with ^100Sn taken as a core and valence neutron pairs confined within the 1d（5/2）, 0g（7/2）, 1d（3/2）, 2s（1/2）, 1h（11/2）orbits in the nucleon-pair orbit and the s-boson independent approximation. The results indicate that the B（E2） values are reproduced well.

Description of ^(150)Nd nucleus by a new alternative scheme

A new scheme was recently proposed in which the usual SU（3） quadrupole-quadrupole interaction was replaced by an O（6） cubic interaction in the Interacting Boson Model, and also successfully applied to the description of 152Sm for the N=90 rare earth isotones with X（5） symmetry. By using this new scheme, in the present work, we further explore the properties of another candidate of 150Nd for the N=90 with X（5） symmetry. The low-lying energy levels and E2 transition rates are calculated and compared with the experimental data. The results show that the new scheme can also reasonably describe the experimental low-lying spectrum and the intraband and the interband E2 transitions for 150Nd. However, for the low-lying spectrum, the O（6） cubic interaction seems better in describing the energy levels, especially in higher excited states and γ band, yet the 02＋ level within the β band is lower than the corresponding experimental value and the U（5）-SU（3） scheme seems better to describe the low-lying levels of β band; and for the B（E2） transition, for the intraband transitions within the ground band and some interband transitions between the β band and the ground band, the results from O（6） cubic interaction are better than those from SU（3） quadrupole-quadrupole interaction, yet of which seems better to describe the intraband E2 transitions within β band. The present work is very meaningful in helping us to understand in depth the new characteristics of symmetry by the higher order O（6） cubic interaction.

Band mixing in ^(96,98)Mo isotopes

We use the two lowest weight states to fit E2 strengths connecting the 0←→2 and 2←→4 transitions in ^(96,98)Mo.Our results confirm that the 2^+ and 4^+ states are maximally mixed,and that the 0^+ states are weakly mixed in both nuclei.An appropriate Hamiltonian to represent the band mixing is found to be exactly solvable,and its eigenstates can be expressed as the basis vectors in the configuration mixing scheme and interacting boson model.The interacting boson model and coexistence mixing configuration under the solvable methods are suitable models for analyzing the band mixing with high accuracy.

Two-neutron transfer reactions as a tool to study the interplay between shape coexistence and quantum phase transitions

The atomic mass table presents zones where the structure of the states changes rapidly as a function of the neutron or proton number.Among them,notable examples are the A≈100 Zr region,the Pb region around the neutron midshell(N=104),and the N≈90 rare-earth region.The observed phenomena can be understood in terms of either shape coexistence or quantum phase transitions.The objective of this study is to find an observable that can distinguish between both shape coexistence and quantum phase transitions.As an observable to be analyzed,we selected the two-neutron transfer intensity between the 0+states in the parent and daughter nuclei.The framework used for this study is the Interacting Boson Model(IBM),including its version with configuration mixing(IBM-CM).To generate wave functions of isotope chains of interest needed for calculating transfer intensities,previous systematic studies using IBM and IBM-CM were used without changing the parameters.The results of two-neutron transfer intensities are presented for Zr,Hg,and Pt isotopic chains using IBM-CM.Moreover,for Zr,Pt,and Sm isotopic chains,the results are presented using IBM with only a single configuration,i.e.,without using configuration mixing.For Zr,the two-neutron transfer intensities between the ground states provide a clear observable,indicating that normal and intruder configurations coexist in the low-lying spectrum and cross at A=98→100.This can help clarify whether shape coexistence induces a given quantum phase transition.For Pt,in which shape coexistence is present and the regular and intruder configurations cross for the ground state,there is almost no impact on the value of the two-neutron transfer intensity.Similar is the situation with Hg,where the ground state always has a regular nature.For the Sm isotope chain,which is one of the quantum phase transition paradigms,the value of the two-neutron transfer intensity is affected strongly.

Neutron─deficientEven─evenNeodymiumIsotopeStructure

The structures of the neutron deficient Nd isotopes of A=128～140 are studied in a schematic hamiltonian in the interacting boson model. The level structure and E2 transitions can be well described in the scheme. In particular, the backbending in the ground state band is well reproduced.