Nuclear Structure in China 2010

The following sections are included:

• PREFACE

• CONTENTS

This article is based on the opening speech given at the thirteenth Chinese biennial Nuclear Structure Conference held in Chifeng, Inner Mongolia, China. The history of this series of Chinese biennial nuclear structure conference is briefly introduced. Personal views on nuclear physics research are presented following the overview of the opportunity provided by main nuclear physics facilities world-wide, important sub-field in nuclear physics, main achievement including important progress in Chinese nuclear physics community, the related important series of international nuclear physics conferences, population of nuclear physicists, newly emerging group in nuclear physics and possible improvement on organizing the Chinese biennial nuclear structure conference.

The high-spin states in ⁸⁹Zr have been studied by in-beam γ-ray spectroscopy using the heavy ion fusion evaporation reaction ⁷⁶Ge(¹⁹F,p5n)⁸⁹Zr reaction at a bombarding energy of 80 MeV. The level scheme of ⁸⁹Zr has been constructed up to . The large-basis shell model code OXBASH was employed to analyze the level structure of ⁸⁹Zr. The results of shell-model calculation are in good accordance with the experiment.

We show in the Skyrme-Hartree-Fock approach that unambiguous correlations exist between observables of finite nuclei and nuclear matter properties. Using this correlation analysis to existing data on the neutron skin thickness of Sn isotopes, we find important constraints on the value E_sym(ρ0) and density slope L of the nuclear symmetry energy at saturation density. Combining these constraints with those from recent analyses of isospin diffusion and double neutron/proton ratio in heavy ion collisions leads to a value of L = 58 ± 18 MeV approximately independent of E_sym(ρ0).

The wobbling states are described microscopically with the Triaxial Projected Shell Model (TPSM), and the experimental wobbling bands firmly established in ¹⁶³Lu have been well reproduced by the present calculation. By using calculated wave functions of wobbling states, the projections of the total angular momentum along the three body-fixed axes are calculated as functions of spin. This calculation results in the dynamic geometry of the angular momentum in the intrinsic frame, and thus promises to provide insight into the wobbling motion in nuclei. The similar TPSM calculations have been performed to study the possible wobbling excitation in the neighboring nucleus ¹⁶⁴Lu. It has been found that the wobbling structure in odd-odd Lu may be modified by the extra neutron, but not completely destroyed, indicating the possibility for observing the wobbling bands in the odd-odd Lu isotopes.

The mixing of scalar mesons is an open problem. In this work, the idea of the mixing of scalar mesons will be applied to dibaryon system on quark level. By introducing the mixing of scalar mesons, we dynamically investigate the structure of possible nonstrange dibaryons in the chiral SU(3) quark model by solving the resonating group method equation. The results show that no matter what kind of mixing is considered, the binding energies of nonstrange dibaryons would become stable if reasonable parameters are used.

The net-baryon number is essentially transported by valence quarks that probe the saturation regime in the target by multiple scattering. The net baryon distributions and nuclear stopping power in the SPS and RHIC energy regions by taking advantage of the gluon saturation model are investigated. A new geometrical scaling variable is used to define the gluon saturation region of central rapidity of central nuclear collisions. Predications for net-baryon rapidity distributions and the mean rapidity loss in central Pb + Pb collisions at LHC are made in this paper.

The dynamics of transfer reactions in collisions between two very heavy nuclei ²³⁸U+²³⁸U is studied within the dinuclear system (DNS) model. Collisions between two actinide nuclei form a super-heavy composite system during a very short time, in which a large number of charge and mass transfers may take place. Such reactions have been investigated experimentally as an alternative way for the production of heavy and superheavy nuclei. The role of collision orientation in the production cross sections of heavy nuclides is analyzed systematically. Calculations show that the cross sections decrease drastically with increasing the charged numbers of heavy fragments. The transfer mechanism is favorable to synthesize heavy neutron-rich isotopes, such as nuclei around the subclosure at N=162 from No (Z=102) to Db (Z=105).

A new shell model method, called as the Projected Configuration Interaction (PCI), has been established recently. The deformed Slater determinants (SD's) are projected onto good angular momentum and form the PCI basis. Using realistic shell model Hamiltonians, very good approximations, relative to the exact solutions, have been achieved by using a small PCI basis space. Our results have shown that, PCI may provide a promising way to extend the large scale shell model calculations to the heaver nuclear system.

Nilsson mean-field plus the extended pairing model for well-deformed nuclei is applied to describe rare-earth nuclei. Binding energies, even-odd mass differences of Er, Yb, and Hf isotopes are calculated systematically in the model with proton pair excitation frozen approximation. Compared with the corresponding experimental data, the results obtained from the standard pairing model with BCS approximation, and the nearest orbit pairing model, it is shown that the extended pairing model is better than the other two models in description of rare-earth nuclei.

We have introduced the complex scaling method and its relativistic extension, and demonstrated the utility and applicability of the extended method. We have shown how the resonance states get exposed and the determination of resonance parameters. We have compared the calculated results with the other methods in satisfactory agreements.

In the framework of Skyrme energy-density functional approach together with the extended semi-classical Thomas-Fermi method, the nuclear equation of state (EOS) is investigated using the nucleus-nucleus potential. The potentials of ⁵⁸Ni+⁵⁸Ni and ³²S+⁸⁹Y are studied in the point of view that the energy at touching point is equal to the threshold energy for hindrance. It is found that MSK3-MSK5, V110 are suitable Skyrme parameters sets and the incompressibility values are in the range of K = 231-234 MeV.

Chiral bands in the A ~105 neutron deficient nuclei have been extensively studied. Doublet structures similar to chiral bands have been found in the nuclei around ¹⁰⁴Rh. Apart from those three signatures suggested for the chiral bands in ¹⁰⁴Rh, alignments and moment of inertia have been discussed for the doublet structures together with the lifetime measurement.

Rotational bands of ²⁵⁰Fm, ^252,253,254No and ²⁵¹Md are studied by the cranked shell model with particle-number conserving treatment for monopole and quadrupole pairing correlations. Observed bands are reproduced very well by theoretical results. Backbendings of kinematic moment of inertia and the alignment of high-j orbital are investigated.

High-spin states in ¹⁵⁷Yb have been populated in the ¹⁴⁴Sm(¹⁶O,3n)¹⁵⁷Yb fusion evaporation reaction at a beam energy of 85 MeV. Two rotational bands built on the νf_7/2 and νh_9/2 intrinsic states, respectively, have been established for the first time. The structural characters observed in ¹⁵⁷Yb provide evidence for shape coexistence of three distinct shapes: prolate, triaxial, and oblate.

We have adopted the multistep shell model in the complex energy plane to study excitations occurring in the continuum part of the nuclear spectrum. In this method of solving the shell model equations one proceeds in several steps. In each step one constructs building blocks to be used in future steps. We applied this formalism to analyze the unbound nucleus ¹²Li. In this case the excitations correspond to the motion of three particles partitioned as the product of a one-particle and two-particle systems.

Protoneutron star models are constructed using a realistic equation of state of hot dense matter, and under three different strongly idealized stages concerning stellar evolution. Stability of protoneutron stars with respect to kaon condensate is studied.

High-spin states in ¹⁵⁹Lu were populated by fusion-evaporation reaction ¹⁴⁴Sm(¹⁹F, 4n) at a beam of 106 MeV. The level scheme for ¹⁵⁹Lu is established up to . with the addition of about 20 new transitions. The possible configurations of the updated bands are suggested by the experiments Routhians, alignments and B(M1)/B(E2) ratios.

With the help of an updated transport model — ultra-relativistic quantum molecular dynamics, the nuclear stopping quantity vartl is used to investigate the stiffness of the equation of state of the nuclear matter as well as medium modifications of nucleon-nucleon elastic cross sections in heavy ion collisions (HICs) at SIS energies. It is found that the excitation function of the vartl value is sensitive to both the mean field and the two-body scattering. Hence, both parts should be taken into account consistently. At low SIS energies, in order to describe the FOPI data, the density dependence of the cross sections should be stronger implying that the effect of the nuclear structure may be noticed in the process of the HICs.

Starting from a covariant density functional of point-coupling, the spectroscopic properties of low-lying states in ^72,74,76,78Kr, including potential energy curves, energy spectrum and electric quadrupole transition strengths, are calculated by mixing of angular momentum projected axially deformed relativistic mean-field+BCS states. The calculated results are compared with the corresponding data. The phenomena of shape coexistence in these nuclei is discussed.

The isospin symmetry-breaking corrections δ_c obtained by the self-consistent relativistic RPA calculations are compared with those obtained by the shell model calculations and the isospin- and angular-momentum-projected nuclear density functional theory. It is found that the present theoretical uncertainty of the isospin symmetry-breaking corrections δ_c is of the order of ~ 0.003, rather than ~ 0.0002 as indicated by the shell model calculations. Whether the unitarity of the CKM matrix is fulfilled or not is still an open question.

The high-spin states in the odd-odd nucleus ¹⁰⁸Ag were populated in the reaction ¹⁰⁴Ru(⁷Li,3n) at a beam energy of 33 MeV. The previously known positive-parity band structures have been extended to higher spins, and their configurations have been discussed. Alignments, band crossing frequencies, and B(M1)/B(E2) ratios have been analyzed in the framework of the cranking model.

High spin states of the odd-odd ^120,122I isotopes have been investigated via the ¹¹⁰Pd (¹⁴N, 4n), ¹¹⁴Cd (¹⁰B, 4n) and ¹¹⁶Cd (¹¹B, 5n) reactions at beam energies of 64, 48 and 68 MeV. In ¹²⁰I, the previously known bands are extended, and a new band structure has been established. In ¹²²I, the yrast band is extended up to (29⁺)and assigned to the [πh_11/2(πg_7/2)²]_23/2- ⊗ νh_11/2)³(νd_5/2)²]_35/2-] configuration, which corresponds to the full alignment of all the valance nucleons outside the semi-closed shell.

The SD-pair shell model (SDPSM) is shown to reproduce approximately typical spectra, E2 transition strengths of the U(5), SO(6), SU(3) and SU*(3) limits of the interacting boson model (IBM). The shape phase transitional patterns of the IBM can also be reproduced in the SDPSM. This analysis confirms that the IBM has a sound shell-model foundation; it also demonstrates that the truncation scheme adopted in the SDPSM is reasonable.

The cross sections of fragments (σ_f) produced in the 100 A MeV even ^36-52Ca projectile fragmentation reactions are evaluated in the framework of the statistical abrasion-ablation model. The distributions of σ_f are compared and the similarities of σ_f distributions are investigated.

The method of excitation energy systematics has been used to help the spin assignment of the πh_11/2 intruder band in ^111,113In. I₀=23/2 and I₀ = 15/2 are assigned to the lowest observed state of the intruder band in ^111,113In. The dynamic moment of inertia and the frequency of the h_11/2 neutrons' aligning of the πh_11/2 intruder band is compared with in the neighboring nuclei. The shift of the crossing frequency is mainly caused by the p-n interaction and the interaction becomes weaker with the number of the neutron increasing.

Two-proton relative momentum from the break-up channels ²³Al → p + p + ²¹Na and ²²Mg → p + p + ²⁰Ne at an energy of 72 AMeV has been measured together with two-proton opening angles at the projectile fragment separator beamline (RIPS) in the RIKEN Ring Cyclotron Facility. The results demonstrate that there exists diproton emission component from single-step ²He for highly excited nuclei of ²³Al and ²²Mg.

The age of the Universe is one of the most important physical quantities in cosmology and it can be determined with the r-process nucleochronometer. Based on the classical r-process model, the r-process abundance patterns and various nuclear chronometers in the metal-poor halo stars are investigated by employing the newly developed nuclear mass models. It is found that the un-certainty of Th/Eu chronometer caused by nuclear mass uncertainties is about 4 Gyr, while the uncertainty of Th/Hf chronometer is so large that it should be taken with caution. With the Th/Eu chronometer, the age of the metal-poor stars CS 31082-001 is determined as 16.3±7.1 Gyr, which agrees well with the results derived from Th/U chronometer.

The chiral doublet bands with π(g_9/2)^-1 ⊗ ν(h_11/2)² configuration are studied by the triaxial particle rotor model. The energy spectra and the in-band B(M1)/B(E2) of the doublet bands with different triaxiality parameter γ are analyzed.

α formation amplitudes extracted from experimental data are presented and an abrupt change around the N = 126 shell closure is noted. It is explained as a sudden hindrance of the clustering of nucleons. The clustering induced by the pairing mode acting upon the four nucleons is inhibited if the configuration space does not allow a proper manifestation of the pairing collectivity.

A number of applications have been proposed concerning the isomers, including the creation of a gamma-ray laser, since some of them may store large amounts of energy for long times. Against this background, the field of triggered gamma emission is entering a new phase in which improved level data allow targeting of specific potentially-useful transitions. In the present work, the configuration-constrained (diabatic blocking) calculations, with inclusion of γ-deformation, are performed to study the multi quasi-particle (multi-qp) excitations of ¹⁷⁸Hf. The detailed excitation energies known in ¹⁷⁸Hf are reasonably reproduced. From our calculations, two levels besides the existing level at 2.573 MeV are found for candidates of these intermediate states (or called depletion levels). Whether these two excited states actually exist will require additional experimentation.

The nuclear giant resonances are studied by using a Fermi-liquid method, and the nuclear collective excitation energies of different values of l are obtained, which are fitted with the centroid energies of the giant resonances of spherical nuclei, respectively. In addition, the relation between the isovector giant resonance and the corresponding isoscalar giant resonance is discussed.

High spin states of ¹¹⁶Sb were populated using the ¹¹⁴Cd(⁷Li, 5n) fusion evaporation reaction at a beam energy of 48 MeV. The previously reported rotational bands, built on πg_9/2 ⊗ νh_11/2 and πg_9/2 ⊗ νd_5/2 configurations, have been extended and a new ΔI = 1 band has been identified.

We use a new scheme to describe the X(5) nuclei, in which the SU(3) quadrupole-quadrupole interaction is replaced by the SO(6) cubic [Q₍₀₎ × Q₍₀₎ × Q₍₀₎]⁰ interaction. Some energy ratios and B(E2) ratios of X(5) nuclei are studied in this work. The results of this new scheme are compared with the corresponding experimental data and those of the traditional U(5)-SU(3) description. It is shown that the results from this new scheme are better than those of the traditional description.

The modes of ternary reaction of ¹⁹⁷Au+¹⁹⁷Au at an energy of 15A MeV are dynamically studied by the improved quantum molecular dynamics model. Three kinds of modes are found by the time evolution of the configurations of the composite reaction systems: One is the direct mode for which the two time separations of the system happen almost simultaneously. Another is the cascade mode for which a two-step process is clearly shown. The third is oblate mode, a kind of very rare fission event. In this case the composite system deforms to a triangle-like configuration with three necks, and then it forms three equally sized fragments along space-symmetric directions in the reaction plane.

The possibility is considered that X(3872) may be a bound state of or . By assuming that the short range force between mesons is governed by one-glue-mediated quark exchange between two mesons and long range force by sigma and pion meson exchange, we calculate the binding energy of system by solving the Schrödinger equation. Results indicate that there exists a weakly bound S-wave state and the binding energy is less sensitive to the parameters of the meson exchange potential.

Based on a semi-empirical nuclear mass formula, the super-heavy stability island is investigated. From the calculated shell corrections of super-heavy nuclei, the region N = 172-178, Z = 116-120 with shell corrections about -6 MeV roughly gives the position of the super-heavy stability island. The probability to synthesize nuclei with Z = 126 may be much smaller than that of produced super-heavy nuclei already, according to the obtained shell corrections and the proton drip line.

High-spin states of ¹¹⁸Sb have been studied by in-beam γ-spectroscopy following the reaction ¹¹⁶Cd(⁷Li, 5n)¹¹⁸Sb. The previously known band structures have been extended. One new rotational band has been identified, and assigned the configuration. Two positive parity bands observed in the present work are suggested as a pair of pseudospin partner bands.

The proton elastic resonance scattering induced by radioactive secondary beams has been studied in inverse kinematics at CIAE since 2005. The so-called thick-target method is applied to obtain the excitation function in a one-shot experiment of a single beam energy. Up to now, several light nuclei systems including ¹³N+p, ¹⁷F+p, and ⁶He+p have been successfully investigated with this method. A general introduction of the method and a summary of the results are presented in this paper.

In this contribution we present some results of a study of the stability of excited superheavy nuclei (SHN) with 100 ≤ Z ≤ 134 against neutron emission and fission. We give a systematic investigation of the survival probability against fission in the 1n-channel of these SHN. The neutron separation energies and shell correction energies are consistently taken from the finite range droplet model which predicts an island of stability of superheavy nuclei around Z = 115 and N = 179. It is found that this island of stability persists for excited superheavy nuclei in the sense that the calculated survival probabilities in the 1n-channel of excited superheavy nuclei at the optimal excitation energy are maximized around Z = 115 and N = 179. This indicates that the survival probability in the 1n-channel is mainly determined by the nuclear shell effects.

A projected Hamiltonian with definite angular momentum from the exactly solvable deformed mean-field plus nearest-orbit pairing model is proposed to study whether the deformed mean-field plus nearest-orbit pairing model can be used to describe low-lying spectra of nuclei reasonably.

The potential energy surfaces of ¹⁵²Sm and its neighboring isotopes are investigated in a constrained reflection-asymmetric relativistic mean-field approach with parameter set PK1. According to the calculations, ¹⁵²Sm has a quadrupole-deformed minimum and an octupole-deformed minimum with similar energies. The low-lying 0⁺ states in the spectrum can be understood as the manifestation of shape coexistence in (β₂, β₃) plane. Furthermore, the neutron gap with N = 88 and proton gaps with Z = 62 in the single-particle levels may be important for this coexistence.

Nuclear pairing gaps of normally deformed nuclei are investigated by using the particle-number conserving formalism for the cranked shell model, in which the blocking effects are treated exactly. Both rotational frequency ω-dependence and seniority ν-dependence of the pairing gap are investigated.

We discuss the Nucleon Pair Approximation (NPA) of the shell model by a short review, which includes a history survey, its physical foundation, validity, and recent applications, as well as our perspectives.

The high-spin states in ¹²⁶I have been investigated by using in-beam γ-ray spectroscopy with the ¹²⁴Sn(⁷Li, 5n)¹²⁶I reaction at a beam energy of 48 MeV. The previously known level scheme of ¹²⁶I has been extended and modified considerably by adding about 60 new γ-transitions and establishing 5 new bands. The backbendings in the yrast band 1 and the yrare band 3 are found both due to a pair of h_11/2 neutrons alignment. The configurations for the newly identified bands 2, 4, 5 and 6 have been assigned.

Lifetimes of the high spin states in a pair of chiral candidate bands in ¹⁰⁶Ag were measured by means of the Doppler-shift attenuation method. The reduced transition probabilities B(M1) and B(E2) were deduced from these measurements. The B(E2) values in both chiral candidate bands behave differently as well as B(M1) values. In addition, the staggering of the B(M1) values with spin was not observed. The experimental results are inconsistent with the ideal chiral predictions.

In the frame of deformed Skyrme Hartree-Fock+BCS model, the effect of tensor interaction is discussed on the shell structure of superheavy nuclei.We compare the results of different Skyrme interactions; SLy5 without tensor interaction, and SLy5+T, T24 and T44 with tensor interaction. The large shell gaps of superheavy nuclei are found at Z=114 and Z=120 for protons and N=184 for neutrons at the spherical shape irrespective of the tensor correlations. It is also shown that the Z=114 and N=164 shell gaps are more pronounced by the tensor correlations in the case of SLy5+T interaction.

The following sections are included:

• LIST OF PARTICIPANTS