International Journal of Modern Physics E

In this talk I shall discuss my perspective of nuclear structure physics. In particular, I would like to discuss the recent RI beam physics, development of nuclear theory including a number of models and unsolved problems.

A microscopic analysis of the asymmetry energy is performed through the investigation of nuclear giant resonances in the relativistic approach. Nuclear ground state properties are calculated in an extended relativistic mean-field theory plus BCS method, where the contribution of the resonant continuum to pairing correlations is properly treated. The nuclear giant resonances are investigated in the relativistic random phase approximation (RRPA) or quasi-particle RRPA. Special emphases are paid to the correlation between the giant dipole resonance or pygmy resonance and the density dependence of the asymmetry energy.

Neutron decay of the isoscalar giant dipole resonance (ISGDR) has been studied in ⁹⁰Zr, ¹¹⁶Sn and ²⁰⁸Pb using the (α,α′) reaction at a bombarding energy of 200 MeV. The same reaction was used to study proton decay of the ISGDR in ⁵⁸Ni and ²⁰⁸Pb. Neutron and proton decay of the ISGDR to low-lying neutron and proton hole states in the daughter nuclei, respectively, allowed an experimental determination of the ISGDR microscopic structures. The determined branching ratios are compared to recent continuum random-phase-approximation (CRPA) calculations. Reasonable agreement was observed for ²⁰⁸Pb and ⁵⁸Ni, whereas strong differences for ⁹⁰Zr and ¹¹⁶Sn were found.

We discuss to what extent information on ground-state properties of finite nuclei (energies and radii) can be used to obtain constraints on the symmetry energy in nuclear matter and its dependence on the density. The starting point is a generalized Weizsäcker formula for ground-state energies. In particular effects from the Wigner energy and shell structure on the symmetry energy are investigated. Strong correlations in the parameter space prevent a clear isolation of the surface contribution. Use of neutron skin-information improves the situation. We find that inclusion of the Wigner effect leads to a larger value of the symmetry energy of nuclear matter at the saturation point.

Recent analysis of the isospin diffusion data from heavy-ion collisions based on an isospin- and momentum-dependent transport model with in-medium nucleon-nucleon cross sections has led to the extraction of a value of L = 88 ± 25 MeV for the slope of the nuclear symmetry energy at saturation density. This imposes stringent constraints on both the parameters in the Skyrme effective interactions and the neutron skin thickness of heavy nuclei. Among the 21 sets of Skyrme interactions commonly used in nuclear structure studies, the 4 sets SIV, SV, G_σ, and R_σ are found to give L values that are consistent with the extracted one. Further study on the correlations between the thickness of the neutron skin in finite nuclei and the nuclear matter symmetry energy in the Skyrme Hartree-Fock approach leads to predicted thickness of the neutron skin of 0.22 ± 0.04 fm for ²⁰⁸Pb, 0.29 ± 0.04 fm for ¹³²Sn, and 0.22 ± 0.04 fm for ¹²⁴Sn.

We study Gamow-Teller strength distributions within a QRPA approach performed on top of a deformed Skyrme-Hartree-Fock+BCS single particle basis with the inclusion of residual spin-isospin interactions in both particle-hole and particle-particle channels. We focus our attention in several problems of interest in Nuclear Structure and Nuclear Astrophysics, such as the β-decay properties of proton-rich medium-mass nuclei of astrophysical interest and the deformation dependence of the Gamow-Teller strength distributions in neutron deficient Pb isotopes. We also discuss the role of deformation in the two-neutrino double beta decay.

The nuclear wobbling motion in the Lu region is studied by the microscopic cranked mean-field plus RPA method. The Woods-Saxon potential is used as a mean-field with a new parameterization which gives reliable description of rapidly rotating nuclei. The prescription of symmetry-preserving residual interaction makes the calculation of the RPA step parameter-free, and we find the wobbling-like RPA solution if the triaxial deformation of the mean-field is suitably chosen. It is shown that the calculated out-of-band B(E2) of the wobbling-like solution depends on the triaxial deformation in the same way as in the macroscopic rotor model, and can be used to probe the triaxiality of the nuclear mean-field.

The time-dependent Hartree-Fock method, using the Skyrme interaction, is used to study the isovector giant dipole response of neutron-rich ³⁴Mg. The response is separately examined along the major and minor axes of this prolate nucleus, with a pygmy-like peak in the direction of the major axis at around 10 MeV. Time-dependent density plots show a superimposed surface mode not fully coupled to the bulk motion.

Recent studies on nuclear structure by using radioactive isotope beams available at the RIKEN projectile-fragment separator (RIPS) are introduced. Special emphasis is given to experiments selected from recent programs that highlight studies; anomalous quadrupole natures in ¹⁶C, new results on ²⁸Ne with respect to the island-of-inversion region. Experimental programs at the new facility called RIBF are also introduced.

Search for low-spin signature inversion in the πi_13/2 ⊗ νi_13/2 bands in odd-odd ^182,184,186Au has been conducted through the standard in-beam γ-spectroscopy techniques. The experiments for ¹⁸²Au and ¹⁸⁶Au have been performed in the Japan Atomic Energy Agency (JAEA) via the ¹⁵²Sm(³⁵Cl,5n)¹⁸²Au and ¹⁷²Yb(¹⁹F,5n)¹⁸⁶Au reactions, respectively. A study of ¹⁸⁴Au has been made using a multi-detector array GASP in LNL, Italy, via the ¹⁵⁹Tb(²⁹Si,4n)¹⁸⁴Au reaction. The πi_13/2 ⊗ νi_13/2 bands in these three nuclei have been identified and extended up to high-spin states. In particular, the inter-band connection between the πi_13/2 ⊗ νi_13/2 band and the ground-state band in ¹⁸⁴Au has been established, leading to a firm spin-and-parity assignment for the πi_13/2 ⊗ νi_13/2 band. The low-spin signature inversion is found in the πi_13/2 ⊗ νi_13/2 bands in ^182,184,186Au according to our spin-assignment and the signature crossing observed at high-spin states.

The recent progress of the relativistic many-body approach by the group at Peking University will be reviewed. In particular, the adiabatic and configuration-fixed constrained triaxial RMF approaches, triaxial RMF approach with time-odd components, a Shell-model-Like APproach (SLAP), a Reflection ASymmetric RMF (RAS-RMF) approach, and a new relativistic Hartree-Fock (RHF) approach with density-dependent σ, ω, ρ and π meson-nucleon couplings for finite nuclei and nuclear matter, will be highlighted.

Sensitivity of the direct nuclear reaction to the exotic structure of the unstable nuclei is outlined. The transfer reaction induced by ⁶He on a ⁹Be target at 25 MeV/u is described. The theoretical analysis using CRC model supports the di-neutron configuration of the two valence neutrons in ⁶He. Preliminary calculation for ¹⁷Ne were introduced which indicates the advantage of using transfer reaction to clarify the s-wave or d-wave configuration of the valence protons.

The derivation of two-neutron separation energies from the direct mass measurement of the neutron-rich nuclei at GANIL has enabled us to establish new neutron magic numbers N=6 and 16 in neutron-rich region for the first time instead of normal 8 and 20 and to confirm the existence of new doubly magic nuclei ⁸He and ²⁴O. Adjunction of a proton to the new doubly magic nuclei ⁸He and ²⁴O enable to accept two or more neutrons by these nuclei and form, respectively, the neutron halo ¹¹Li nucleus and create a very neutron-rich set of ^27,29,31F isotopes. The connection between doubly magic nuclei and the neutron halo and/or very neutron-rich odd-Z nuclei is studied by analysis of triton separation energies S_t of light neutron-rich nuclei.

Large scale nuclear structure studies within the complex Excited Vampir model involving rather large single particle basis systems as well as general two-body interactions are used to investigate exotic phenomena in medium mass nuclei. Results are presented on the influence of Coulomb induced isospin-mixing on the superallowed Fermi β decay in isovector triplets of nuclei, as well as the mechanism responsible for the generation of magnetic bands in the A ≃ 80 mass region.

The properties of light exotic nuclei far off β-stability are studied using relativistic mean field (RMF) models considering the nonlinear isoscalar-isovector coupling terms that modify the density dependence of the symmetry energy. The ρNN tensor coupling is included. The neutron thickness of some light exotic nuclei near neutron drip lines is as uncertain as that of heavy nuclei. The uncertainty of these light exotic nuclei is enhanced by the inclusion of the ρNN tensor coupling subject to the 2s_1/2 occupation of the out-layer neutrons. The charge density distribution of exotic nuclei on both sides of drip lines are considerably modified by the isospin dependent interactions. The role of multi-Λ hypernuclei in extending the drip lines are discussed.

The RISING fast beam campaign aims at high resolution γ-ray spectroscopy experiments with relativistic radioactive beams at GSI. The secondary beams produced by fragmentation or fission are used for Coulomb excitation or secondary fragmentation experiments to perform studies of nuclei far off stability. The physics phenomena studied with this method include nuclear structure experiments targeting at the evolution of shell structure toward the drip lines, mirror symmetry, collectivity and electromagnetic transition strengths. Example results of this fast beam campaign are presented and compared to various shell model calculations and nuclear structure models.

We report on the first use of post-accelerated radioactive isomeric beams. Long-lived isomeric states in ⁶⁸Cu and ⁷⁰Cu have been produced and separated at ISOLDE, CERN. Subsequently they were post-accelerated to 2.86 MeV/u and sent to a target in the center of the MINIBALL spectrometer, used for the detection of the γ-rays of interest. The preliminary results from the Coulomb excitation of the I^π=6^-, 1⁺ states in ⁶⁸Cu and the I^π=6^- one in ⁷⁰Cu, compared to a large-scale shell model calculations, hint the importance of the excitations across the Z=28 gap for the understanding of the nuclear structure in the neutron-rich N=40 region.

Properties of the odd-odd mirror nuclei ¹²B and ¹²N have been investigated in the time-odd triaxial relativistic mean field approach. Influences of the nuclear magnetism, the mass difference between neutron and proton, the isovector meson field ρ and the Coulomb field on the properties of mirror nuclei have been discussed in detail.

The longitudinal momentum (p_//) distributions of fragments after one-proton removal and reaction cross sections (σ_R) for several N = 10 isotones at intermediate energy (~ 70A MeV) have been measured simultaneously at the RIken Projectile fragment Separator (RIPS). p_// was measured using a direct time-of-flight (TOF) technique, while σ_R was determined using a transmission method. An enhanced σ_R is observed for ²³Al comparing with its neighbors. The p_// distribution for ²²Mg fragments from ²³Al one-proton removal reaction has been obtained for the first time. The experimental data are discussed within a Few Body Glauber (FBG) framework. Analysis of p_// indicates a dominant d-wave component in the ground state of ²³Al. This agrees with recent experimental results. We also suggest the possibility of an enlarged ²²Mg core for proton-rich nucleus ²³Al.

Lifetimes of exited states in ¹³⁴Pr were measured be means of the recoil distance Doppler-shift and Doppler-shift attenuation techniques. The experiments were performed at IReS, Strasbourg using the EUROBALL IV spectrometer, in conjunction with the inner BGO ball and the Cologne coincidence plunger apparatus. Exited states in ¹³⁴Pr were populated in the fusion-evaporation reaction ¹¹⁹Sn(¹⁹F, 4n)¹³⁴Pr. Reduced transition probabilities in ¹³⁴Pr are compared to the predictions of the two quasiparticle+triaxial rotor and interacting boson fermion-fermion models. The experimental results do not support the presence of static chirality in ¹³⁴Pr underlying the importance of shape fluctuations. Only within a dynamical context the presence of intrinsic chirality in ¹³⁴Pr can be supported.

Structures of excited states in ¹¹C and ¹¹B were studied based on variational calculations after spin-parity projection in a framework of antisymmetrized molecular dynamics (AMD). The calculations systematically reproduce the experimental data of the transition strengths such as Gamov-Teller and M1 transitions. A well-developed cluster structure of 2α+³He(t) was found in the state of ¹¹C(¹¹B), which can be assigned to the observed state at 8 MeV. The calculations reproduce the small measured in the recent experiments. It was suggested that the state has a dilute cluster state, and its features are similar to those of the which is considered to be a gas state of three α clusters. The structures of ¹³C were also discussed.

We present a brief review of some static properties of metal clusters. We emphasize relations with atomic nuclei and focus on cluster quantities which have counterparts in nuclei. We discuss in particular the case of the optical response which provides a key tool of analysis of the structure and shape of simple metal clusters.

We have calculated the strength functions of the Gamow-Teller transition processes from mirror pairs ⁴⁶Ti–⁴⁶Cr and ⁵⁰Cr–⁵⁰Fe to the odd-odd N = Z nuclei ⁴⁶V and ⁵⁰Mn. The calculations are carried out in fp model space with shell model diagonalization method. Calculations are compared with experimental observations. We have also discussed the effects of isospin symmetry breaking on the analogous transitions.

We systematically investigate the half-lives of exotic radioactivities in the framework of the density-dependent cluster model. Simple analytical formulas between lifetime and decay energy are also derived for the exotic radioactivities based on the Gamow quantum tunnelling theory. The theoretical results from the density-dependent cluster model and from the analytical formulas agree well with the experimental data. A unified description is achieved for proton emission, α-decay and cluster radioactivity by both phenomenological and microscopic methods.

The elements with Z = 107 - 112 have been successfully synthesized at GSI employing ²⁰⁸Pb and ²⁰⁹Bi targets and producing relatively cold compound systems. The unambiguous identification of these elements via evaporation residue(ER)-α correlations and the link to known α emitters has been confirmed by independent measurements performed at RIKEN, Japan and partly by chemistry experiments. An impressive body of data which is interpreted as the synthesis of isotopes with Z = 114 - 116 and 118 has been accumulated at the FLNR, Dubna, where the alternative approach of reactions with actinoide targets forming more excited compound nuclei was pursued. Despite of a consistent systematic picture, the final confirmation, however, is still missing. These exciting results together with the possibilities opened up by the advanced experimental techniques and the nowadays available beam intensities with their expected future increase have triggered a broad range of activities. Apart from experiments to attempt the synthesis of new elements, nuclear structure investigations in the transactinoide region has become possible for Z up to 108 or 110. Heavy element chemistry has successfully placed Hs in the periodic table and is now attacking element 112. The development of accelerators and experimental methods promises advances to enable the extension of these investigations in regions closer to the "island of stability". Mass measurements using ion traps and neutron rich unstable beam species for the systematic investigation of nuclear structure and reaction mechanisms for heavy neutron rich systems are believed to complete the variety of tools in future.

Superheavy elements have provided a good test of the validity of both nuclear structure models and nuclear decay models in a large mass region. We firstly review the recent progress on theoretical studies of superheavy nuclei. Emphasis is placed on the structure and decay of superheavy nuclei. Then theoretical results of odd-odd nuclei with Z = 109 - 115 are presented and discussed. It is clearly demonstrated that there is shape coexistence for the ground state of many superheavy nuclei from different models and many superheavy nuclei are deformed. In some cases superdeformation can become the ground state of superheavy nuclei and it is important for future studies of superheavy nuclei. This can lead to the existence of low-energy isomers in the superheavy region and it plays an important role for the stability of superheavy nuclei. As α-decay and spontaneous fission plays a crucial role for identifications of new elements, we also review some typical models of α-decay half-lives and spontaneous fissions half-lives. Some new views on superheavy nuclei are presented.

Based on the improved isospin dependent molecular dynamics model in which the shell correction energy of the system is calculated by using deformed two-center shell model and the surface energy of the system is improved by introducing a switch function that combines the surface energies of projectile and target with the one of the compound nucleus. The importance of shell correction energy on synthesis of superheavy nuclei is studied systematically. For reaction systems induced by of ¹⁶O and ^40,48C at low energies near Coulomb barrier, it is found that the calculated fusion cross sections show a strong enhancement for the neutron-rich combinations, which can regenerate the experimental data quantitatively.

In the framework of the relativistic mean field (RMF) theory, the stability and ground properties of super-heavy nuclei are discussed. Our study indicated that the current synthesized super-heavy nuclei (SHN) actually appear in the stable region, and adding more neutrons will not increase their stability. The study of nuclei from ²⁸⁷115 α decay chain showed that they are usually deformed, the magnitudes of their shell gaps are much smaller than those of nuclei before the actinium region, so that the shell effect is weakened, and SHN are usually not stable. A common phenomenon is that the Fermi surface of the proton is close to the continuum, the resonant continuums exist in SHN, because the SHN are usually neutron deficient. Although bulk properties can be described by the RMF+BCS theory, further study is needed. Density dependent delta pairing interaction can improve the treatment of the pairing and thus improve the level distribution in the continuum.

Dynamics of fusion of massive nuclei is described by a simple diffusion model in terms of the two-center shape parameterizations {z, ε} and the fusion probability is calculated by a Brownian particle passing over the top of a parabolic potential along the elongation coordinate z. The neck variable ε at initial shape is supposed to be a Gaussian distribution after a transitive process, and the average initial kinetic energy of the fusing system is determined by energy conservation. The fusion probabilities of several symmetric or nearly symmetric systems in central collisions are calculated as functions of the center-of-mass energy and compared with the experimental data. Effects of energy loss and neck folding on the fusion hindrance are discussed.

As a subset of radioactive beams, isomer beams open up the dimensions of excitation energy and angular momentum. The problem of isomer decay rates is briefly presented, as they are not yet well understood. The use of isomer beams for nuclear structure investigations is reviewed, using examples related to exotic decay modes, charge radii, and Coulomb excitation. There are also unique possibilities for the study of induced electromagnetic depopulation. A key aspect is beam purification, for which different techniques are discussed.

Masses of neutron-rich nuclei ranging from ytterbium to uranium were investigated using the Schottky Mass Spectrometry (SMS) method. Special efforts were devoted to exploring long-lived K-ismoers in the mass 180-region. New ground state masses, new isotopes and isomers are also identified in the sub-uranium region and ²⁰⁸Pb region. Some preliminary results from this experiment are presented.

Using deformed Hartree-Fock and angular momentum projection (PHF) technique we try to understand the intrinsic structure and the systematics in the life times of K = 6⁺ isomers in the Hf isotopes (in ^172-178Hf nuclei) and N = 104 Yb, Hf and W isotones. The band structure in ¹⁷²Hf is reasonably well reproduced. The variation in the B(E2;2⁺ → 0⁺) values in the Hf isotopes as well as N = 104 isotones are well reproduced. The calculated K-forbidden E2 transition probabilities from the isomer bandheads to the 4⁺ yrast states qualitatively explain the variation of the lifetimes with N and Z.