A New Era of Nuclear Structure Physics

Preface.

Contents.

Welcome address.

Opening address.

After a brief review on the status of few–nucleon studies based on conventional nuclear forces, we sketch the concepts of the effective field theory approach constrained by chiral symmetry and its application to nuclear forces. Then first results for few–nucleon observables are discussed.

Precise data on the cross section and analyzing powers were measured for the d–p elastic scattering at 70, 100 and 135 MeV/u. Also deuteron to proton polarization transfer coefficients , , , were measured at 135 MeV/u. The measurement yielded proton induced polarization P^{y '}. The data were compared with Faddeev calculations with high precision nucleon–nucleon forces combined with different three-nucleon forces(3NFs), the 2π-exchange Tucson-Melbourne model, a modification thereof closer to chiral symmetry TM′, and the Urbana IX 3NF.

The Complex Energy Method [Prog. Theor. Phys. 109, 869L (2003)] is applied to the four body Faddeev-Yakubovsky equations in the four nucleon system. We obtain well converged solutions in all energy regions below and above the four-nucleon breakup threshold.

The recent quark-model baryon-baryon interaction by the Kyoto-Niigata group is applied to the triton, hypertriton, 2αΛ and 2Λα systems, in which a new three-cluster Faddeev formalism, using the 2-cluster resonating-group method (RGM) kernel, is developed for the exact treatment of the Pauli forbidden states between clusters.

Reaction spectroscopy and γ-ray spectroscopy of Λ hypernuclei has made significant progresses and has provided indispensable information on Λ hypernuclear structure and ΛN interaction in the recent years. In addition, the (e,e’K⁺) spectroscopy was, for the first time, successfully carried very recently. Based on these development, the future prospect of hypernuclear physics is discussed.

We consider rearrangement effects in light hypernuclei in the framework of the lowest order Brueckner theory. The energy change of the ⁴He core of when the Λ hyperon is added to ⁴He is first estimated without much numerical computations. Next, rearrangement contributions in are estimated, which are important to deduce the strength of the ΛΛ interaction from the experimental .

The Particle Listings 2000 edition gave the recommended value of antiproton mass, for the first time, to be within 5 × 10⁻⁷ in the relative deviation from the proton mass; this can be a test of the CPT invariance. The value was derived by our precision 3-body calculation, using the Gaussian Expansion Method, to analyze the laser spectroscopy data of metastable states in antiprotonic helium atoms taken at CERN. The 2002 edition and the 2003 updated version reported an one-order smaller value, 6 × 10⁻⁸, based on further development of both the experiment and our calculation.

We calculated resonances of positronium complexes, Ps⁻ and Ps₂, with the stochastic variational method combined with the complex scaling method (SVM+CSM). The method was successfully applied to predict resonances with nonzero angular momentum with high accuracy.

An ab-initio description of atomic nuclei that solves the nuclear many-body problem for realistic nuclear forces is expected to possess a high degree of predictive power. In this contribution we treat the main obstacle, namely the short-ranged repulsive and tensor correlations induced by the realistic nucleon-nucleon interaction, by means of a unitary correlation operator. This correlator applied to uncorrelated many-body states imprints short-ranged correlations that cannot be described by product states. When applied to an observable it induces the correlations into the operator, creating for example a correlated Hamiltonian suited for Slater determinants. Adding to the correlated realistic interaction a correction for three-body effects, consisting of a momentum-dependent central and spin-orbit two-body potential we obtain an effective interaction that is successfully used for all nuclei up to mass 60. Various results are shown.

Shell structures in the N ≃ Z nucleus ¹⁷O and the neutron-rich oxygen isotopes ²³O and ²⁵O are microscopically described by calculating single-particle energies with modern nucleon-nucleon interactions within the framework of the unitary-model-operator approach. It is found that the effect of three-body cluster terms on the single-particle energy is more important in ²³O and ²⁵O than ¹⁷O.

Triaxial strongly deformed and superdeformed (TSD) structures have been observed in Lu-Hf nuclei. Wobbling motion, a characteristic excitation mode of triaxial nuclei, has been established in odd-Z even-N ^163,165,167Lu. The aligned i_13/2 proton plays a crucial role to realize 𝔍_x > 𝔍_y in positive-γ shapes and allowing the wobbling motion compete energetically with other excitations. No evidence for wobbling exists, up to date, for even-even system that was originally predicted. Theoretical calculations successfully predicted the existence of an island of TSD structures in Lu-Hf isotopes, but face great challenges regarding the wobbling mechanism and the calculated proton and neutron shell gaps.

We report on pair-truncated shell-model calculations of low-lying yrast and quasi-γ bands of nuclei around mass 130 using phenomenological effective interactions of pairing plus quadrupole type, where the strengths of interactions are gradually changed as functions of numbers of valence nucleons. The calculations start with even-even nuclei of low-lying states, which exhibit typical features of γ-instability. The model reproduces well experimental energy levels and E2 transition rates. We calculate energy levels of odd-A nuclei, where the effective interactions identical to those obtained from the calculations of the even-even nuclei are employed. The agreement between the theoretical values and the experimental observations is rather well.

In order to search for high-spin isomers in N=51 isotones, an unstable nuclear beam ¹⁷N was developed using the low-energy radioisotope beam separator(CRIB) of the Center for Nuclear Study(CNS), University of Tokyo, in RIKEN.

High-spin isomers in N=83 isotones have been systematically studied. These isomers are of stretch coupled configurations and oblate shape. High-spin isomers of N=51 isotones are expected to be stemmed from the same isomerism appeared in N=83 isotones.

Since the nuclei with Z <40 of N=51 isotones are close to the stability line, it is difficult to produce high-spin states in these nuclei using reactions by combinations of stable beams and targets. Therefore, it is very effective to use the radioisotope beam. Experiment was carried out by means of the γ spectroscopy method, Seven γ-rays emitted from Nb nuclei which were produced by the secondary fusion reaction of ⁸²Se + ¹⁷N were observed.

Multiple Coulomb excitation of ^66,68Zn was carried out. The experimental data were analyzed with the least-squares search code GOSIA. E2 matrix elements and quadrupole moments of states were obtained. The ground band structures are explained to some extent with the asymmetric rotor model (ARM) and the interacting boson model (IBM) in O(6) limit. Potential energy surfaces (PES) calculated with the Nilsson-Strutinsky model show γ-unstability for ⁶⁶Zn and shallow two minima for ⁶⁸Zn. According to the experimental results and induction from the theoretical calculations, it seems that ^66,68Zn would be explained with such a model with soft triaxial potential.

A technique for providing high-spin isomers as probes of fusion reaction and measurement of g-factor has been worked out at RIKEN. In the study of the secondary fusion reaction ¹²C(^145mSm,xn)^157−xEr, the γ rays emitted from the fusion-evaporation residue ¹⁵⁴Er have been successfully observed. The nuclear g-factor of the T_1/2 = 28 ns high-spin isomer in ¹⁴⁹Dy has been measured with the γ-ray TDPAD method.

The role of continuum states in nuclei is considered, along with use of breakup theories of stripping and diffractive dissociation in probing nuclear structure. In the breakup of three-body nuclei such as Borromean halo systems, both three-body and two-body continuum final states need to be modelled and measured.

The reaction cross section for the neutron-rich nucleus ¹⁷B on a carbon target has been measured at an energy of 77 AMeV by a transmission method. A large enhancement of ¹⁷B reaction cross section at low energy was observed. The density distribution of ¹⁷B was deduced through the energy dependence of the reaction cross section together with high-energy data using a finite-range Glauber-model calculation under an optical-limit approximation. It is confirmed that the neutron-tail in the density distribution is necessary for ¹⁷B in order to reproduce the measured reaction cross sections. Based on the assumption of a core (¹⁵B) plus valence two-neutron picture, the mixture of ν(2s_1/2) and ν(1d_5/2) was studied without treating the correlation between two neutrons.

The breakup of halo nuclei can be studied in a semi-classical approximation by solving the time-dependent Schrödinger equation. The resolution is performed numerically. A high accuracy is required to extract the breakup component. A fourth-order algorithm is proposed and tested. The Coulomb breakup of ¹⁵C on a lead target is analyzed and compared with existing data.

The semiclassical method of Alder and Winther is generalized to study fusion reactions. As an illustration, we evaluate the fusion cross section in a schematic two-channel calculation. The results are shown to be in good agreement with those obtained with a quantal Coupled-Channels calculation. We suggest that in the case of coupling to continuum states this approach may provide a simpler alternative to the Continuum Discretized Coupled-Channels method.

The low to medium energy acceleration of radioactive beams opens up specific possibilities for the study of nuclear reactions and nuclear structure. This energy domain is particularly well suited for the study of direct transfer reactions and resonant scattering. The study of nuclei far from stability interacting with simple target nuclei, such as protons, deuterons, ³He and ⁴He implies the use of inverse kinematics. The kinematics, together with the low intensities of the beams call for special techniques. We tested a new detector, in which the detector gas is the target, an active target. This allows in principle a 4π solid angle of the detection, and a big effective target thickness without loss of resolution. The detector developped, called Maya, used isobutane C₄H₁₀ as gas in the first experiment, and other gases are possible. The multiplexed electronics of more than 1000 channels allows the reconstruction of the events occurring between the incoming particle and the detector gas atoms in 3D. Here we were interested in the reactions induced by ⁸He on protons at 2-3.5MeV/n. The design of the detector is shown, and some first results are discussed.

Four treatments of resonance states are outlined: direct search of the S-matrix pole, complex scaling, analytic continuation in the coupling constant and Berggren’s theory. Examples for the latter two show their feasibility and usefulness.

A generalized two-center cluster model (GTCM), including various partitions of the valence nucleons around two α-cores, is proposed for studies on the exotic cluster structures of Be isotopes. This model is applied to the ¹⁰Be=α + α + 2n and the ¹²Be=α+α+4n systems. The adiabatic energy surfaces for α − α distances are calculated. It is found that this model naturally describes the formation of the molecular orbitals as well as that of asymptotic cluster states depending on their relative distance.

In this contribution one example of challenging new experimental developments will be presented: direct mass measurements in the GSI experimental storage ring. The exploration of the nuclear mass surface in exotic regions gives first information on the location and persistence of nuclear shells far-off stability and isospin effects e.g. on the pairing strength. An outline of the the recently approved GSI project for an extended new synchrotron facility including an overview over the experimental program, new experimental developments, and the perspectives for nuclear structure research is given.

The progress in the modeling of exotic nuclei with an extreme neutron-to-proton ratio is discussed. Two topics are emphasized: (i) the quest for the universal microscopic nuclear energy density functional and (ii) the progress in the continuum shell model.

Proton radioactivity from deformed drip–line nuclei is discussed. It is shown how it is possible to describe all experimental data currently available for decay from ground and isomeric states, and fine structure of odd-even and odd–odd nuclei, within a consistent theoretical approach.

The Skyrme-HFB equations are solved in coordinate space on a 2-D lattice for deformed axially symmetric nuclei. Using B-Spline techniques, we focus on an accurate representation of the HFB continuum states for neutron-rich exotic nuclei. Results are presented for the sulfur isotope chain ^34–52S up to the two-neutron dripline. We also study the g.s. properties of neutron-rich heavier nuclei (^102,104Zr,¹⁵²Ce,¹⁵⁶Nd, and ^158,160Sm) some of which exhibit very large prolate quadrupole deformations.

M3Y-type interactions are developed and applied to mean-field calculations. By comparing results of an M3Y-type interaction on the uniform nuclear matter with those of the Skyrme and the Gogny interactions, we find a remarkable difference in the spin-isospin properties, to which the one-pion-exchange potential gives significant contribution. Correlating to variation of the shell structure, these spin-isospin properties play a certain role in the new magic numbers near drip lines such as N = 16 and N = 32.

We study the connection between relativistic mean field models and the bare nucleon-nucleon interaction. We start from a bare interaction, and by employing a G-matrix formalism we derive a density dependent realistic interaction in the medium. We introduce a one-boson-exchange potential and we extract the masses and the coupling strengths of the meson fields through a fit to the G-matrix potentials. The parameters and their density dependence are compared with those of other one-boson-exchange parametrizations.

The Hartree-Fock + BCS model with a separable monopole nucleon-nucleon interaction is applied to calculate the charge density distribution in selected even-even nuclei. The charge r.m.s. of ^40–48Ca isotopes and binding energies of even-even Cd nuclei are discussed. The Q_β value for ¹³⁰Cd → ¹³⁰In is calculated, giving good agreement with experiment.

The evolution of shell structure in exotic nuclei is discussed. There are two major aspects of this shell evolution : one is related to the spin-isospin dependent central part of the nucleon-nucleon interaction, while the other is the tensor interaction. I shall mainly discuss the latter case, since the former one has been discussed to some detail. It will be suggested that the tensor interaction can change the shell structure, for instance, by varying the spin-orbit splitting considerably as a function of N and Z.

Excited states in the ¹³B nucleus were investigated by a measument of the proton transfer reaction (α,t) at 50 MeV per nucleon in the inverse kinematics. From an analysis on the angular distribution of the ¹³B for the 4.83-MeV excited state, its spin and parity was assigned to be 1/2⁺ for the first time.

A new experimental method has been developed to measure the mean-life of the first excited state of ¹⁶C. The method uses a concept of the shadow technique with high velocity (β ≃ 0.3) of the excited nucleus. The mean-life was determined to be τ = 77 ± 14 (stat) ±19 (syst) ps. The central value of mean-life corresponds to , or 0.26 Weisskopf units. This transition strength was found to be anomalously small compared to the empirically predicted value.

Structure of Carbon isotopes are investigated by deformed Skyrme Hartree-Fock and shell model calculations. We point out that the quadrupole deformations of C–isotopes have a strong isotope dependence as a manifestation of nuclear Jahn-Teller effect. It is shown also that the quadrupole moments and the magnetic moments of the odd C isotopes depend clearly on assigned configurations, and their experimental data will be useful to determine the spin-parities and the deformations of the ground states of these nuclei. The electric quadrupole (E2) transitions in even C isotopes are also studied. The isotope dependence of the E2 transition strength is reproduced properly, although the calculated strength overestimates extremely small observed value in ¹⁶C.

On the basis of the Hartree-Fock-Bogoliubov (HFB) plus quasiparticle random phase approximation method (QRPA) based on the Green’s function approach with Skyrme force, we discuss the anomalous E2 properties of the first 2⁺ states in neutron-rich nuclei ³²Mg and ³⁰Ne. The B(E2) values and the excitation energies of the first 2⁺ states are well described within HFB plus QRPA calculations with spherical symmetry. We conclude that pairing effects account largely for the anomalously large B(E2) values and the low excitation energies in ³²Mg and ³⁰Ne.

The magnetic moment of ¹⁹N was measured by using a β-NMR method and a spin-polarized ¹⁹N beam from the fragmentation reaction. As a result, the g value for the ¹⁹N ground state, g = 0.61 ± 0.03(preliminary), was obtained. The value was compared with those of ¹⁵N and ¹⁷N. Contrary to shell-mode predictions that the g value should increase with increasing number of neutrons in the sd shell, the obtained g for ¹⁹N_g.s. is significantly smaller than the g factor for ¹⁷N_g.s..

Reactions of secondary beams at energies of several hundred MeV/u are utilized at the GSI radioactive beam facility to explore the structure of unstable nuclei. Scattering of radioactive nuclei can be studied by kinematically complete measurements with the LAND reaction setup. In the present article, experiments concerning inelastic excitations to the continuum will be discussed utilizing the electromagnetic excitation process at high energies. First experiments in this direction were performed for light neutron-rich nuclei. Two aspects are of particular interest: i) Non-resonant transitions to the continuum just above the threshold, which have been established as a spectroscopic tool to study the ground state single-particle structure of the projectile. ii) The dipole excitations of neutron-proton asymmetric systems, in particular collective excitations such as the giant dipole resonance or low-lying soft modes.

Pair correlation effects on the soft dipole excitation in medium mass nuclei near neutron drip-line are investigated by means of the continuum quasiparticle random phase approximation. The correlation of di-neutron type found in the ground state affects strongly the soft dipole excitation, and enhances the transition amplitude for two-neutron pair transfer.

The time-dependent Hartree-Fock calculation with a full Skyrme energy functional has been carried out on the three-dimensional Cartesian lattice space to study E1 giant dipole resonances (GDR) in light nuclei. The outgoing boundary condition for the continuum states is treated by the absorbing complex potential. The calculation for GDR in ¹⁶O suggests a significant influence of the residual interaction associated with time-odd densities in the Skyrme functional. We also predict a large damping for superdeformed ¹⁴Be at the neutron drip line.

We present the first application of an extended RPA (ERPA) with ground-state correlations. The ERPA is formulated as the small amplitude limit of the time-dependent density-matrix theory, which is an extended version of the time-dependent Hartree-Fock theory. We obtain the correlated ground states of ^20,22O using an iterative gradient method and calculate the first 2⁺ states and their two-phonon states using the ERPA.

Cross sections and analyzing powers of proton elastic scattering off ⁵⁸Ni and ^{116,118,120,122,124}Sn at 295 MeV have been measured up to the angle of about 4 fm⁻¹ in momentum transfer to deduce a systematic change of neutron density distribution. Since the shapes of neutron and proton distributions are supposed to be the same in ⁵⁸Ni, we have used the ⁵⁸Ni elastic scattering as a reference to tune the relativistic Love-Franey interaction used in the relativistic impulse approximation by introducing a medium effect. Then, we have applied the elastic proton scattering to deduce the neutron density distribution of tin isotopes. The result of our analysis shows a clear systematic behavior which shows a gradual filling in the 3s_1/2 neutron single particle orbit. A recoil particle spectrometer(RPS) project at RIKEN to deduce the density distribution for unstable nuclei is reported.

I report the recent progress of our study on the determination of the nuclear density distributions from the proton-nucleus elastic scattering cross sections.

We report preliminary results from ultra-fast time-delayed γγ(t) measurements on exotic nuclei just below ¹⁰⁰Sn. The measurements were performed at the LISE spectrometer in GANIL. Nuclei of ⁹⁴Ru and ⁹⁶Pd were populated in the isomeric states via the fragmentation of energetic ¹¹²Cd beam. Preliminary lifetime or lifetime limits are reported for the 6⁺, 4⁺, and 2⁺ states in ⁹⁶Pd and the 4⁺ and 2⁺ states in ⁹⁴Ru. These results indicate an unexpected and strong quenching of the B(E2) strength for the 4⁺ to 2⁺ E2 transition in ⁹⁶Pd in comparison with model predictions and the equivalent B(E2) strength in ⁹⁴Ru. The sequence of quenched B(E2) rates for the 8⁺ → 6⁺ E2 transition in ⁹⁴Ru, 4⁺ → 2⁺ E2 transition in ⁹⁶Pd and for the 8⁺ → 6⁺ E2 transition in ⁹⁸Cd, seems to represent a systematic pattern along the N=50 neutron number just below Z=50 and could imply a weak N=50 shell closure when approaching the doubly magic ¹⁰⁰Sn.

We calculate energies E₂₊ and transition strengths B(E2) ↑ of the lowest 2⁺ states of even neutron-rich Te and Sn isotopes, using the quasiparticle random phase approximation with simple separable interactions. With those calculations reproducing the experimental systematics very well, we discuss, first, an unusual relation between E₂₊ and B(E2)↑ in the nuclei ^132,136Te; the relation does not follow the empirical formula B(E2) ↑ ∝ 1/E₂₊. Second, we discuss the B(E2) ↑ of ¹³²Sn, which is larger than those of the neighboring even Sn isotopes. We also calculate g-factors for some of those 2⁺ states. Finally, we argue that ⁶⁸Ni is not a doubly-magic nucleus.

Complications which arise when the Transient Field method for determination of nuclear excited state g-factors is used with radioactive isotope beams, are surveyed. Ways to overcome the problems include allowing the Coulomb excited nuclei to recoil into vacuum. This has the disadvantage that the angular distribution of their gamma de-excitation, which forms the basis for the TF method, becomes attenuated. However it is argued that these attenuations may, in themselves, form the basis of a simple way to study g-factors. A simple theoretical introduction is given and recent preparatory experiments are outlined.

Nuclear magnetic resonance on oriented nuclei for ⁹¹YFe experiments have been performed. Comparing the external field dependence of resonance frequencies with ⁹¹YFe and ^91mYFe, the hyperfine anomaly in Fe was determined as ^91mΔ⁹¹ = +4.2(8)%. The measured hyperfine anomaly was interpreted in terms of a microscopic theory including core polarization and meson exchange currents.

A total absorption spectrometer, dedicated to the study of very short lived atomic species, has been built and installed at the CERN/ISOLDE mass separator. The β decays of the neutron-deficient ⁷⁴Kr and ⁷⁶Sr nuclei have been studied using this new device. The experimental Gamow-Teller strength distributions obtained over the full Q_EC windows are presented and compared with self-consistent, deformed, HF-BCS-QRPA calculations.

The atomic nucleus is the first major step of nature towards complexity. It links the fundamental physics and our real world. Various approaches are needed in experiment and theory to explore and understand its nature. The progress in creating a consistent picture, a common challenge for experiment and theory, was the topic of the symposium.

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International Symposium "A New Era of Nuclear Structure Physics" (NENS03) Program.

List of Participants.