Frontiers of Collective Motions

Preface.

Photo of Participants of Frontiers of Collective Motions.

CONTENTS.

No abstract received.

The moment of inertia, Θ, is one of the possible observables for the experimental determination whether a trapped Fermi system has reached the BCS transition or not. In this article we investigate in detail the temperature dependence of Θ below the critical temperature T_c. Special care is taken to account for the small size of the system, i.e., for the fact that the trapping frequency ħω is of the same order of magnitude as the gap Δ. It turns out that Θ does not change rapidly if T becomes smaller than T_c, but it rather decreases smoothly. Qualitatively this behavior can be explained within the two-fluid model, which corresponds to the leading order of an ħ expansion. Quantitatively we find deviations from the two-fluid model due to the small system size.

Structure study by the use of AMD in stable and unstable nuclei is reviewed. We put some emphasis on the characteristic features of AMD approach which include variation after parity projection, variation after angular momentum projection, superposition of parity-spin projected AMD Slater determinants. Since AMD is an ab initio theory of nuclear structure, we can study cluster structure without assuming the existence of any clusters and can describe the coexistence of mean-field-type structure and cluster structure.@ Some examples of calculated results are shown by comparing with the experimental data. They are the studies on neutron-rich Li, BeCB isotopes, on the island of inversion around N=20, and on the excited bands with many-particle many-hole structure in ⁴⁴Ti.

Measurements on ⁹⁰Zr(p, n) and ⁹⁰Zr(n, p) reactions at 300 MeV were made and reliable S_β− and S_β+ values are successfully extracted. A Gamow-Teller quenching factor (Q) in terms of the spin sum rule of S_β− – S_β+ = 3(N – Z) is derived as Q = 0.89 ± 0.04(MDA) ± 0.04(IVSM) apart from the systematic uncertainty of . The Landau-Migdal (LM) parameters representing a short-range correlation in an isospin-spin channel are deduced to be and with the Chew-Low coupling constant f_Δ/fπ = 2. The critical density of the pion condensation is estimated to be ρ_c ~ 2_ρ0 which can be easily realized in the neutron stars. Recent observation of the surface temperature of the neutron star 3C58 supports the pionic cooling mechanism and consequently manifestation of the pion condensation in neutron stars.

The excitation of isospin and spin-isospin modes has been a topic of much interest in the last two decades because of their importance to various astrophysical phenomena next to the intrinsic interest in their microscopic structure. (p, n) and other (p, n)-type reactions, such as (³He,t), at intermediate energies have been used to map spin-isospin-flip strength in the β⁻ direction. For the β⁺ direction the spin-isospin-flip strength can, in principle, be mapped with the (n, p) reaction at intermediate energies. However, the resolution that can be obtained with secondary neutron beams is hardly useful to map accurately this strength. Better reactions could be (d, ²He) and (t, ³He) reactions at intermediate energies. Recently, at KVI a primary triton beam has been accelerated to energies of about 45 MeV/u. It is planned to use this beam to study isospin excitations in ‘neutron-rich’ nuclei. Furthermore, an unprecedented high resolution of 150 keV has been achieved with the (d,²He) reaction, which is a reaction of essentially pure spin- and isospin-flip character. This allows to map the spin-isospin strength and study its microscopic and multipole structure. Recent experimental results are discussed.

High-resolution (³He, t) reaction at 0° and at intermediate incident energies is a new spectroscopic tool for studying Gamow-Teller (GT) excitations up to highly excited region. With an achieved resolution of well less than 50 keV, bump-like structures of “GT resonances” have been resolved into “discrete GT states” for fp-shell nuclei, where the level density is relatively high. One-to-one comparison of strengths is now possible for isospin analogous transitions, i.e., the transitions among isospin analog states. Isospin T of excited GT states were identified through the comparison with (p, p′) experiments based on different enhancements of analog M1 states compared to the GT states depending on different T values. Isospin symmetry of T_z = T₀ → T₀ – 1 and –T₀ → –T₀ + 1 transitions (T₀ > 0) is investigated by comparing the (³He, t) experiments that can study the former part with the β-decay study that can investigate the latter. The GT transition strengths in Fe isotopes are by itself key parameters for presupernova models in the core collapse stage. Fine structures of GT states are also observed in the low-lying region of medium-heavy nuclei.

With the use of the symmetry-unrestricted cranked SHF method in the 3D coordinate-mesh representation, a systematic search for the SD and HD rotational bands in the N=Z nuclei from ³²S to ⁴⁸Cr has been done, and SD and HD solutions have been found in ³²S, ³⁶Ar, ⁴⁰Ca, ⁴⁴Ti, and in ³⁶Ar, ⁴⁰Ca, ⁴⁴Ti, ⁴⁸Cr, respectively. The SD band in ⁴⁰Ca is found to be extremely soft against both the axially symmetric (Y₃₀) and asymmetric (Y₃₁) octupole deformations. Possible presense of SD states in neutron-rich sulfur isotopes from ⁴⁶S to ⁵²S has also been investigated, and deformation properties of neutron skins both in the ground and SD states are discussed.

The observation of chiral doublet bands in odd-odd triaxial nuclei will be reviewed. Experimental verification of nuclear chirality is outlined. The specific fingerprints related to chirality in the intrinsic system will be discussed as interpreted by theoretical considerations.

The reflection asymmetric shell model approach has been introduced for the description of octupole bands. The Q · Q forces of quadrupole, octupole and hexadecapole as well as the monopole and quadrupole pairings are included in the hamiltonian. The shell model space is spanned by a selected set of the projected axial and octupole Nilsson plus BSC basis. The calculated results for the octupole bands in the A=220 region are in a good agreement with the experimental data. The experimental SD bands 1 and 3 in ¹⁹⁴Hg are well reproduced by the present calculation and interpreted as the parity partner octupole SD bands with K^π = 0⁺ and K^π = 0⁻ respectively.

Systematic trends of reduced transition probabilities within πh_11/2⊗νh_11/2 doublet bands in odd-odd Cs isotopes are interpreted as a result of selection rules unique to chiral geometries. Calculated B(E2) and B(M1) strengths based on a particle/hole plus triaxial rotor model with γ=30° are presented.

Proton decay from deformed nuclei is studied, assuming that the emitted proton moves in a deformed single particle Nilsson resonance and the half–lives for decay are evaluated exactly. All measured deformed proton emitters are perfectly described by this model.

Beta-decay is described here as an alternative to charge- exchange reactions to populate spin-isospin excitations in nuclei. Its advantages and disadvantages are discussed and the Total Absorption Technique, a reliable method of measuring Gamow-Teller transition probabilities is described. An illustrative example is given where single particle and collective excitations are observed in the beta decay. Problems such as the spreading width, mixing of the states and the high energy tail of the resonance are discussed.

Substantially large E1 strength at low excitation energies, which appears characteristically for the Coulomb dissociation of halo nuclei, has been investigated by using the ¹¹Be+Pb reaction at 68A MeV. We study the effects of higher order excitation and the nuclear breakup contribution in this reaction. These contaminants have been found very small and can be discriminated by using the impact parameter analysis. The method is then successfully applied to the case of ¹⁵C. We have also studied the ¹¹Be breakup on C target to understand the nuclear breakup mechanism of halo nuclei.

The double differential cross sections at 0°–12° were measured for the ⁹⁰Zr(n, p) reaction at 293 MeV in a wide excitation energy region of 0–70 MeV. The experiment was performed by using the (n, p) facility at the Research Center for Nuclear Physics. The multipole decomposition (MD) technique was applied to the measured cross sections to extract the GT component in the continuum. After subtracting the contribution of the isovector spin-monopole excitation we obtained the GT strength of S_β+ = 3.0±0.3±0.8±0.5 up to 31 MeV excitation. The quenching factor Q was deduced by using the present result and the S_β− value obtained from the MD analysis of the ⁹⁰Zr(p, n) spectra. The result is Q = 0.88±0.03±0.05±0.14 in regard to Ikeda’s sum rule value of 3(N – Z) = 30.

Collective excitations of a trapped bose-fermi mixture of cold atomic gases are studied in RPA. Selfconsistent mean-field equations of coupled bosons and fermions are solved and the ground-state properties are studied for a variable boson-fermion interaction strength. Collective excitations with angular momentum 0 to 3 are calculated and the strength distributions and dynamical form factors are studied. In particular, boson-fermion out-of-phase dipole oscillation is shown to appear at low energy, which is analogous to the nuclear soft dipole oscillation. It is shown that the boson-fermion interaction gives rise to an effective fermion-fermion attraction which induces a concentration of the monopole strength. We comment also on the possible instability of the system due to the boson-fermion attractive interaction.

Starting from a Green function approach to nuclear matter, the formation of bound states and quantum condensates is treated within the cluster-mean field approach. In particular, quartetting in symmetric matter is considered. Nucleonic correlations are of importance in low-density matter, e.g. near the surface of nuclei. Self-conjugate 4n nuclei exhibit an α-like cluster structure. A new α-cluster wave function is proposed which is of the α-particle condensate type. Applications to ¹²C and ¹⁶O show that states of low density close to the three- resp. four-α-particle threshold in both nuclei are possibly of this kind. Furthermore, the occurrence of deformed condensates is discussed. In particular, excited ⁸Be is described as deformed gas-like two-α-particle states.

The upgraded Gas-Filled Recoil-Ion Separator (GARIS) has been operated in RIKEN with the high-intensity heavy-ion linac (RILAC). Three alpha-decay chains of ²⁷¹[110], which were produced by the ²⁰⁸Pb(⁶⁴Ni, n)²⁷¹[110] reaction, have been identified and thus confirmed the observation at GSI. The same system was used to observe a new isotope ²³⁴Bk by ¹⁹⁷Au(⁴⁰Ar, 3n)²³⁴Bk reaction. The data indicate a possible existence of two states in ²³⁴Bk. The decay product of ²³⁴Bk, ²³⁰Am decays mainly by β decay because no α decay has been observed. The estimated halflife of ²³⁰Am is 17 ⁺¹⁵_-12 s. We also report the results of search of Z=118 element.

Properties of collective modes in very neutron-rich nuclei are discussed. From one side, we overview the effect of the occurrence of neutron skins on the properties of the traditional collective modes, such as the Giant Dipole Resonance and the Giant Quadrupole Resonance. On the other side, we briefly discuss the occurrence of low-lying multipole strength in the case of weakly-bound nuclei close to the drip-lines. Application to the multipole response of weakly-bound cluster nuclei, such as ⁷Li, is presented.

We report on recent advances in the description of weakly bound and unbound nuclear states using either a real ensemble representing (quasi-)bound single-particle states and non-resonant continuum states (the so-called Shell Model Embedded in the Continuum) or a complex Berggren ensemble representing bound single-particle states, decaying resonant states, and non-resonant continuum states (the so-called Gamow Shell Model). These two different strategies in formulating the multiconfigurational Continuum Shell Model are illustrated by showing how the non-resonant continuum impacts the mechanism of nuclear binding.

The electric quadrupole moments Q of the B isotopes have been measured recently up to the mass number A = 17. The observed Q moment for ¹⁷B as well as that for ¹⁵B are very close to that for the N = 8 isotope ¹³B, contrary to the shell-model expectation with constant effective charges that Q increases rapidly with increasing number of neutrons added to the ¹³B core. Analysis of these results reveals substantial reductions of the E2 effective charges for nuclei with large (N–Z)/A ratios, and cautions that the commonly accepted notion of constant effective charges may not hold in nuclei far from the β-stability line. We discuss the variation of effective charges in relation to the change in properties of the isoscaler and isovector giant resonances in neutron rich nuclei.

The evolution of structure in nuclei as a function of nucleon number is discussed and it is shown that finite nuclei can exhibit phase transition-like behavior, and that nuclei at the phase transition points can be described by the new symmetries X(5) and E(5). The evolution of structure as a function of angular momentum has received new attention lately. We briefly discuss the concept of E-GOS plots and the possibility of wobbling-like motion in γ-soft nuclei.

The evolution of shell structure and the consequent variation of the magic numbers are discussed for exotic nuclei. A major origin of the shell evolution is shown to be the spin-isospin dependent central part of the nucleon-nucleon interaction in nuclei. The importance and robustness of this mechanism is shown in connection to the τ · τ σ · σ interaction. In neutron-rich exotic nuclei, magic numbers such as N=8, 20, etc. can disappear, while N=6, 16, etc. arise. The τ · τ σ · σ interaction should be related to Gamov-Teller and magnetic properties. Another mechanism of the shell evolution is shown to be the tensor interaction.

Following a brief reminder of how pairing models can be solved exactly, we discuss two examples in which this exact solvability has been used to provide interesting insight into issues of importance in nuclear structure physics. One concerns the uncovering of a new mechanism for sd dominance in interacting boson models of nuclei and the other concerns a mapping of nuclear pairing onto a classical electrostatic problem and the insight it provides into nuclear superconductivity.

In this contribution, we review recent results obtained for the excited collective states in several isotopic chains with a Gogny force. In the second part, the role of many-body effects beyond mean field on the pairing properties is discussed.

The structure of low-lying states in nuclei can be described by the shell model, the collective model and by cluster models. With a large enough basis and a suitable interaction the shell model is capable of describing all nuclear states. In the collective model, the single particle basis of the deformed shell model is optimized for describing the particular collective states under consideration. Phenomenological cluster models are able to provide a very simple description of certain bands of states which are observed experimentally, and microscopic cluster models relate phenomenological descriptions to the shell model and collective models. The purpose of this contribution is to review some binary cluster models and discuss their relation to the collective model and shell model.

No abstract received.

Isoscalar quadrupole and isovector dipole excitations in neutron-rich oxygen isotopes are studied by QRPA calculations with the Green’s function method. The residual interaction between the quasiparticles is self-consistently derived from the mean-field hamiltonian that has an explicit velocity dependence. We discuss the importance of the velocity-dependent terms for the description of these collective excitations.

Ground state properties of C isotopes, deformation and elecromagnetic moments, as well as electric dipole transition strength are investigated. We first study the ground state properties of C isotopes using a deformed Hartree-Fock (HF) + BCS model with Skyrme interactions. Isotope dependence of the deformation properties is investigated. Shallow deformation minima are found in several neutron-rich C isotopes. It is also shown that the deformation minima appear in both the oblate and the prolate sides in ¹⁷C and ¹⁹C having almost the same binding energies. Next, we carry out shell model calculations to study electromagnetic moments and electric dipole transitions of C isotopes. We point out the clear configuration dependence of the quadrupole and magnetic moments in the odd C isotopes, which will be useful to find out the deformation and spin-parities of the ground states of these nuclei. Electric dipole states of C isotopes are studied focusing on the interplay between low energy Pigmy strength and giant dipole resonances. Low peak energies, two-peak structure and large widths of the giant resonances show deformation effects. Calculated transition strength below dipole giant resonance in heavier C isotopes than ¹⁵C is found to exhaust 12 ~ 15% of the Thomas-Reiche-Kuhn sum rule value and 50 ~ 80% of the cluster sum rule value.

The strength functions of quadrupole modes in ²²O and ²⁴O are calculated using the time-dependent density-matrix theory (TDDM). It is found that TDDM gives the lowest quadrupole states which are energetically shifted upward and become significantly collective due to the coupling to two-body configurations. It is pointed out that these features of the lowest quadrupole states are similar to those obtained in the quasi-particle random phase approximation.

An α-boson model was applied to examine the possibility of α-cluster condensation in ¹²C and ¹⁶O. The amount of α condensation was quantified by diagonalizing density matrices. The probabilities that the α-particles occupy an S-orbit were 30–40% for some candidate states of α condensation.

Shape coexistence problems in N = 14 isotones are studied with a microscopic method of antisymmetrized molecular dynamics. The present calculations reproduce features of deformation in ²⁸Si, and predict possible shape coexistence of neutron density in neutron-rich nuclei(¹⁹B and ²⁴Ne). We also systematically study the structures of the ground and excited states, and the molecular resonances of ²⁸Si. Besides the shape coexistence in the low-energy region, the results indicate the high-lying levels with α-cluster and ¹²C+¹⁶O molecular structures in ²⁸Si, which are consistent with the observed spin-assigned resonances. The resonance states above the threshold energies are connected with the low-lying deformed states from a view point of molecular excitation by discussing inter-cluster wave functions.

No abstract received.

Absorbing-boundary-condition method and its applications to nuclear responses and breakup reactions are reported. The method facilitates calculations of the continuum states in the coordinate space of many degrees of freedom. Properties of nuclei near drip lines are discussed.

We study the monopole oscillation in the bose-fermi mixed condensed system by performing the time-dependent Gross-Pitaevsky (GP) and Vlasov equations. We find that the big damping exists for the fermion oscillation in the mized system even at zero temperature.

In this talk we shall present our recent understanding on the angular momentum 0 ground state dominance of even-fermion systems and boson systems in presence of two-body random interactions. We give only two simple examples which are analytically solvable. However, we stress that our approach can be generalized to more complicated systems: both (even or odd number of) fermions in a single-j shell (or many-j shells) and bosons. We emphasize without details that the angular momentum 0 ground state dominance is essentially given by interactions with specific features.

Recent experimental results from the interaction of electromagnetic and hadronic probes with nuclei are discussed in the light of the role of orbital motion in collective nuclear excitations. First, in a high-resolution study of the electric dipole response in ²⁰⁸Pb at the superconducting Darmstadt electron linear accelerator (S–DALINAC) a resonance structure located around the neutron emission threshold has been identified. It is interpreted to result from surface density oscillations of the neutron skin relative to an almost isospin-saturated core. It may be an integral part of a toroidal E1 mode and thus be an example of vortex collective motion in nuclei. Second, earlier experiments on the search for a magnetic quadrupole resonance in ⁴⁸Ca and ⁹⁰Zr with high-resolution backward angle inelastic electron scattering at the S–DALINAC were extended to ⁵⁸Ni and in the latter case supplemented by forward angle inelastic proton scattering in Groningen. The results provide ample evidence for the existence of a so-called nuclear twist mode, i.e. a zero sound mode which should also be present in other finite Fermi systems. Finally, some salient features of the prime example of an orbital magnetic dipole mode, the scissors mode, are briefly revisited.

We examine how pairing and continuum effects can be treated self-consistently in the microscopic description of ground states and excited states of neutron-rich nuclei. Assuming an effective interaction of the Skyrme type we show how the self-consistent fields of the Hartree-Fock-Bogoliubov (HFB) theory can be constructed with the inclusion of the continuum. The effects of continuum are shown to be more pronounced in the vicinity of the drip lines. On the basis of the continuum-HFB solution one can build the continuum-QRPA approach which provides a consistent description of the excitations. As an illustration, we present and discuss some results obtained for low-lying excitations and giant resonances in neutron-rich Oxygen isotopes and in ²⁶Ne.

Isovector non-spin-flip giant resonances were observed in the reaction ⁶⁰Ni(¹³C, ¹³N)⁶⁰Co at E/A = 100 MeV. Besides the giant dipole resonance at E_x = 8.7 MeV, another resonance has been observed at E_x = 20 MeV with a width of 9 MeV. A comparison of its angular distribution with Distorted-wave Born approximation calculations indicates that this resonance is excited by L=2 and carries about 50 % of the sum-rule limit strength for the giant quadrupole resonance.

By using the continuum quasiparticle random phase approximation, which we recently formulated on the basis of the coordinate-space Hartree-Fock-Bogoliubov theory, we investigate pairing effects on the low-lying dipole strength in neutron rich oxygen isotopes near the drip-line. The neutron pairing enhances the dipole strength near the threshold, especially in the case of the surface pairing. Analysis shows that spatially correlated spin-singlet neutron pairs (di-neutrons) are formed in the external region, and the low-lying dipole strength is characterized by motion of the correlated neutron pairs against the core.

The new neutron-rich radioactive ion beams available from the HRIBF allow a variety of exciting measurements around the ¹³²Sn region, including Coulomb excitation, fusion-evaporation, and neutron transfer. Experiments using these beams also provide an excellent training ground for developing techniques to be used at the future high-intensity Rare Isotope Accelerator facility, RIA. The B(E2; 0⁺ → 2⁺) value for first 2⁺ excited states of neutron-rich ^132,134,136Te and ^126,128,130Sn have been measured by Coulomb excitation in inverse-kinematics. The B(E2) values obtained for ^132,134Te are in excellent agreement with expectations based on the systematics of heavy stable Te isotopes, while that for ¹³⁶Te is unexpectedly small. These results are discussed in terms of the shell model and the quasiparticle random phase approximation. Neutron transfer onto a ¹³⁴Te beam, from ⁹Be and ¹³C targets to populate single-particle states in ¹³⁵Te, has also been studied. Results, and plans for future experiments with these neutron-rich beams, are presented.

We first review the current status of Hartree-Fock (HF) based random phase approximation (RPA) as applied to the study of the properties of isoscalar giant resonances. We then provide assessments of the consequences due to certain violations of self-consistency in implementing HF–RPA, as often encountered in the published literature. Next, we present results of microscopic calculations of excitation cross sections, σ(E), for the isoscalar giant dipole resonance (ISGDR) and provide a resolution of the long standing problem concerning the value of the nuclear matter incompressibility coefficient, K_nm, deduced from experimental data on σ(E) for the ISGDR.

Recently, γ-ray spectroscopy with radioactive ion beams has been successfully studied for investigating the low-lying structure of unstable nuclei. In this report, recent experimental results on the neutron-rich nuclei ¹²Be and ³⁴Mg are presented. The level schemes and transition probabilities are determined for the low-lying excited states in these nuclei, and discussed in relation to the modification of nuclear shell structure around N=8 and 20 far from the stability line.

High-spin negative-parity states in ⁴⁰Ca have been investigated by using the ²⁸Si(²⁰Ne,2α)⁴⁰Ca reaction. The level scheme of ⁴⁰Ca was extended to a 17⁽⁻⁾ state at 23.5 MeV and three rotational band structures were found. Transition quadrupole moments of the bands were deduced based on the residual Doppler shift analysis, and they show significant collectivity. The observed band structures were compared with cranked relativistic mean field calculations.

High-spin isomers in N=83 isotones have been systematically studied. Spin-parities of these isomers are 49/2⁺ and 27⁺ for odd and odd-odd nuclei, respectively. These isomers are of stretch coupled configurations and have oblate shapes.

Experimental results were compared with those calculated by a deformed independent particle model(DIPM). Excitation energies of high-spin isomers in N=83 isotones with 60≦Z≦66 are almost constant. This constancy can be attributed to a decrease of the shell gap energy of Z=64 from 2.4 to 1.9MeV, as a proton number decreases from Z=64 to 60. These isomers are considered to be shape isomers, as the results of the DIPM calculation indicates that high-spin isomers may be caused by the sudden shape change from a near spherical to an oblate shape.

Search for high-spin isomers with the same isomerism has been experimentally started in N=51 isotones.

The g factor of the high-spin isomer in ¹⁴⁹Dy (t_1/2 = 28 ns) has been measured using the γ-ray time-differential perturbed angular distribution (TDPAD) technique with a pulsed beam of ¹³²Xe. The experimental result indicates a main configuration of the isomer to be . A deformed independent particle model (DIPM) calculation predicts that a large oblate deformation is caused by breakdown of the N = 82 shell-closure at this isomeric state.

The three moments of inertia associated with the wobbling mode built on the triaxial superdeformed states in Lu-Hf region are investigated by means of the cranked shell model plus random-phase approximation to the configurations with aligned quasiparticle(s). The result indicates that it is crucial to take into account the direct contribution to the moments of inertia from the aligned quasiparticle(s) so as to realize in positive-γ shapes.

The wobbling mode is uniquely related to triaxiality and introduces a series of bands with increasing wobbling phonon number, n_w, and a characteristic large Δn_w = 1 E2 strength between the bands. The pattern of γ-transitions between the wobbling excitations will be influenced by the presence of an aligned particle. Evidence for the wobbling mode was obtained recently, and even a two-phonon wobbling excitation has now been identified in ¹⁶³Lu. The similarity of the data in ¹⁶³Lu to new strongly deformed triaxial bands and connecting transitions in the neighbouring nuclei, ¹⁶⁵Lu and ¹⁶⁷Lu, establishes wobbling as a more general phenomenon in this region.

Being stimulated by the recent identification of the two-phonon wobbling excitation, first I make a brief survey of various two-phonon states in nuclear physics, in connection with experimental observations. Then, I discuss the wobbling-phonon excitation in the presence of particle alignments, which is nicely pinned down in the recent experiments of the nucleus .

Please refer to full text.

No abstract received.

No abstract received.

Program.

List of participants.