Session CL: Nuclear Structure I

Instability of N$=$Z$=$28 shell closure against quadruple deformation in $^{56}$Ni

$^{56}$Ni is expected to have a doubly closed shell configuration with the magic number N$=$Z$=$28 in a simple picture. However, the observed $E$(2$^{+}_{1})$ and $B(E$2) suggest the collectivity of $^{56}$Ni and weakened N$=$Z$=$28 shell closure. Furthermore, in the low-lying states, a super deformed (SD) band with an (f$_{7/2})^{-4}$(p$_{3/2})^{4}$ configuration is experimentally observed and it shows the existence of the SD shell gap with N$=$Z$=$28. Therefore, the detailed study of the low-lying spectrum will provide us important information on the N$=$Z$=$28 magic number in the proton-rich nuclei. In this contribution we will discuss the positive-parity excited states of $^{56}$Ni and the instability of N$=$Z$=$28 shell closure on the basis of the antisymmetrized molecular dynamics calculation. It is shown that the N$=$Z$=$28 shell closure is unstable against oblate deformation and it leads to the appearance of low-lying $\beta $- and $\gamma $-bands. It is also shown that by prolate deformation the spherical N$=$Z$=$28 shell gap easily disappears and the SD shell gap appears, which generates SD bands with (f$_{7/2})^{\mathrm{-m}}$(p$_{3/2})^{\mathrm{m}}$ configurations. These two aspects of the N$=$Z$=$28 shell closure lead the coexistence of the almost spherical ground band, $\beta $ - and $\gamma $ -bands and SD bands within small excitation energies.   

A Quantum Mechanical Approach to Nuclear Rotations

We deal with the study of collective motion within the context of a quantum mechanical method -- the nuclear Born--Oppenheirmer (NBO) method. We focus in particular on a quantum mechanical approach to nuclear rotations. As an illustration, we utilize the NBO method to study non-spherical, permanently deformed nuclei; in particular, we study nuclei that are axially-symmetric and even, but with non-closed shells. We also focus on a quantum mechanical derivation of formal expressions for the energy and for the moment of inertia. Using trial functions in which the intrinsic structure is described by a mean-field approximation, we then show that the NBO formalism yields the Thouless-Valantin formula for the moment of inertia and that this moment of inertia increases with angular momentum, in agreement with experimental data. We show that the NBO formalism is well equipped to describe low-lying as well as high lying rotational states. Additionally, we establish a connection between the NBO method and the self-consistent Cranking (SCC) model.   

Superdeformation in $^{35}$S

Recent investigations of superdeformed bands have focused on the A$\sim$40 region. It was suggested that the $f_{7/2}$ intruder orbital is the driving force behind the onset of superdeformation in A$\sim$40, although this was not con firmed experimentally. The high-spin states in $^{35}$S were investigated using $^{26}$Mg($^{18}$O, 2 1n)$^{35}$S fusion evaporation reaction. A level scheme for $^{35}$S was deduced. The half-life of the transition in the band was estimated by measuring the residual Doppler shift. The deduced half-life shows the large collectivity of the band. The result indicates that the superdeformed band in $^{35}$S is associated with the excitations of nuclei to the $f_{7/2}$.   

A study of the tetrahedrally deformed nuclei by using the quantum number projection method with Gogny interaction

Possible existence of the tetrahedrally symmetric nuclei was suggested from mean-field calculations such as the Skyrme (SIII) Hartree-Fock-Bogoliubov (HFB) and the Woods-Saxon Strutinsky methods. Because of large energy gaps of the single particle levels, the tetrahedrally deformed nuclei become stable for the particular particle numbers, i.e., the tetrahedral magic numbers. We have recently performed Gogny (D1S) HFB calculations and obtained the tetrahedrally deformed states for nuclei with such magic numbers. The resultant spectra calculated by the quantum number projection nicely follow the predicted spin-parity combinations by the group theory. One of the important findings is that the tetrahedral energy gain by the projection from the spherical configuration is very large, e.g., about 10MeV for the cases of $^{80,96,110}$Zr nuclei, in contrast to the fact that the HFB energy curve is rather shallow. However, the tetrahedral deformation is one of the octupole deformations; new calculations under investigation suggest that the energy gains for the other octupole deformations are of the similar amount for Zr isotopes. We would like to discuss these multiple softness of octupole shape including the tetrahedral deformation.   

Lifetime measurements for the proposed antimagnetic rotational band in $^{101}$Pd

It has become well known by active researches in the last two decades that particle-hole combinations of dissimilar nucleons in high-$j$ orbitals can create novel structures such as magnetic rotation (MR) bands and antimagnetic rotation (AMR) bands around doubly magic nuclei. We proposed an antimagnetic rotational band including the $h_{11/2}$ neutron orbital in $^{101}$Pd based on the previous in-beam $\gamma$-ray spectroscopy by using the reaction $^{68}$Zn($^{37}$Cl,1p3n). However, we could not confirm the antimagnetic rotational character at that time for lack of lifetime data. Since a thick target was used in that experiment, it was possible to extract lifetimes for several levels in the ${\nu}h_{11/2}$ band through the analysis of Doppler broadened line shapes of $\gamma$-rays. The results of those analyses will be presented in this talk.   

Study of high spin states in the triaxial deformed nuclei using an angular momentum projection method

Although the well-known deformation in nuclei is the axially symmetric ellipsoidal deformation, the existence of triaxial deformation is suggested theoretically and experimentally. At high-spin states of the triaxially deformed nuclei, there are many interesting rotational bands such as the chiral doublet band and the wobbling band. In the odd-odd nuclei with a high-j particle and a high-j hole, the three angular-momentum vectors, those of the core, the high-j particle and the high-j hole, align along the three mutually perpendicular directions. These angular-momentum vectors give rise to a chiral geometry, which leads to the degenerate pair of bands. The chiral doublet band and the wobbling band have been first predicted by the macroscopic models. However, their microscopic understanding is necessary. We have recently developed an efficient method to perform the angular momentum projection, which is a fully microscopic approach to the nuclear rotational motion. With this approach, we investigate the high-spin rotational bands in the triaxially deformed nuclei. We will report on the results of the energy spectra and the electromagnetic transition rates, and discuss them in comparison with experimental data.   

Isocranking calculation with proton-neutron mixed energy density functionals

We present results of calculations based on the Skyrme energy density functional that include arbitrary mixing between protons and neutrons. In this framework, single-particle states are superpositions of proton and neutron components and the energy density functional is fully invariant with respect to three-dimensional rotations in the isospin space. In this proton-neutron (p-n) mixing calculation, the isospin of the system is controlled by means of the isocranking method, which carries the standard tilted-axis cranking approach over to isospin space. By adjusting the isocranking frequency, we can control the size and direction of isospin of the system. We show selected numerical results of the p-n mixed Hartree-Fock calculations including those for the T$=$4 isobaric analogue states in A$=$40-56 nuclei and demonstrate that this approach is capable of describing quantitatively the isobaric analogue excited states. We also present the results of a systematic calculation for T $=$ 1 triplets in the A $=$ 10-66 region, and discuss a possible extension of the p-n mixed energy density functionals including the isospin breaking interaction.   

8Be+alpha rotational states and alpha condensate in 12C

The Hoyle state, the second 0+ state in 12C, is known to have the nature of alpha condensation, in which the 3alpha particles occupy an identical S-orbit, with a dilute gaslike structure of weakly interacting alpha particles. The second 2+ state in 12C was observed at a few MeV above the Hoyle state in experiments. It is also reported that the new 4+ state is observed at around 13.3 MeV. The candidates of the third and fourth 0+ states, which are close to the second 2+ state, are also reported recently. While all these states are expected to have well developed 3-alpha-cluster structure, a band nature of these states are completely unknown. 8Be+alpha rotational band is one interpretation and the alpha condensate nature might be deeply related to the band nature. Some authors argure that some of these states form a rotational band with triangular shape. Aiming at solving this puzzling situation, we employ an extended version of the so-called Tohsaki-Horiuchi-Schuck-Ropke (THSR) wave function, which inherently has structures of 2-alpha +alpha clusters as well as of the gaslike 3alpha clusters. With this model wave function, we discuss the band nature and mutual relation between these excited states, focusing on the strength of E2 transition.   

Two center molecular structures in light nuclear systems

In light neutron-excess systems, many kinds of molecular structures are discussed from the viewpoint of the clustering phenomena. In particular, much attention has been concentrated on Be isotopes, and their low-lying states are nicely described by the molecular orbit (MO) model based on the $^{\mathrm{8}}$Be $=\alpha +\alpha $ core. The neutron MO generated around $^{\mathrm{8}}$Be core, such as $\pi^{\mathrm{-}}$ and $\sigma ^{\mathrm{+\thinspace }}$associated with the covalent orbit of atomic molecules, have been shown to give a good description for the low-lying states of these isotopes. In addition, many resonant states, decaying into the fragments of $^{\mathrm{6,8}}$He, have been observed in recent experiments of Be isotopes. Furthermore, the experimental data of the highly excited states have been accumulated for other systems, $^{\mathrm{18}}$O, for instance. In this report, we will discuss the molecular structures, which are generated by various two center cores, such as $^{\mathrm{10,12}}$Be ($=\alpha +\alpha +$2,4N), $^{\mathrm{18}}$O ($=\alpha +^{\mathrm{12}}$C$+$2N) and $^{\mathrm{10,12}}$C ($=\alpha +\alpha +$2,4P). We employ the generalized two-center cluster model, which has been successful in the studies of $^{\mathrm{10,12}}$Be from bound region to continuum region. In particular, we focus on the variation of the molecular structure, which are generated by changing a combination of the cores and excess nucleons. The enhancement factors in reactions, which can identify the intrinsic structures, will also be discussed.   

$\alpha + ^{15}$O cluster structures in $^{19}$Ne and the $\alpha$ resonant scattering

Cluster structures are well known to appear in the excited states of light nuclear systems. A typical example is the $\alpha + ^{16}$O cluster structures in $^{20}$Ne, and the $\alpha + ^{15}$N structures are also deeply analyzed in $^{19}$F, which is one proton deficient system of $^{20}$Ne. However, the $\alpha + ^{15}$O structure, corresponding to the neutron deficient system of $^{20}$Ne, still remains unclear. In the present study, we investigate the $\alpha + ^{15}$O structure in $^{19}$Ne by employing a simple potential model. We assume the Wood-Saxon potential for the nuclear potential of $\alpha + ^{15}$O, and its parameter set is fixed by solving the $\alpha + ^{15}$N elastic scattering. From the nuclear potential determined from the $\alpha + ^{15}$N scattering problem, we calculate the energy levels in the $^{19}$Ne $= \alpha + ^{15}$O system by adding the Coulomb interaction to the $\alpha + ^{15}$N system. The absorbing boundary condition is imposed on the unbound states in $\alpha + ^{15}$O, and the resonant levels in $^{19}$Ne are identified. We have also calculated the excitation function of the resonant $\alpha + ^{15}$O elastic scattering under the same condition as the recent experiments. In the present report, we will show our prediction of the $\alpha + ^{15}$O rotational bands and the cross sections in the resonant $\alpha $ scattering. Moreover, we will also report the application of the microscopic cluster model to the $^{19}$Ne $= \alpha + ^{15}$O system.   

Alpha-cluster excited states in $^{32}$S

Excited states having core$+$alpha cluster structure called the alpha-cluster excited state are known to exist in such nuclei as $^{16}$O and $^{20}$Ne. Meanwhile, the existence of alpha-cluster excited states in the middle of sd-shell nuclei is an open problem. Recently, the alpha-cluster excited state in $^{32}$S is suggested by experiments. In order to understand the dynamics of the core-alpha relative motion, we focus on the structure change of the core nuclei and the breaking of the alpha-cluster. In the present work, we construct $^{28}$Si$+$alpha model which has the structure change of the $^{28}$Si core and the alpha-cluster breaking. Using the present model, we calculate the energy expectation value of $^{28}$Si$+$alpha system. We found that the structure change of the core nuclei is energetically rather important while the alpha-cluster breaking is not significant when the alpha-cluster exists at the surface of the $^{28}$Si core. We calculate the ground and excited states with the generator coordinate method. As a result, we suggest the existence of alpha-cluster excited states in $^{32}$S.   

$^{16}$O + $^{16}$O molecular structures of superdeformed bands in S isotopes

Structures of excited states in $^{33\mbox{-}36}$S have been investigated by using the antisymmetrized molecular dynamics and the generator coordinate method (GCM). GCM basis wave functions are calculated by energy variation with a constraint on a quadrupole deformation parameter $\beta$. By performing GCM after parity and angular momentum projections, coexistence of positive- and negative-parity superdeformed (SD) bands are obtained, as well as low-lying states. The SD bands have structures of $^{16}$O + $^{16}$O + valence neutrons in molecular orbitals around two $^{16}$O cores in a cluster picture.   

Linear-chain structure of alpha clusters in Carbon isotopes

The linear-chain structure of $^{\mathrm{12}}$C in which three alpha particles are linearly aligned has long been interested and investigated since its proposal by Morinaga, but nowadays, its existence is doubt, because its instability was shown by fill-microscopic nuclear models. However, the possible existence of linear-chains in neutron-rich carbon isotopes assisted by the valence neutrons was recently suggested based on the cluster model. Therefore, it is of importance and interest to examine their stability and investigate the stabilization mechanism based on full-microscopic model. In this presentation, we will discuss the alpha cluster states of carbon isotopes including the linear-chains based on the antisymmetrized molecular dynamics (AMD) model. For, example, we will demonstrate two different types of the alpha cluster states, that are, triangular and linear-chain configurations. Four valence neutrons occupy the molecular-orbit surrounding the cluster cores, in particular, their orbits of the linear-chain structure are $\pi $-orbit and $\sigma $-orbit as suggested by the cluster calculation. In addition, we predict the excitation energies of two structures. We will show that the linear-chain states have very large moment of inertia and they appear near the $^{\mathrm{6}}$He$+^{\mathrm{10}}$Be threshold energy.