Kenjiro Takada

Dyson-type boson mapping and SU(6) boson model

Abstract The Dyson-type boson mapping is applied to realistic cases to show that it is a very promising method for describing nuclear collective motion. Eigenvectors are obtained in the corresponding hermitian boson theory from the results of right- and left-hand-side eigenvalue problems in the Dyson boson theory. The numerical results are compared with those of the SU(6) boson model and exact quasiparticle shell-model calculations within the multi-phonon subspace.

Application of Dyson boson mapping to the analysis of mode-mode coupling in Ge and Se isotopes

Abstract The Dyson boson mapping is applied to the analysis of the coupling between the quadrupole phonon mode and the pairing-vibrational modes. The original fermion (quasiparticle) space consisting of a product of multi-quadrupole-phonon space and multi-pairing-vibration space is transformed into a boson space by the Dyson boson mapping. In this boson space, numerical analyses are carried out for the cases of the Ge and Se isotopes. The results show that the so-called “mysterious” 0 + states in the Ge and Se isotopes are reasonably explained and that the Dyson boson mapping is quite applicable to analyses of the couplings between various kinds of collective modes.

Application of the dyson boson mapping to the analysis of the phase transition at N = 88–90

Abstract The Dyson boson mapping theory is applied to the analysis of the phase transition from vibrational to rotational spectra in the Sm isotopes. The original quasiparticle space consisting of multi-quadrupole collective-phonon states on the spherical shell-model bases is transformed into a boson space by the Dyson mapping. In this boson space, numerical analysis is carried out for 146–154 Sm. In addition, the boson space is extended to contain non-collective phonon degrees of freedom and in this extended space the coupling effect between collective and non-collective phonons is precisely estimated. The numerical results show that the contribution from the noncollective phonon degrees of freedom cannot be neglected in the transitional region.

E0 transition and coupling between quadrupole and pairing-vibrational modes

Abstract Using a theory of mode-mode coupling between the two-phonon 0 + mode and the pairing-vibrational mode, we have extensively investigated the first excited 0 + (0 2 2 ) states in spherical and transitional nuclei. The results tell us that the 0 2 + states in a wide range of nuclei are strongly mixed states of both the modes. By making use of these results, the matrix elements for the E0 transitions from the 0 2 + states to the ground states are calculated for the Zn, Ge, Se, Kr, Sr, Zr, Mo, Ru, Pd, Cd and Sn isotopes. For some of the Cd and Sn isotopes, the matrix elements between the 0 2 + and 0 2 + states are also obtained. These numerical calculations make a rather good fit to the E0 experiments.

Application of Dyson mapping to odd-mass nuclei

Abstract The Dyson mapping is applied to the analysis of low-lying collective states in odd-mass nuclei. The original fermion (quasiparticle) space is truncated to a collective subspace which consists of products of collective phonons and a single fermion (quasiparticle). This subspace is mapped on an ideal boson-fermion space by the Dyson mapping and a simple but non-hermitian hamiltonian is obtained. The eigenvalue equations for the hamiltonian are numerically solved for the cases of the unique-parity states in the odd-mass Rh isotopes. The results show that the Dyson mapping is quite useful for analyses of phonon-particle coupling in odd-mass nuclei.

Structure of excited states in Se-isotopes

Energy systematics of the anomalously low-lying excited 0+ states and the systematic behaviour of theB(E2: 0+→21+) values in Se-isotopes are investigated by taking the important effect of mutual interplay between dynamical pairing and quadrupole correlations into account.

Alpha-Like Spatial Four-Body Correlations in Light Nuclei Vertically-Truncated-Subspace Shell Model for the Core Plus Four-Particle System

Spatially correlated modes of the extra four particles in the core plus four-particle system are investigated on the basis of the (major-shell-mixing) shell-model picture. New bases of the four-body configurations are introduced to represent both the shell-model character and the a-like-clustering nature of the four particles. The bases define a subspace in which the single-particle shell-model states are vertically truncated with the [ 4] symmetry. The model is applied to the study of the low-lying even-parity levels of 20Ne, reproducing well the levels in the ground band with the use of the residual interaction much weaker than that used in the sd shell model. Spatial correlations and higher-shell-mixing effects in the calculated states are investigated from the various viewpoints.

Microscopic study on the shape phase transition in the sm isotopes: st(I). Effect of ground-state correlation

Abstract The phase transition from vibrational to rotational spectra in the Sm isotopes is analyzed by using two newly-developed types of Dyson boson mapping methods. One is a Dyson boson mapping based on the random-phase-approximation phonon and the other is an application of the first-order Dyson-type self-consistent collective-coordinate method. Both the methods aim at including the ground-state correlation in the Dyson boson mapping theory, and the numerical results on the Sm isotopes show that its effect is rather large in the transitional region but it fails to reproduce the shape transition in the experimental data.

Coupling effect between quadrupole phonon and pairing vibration in odd-mass nuclei

Abstract The dynamical anharmonicity effect due to the coupling between a quadrupole-phonon mode and a pairing-vibrational mode is analyzed by applying the Dyson mapping theory to odd-mass nuclei. The original fermion (quasiparticle) space consisting of a product of multi-quadrupole-phonon states, multi-pairing-vibration states, and single-quasiparticle states is transformed into an ideal boson-fermion space by the Dyson mapping. In this ideal boson-fermion space, numerical analyses are carried out for some odd-mass nuclei, by putting special emphasis on 93 Nb. The results show that the effect of many-phonon states including both of the quadrupole phonon and the pairing vibration is very important and the Dyson mapping theory is quite useful for such analyses.

Non-Unitary Realization of the Selfconsistent Collective-Coordinate Method

Recently we reformulated the selfconsistent collective·coordinate (See) method of Marumori, Maskawa, Sakata and Kuriyama. In this reformulation, biunitary forms of state vectors are used and the resultant representation corresponds to a c-number image of the Dyson-type boson expansion theory. This non-unitary version of the see method is rederived from a general point of view in order to clarify the relation to the original unitary version. Moreover, it is shown that the expansion technique to solve the basic equations is as applicable to this new version as to the unitary one, so that applications to realistic problems are easily done.