Masahiko Fuyuki

Property of Many-Phonon Norm Matrix

It is shown that the many-phonon states built up from collective quasiparticle pairs satisfy the orthogonality condition in a good approximation, if the approximation scheme recently proposed by Holzwarth, Janssen and Jolos is applied to the intrinsic space in the quasiparticle state space, which is orthogonal to the pairing rotational and vibrational excixad tations. Recently, Holzwarth, Janssen and Jolos 1l have proposed a new approximation method to evaluate anharmonicity effects associated with low-frequency quadrupole modes in transitional nuclei_ The essence of this method consists in truncating the quasiparticle state space by building up many-phonon states from collective two-quasiparticle operators with J = 2+ and evaluating the fermion matrix elements within this collective phonon space. According to a more rigorous formulation given by Iwasaki, Sakata and Takada,) this method is regarded as the first-order approximation in the expansion with respect to the order of commutators involving phonon operators_ In principle, the norm matrix of many-phonon states have to be diagonalized in order to exactly take account of the Pauli principle. However, if the many-phonon states satisfy the orthogonality property in a good approximation, our task is reduced to calculating only normalization constants and, accordingly, physical interpretation of the resulting expressions may be greatly simplified_ The orthogonality implies that we can classify the many-phonon states defined in fermion space in terms of the quantum numbers which characterize the five-dimensional harmonic oscillators (i.e., the quadrupole boson states). In this paper, we show that this property holds in a good approximation, if the collective phonon sPace is defined in the intrinsic sPace of the quasiparticle state space_ The concept of intrinsic space has been introduced in Ref. 3), which is defined to be orthogonal to the pairing degrees of freedom (pairing rotation and pairing vibration). In § 2, the method of Holzwarth et al. D is applied to the intrinsic space so that the collective phonon space never involves the spurious components associated with the nucleon-number non-conservation in the quasiparticle representation. The condition under which the many-phonon states satisfy the orthogonality property is given in

Dynamical Interplay of Pairing and Quadrupole Modes in Transitional Nuclei. III

Using the single j-shell model with the pairing plus quadrupole force, we show that l) the transition from vibrational to rotational excitation structure can be reproduced within the collective model space built up from the J =0- and J =2- coupled nucleon pairs, 2) change of the monopole pair field due to many-quasiparticle excitations does accelerate the transition; this fact indicates the importance of taking explicit account of the couxad pling between pairing rotation and many-phonon excitations in transitional nuclei.

Gamow-Teller Beta Transition between Collective and Single-Particle States in Spherical Odd-Mass Nuclei

Gamow-Teller beta transitions between the anomalous coupling state with spin 7 j2+ in odd-proton nuclei with filling lg!l(20rbit and the 2d5/2 single-particle state.in ~dd-neutron nuclei are calculated by t?e method of many-quasi-particle newTamm-Dancoffspace. The effect of the proton-neutron cotrelation with spin I+ is taken into account on an equal footing as the quadrupole correlation. Calculated results are compared to the experimental data.