Spherical Odd-mass Nuclei Research Articles

GUE-type energy level statistics for spherical odd-mass nuclei

The spectral statistics of spherical nuclei are steadily considered with emphasis on nearest-neighbor spacing statistics. Sequences are constructed by using all the available empirical data for the considered nuclei in different mass regions and analyzed via the generalized Brody distribution and the maximum likelihood estimation technique. Our results indicate an approach to chaotic dynamics for the nuclei considered in this work. Also, spherical odd-mass nuclei in the 50A ≤ 100 mass region exhibit a slight deviation to the GUE spectral statistics rather than to the GOE.

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

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

Theory of Collective Excitations in Spherical Odd-Mass Nuclei. IV: Formulation in the General Many-j-Shell Model

Theory of Collective Excitations in Spherical Odd-Mass Nuclei. IV: Formulation in the General Many-j-Shell Model

Theory of Collective Excitations in Spherical Odd-Mass Nuclei. III: Electromagnetic Properties of the Anomalous Coupling States

Various electromagnetic properties of the anomalous coupling states with spin (j-1) are shown to be well explained by the new viewpoint of the dressed n-quasi-particle modes proposed in a previous paper. In this point of view, the anomalous coupling collective states with spin (j -1) are considered as the dressed three-quasi-particle modes, which are regarded as a kind of elementary excitation modes in odd-mass nuclei. The effects of couplings between dressed three-quasi-particle modes and one-quasi-particle mode~ are also discussed in this connection, including those with spin j, (j-1) and (j-2).

Theory of Collective Excitations in Spherical Odd-Mass Nuclei

Theory of Collective Excitations in Spherical Odd-Mass Nuclei

Projected spectra of heavy nearly spherical odd- A nuclei

The energy spectra of heavy odd- A nuclei are investigated, using the angular momentum states projected from a BCS internal wave function with small value of deformation parameter. In this way the vibrational motion of spherical odd-mass nuclei can be studied in the frame-work of microscopic model. The results presented exhibit some similarity to the phenomeno-logical weak-coupling model of de-Shalit.

Theory of Collective Excitations in Spherical Odd-Mass Nuclei. II

A new point of view on the structure of the anomalous coupling states is proposed. In this point of view, the main component of the anomalous coupling states with spin I = (j-1) is considered to be the dressed three-quasi-particle mode, which has been developed in a previous paper, part I, as a new collective mode in spherical odd-mass nuclei. The excitation-energy systematics of the anomalous coupling states is theoretically made with the use of the pairing-plus-quadrupole force. From the numerical results, it is concluded that the excited anomalous coupling states with spin I = (j-1) can be recognized very well as the dressed three-quasi-particle states. The role of the three-quasi-particle correlation in characterizing the anomalous coupling states is investigated, and the importance of the three-quasi-particle correlation in the collective excitations in odd-mass nuclei is demonstrated.

Theory of Collective Excitations in Spherical Odd-Mass Nuclei. I

A new systematic theory of describing the collective excitations in spherical odd-mass nuclei is developed. The theory can be regarded as a direct extension of the conventional quasi-particle-new-Tamm-Dancoff method (i.e. the quasi-particle-random phase approximation) for spherical even-mass nuclei into the case of spherical odd-mass nuclei. order to con­ struct properly the theory within the framework of the quasi-particle-new-Tamm-Dancoff method, it is shown to be decisive to introduce a new concept which precisely specifies the dressed three-quasi-particle modes. The new concept is recognized in connection with the space which has been introduced through the quasi-spin formalism for the pairing correlations. It is not the purpose of this paper, part I, to go into a clear-cut formulation of the theory and into detailed quantitative calculations, but rather to put an emphasis on the explanation of basic ideas. § I. Introduction Recent accumulation of the experimental data illuminating the structure of low-lying collective excited states in spherical odd-mass nuclei has stimulated the investigation of problems on particle-vibration coupling. An important effect of particle-vibration which has been neglected for a long time, has been emphasized by Bohr and Mottelson 1 ) in the Tokyo Conference in 1967: In the phenomenological coupling model, the lowest-order-perturbation effects which contribute to energies of the excited states composed of the odd quasi-particle and the one-phonon, are shown in Figs. lA and lB. The diagrams of type lA are nothing but the conventional ones which have so far been treated as phonon-quasi-particle coupling, while the diagrams of type lB have usually been neglected so far. The physical effect underlying the diagrams lB is that the phonon disassociates into a pair of quasi­ particle, one of which reassociates with the odd-quasi-particle while the remain­ ing quasi-particle is now the odd-quasi-particle. Thus this effect is essentially based on the Pauli principle between the quasi-particles composing the phonon and the extra quasi-particle outside the core. The extreme importance of the diagrams of type lB can be recognized as follows. The diagrams of type lA consist of the coupling with the factor (u!'u 2 - v 1v 2) which can be quite small,

N-p Surface delta interaction and coupled BCS equations in spherical odd-mass nuclei

Detailed numerical work on pairing correlations in spherical odd-mass (s.o.m.) nuclei has been done recently (~). While one usually takes into account the pairing of identical nucleons as exactly as possible, effects of n-p pairing are only treated in a rough manner, if at all. As was mentioned in (2.a) no convincing theoretical and experimental agreement justifies the neglect of n-p interactions. Especially in the regions

On the wave functions of spherical odd-mass nuclei

A procedure presented in a previous paper has been generalized in order to describe collective properties of odd-mass nuclei. The problem has been considered first in the general case of fermions interacting by realistic two-body forces. The present classification of low lying states of odd nuclei has been confirmed. The lowest states can be separated in two groups: one-quasi-particle and phonon-particle states. From the general case a schematic model grounded on (pairing+P(2)) forces has been derived and applied to205Pb, in order to study the general features of wave functions.

Odd-even staggering in the isotope shift of the nuclear radius

It is shown that spherical odd-mass nuclei are expected to have smaller mean square deformations than the neighboring even ones by an amount sufficient to explain the odd-even staggering of the isotope shift.

Collective excitations in spherical odd-mass nuclei

The random-phase approximation is modified to study the vibrational motion of spherical odd-mass nuclei. It is shown that there is no need to introduce empirical parameters to describe the interaction of the odd particle and the core, but that this interaction may be related naturally to the same Hamiltonian which describes the collective motion of even nuclei. The relationship with recent work of Kisslinger and Sorensen is also studied; though formally distinct, it is seen that the methods should in practice yield comparable results. The results of de-Shalit's weak-coupling model are seen to be included in the present formulation, which should be valid, however, for a wider range of interaction strengths. It is also shown how the method can be generalized to take into account higher-order corrections.