Masatoshi Yamamura

A Microscopic Theory of Collective and Independent-Particle Motions

A microscopic theory of collective and independent·particle motion in many· fermion system is developed in the framework of the classical theory. The basic idea is an extention of the conventional time-dependent Hartree-Fock method with the use of fermion coherent state representation. Equation to determine collective path and constraints to govern the collective and the independent-particle variables are given. Hamiltonian and other physical quantities given with the original fermion variables are rewritten to the forms expressed in terms of the collective and the independent-particle variables.

On the New Kinematical Constraints of the Pair Operators in the Algebraic Approach to the Theory of Collective Motion

New kinematical constraints of the pair operators in the algebraic approach to the theory of collective motion are proposed. These relations are the. natural extension, to the operator forms, of the well-known constraints of the generalized density inatrix in the Hartree-Bogoliubov theory. On the basis of the new constraints; a microscopic theory of rotational motion given by Belyaev and Zelevinsky is reconstructed. § I. Introduction In 1968 Marumori, Miyanishi, Nishiyama and the present author proposed a new microscopic theory, which is called the algebraic approach, with the aim of achieving a unified understanding of the vibrational and rotational motions in even nuclei. 1> The basic standpoint of this approach is the following: . For getting the composite nature of the pair operators composed of fermion operators, the dynamics of the system under consideration can be solved with the use of certain dynamical and kinematical constraints of the pair operators. More concretely, the procedure is the following: (i) We introduce a sub-space consisting of the eigenstates of the Hamiltonian which are strongly connected with one another through the specific pair operators. (ii) A set of equations can. be obtained by making a spectral decomposition within the sub-space to the above-mentioned constraints. The unknown quantities of the equations are the matrix elements of the pair operators and the excitation energies in the sub-space. (iii) Thus, solving these equations, we can understand the structure of the states belonging to the sub-space. In this approach, the equations of motion for pair operators are adopted as dynamical constraints. The kinematical constraints consist of the commutation relations among the pair operators and a certain relation that the special quadratic combination of pair operatars is reduced to the total nucleon number. In this framework, vibrational motion could be well described; results equivalent to those of the quasi-particle RP A could be obtained without using the quasi-particle representation. The direct development of this theoretical framework has been performed by Klein et aJ.2> They have investigated various types of collective motions in the above-mentioned framework supplementing the variational concept, which they call the algebraic-variational approach to the theory

A POSSIBLE DESCRIPTION OF ''ROTATION-LIKE EXCITATIONS'' IN Te, Xe, AND Ba ISOTOPES.

Abstract A possible description of rotation-like excitation in “spherical” nuclei is proposed.

On the Ground-State Correlations of Vibrating Closed-Shell Nucleus Due to the Residual Interaction

The strength of ground-state correlations calculated from the RPA with quasi-boson approximation is known to differ by a factor of two from that calculated in various other methods. This contradiction is investigated in detail in the case of closed-shell nucleus with any single multi-pole interaction. It is proved that the ground-state correlations calculated by the RPA with the quasi-boson approximation are correct if only collective states are included, as suggested by Rowe, in the case of negligible exchange matrix elements of the interaction.

A Description of the Rotator as an Example of Hamiltonian with Coordinate-Dependent Mass Semi-Classical Theory

A description of the rotator is given as an example of large amplitude oscillation. The basic idea is a quasi-harmonic approximation proposed by the present author. Classical solution is quantized in the framework of the old quantum theory. The results are qualitatively consistent with the exact ones in the region from the small to the large amplitude.

A Note on Microscopic Description of Rotational Motion

The theoretical framework of the method developed by Gross and one of the preaent authors (M. Y.) for the description of rotational motion is shown to be completely equivalent to that of Bohrs rotational model for the case of the ground-state rotational band of deformed even nuclei. For simplicity, we restrict ourselves to the case of a single-j shell system of even identical particles with a quadrupole interaction. (auth)

Two-Nucleon Transfer Amplitudes in the Ground-State Rotational Bands of Even Nuclei

It has been hoped in the the study of collective motions to make a bridge between quadrupole vibration and rotation on the basis of pairing plus quadrupole forces. Compared with one of the feet of the bridge (pairing force only), the foundation of the other foot (quadrupole force only) is not so firm. This is one of the reasons why the construction of the bridge has been unsuccessful. With the intention of filling this gap, the present author and others have successfully related the electromagnetic properties (induced by the quadrupole force) to rotation (referred to as (I)) .1l However, certain kinds of pairing modes are expected to become important in the intermediate regions. Then, as an approach to this problem from the side of quadrupole force, it is also inevitable to investigate two-nucleon transfer in the case of quadrupole force only even if they are not expected to enhance from the character of the force. This is the motivation of this work. Hereafter we will use the basic idea and results of (I) . For simplicity, we consider the system of identical particles in the single-j orbit with a quadrupole force. The Hamiltonian is given by

A Consistent Microscopic Description of Rotational Motion in Even-Even Deformed Nuclei

The idea of using sum rules expressing different single-particle transition operators in terms of higher powers of other operators, recently devised by D. H. E. Gross and the present author, is applied to the description of nuclear rotational motion in a proton-neutron system. For simplicity, we restrict ourselves to the single jp-and jn-shell model with a quadrupole interaction. Moment of inertia, quadrupole moments; transition probabilities and collective g-factor show excellent agreement with those given by the cranking model.

A Quantal Theory of Pairing Rotation, Pairing Vibrations and Independent-Particle Motions

A microscopic theory is proposed to describe not only the pairing rotation, the pairing vibrations and the independent· particle motions, but also their mutual couplings in a consistent manner. With the aid of a BCS·type wave packet and a quasi-particle coherent state, the quantal system is translated into a corresponding classical one. First, we develop a canonical form in a classical image. This classical system obeys certain constraints, by which the double counting in the degrees of freedom is avoided. Then, the quantization is performed with the use of the Dirac theory of a canonical system with constraints. The original fermion operators themselves are expressed in terms of three types of degrees of freedom, which correspond to the pairing rotation, the pairing vibrations and the independent-quasi-particle motions, respectively.

A Microscopic Theory of Rotational Motion in Deformed Odd-Mass Nucleus An Additional Term to the Cranking Moment of Inertia

Nuclear rotational motion has been regarded as one of the most mportant problems in the theory of nuclear collective excitations. One of the reasons is that a consistent description of the rotation is of fundamental significance in quantum theory of many-body system. In addition to the above-mentioned reason, we can find the importance in the recent experimental studies of medium and heavy nuclei. Through the experimental information, we have already known that there exist many nuclei which show, more or less, the rotation-like excitations. Therefore, it is an important task to develop a powerful theory for analysing the structure of such nuclei. A conventional description of the rotation is to take into account the change of the self-consistent Hartree-Bogoliubov field induced by an external field iuJx. By applying this idea to the case of even-mass nucleus, we can obtain a set of inhomogeneous linear equations, the homogeneous parts of which are very similar to the equations for conditions of the stability of the Hartree-Bogoliubov field.n The interaction parts contained in these equations generally give rise to additional term to the standard cranking moment of inertia. However, in the case of the quadrupole force, such a term does not appear. Therefore, for the sake of investigating the deviation from the simple cranking formula, the pairing type or T-odd particle-hole type interaction*) has been inevitably introduced. The additional