Boson Expansion Research Articles

Measurements of static electric quadrupole moments of the 2 +1, 2 +2, 4 +1 and 6 +1 states of 196Pt

Coulomb excitation of 196Pt with 4He, 7Li, 12C aand 58Ni projectiles and the particle-singles spectroscopy and particle-gamma coincidence techniques have been used to measure the static electric quadrupole moments of the 2 + 1, 2 + 2, 4 + 1 and 6 + 1 states as well as other E2 and E4 matrix elements of 196Pt. The results are compared with the predictions of the boson expansion theory, the general collective model, the O(6) and U(5) limits of the interacting boson model and the pairing-plus-quadrupole model; best agreement is obtained with the boson expansion theory.

On a Boson Expansion Method with Two-Body Correlations

Dynamical Nuclear Field Theory which was modified in the previous paper so as to bring complete equivalence with Boson Expansion Theory (BET) is now extended to derive a BET under the influence of two-body correlations. For this purpose, the driving Hamiltonian of the vibrating Hartree field approximation is supplemented by the residual two-body interaction. Effective forms of Tamm-Dancoff fermion-pair and scattering operators are expanded perturbatively. Effects of three kinds of bubble diagrams can be incorporated by the renormalization procedure, but the contributions from unlinked diagrams remain uncancelled. Comparisons with Nuclear Field Theory are discussed.

On a Boson Expansion Method with Two-Body Correlations

Dynamical Nuclear Field Theory which was modified in the previous paper so as to bring complete equivalence with Boson Expansion Theory (BET) is now extended to derive a BET under the influence of two-body correlations. For this purpose, the driving Hamiltonian of the vibrating Hartree field approximation is supplemented by the residual two-body interaction. Effective forms of Tamm-Dancoff fermion-pair and scattering operators are expanded perturbatively. Effects of three kinds of bubble diagrams can be incorporated by the renormalization procedure, but the contributions from unlinked diagrams remain uncancelled. Comparisons with Nuclear Field Theory are discussed.

On the Canonical Equivalence of Classical Boson Expansions for Mixed States

The theoretical study of nuclear phenomena observed in highly excited states has been one of the interesting problems in nuclear theory. In response to the situation mentioned above, a thermal boson expansion was developed, as a basis for the derivation and possible generalization of the thermal random phase approximation.),2) More recently, a classical microscopic theory of mixed states has been proposed. ),4) The basic concept of this theory can be expressed by interweaving the time-dependent Hartree-Fock theoryS) with the formalism of thermo field dynamics) in Dirac's canonical theory for a constrained system.7) Although both theories start from different ideas, the final aims are similar: to express the ensemble averages of density type fermion pairs in terms of canonical variables. Formally, the averages can be written as

On the Canonical Equivalence of Classical Boson Expansions for Mixed States

On the Canonical Equivalence of Classical Boson Expansions for Mixed States

Collective motion of nuclear mixed states: Thermal boson expansions.

A classical microscopic theory of mixed states has recently been formulated in order to deal with the theoretical description of nuclear phenomena observed in highly excited states. In this theory, which is here briefly reviewed, the degrees of freedom of real fermions are doubled by fictitious fermions, in the context of the formalism of thermofield dynamics. The requirement of static stability of the thermal state of equilibrium plays, in the theory, a relevant role. The possibility of constraining the dynamics of the fictitious degrees of freedom, in such a way as to eliminate spurious thermal excitations, is discussed. The concept of canonical collective variables for mixed states is analyzed. Boson expansions appropriate to describe collective excitations of hot quantal systems are introduced and their properties investigated. It is shown that thermal boson expansions based on the formalism of thermofield dynamics are free from formal inconsistencies which may be present in boson expansions derived by an {ital ad} {ital hoc} quantization of conventional thermal mean field theories. The formalism is applied to the Lipkin model, and the correlation energy of a hot system is discussed.

Generalized Holstein-Primakoff images of fermion operators

The generalized Holstein-Primakoff (GHP) boson expansion is used to derive the images of single-fermion creation and annihilation operators in terms of collective bosons and ideal fermions for the case of well-deformed nuclei. The boson-fermion image of the quadrupole operator is then obtained, and is found to include a pure boson term, a pure fermion term, a boson-fermion exchange term and a further exchange term that mixes bosons with two quasifermions. We apply this method to a single- j model and show that in the deformed limit, the GHP expansion for the quadrupole operator gives a more appropriate description of quasiparticle energy systematics than does the corresponding operator obtained from a generalized seniority mapping. Finally, we consider the term that mixes bosons and quasifermion pairs within the context of the single- j model and show that it has precisely the form proposed phenomenologically in an extension of the IBM to high-spin states.

A boson representation of the nuclear charge and current densities

We derive a formally exact normal-ordered boson expansion in terms of harmonic oscillator bosons, for the nuclear charge and current densities. This expansion separates the dependence on the momentum transfer from the dependence on the nuclear structure, and is exact in the case of the harmonic oscillator shell-model space. Our boson expansion provides a mechanism for expressing the multipole operators in terms of SU(3) tensors. Thus, we perform an SU(3) tensor analysis of the multipole operators, since this is of major importance for shell-model calculations in an SU(3) basis.

Iterative boson expansions and mean-field approximations for boson systems

Iterative boson expansion techniques are suggested as a systematic procedure to incorporate correlations into a mean-field description of both the ground state and excited bands of many-boson systems. The method is illustrated by applying it to an exactly solvable system of interacting bosons which exhibits a phase transition from a deformed mean field to a boson superfluid state.

Electromagnetic decay of two-phonon states

Abstract We study the electromagnetic decay of two-photon states corresponding to the multi-excitation of giant resonances. The calculations are performed within a boson expansion approach and the elementary modes are constructed in RPA. The rates for direct transition of two-phonon states to the ground states turn out to be not negligibly smaller than those from the (single) giant resonances. The former transitions are accompanied by a γ-ray whose energy is equal to the sum of the two-phonon energies. Thus the detection of such high energy γ-rays could provide a signature of the excitation of two-phonon states.

Unique boson expansion for spin systems

A boson expansion for generators of the SU(2) group has been constructed for arbitrary dimension. It is unique provided that certain physically motivated restrictions are imposed. An approximation strategy alternatice to the large S expansion is suggested. It allows one to incorporate the kinematic interaction more correctly than in the case of the Holstein-Primakoff expansion.

The σ→ππ decay width in the linear sigma model

>Using a boson expansion that includes appropriate anharmonic terms, the decay width of a scalar-isoscalar meson into two pseudoscalar-isovector meson is calculated. A constrained RPA approach, leading to a discretization of the modes in the quark-antiquark continuum, is incorporated in the model. The technique is applied to the bound state solution as well as to the discretized solution.

The 2νββ decay rate within a boson expansion formalism

A microscopic hamiltonian consisting of a one-body term and a realistic two-body interaction, corresponding to the G-matrix of the Bonn potential, is treated within the QRPA formalism including both particle-hole (ph) and particle-particle (pp) channels. The β ± transition operators are expanded up to the first order in terms of the dipole and quadrupole RPA bosons. The influence of the higher RPA terms on the ββ matrix elements M GT (00) and M GT (02), associated with the transitions 0 i + → 0 i + → 0 i + → 2 f + respectively, is studied as a function of the strength of the dipole pp interactions g pp (1). The HRPA terms shift the zero ( g pp (1) = 1) of the RPA function M GT (00) to the region where QRPA collapses. The M GT (02) value is an increasing function of g pp (1).

Relation between spin-coherent states and boson-coherent states in the theory of magnetism.

It is shown that the application of both the spin-coherent states and the Holstein-Primakoff representation with boson-coherent states leads to the same classical limit for the spin-operator average values, if the proper procedure for normal ordering is applied. A general expression for the boson expansion is derived, and the first quantum correction is obtained. Consequences of the study of nonlinear excitations in magnetic systems are presented.

Boson-Fermion Expansion of Correlated Pair Modes

We propose a new method that transcribs the fermion system to the boson-fermion system by introducing a unitary operator defined in the whole boson-fermion space. We obtain the boson-fermion expansion of the fermion pair operators such that only the collective pair modes are transformed into boson operators while the non-collective modes are unchanged in the lowest order approximation. The odd-A system is treated in the same formalism as the even-even nuclear system. We briefly discuss the relation between our method and the conventional boson expansion theory

Boson-Fermion Expansion of Correlated Pair Modes

We propose a new method that transcribes the fermion system to the boson-fermion system by introducing a unitary operator defined in the whole boson-fermion space. We obtain the boson-fermion expansion of the fermion pair operators such that only the collective pair modes are transformed into boson operators while the non-collective modes are unchanged in the lowest order approximation. The odd- A system is treated in the same formalism as the even-even nuclear system. We briefly discuss the relation between our method and the conventional boson expansion theory.

Microscopic analysis of nuclear collective motions in terms of the boson expansion theory: (II). Numerical calculations

Anharmonicities in nuclear quadrupole collective motions are studied by applying the self-consistent effective interactions derived in our previous work. Numerical calculations are made in terms of the boson expansion technique of Kishimoto-Tamura with several new refinements developed in the first paper of this series. It is shown that the three-body interaction is necessary to maintain the integrity of the collective modes in the presence of coupling with quasi-particle modes. General agreements with experimental data on nuclei in various mass region have confirmed that our theory is capable of describing various types of anharmonicities characteristic to the nuclei in question.

Exact Relation between Dynamical Nuclear Field Theory and Boson Expansion Theory in a Tamm-Dancoff-Boson System

In the treatment of the vibrational mode of even-even nuclei, Dynamical Nuclear Field Theory (DNFT) in the Tamm-Dancoff (TD) representation exhibited the defect to include unlinked cluster terms. We aim to remove this deficiency. In lowest order of the repetitive actions of the particle-boson couplings, we generate |0)B⊗|nTD fermion pairs> states out of |0>F⊗|nbosons) states. We impose the lowest order self-consistency. The modified DNFT gives the normal-ordered linked-cluster expansion, in complete equivalence with the boson expansion theory (BET), of Kishimoto, Tamura and Sakamoto.

Exact Relation between Dynamical Nuclear Field Theory and Boson Expansion Theory in a Tamm-Dancoff-Boson System

In the treatment of the vibrational mode of even-even nuclei, Dynamical Nuclear Field Theory (DNFT) in the Tamm-Dancoff (TD) representation exhibited the defect to include unlinked cluster terms. We aim to remove this deficiency. In lowest order of the repetitive actions of the particle-boson couplings, we generate |0) B ⊗|n TD fermion pairs> states out of |0> F ⊗|n bosons) states. We impose the lowest order self-consistency. The modified DNFT gives the normal-ordered linked-cluster expansion, in complete equivalence with the boson expansion theory (BET), of Kishimoto, Tamura and Sakamoto

Pseudo-symplectic model for strongly deformed heavy nuclei

An extension of the strong-coupled pseudo SU(3) model, which is a scheme that has found application in the study of superdeformed bands in heavy nuclei, is introduced. The theory includes multiple inter-shell excitations of the monopole and quadrupole type. It is an extension to heavy ( A ≳ 100) nuclei of the microscopic collective model which applies for light ( A ≲ 28) systems. Because the scheme has a Sp(3, R) ⊃ SU(3) group theoretical structure, it is called the pseudosymplectic model. A boson expansion for the model hamiltonian is given and results for an application of the theory to 238U presented.