Correlated Nucleon Pair Model and Microscopic Basis of Interacting Boson

An earlier work dealing with low-lying collective states in nuclei is revised and improved. Correlated and independent nucleon S and D pairs properly modified so that they behave approximately like bosons are constructed in terms of which a model space for lowlying collective states is defined, and a microscopic basis for IBM is thus set up. All dynamical variables can also be "bosonized", i.e., expressed in terms of these "bosons" but with statedependent coefficients or operators to incorporate their state dependence in model space.     

Proton-neutron sdg boson model and spherical-deformed phase transition

The spherical-deformed phase transition in nuclei is described in terms of the proton-neutron sdg interacting boson model. The sdg hamiltonian is introduced to model the pairing+quadrupole interaction. The phase transition is reproduced in this framework as a function of the boson number in the Sm isotopes, while all parameters in the hamiltonian are kept constant at values reasonable from the shell-model point of view. The sd IBM is derived from this model through the renormalization of g-boson effects.     

Hermitian Boson Expansion Approach of IBM Toward Cross Shell Excitation

By the Holstein-Primakoff boson expansion,an hermitian supplementary term with finite form is introduced into the IBM hamiltonian to describe the cross shell excitations.The method of intrinsic condensate is generalized to treat the intruder states.According to this scheme,the low-lying spectra of the Sn isotopes are calculated.Both the vibrational spectra and the additional rotational spectra are obtained.     

U(5)-SU(3) nuclear shape transition within the interacting boson model applied to dysprosium isotopes

In the framework of the interacting boson model (IBM) with intrinsic coherent state, the shape Hamiltonian from spherical vibrator U(5) to axially symmetric prolate deformed rotator SU(3) are examined. The Hamiltonian used is composed of a single boson energy term and quadrupole term. The potential energy surfaces (PES’ s) corresponding to the U(5)-SU(3) transition are calculated with variation of a scaling and control parameters. The model is applied to ^150–162Dy chain of isotopes. In this chain a change from spherical to well deformed nuclei is observed when moving from the lighter to heavier isotopes. ¹⁵⁶Dy is a good candidate for the critical point symmetry X(5). The parameters of the model are determined by using a computer simulated search program in order to minimize the deviation between our calculated and some selected experimental energy levels, B(E2) transition rates and the two neutron separation energies S_2n. We have also studied the energy ratios and the B(E2) values for the yrast state of the critical nucleus. The nucleon pair transfer intensities between ground-ground and ground-beta states are examined within IBM and boson intrinsic coherent framework.     

The Analytical Wavefunctions of SU(3) Limit in the Interacting Boson Model

A projection method to calculate the physical states from intrinsic states is put forward. Using this projection method, the physical states of the ground state band in the interacting boson model (IBM) SU(3) limit are calculated. The wave functions are expressed in terms of the building blocks of the IBM wave functions.     

The geometric content of the interacting boson model for molecular spectra: A testground for the nuclear IBM

The recently proposed algebraic model for collective spectra of diatomic molecules is analysed in terms of conventional geometrical degrees of freedom. We present a mapping of the algebraic hamiltonian onto an exactly solvable geometrical hamiltonian with the Morse potential. This mapping explains the success of the algebraic model in reproducing the low-lying part of molecular spectra. At the same time the mapping shows that the expression for the dipole transition operators in terms of boson operators differs from the simplest IBM expression and in general must include many-body boson terms. The study also provides an insight into the problem of possible interpretations of the bosons in the nuclear IBM.     

Do we understand IBM parameters?

A microscopic calculation of interacting-boson model (IBM) parameters is performed for Xe isotopes within the framework of the broken-pair model. We employ a shell-model hamiltonian which reproduces the spectra of near-magic and semi-magic nuclei. As a first approximation we adopt the idea of Otsuka, Arima and Iachello, that IBM states represent fermion states built from collective S- and D-pairs — the SD space. We show that at least two effects are needed to explain the empirical values of IBM parameters. Firstly there is a reduction in collectivity of S- and D-pairs in states with several broken pairs, due to the Pauli-blocking effect of the latter. Secondly the shell-model hamiltonian mixes the SD space with other fermion states which are not explicitly represented in the IBM. Among the latter, states with a collective G-pair (J = 4) are the most important, but they contribute less than half of the total renormalization of the parameters. The calculated IBM parameters χ of the E2 transition operators exhibit similar trends to those which occur in the IBM hamiltonian.We explain the IBM Majorana force as a renormalization effect on states with even J; not as a repulsion in states with odd J. The latter emerge as rather pure states which mix little with the non-collective fermion space. This indicates that they may be experimentally observable.With our calculated parameters the IBM spectra and E2 transitions are of comparable quality to those obtained in IBM fits of the data.     

On the boson mapping of fermion collective pairs

We study the problem of the mapping of fermion collective pairs onto particle-particle bosons and of different fermion operators (hamiltonian, one- and two-particle transfer operators) onto corresponding boson ones and we test the consequences of the truncation to lowest orders of these boson operators. We find that, although the lowest-order terms in the expansion of the operators in boson space lead to matrix elements between boson states which display the qualitative behaviour of the corresponding ones between fermion states, higher-order terms are required to get a quantitative agreement when a large number of particles are involved, as a direct consequence of the increased role of the Pauli principle.     

Quasiparticle shell-model calculation within multi-phonon subspace and SU(6) boson model

The hamiltonian with quadrupole interaction is diagonalized within the multi-phonon subspace for the cases of ⁷⁴Se, ¹¹⁴Cd and ¹²⁶Xe. The results are compared with those of the SU(6) boson model based on the Tamm-Dancoff phonon and the applicability of the boson model is discussed. As a by-product, the applicability of the quasiparticle random-phase approximation (QRPA) is investigated. It is shown that the SU(6) boson model is much better than the QRPA. The contribution from non-collective phonon degrees of freedom to the many-phonon high-spin states is also discussed.     

An IBM2 Description of the E(5) Symmetry in 134Ba and 108pd

With the low-lying energy levels, E2 transition branching ratios and absolute transition rates of the 134Ba and 108Pd, are investigated in the neutron-proton interacting boson model (IBM2) which includes the quadrupole quadrupole interaction between like bosons and the E(5) symmetry, it shows that the IBM2 can describe the nuclei at critical point of a phase transition well.     

Superdeformation in the N = Z nucleus 36Ar: experimental, deformed mean field, and spherical shell model descriptions

A superdeformed rotational band has been identified in 36Ar, linked to known low-spin states, and observed to its high-spin termination at Ipi = 16(+). Cranked Nilsson-Strutinsky and spherical shell model calculations assign the band to a configuration in which four pf-shell orbitals are occupied, leading to a low-spin deformation beta(2) approximately 0.45. Two major shells are active for both protons and neutrons, yet the valence space remains small enough to be confronted with the shell model. This band thus provides an ideal case to study the microscopic structure of collective rotational motion.     

Studies of low-lying states of even-even Xe isotopes within the nucleon pair approximation

We study the relevance of nucleon pairs with higher spins, in addition to spin-zero and spin-two pairs (i.e., S D pairs), in low-lying states of even-even Xe nuclei. By including those higher-spin pairs in our configuration, we recalculate energy level schemes, elec trical quadrupole moments, magnetic moments and electric quadrupole transition rates, for low-lying states of even-even 128-142Xe nuclei. The agreement between our calculated results and the experimental data is substantially improved in compari...     

Cranking Calculation in the sdg Interacting Boson Model

A self-consistent cranking calculation of the intrinsic states of the sdg interacting boson model is performed. The formulae of the moment of inertia are given in a general sdg IBM multipole Hamiltonian with one- and two-body terms. In the quadrupole interaction, the intrinsic states, the quadrupole and hexadecapole deformation and the moment of inertia are investigated in the large N limit. Using a simple Hamiltonian, the results of numerical calculations for ¹⁵²,¹⁵⁴Sm and ^154-160 Gd satisfactorily reproduce the experimental data.     

Shell model description of interacting bosons

The interacting boson model, describing collective states of even-even nuclei, is introduced as a drastic truncation of large scale shell model calculations. The shell model hamiltonian can be diagonalized by using a correspondence, or mapping, of the nucleon states in the truncated space into states obtained by coupling proton and neutron s- and d-bosons. The equivalent boson hamiltonian in a simple case is obtained and diagonalized. Eigenstates with definite proton-neutron symmetry (good F-spin) emerge for certain values of proton and neutron numbers. In general the situation is more complex but the results obtained follow closely the experimental data.     

ΔI= 4 Bifurcation and the sdg Interacting Boson Model

We show that the superdeformed nuclear states can be described in the framework of the interacting boson model (IBM) with the g-bosons being taken into account in this paper.The ΔI= 4 bifurcation in superdeformed rotational bands can be reproduced in the SU(5) limit of the sdg IBM. The perturbation causing the ΔI= 4 bifurcation to emerge in the ΔI= 2 superdeformed rotational band may possess the SU(5) symmetry.     

An exactly solvable anharmonic Bohr hamiltonian and its equivalent boson hamiltonian

The eigenenergies and eigenfunctions of the bound states of an anharmonic quadrupole oscillator are derived in closed form. An interacting boson model hamiltonian is found which has the same eigenspectrum.     

Boson image of the quadrupole operator in deformed nuclei

In this paper the boson image of the quadrupole operator is discussed. The boson image is obtained via a Dyson mapping of the expectation values of this operator between coherent states. The effect of truncating the boson space to particular collective bosons is investigated. The truncation to the sd-boson space introduces nonphysical (spurious) states. The introduction of s′- and d′-bosons is necessary to avoid these spurious states.