Strong coupled and doubly decoupled bands in the SU BF (3) ⊗ U F (2j + 1) limit of interacting boson — fermion — fermion model

The quantum numbers labelling the basis states and the corresponding strong coupled wavefunctions in the SU ^BF (3) ? U ^F (2j + 1) limit of interacting boson — fermion — fermion model are given. This dynamical symmetry limit is appropriate for heavy deformed odd — odd nuclei for configurations with one of the odd particle (proton or neutron) occupying all the natural parity orbits in the corresponding valence shell and the other particle occupying a single j — orbit. A boson — fermion — fermion interaction that can change the positions of the strong coupled bands without admixing and generate degenerate quadruplet of bands is constructed. A simple spin — spin and spin — orbital interaction that splits and changes the positions of the members of the quadruplet of bands is given. Adding a coriolis term to the hamiltonian generates doubly decoupled bands such as those seen in ¹⁷⁶Re nucleus.     

On the correspondence between fermion and boson states and operators

Mapping of shell-model (fermion) Hamiltonians onto boson Hamiltonians which underly the interaction boson model ^1–5) is investigated. A simple correspondence is defined and a sufficient condition given for shell-model Hamiltonians to simply correspond to finite hermitian boson Hamiltonians. A special case is discussed where diagonalization of a shell-model Hamiltonian for valence protons and neutrons can be exactly carried out in an equivalent (but different) boson space. If, however, the proton Hamiltonian and neutron Hamiltonian are diagonal in the seniority scheme, mapping of fermion states onto orthogonal boson states cannot be a simple correspondence. In that case the boson quadrupole operators equivalent to fermion guadrupole operators cannot be single-boson operators but must be more complicated, ones.     

A schematic model for monopole and quadrupole pairing in nuclei

A schematic Hamiltonian with a pairing interaction plus a quadrupole-quadrupole interaction between nucleons is presented. It is shown that all the states of the fermion system can be classified according to the number of nucleons u not coupled to coherent monopole or quadrupole pairs. The states with u = 0 are shown to have a one-to-one correspondence to the states of the interacting boson model. The spectra for these states are derived analytically for various limits of the pairing strength and the quadrupole strength. Analytical forms for the matrix elements of operators are derived for these limits. The operators in fermion space are mapped onto boson operators. The matrix elements of operators in the fermion space are shown to be equal to matrix elements of the boson operators multiplied by analytical Pauli factors which are state dependent. The two-nucleon transfer strength is calculated in two limits and is compared to experimental values.     

Ground state correlations and structure of odd spherical nuclei

It is well known that the Pauli principle plays a substantial role at low energies because the phonon operators are not ideal boson operators. Calculating the exact commutators between the quasiparticle and phonon operators, one can take into account the Pauli principle corrections. Besides, the ground state correlations due to the quasiparticle interaction in the ground state influence the single-particle fragmentation as well. In this paper, we generalize the basic equations of the quasiparticle-phonon nuclear model to account for both effects mentioned. As an illustration of our approach, calculations on the structure of the low-lying states in ¹³³Ba have been performed. The text was submitted by the authors in English.     

Boson expansions and quantization of time-dependent self-consistent fields (I). Particle-hole excitations

Two concrete methods are presented for quantizing the time-dependent Hartree equations in terms of boson operators. The first is the well-known infinite boson expansion analogous to the Holstein-Primakoff representation of angular momentum operators. The second, a new development, consists of finite boson quadratic forms, and is analogous to the Schwinger representation of angular momenta. In each case, a physical boson subspace can easily be constructed within which the full fermion dynamics is exactly duplicated. It therefore follows that quantization of the time-dependent Hartree equations, including all degrees of freedom, retrieves the exact many-body problem. The discussion in this paper is limited to particle-hole excitations of an N-particle system. A generalization to one-nucleon transfer processes on the N-particle system is also given in terms of ideal odd nucleons, but this brings in infinite expansions.     

Microscopic analysis of nuclear collective motions in terms of the boson expansion theory: (I). Formulation

A normal-ordered linked-cluster boson expansion theory, previously worked out by one of the authors (T.K.) and Tamura, has been developed further by reformulating it in a “physical” quasiparticle subspace which contains no spurious particle-number excitation modes. The expansion coefficients of the collective hamiltonian for low-lying quadrupole motions are determined starting from a microscopic fermion hamiltonian including self-consistent higher-order (many-body) interactions derived in our previous work. The contributions from the non-collective states with all possible non-collective one-boson excitations having I^π = 0⁺− 4⁺, which can directly couple to the collective states with one or two phonons, are taken into account in a systematic and compact way.     

玻色算符的逆算符及其相关的奇偶相干态

利用玻色算符的逆算符a^^-1和a^^+-1，定义了一类新的奇偶相干态 ，即增、减光子奇偶相干态.它们分别是算符为a^^-ka^^k+2,a^^+-ka ^²a^^+k的本征态，可由a^^-k和a^^+-k分别作用于通常的奇偶相干态来产生. 数值计算结 果表明，这类新的奇偶相干态都是非经典的光场态，它们都能呈现出光子反群聚效应 关键词： 玻色算符的逆算符 奇偶相干态 光子反群聚效应 量子压缩效应     

Influence of particle-number projection on potential energy surfaces of fissioning nuclei

The structure of high-spin states in the transitional nuclei^191,193Hg is described in the framework of the interacting boson fermion model with one broken pair. The results of model calculation reproduce in detail the structure of yrast states up toJ=49/2⁺ ?, including the first backbending, and the two lowest three-neutron negative parity bands.     

SU(3) coupling schemes for odd-odd nuclei in the interacting boson – fermion – fermion model with both odd proton and odd neutron in natural parity orbits

The SU^BFF(3) dynamical symmetry limits of interacting boson – fermion – fermion model are identified and they are appropriate for heavy deformed odd – odd nuclei for configurations with both the odd proton and odd neutron occupying all the natural parity orbits in the corresponding valence shells. There are three symmetry limits and their correspondence with two quasi-particle (proton-neutron) Nilsson configurations is established; one of the limits mixes both Nilsson n_z's and Λ's and other two limits mix only Nilsson Λ's. The ¹⁹¹Ir (d,t) ¹⁹⁰Ir single nucleon transfer spectroscopic strengths are well described by one of the symmetry limits that mixes only Nilsson Λ's. Received: 22 June 1998     

S-Matrix formalism for particles interacting with phonon fields: Coherent state representation

We apply the quasiparticle picture to the interaction between a fermion and a boson field using a coherent states representation of theS matrix. Its matrix elements between single particle states are explicitly evaluated in terms of a path integral. The method is extended to include dispersion in the excitation spectrum and applied to the case of a metal with electron-hole symmetry. Its relation with perturbation theory is discussed and the second order perturbative result for polarons in insulators is recovered.     

Positive parity low spin states of odd-mass tellurium isotopes

In this work, we analyse the positive parity of states of odd-mass nucleus within the framework of interacting boson fermion model. The result of an IBFM-1 multilevel calculation with the lg_9/2, 2d_5/2, 2d_3/2, 3s_1/2 and one level, 1h_11/2 with negative parity, single particle orbits is reported for the positive parity states of the odd mass nucleus ^123-125Te. Also, an IBM-1 calculation is presented for the low-lying states in the even-even ^124-126Te core nucleus. The energy levels and B (E2) transition probabilities were calculated and compared with the experimental data. It was found that the calculated positive parity low spin state energy spectra of the odd-mass ^123-125Te isotopes agree quite well with the experimental data.     

Fermions and bosons in a two-dimensional world

We derive the formal equivalence of a free massless two-dimensional theory and a free massless two-dimensional boson theory constructed from the bilinear products of the self-same fermion theory. The sense of this equivalence is investigated. Using a box normalization, it is found that the fermion states are Glauber coherent states of bosons, where the boson vacuum is the ground state of the charge sector corresponding to the given fermion state. The massless boson is the Goldstone boson and the degenerate vacua are the ground states of the various charge sectors. A complete operator identity between fermion and boson operators can be obtained, but to do this an additional boson operator must be introduced which cannot be defined in terms of bilinear products of the fermion operators. Doing this makes the charge spectrum continuous.     

The interacting quasiparticle–phonon picture and odd–even nuclei. Overview and perspectives

The role of the nucleon correlations in the ground states of even–even nuclei on the properties of low-lying states in odd–even spherical and transitional nuclei is studied. We reason about this subject using the language of the quasiparticle–phonon model which we extend to take account of the existence of quasiparticle?phonon configurations in the wave functions of the ground states of the even–even cores. Of paramount importance to the structure of the low-lying states happens to be the quasiparticle–phonon interaction in the ground states which we evaluated using both the standard and the extended random phase approximations. Numerical calculations for nuclei in the barium and cadmium regions are performed using pairing and quadrupole–quadrupole interaction modes which have the dominant impact on the lowest-lying states’ structure. It is found that states with same angular momentum and parity become closer in energy as compared to the predictions of models disregarding the backward amplitudes, which turns out to be in accord with the experimental data. In addition we found that the interaction between the last quasiparticle and the ground-state phonon admixtures produces configurations which contribute significantly to the magnetic dipolemoment of odd-A nuclei. It also reveals a potential for reproducing their experimental values which proves impossible if this interaction is neglected.     

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.     

Microscopic calculation of IBM parameters by using intrinsic states

The overlaps between intrinsic fermionic and bosonic wave functions are required to be the same. This provides relations between fermion and boson variables. These relations are used in conjunction with an OAI procedure for intrinsic states to map the shell-model space operators onto their equivalent boson space operators. As an example, a QQ interaction is mapped.     

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.     

Composite-Particles (Boson,Fermion) Theory of Fractional Quantum Hall Effect

A theory is developed for fractional quantum Hall effect in terms of composite (c)-bosons (fermions) without useing Laughlin’s results about the fractional charge. Here the c-particle (fermion, boson) is defined as a bound composite fermion (boson) containing a conduction electron and an even (odd) number of fluxons (elementary magnetic fluxes). The Bose-condensed c-bosons, each containing an electron and an odd number m of fluxons at the filling factor ν=1/m is shown to generate the Hall conductivity plateau value m e ²/h, where the density of c-particles, \(n_{\phi }^{(m)}\), either bosonic or fermionic, with m fluxons is given by \(n_{\phi }^{(m)}=n_{\mathrm {e}}/m\), n _e = electron density. The only assumption is that any c-fermion carries a charge magnitude equal to the electron charge e. The quantum Hall state is shown to be more stable at ν=1/3 than at ν=1.     

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 sound velocity in heavy fermion systems

The influence of the quasiparticle-phonon interaction on a sound velocity in heavy fermion systems in the presence of an external magnetic field is studied. It is shown that for temperatures less than spin fluctuation temperatureT ^* the change of sound velocity depends strongly on the detailed shape of the quasiparticle density of states.     

A unification of boson expansion theories: (I). Functional representations of fermion states

The method for obtaining boson expansion by representing the fermion states as holomorphic functions of many complex variables is presented. Such functional representation is explicitly constructed for each space which is the carrier space of an irreducible representation of a semisimple compact Lie group. This is achieved by proving the unity resolution in terms of holomorphically parametrized Perelomov's generalized coherent states. The functional images of fermion states are polynomials of complex variables, while those of fermion operators are differential operators of finite order with polynomial coefficients.