Proton-neutron interaction near closed shells

Odd-odd nuclei around double shell closures are a direct source of information on the proton-neutron interaction between valence nucleons. We have performed shell-model calculations for doubly odd nuclei close to ²⁰⁸Pb, ¹³²Sn, and ¹⁰⁰Sn using realistic effective interactions derived from the CD-Bonn nucleon-nucleon potential. The calculated results are compared with the available experimental data, attention being focused on particle-hole and particle-particle multiplets. While good agreement is obtained for all the nuclei considered, a detailed analysis of the matrix elements of the effective interaction shows that a stronger core-polarization contribution seems to be needed in the particle-particle case.     

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     

Triaxiality, chirality and γ-softness

Current work explores the impact of γ-softness on partner bands built on the πh_11/2νh_11/2 particle-hole configurations in triaxial odd-odd nuclei. The results of calculations conducted using a core-particle-hole coupling are presented. The model Hamiltonian includes the collective core, the single-particle valence nucleons, and separable quadrupole-quadrupole interactions. The Kerman-Klein method was applied to find eigenstates, which provided a convenient way for exploring core effects. Calculations were made for triaxial cores with various γ-softness using the General Collective Model keeping the expectation value for the triaxiality parameter fixed at (γ)=30°. The degeneracy in the πh_11/2νh_11/2 bands results from the calculations for the γ-rigid core but is lifted for the γ-unstable core.     

Magnetic dipole transitions and proton-neutron degrees of freedom in nuclear deformation

The M1 transitions between low-lying collective states are discussed from the viewpoint of the Proton-Neutron Interacting Boson Model, with particular emphasis on the mixed-symmetry states. Mixed-symmetry 2⁺ states are studied for⁵⁶Fe and⁵⁴Cr in terms of realistic and large-scale shell-model calculations, including M1 properties. The Doorway-state character of the mixed-symmetry 2⁺ state is proposed with examples in these nuclei. The possible candidate of the mixed-symmetry 2⁺ state in¹³⁴Ba is analyzed based on recent experiment by Molnaret al. on M1 transitions. The M1 transitions from the quasi-γ to quasi-g bands in γ-unstable or O(6) nuclei are discussed next, by taking Ba isotopes as an example. It is suggested that such M1 transitions are enhanced compared to axially symmetric nuclei as an indication of softness towards proton-neutron incoherent motion in γ-unstable nuclei,i.e., mixture of mixed-symmetry states. A new mirror-type symmetry is introduced for γ-unstable nuclei, and the M1 selection rule due to this symmetry is presented, making 4 ₂ ⁺ →4 ₁ ⁺ transition allowed but 3 ₁ ⁺ →2 ₁ ⁺ forbidden, for instance.     

Complex Harmonic-Oscillator Basis for the Relativistic Three-Body Problem

A complex harmonic-oscillator basis is employed for the three-body problem obeying S ₃-symmetry. Unlike a real basis it generates an additional quantum number (N _a ), in addition to the standard principal quantum number (N), and thus facilitates a more quantitative S ₃-classification of the various states than is usually possible. It is shown that certain bilinear forms with definite S ₃-symmetry properties, which can be constructed out of the linear harmonic-oscillator operators (a, a ^†) satisfy several uncoupled sets of SO(2, 1) algebras with spectra bounded from below. It is also briefly indicated how this S ₃-formalism can be adapted to the core structure of a more general relativistic three-particle system with unequal-mass kinematics through an appropriate choice of internal variables. Received May 11, 1994; revised November 3, 1994; accepted for publication November 23, 1994     

Proton-neutron quasiparticle RPA with separable Gamow-Teller forces

A comprehensive representation is presented of a generalized form of the proton-neutron quasiparticle RPA model, originally introduced by Halbleib and Sorensen almost thirty years ago. The model uses separable Gamow-Teller forces, including, in addition to the particle-hole force of the former model, the particle-particle force, which is of decisive importance for β⁺ decay andββ decay. The above model has further been extended to the treatment of odd-odd nuclei. An extension is also made to transitions from nuclear excited states. This is essential for calculations of nuclear weak transition rates in the high-temperature interior of massive stars. Complementing the discussion of Halbleib and Sorensen on the particle-hole force, the structure of the RPA dispersion relation is discussed with emphasis on effects of the particle-particle force.     

Construction of microscopic boson states and their relevance for IBM-2

We investigate four methods for the construction of collective shell model states which may be mapped onto boson states of the IBM-2. These methods use, as building blocks for the wave functions, particle-particle pair operators, particle-hole operators, pair operators with seniority projection and energy-weighted quadrupole operators. It is demonstrated that one obtains stronger collectivity with the energy-weighted quadrupole operator than with the other methods.On the basis of a comparison of calculated and empirical IBM-2 interaction parameters we can rule out the seniority projection method. This implies that particle-particle and particle-hole approaches difler.The ratios between quadrupole matrix elements of the microscopic boson states appear to be similar to the IBM predictions. For states corresponding to those with two d-bosons coupled to J = 0 there is a smaller quadrupole matrix element when subshells with small angular momenta dominate near the Fermi level. Especially for this type of states the collective quadrupole space will be larger than represented in the IBM, however, which may compensate the smaller proton-neutron quadrupole coupling.The calculated bare quadrupole interaction between like bosons is found to be weak.     

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.     

U(3) symmetry: a link between nuclear models and phenomena

Light nuclei show evidence for aU(3) symmetry. This symmetry appears in all of the basic models of these nuclei, such as the shell, collective and cluster model. It has a microscopic origin which is related to the shell structure and to the nature of the effective two-nucleon forces, but it determines macroscopic characteristics as well, such as the amount of quadrupole deformation, moment of inertia, etc. We show that this symmetry also serves as a basis for interrelating various cluster configurations of the same (compound) nucleus, offering a natural link between seemingly unrelated phenomena, like nuclear molecular resonances and excitations in the low-lying nuclear spectra.     

A valence space solution to the B(E2) saturation problem in deformed nuclei

The empirically observed saturation in B(E2: 0⁺₁→2⁺₁) values in deformed nuclei near mid shell is interpreted in terms of a reduced integrated valence proton-neutron interaction arising from reduced spatial overlaps. This analysis, based on very general properties of the deformed field, removes a serious difficulty encountered by simple valence space models and may provide a simpler interpretation of other observables as well.     

Direct empirical correlation between proton-neutron interaction strengths and the growth of collectivity in nuclei

A direct correlation between experimental values of proton-neutron interaction strengths and experimental measures of the growth of collectivity in nuclei is found. In particular, differences in the p-n interaction strengths and differences in growth rates of collectivity in particle-particle (or hole-hole) and particle-hole regions are found to correspond.     

Proton-neutron correlations in nuclei with N = 30

Structure of the nuclei with N = 30 and Z = 20–28 is investigated by the nuclear shell model within the proton-neutron configurations (1f_{$\text{7}\text{2}$})^z?20_p × (2p_{$\text{3}\text{2}$}, 2p_{$\text{case1}\text{2}$}, 1f_{$\text{case5}\text{2}$})²_n. Effective proton-neutron interactions determined by a least-squares fit to the observed spectra of N = 29 nuclei are adopted. Agreement of the calculated spectra with experimental spectra is satisfactory. Strong correlations between protons and neutrons break down the pairing scheme and lower the first J = 2 levels in doubly even nuclei, which is shown from the resultant wave functions. A relation between the shell model and collective rotational model is discussed concerning the calculated rotation-like spectrum of ⁵⁶Fe. Electromagnetic properties and spectroscopic factors of single-nucleon transfer reactions are calculated. They are in good agreement with experiments.     

Nucleon channel coupling in electrodisintegration of nuclei

The process of nuclear excitation above threshold for nucleon decay in high energy electron scattering is considered. On the basis of the particle-hole shell model a formalism is proposed which allows one to describe electroexcitation of nuclei in a unified manner both in the resonance and quasielastic scattering regions. Numerical calculations were made for the ¹²C nucleus taking into account the mixing of proton and neutron configurations (channels) of the particle-hole type in the continuum.     

On an intermediate structure of giant analog resonances in medium and heavy nuclei

The effect of coupling of the usual particle-hole states to particle-hole states built above a collective state on the decay characteristics and structure of a giant resonance with higher isospin (T _>) has been estimated. Numerical calculations are carried out for⁶⁰Ni,⁹⁰Zr and²⁰⁸Pb.     

Quark-lepton compositeness: A three-body scenario

The Harari-Shupe model of quarks and leptons is viewed, not as a gauge theory, but as a quantum-mechanical three-body problem of the extreme relativistic type involving massless preons. Considerations based onS ₃-symmetry in the available degrees of freedom (spin, isospin, space and hypercolour) are employed in conjunction with a spin-dependence ansatz on the three-preon forces (Σ ^a =σ _μv ⁽¹⁾ σ _λμ ⁽³⁾ ) for an understanding of the three basic issues of (i) spin-1/2, (ii) generation structure and (iii) steeply rising mass patterns of quark-lepton families. The Σ ^a -dynamics is compatible with the interpretation of colour as a manifestation ofS ₃-symmetry, as envisaged in the original Harari-Shupe proposal, while the interpretation of the generation structure devolves on the role of a certain quantum numberN which takes on three different classes of values (3n, 3n ± 1;n = 0, 1, 2, ...) according to theS ₃-symmetry of thespatial wavefunction.     

Pairing correlations and soft dipole excitations in nuclei on the neutron-drip line

Paring correlations and soft dipole excitations in weakly bound nuclei on the edge of neutrondrip line are studied by using a three-body model. A density-dependent contact interaction is employed to calculate the ground state of halo nuclei ⁶He and ¹¹Li, as well as a skin nucleus ²⁴O. Dipole excitations in these nuclei are also studied within the same model. We point out that the dineutron-type correlation plays a dominant role in the halo nuclei ⁶He and ¹¹Li having the coupled spin of the two neutrons S = 0, while the correlation similar to the BCS type is important in ²⁴O. Contributions of the spin S = 1 and S = 0 configurations are separately discussed in the low-energy dipole excitations. The calculated results are compared with recent experimental data of ⁶He and ¹¹Li. The text was submitted by the authors in English.     

Present status and future aspects of nuclear structure close to 100Sn

The present status of experimental approach to ¹⁰⁰Sn in the spectroscopy of excited states is landmarked by the T_z=3/2 nuclei between ⁹⁵Pd and ¹⁰¹In and the T_z=1 nuclei ⁹⁴Pd and ⁹⁸Cd. The detection limits with Pre-EUROBALL γ-arrays and ancillary detectors are below the 10^?5 level of the total fusion- evaporation residue cross section. A large scale shell model analysis of the existing data reveals the shell structure at ¹⁰⁰Sn, which shows a remarkable similarity to ⁵⁶Ni. Evidence for an increasing proton-neutron interaction in approaching the N=Z line is deduced from high spin isomers and spherical yrast lines. The effective E2 operator for protons and neutrons and implications for a low lying particle-hole (ph) E2 excitation in ¹⁰⁰Sn are discussed.     

Heat dissipation in two-terminal Benzene junction

We investigate the heat dissipation mechanism in the Benzene molecular junctions. Using the tight-binding model and the generalised Green’s function formalism, heat dissipation in the electrodes is studied numerically. Results reveal a strong dependence of heat dissipation on the transmission characteristics and the bill polarity. For a pure Benzene molecular junctions, regardless the electrodes positions, namely meta, ortho and para configurations, heat dissipates in a symmetric fashion at both electrodes and does not rely on the bias polarity. This feature is a consequence of a symmetric transmission function over the energy spectrum of incoming electrons. Introducing a single impurity on the Benzene molecule, we force the model to lose its particle-hole symmetry and a drastic change occurs in the heat dissipation of the junction.