Charge-changing transitions in an extended Lipkin-type model

Charge-changing transitions are considered in an extended Lipkin-Meshkov-Glick (LMG) model taking into account explicitly the proton and neutron degrees of freedom. The proton and neutron Hamiltonians are taken to be of the LMG form and, in addition, a residual proton-neutron interaction is included. Model charge-changing operators and their action on eigenfunctions of the model Hamiltonian are defined. Transition amplitudes of these operators are calculated using exact eigenfunctions and then the RPA approximation. The best agreement between the two kinds of calculation is obtained when the correlated RPA ground state, instead of the uncorrelated HF ground state, is employed and when the proton-neutron residual interaction, besides the proton-proton and neutron-neutron residual interactions, is taken into account in the model Hamiltonian. Received: 4 May 1998     

The use of coherent states in the variational treatment of proton-neutron interactions

Coherent states are used as trial states to determine, variationally, the structure of the eigenvectors belonging to a schematic Hamiltonian consisting of single-particle, pairing and residual proton-neutron interaction terms. It is shown that the standard proton-neutron quasiparticle random-phase approximation (pn-QRPA) is recovered, as a variational theory, by replacing quasiparticle pair creation and annihilation operators by bosons. It is also shown that an exact, algebra preserving, mapping of the Hamiltonian is needed to describe the spectrum beyond the QRPA phase transition. The role of the spurious components of the trial wave functions is discussed. Received: 19 February 2002 / Accepted: 3 May 2002     

Pair-vibrational states in the presence of neutron–proton pairing

Pair vibrations are studied for a Hamiltonian with neutron–neutron, proton–proton and neutron–proton pairing. The spectrum is found to be rich in strongly correlated, low-lying excited states. Changing the ratio of diagonal to off-diagonal pairing matrix elements is found to have a large impact on the excited-state spectrum. The variational configuration interaction (VCI) method, used to calculate the excitation spectrum, is found to be in very good agreement with exact solutions for systems with large degeneracies having equal T=0$T=0$ and T=1$T=1$ pairing strengths.     

Self-consistent medium polarization in RPA

The standard random-phase approximation for finite systems is extended by including the effect of the exchange of the RPA phonons in the residual interaction selfconsistently. It is shown that this particle-hole interaction is strongly energy dependent due to the presence of poles corresponding to 2p2h (and more complex) excitations. The RPA eigenvalue problem with this energy-dependent residual interaction also provides solutions for these predominantly 2p2h-like states. In addition a modified normalization condition is obtained.This new scheme is applied to ⁵⁶Ni (⁵⁶Co) in a large (up to 7ħω) configuration space using a residual interaction of G-matrix type. It is shown that the lowest 2⁺ eigenvalue, which in the standard RPA becomes imaginary, is stabilized when the selfconsistent screening is taken into account. Another feature observed is the splitting of the M1 strength as an example of 1p1h and 2p2h mixing.     

Influence of non-central interactions on low lying states of24Mg

Shell model calculations of low lying positive parity states of²⁴Mg have been performed in anSU(3) truncated space. In contrast to previousSU(3) model calculations the experimental spectrum can be reproduced well. This is attained by variation of a certain non-central component of the residual interaction.     

RPA description of the electric polarizability of the nucleon

Excited states of the nucleon are described as RPA configurations on a mean-field ground state taken from the MIT bag model. A residual interaction of a structure as in the Nambu-Jona-Lasinio model is used. The particlehole states are coupled to good total angular momentum and isospin. Valence excitations of particle-hole type and quark-antiquark (q $\bar q$ ) states from the Dirac-sea are included. The dependence of the baryon spectrum and multipole response functions on the coupling constantG is studied. At critical values ofG the 3q-ground state becomes degenerate with strongly collectiveq99-2 modes. The model is used to calculate the averaged electric polarizability of the neutron and the protonα. Without residual interactionα=7·10^?4 fm ³ is found. With residual interaction the value increases toα=(?11)·10^?4 fm ³. The measured value ofα is reproduced within experimental error bars.     

Proton and neutron contributions to the charge longitudinal response

The charge longitudinal response of nuclei, as measured by inclusive inelastic electron scattering, is investigated in the semiclassical RPA framework. The proton and neutron contributions to the total response are explicitly separated out. It is found that a sizable neutron ejection can be induced by RPA correlations, particularly at low momentum and energy transfer. A comparison of our theory with the experimental data is presented, also in the case of asymmetric nuclei (N ≠ Z). In particular, the differences in the neutron contributions between ³⁰Ca and ⁴⁸Ca are discussed.     

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.     

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     

Microscopic calculations of beta decay far from stability

Beta decay properties of nuclei far from stability are of decisive importance for the understanding of the element synthesis in the universe and the determination of the age of the universe by means of cosmochronometers. A new large scale microscopic calculation ofβ ^?-decay half-lives up to the neutron drip line is presented. This new approach uses the proton-neutron quasiparticle random phase approximation with a Gamow-Teller residual interaction.     

Empirical Proton-Neutron Interaction Energy

A method for extracting the empirical proton-neutron interaction energy between the last proton and the last neutron,δV_pn has been discribed and developed.The results for ground states of all even-even nuclei with N not less than 40 and for high spin states of some nuclei have been discussed.δV_pn values at high frequency for given configuration of some odd a nuclei were shown as well.It is found that these empirical δV_pn values include all multipole (mostly the monopole and quadrupole) terms of proton-neutron interaction and sensitively depend on nuclear deformation,configuration and rotational frequency.     

Effective SU(2) × SU(2) symmetry violations generated by electromagnetic and weak interactions

The interplay among the SU(3) × SU(3) violating interaction and the electromagnetic and weak interactions is considered in the context of the (3,3^∗)+(3^∗,3) symmetry breaking model. It is argued that the symmetry breaking Hamiltonian determined phenomenologically represents the effective interaction which generates the tadpole contributions coming from all symmetry violating interactions.     

Algebraic realization of the quantum rotor — odd-A nuclei

An algebraic realization of the quantum rotor for non-zero spin values (integer as well as half-integer) is established by constructing a model Hamiltonian out of rotationally invariant functions of the generators ofSU(3). The eigenvalues of this Hamiltonian in the leading normal-SU(3) symmetry for²⁵Mg and the so-called leading pseudo-SU(3) symmetries for¹⁵⁹Dy and¹⁶⁵Er are compared with the corresponding rotor results. For spinfree systems the internal symmetry group of the rotor and itsSU(3) realization are known to be D₂, the Vierergruppe. This symmetry extends to integral spin values, while for half-integer spins the rotor and itsSU (3) realization are shown to display an internal quaternion group symmetry. The theory points to a microscopic (many-particle shell-model) picture of nuclear rotational motion with spin degrees of freedom taken fully into account. An algebraic realization of the many-particle Nilsson model for odd-A nuclei, with the orbit-orbit and spin-orbit terms included, is given and applied to²³Na.     

Neutrino-nucleon scattering rate in proto-neutron star matter

We present a calculation of the neutrino-nucleon scattering cross-section which takes into account the nuclear correlations in the relativistic random phase approximation (RPA). Our approach is based on a quantum-hadrodynamics model with exchange of σ, ω, π, ρ and δ mesons. In view of applications to neutrino transport in the final stages of supernova explosion and proto-neutron star cooling, we study the evolution of the neutrino mean free path as a function of density, proton-neutron asymmetry and temperature. Special attention was paid to the issues of renormalization of the Dirac sea, residual interactions in the tensor channel, coupling to the delta-meson and meson mixing. In contrast with the results of other authors, we find that the neutral-current process is not sensitive to the strength g' of the residual contact interaction. As a consequence, it is found that RPA corrections with respect to the mean-field approximation amount to only 10% to 15% at high density. Received: 27 June 2001 / Accepted: 14 January 2002     

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.     

Spontaneously broken quark helicity symmetry

We discuss the origin of chiral-symmetry breaking in the light-cone representation of QCD. In particular, we show how quark helicity symmetry is spontaneously broken in SU (N) gauge theory with massless quarks if that theory has a condensate of fermion light-cone zero modes. The symmetry breaking appears as induced interactions in an effective light-cone Hamiltonian equation based on a trivial vacuum. The induced interaction is crucial for generating a splitting between pseudoscalar and vector meson masses, which we illustrate with spectrum calculations in some 1 + 1-dimensional reduced models of gauge theory.     

Integrable string models of WZNW model type with constant SU(2), SO(3), SP(2) and SU(3) torsion and hydrodynamic chains

The integrability of string model of WZNW model type with constant SU(2), SO(3), SP(2) torsion is investigated. The closed boson string model in the background gravity and antisymmetric B-field is considered as integrable system in terms of initial chiral currents. The model is considered under assumption that internal torsion related with metric of Riemann-Cartan space and external torsion related with antisymmetric B-field are (anti)coincide. New equation of motion and exact solution this equation was obtained for string model with constant SU(2), SO(3), SP(2) torsion. New equations of motion and new Poisson brackets (PB) for infinite dimensional hydrodynamic chains was obtained for string model with constant SU(n), SO(n), SP(n) torsion for n → ∞.     

On the projected spectra from a deformed correlated intrinsic state

It is argued that the residual interaction being relatively of long range, should produce Random Phase Approximation (RPA) type of correlations in the Hartree-Fock (HF) intrinsic state. A model is described to take these correlations inti account in the intrinsic state. A comparison of the projected spectra from this state with the exact shell model diagonalization for a model problem bears out this point. An application of the model is distinguishing two almost degenerate HF solutions for the 2s-1d shell nuclei is mentioned.     

On the role of image forces in chemisorption theory

The Extended Anderson Hamiltonian is used to study the effect of fluctuations of an adatom charge Q on the ionic part of the chemisorption energy. It is shown that dynamical effects essentially modify the classical expression E = ? ?Q² for the energy of interaction between a static charge Q and a metal (? is the interaction energy for a unit charge). The exact solution for the one-electron two-level model as well as a variational solution for the Extended Anderson Hamiltonian model are given. Validity conditions for a variety of approximate schemes are studied. The results are presented for the Extended Anderson Hamiltonian model parameterized so as to describe some aspects of the Li/W and Li/Mo chemisorption systems.