Parameter Symmetry of the Interacting Boson Model

We discuss the symmetry of the parameter space of the interacting boson model (IBM). It is shown that for any set of the IBM Hamiltonian parameters (with the only exception of the U(5) dynamical symmetry limit) one can always find another set that generates the equivalent spectrum. We discuss the origin of the symmetry and its relevance for physical applications.Comment: Minor changes; Revtex, 14 pages with 1 figur

P-matrix and J-matrix approaches. Coulomb asymptotics in the harmonic oscillator representation of scattering theory

The relation between the R- and P-matrix approaches and the harmonic oscillator representation of the quantum scattering theory (J-matrix method) is discussed. We construct a discrete analogue of the P-matrix that is shown to be equivalent to the usual P-matrix in the quasiclassical limit. A definition of the natural channel radius is introduced. As a result, it is shown to be possible to use well-developed technique of R- and P-matrix theory for calculation of resonant states characteristics, scattering phase shifts, etc., in the approaches based on harmonic oscillator expansions, e.g., in nuclear shell-model calculations. P-matrix is used also for formulation of the method of treating Coulomb asymptotics in the scattering theory in oscillator representation.Comment: Revtex, 57 pages including 15 figures; to be published in Annals of Physic

Two-body correlations in Bose condensates

We formulate a method to study two-body correlations in a condensate of N identical bosons. We use the adiabatic hyperspheric approach and assume a Faddeev like decomposition of the wave function. We derive for a fixed hyperradius an integro-differential equation for the angular eigenvalue and wave function. We discuss properties of the solutions and illustrate with numerical results. The interaction energy is for N~20 five times smaller than that of the Gross-Pitaevskii equation

Creation of the precision magnetic spectrometer SCAN-3

The new JINR project [1] is aimed at studies of highly excited nuclear matter created in nuclei by a high-energy deuteron beam. The matter is studied through observation of its particular decay products - pairs of energetic particles with a wide opening angle, close to 180°. The new precision hybrid magnetic spectrometer SCAN-3 is to be built for detecting charged (π±, K±, p) and neutral (n) particles produced at the JINR Nuclotron internal target in dA collisions. One of the main and complex tasks is a study of low-energy ηA interaction and a search for η-bound states (η-mesic nuclei). Basic elements of the spectrometer and its characteristics are discussed in the article

Coulomb Energy Averaged over the nℓNn\ell^N-Atomic States with a Definite Spin

12 pages, Tex FileA purely group-theoretical approach (for which the symmetric group plays a central rôle), based upon the use of properties of fractional-parentage coefficients and isoscalar factors, is developed for the derivation of the Coulomb energy averaged over the states, with a definite spin, arising from an atomic configuration $n \ell^N$

Tomographic representation of spin and quark states

We present a short review of the general principles of constructing tomograms of quantum states. We derive a general tomographic reconstruction formula for the quantum density operator of a system with a dynamical Lie group. In the reconstruction formula, the multiplicity of irreducible representation in Clebsch-Gordan decomposition is taken into account. Various approaches to spin tomography are discussed. An integral representation for the tomographic probability is found and a contraction of the spin tomogram to the photon-number tomography distribution is considered. The case of SU (3) tomography is discussed with the examples of quark states (related to the simplest triplet representations) and octet states