Completely analytical interactions: Constructive description

An interactionU is called a completely analytical (CA) interaction, if it satisfies one of 12 given conditions formulated in terms of analyticity properties of the partition functions Z_v(u), or correlation decay, or truncated correlation bounds, or asymptotic behavior of ln Z_v(u), v→∞. The 12 conditions are presented, together with part of the proof of their equivalence. The main result of the paper is that each condition is constructive in the following sense: instead of checking it in all finite volumesv??^v, it is enough to consider only (a finite amount of) volumes with restricted size. In particular, the partition functions Z _v (u+?) for the complex perturbationsu+? ofu do not vanish for all V? ^v and all ? with ∥?∥<?, provided this is true only forv with diam v?C(?) and ∥?∥<?′ (but with?<?′).     

Molecular and compact four-quark states

We study charmonium (c(c)n(n)), bottomonium (b(b)n(n)) and exotic (cc(n)(n) and bb(n)(n)) four-quark states by means of a standard non-relativistic quark potential model. We look for possible bound states. Among them we are able to distinguish between meson-meson molecules and compact four-quark states.     

Molecular and compact four-quark states

We study charmonium （ccnn）,bottomonium （b bnn） and exotic （ccnn and bbnn） four-quark states by means of a standard non-relativistic quark potential model.We look for possible bound states.Among them we are able to distinguish between meson-meson molecules and compact four-quark states.     

Coherent states for quantum compact groups

Coherent states are introduced and their properties are discussed for simple quantum compact groupsA _l, B_l, C_l andD _l. The multiplicative form of the canonical element for the quantum double is used to introduce the holomorphic coordinates on a general quantum dressing orbit. The coherent state is interpreted as a holomorphic function on this orbit with values in the carrier Hilbert space of an irreducible representation of the corresponding quantized enveloping algebra. Using Gauss decomposition, the commutation relations for the holomorphic coordinates on the dressing orbit are derived explicitly and given in a compactR-matrix formulation (generalizing this way theq-deformed Grassmann and flag manifolds). The antiholomorphic realization of the irreducible representations of a compact quantum group (the analogue of the Borel-Weil construction) is described using the concept of coherent state. The relation between representation theory and non-commutative differential geometry is suggested. Dedicated to Professor L.D. Faddeev on his 60th birthday     

Translationally invariant description of particle-hole states

A translationally invariant model is proposed which allows to calculate one-particle excitations and dipole transition probabilities of closed-shell nuclei with inclusion of the continuum. The connection of this model with the nuclear shell model is shown, and it is applied to the calculation of the photodisintegration cross section of⁴He.     

Positive distribution description for spin states

We investigate a possibility of describing spin states in terms of a positive distribution function depending on continuous variables like Euler's angles. A spin state reconstruction procedure similar to the symplectic tomography is considered. A quantum evolution equation for the classical-like positive distribution function is found. Generalization to arbitrary values of angular momentum is discussed.     

Analytic description of the fusion and fission processes through compact quasi-molecular shapes

Recent studies have shown that the characteristics of the entrance and exit channels through compact quasi-molecular shapes are compatible with the experimental data on fusion, fission and cluster radioactivity when the deformation energy is determined within a generalized liquid drop model. Analytic expressions allowing to calculate rapidly the main characteristics of this deformation path through necked shapes with quasi-spherical ends are presented now; namely formulas for the fusion and fission barrier heights, the fusion barrier radius, the symmetric fission barriers and the proximity energy.     

Microscopic description and excitation of unitary alalog states

A microscopic investigation in a self-consistent particle-hole model reveals approximate unitary analog states in spite of large symmetry breaking. The K-nucleus elastic scattering and (K^?, π^?) excitation of these states are studied, showing strong surface effects.     

Continuum three-body states using the hyperspherical adiabatic basis set

In this paper we investigate the feasibility of employing the hyperspherical adiabatic (HA) basis set to describe continuum three-nucleon states. In particular, the HA expansion is compared with the simpler expansion on hyperspherical harmonics (HH). A practical numerical application is presented using the MT-III potential.     

Some new consequences of the order parameter description of glassy states

By extending the classical order parameter theory of glassy states to the case of inhomogeneous glassy states, some new consequences of the theory are derived. It is shown that the phase boundaries, critical points, and the kinetics of phase transition differ in the annealed and the quenched states. For example, the critical point of phase separation is always suppressed in the quenched states. Cahn's analysis of elastic energy effects is shown to be a special case of the present formalism.     

IBFA description of high-spin positive-parity states in Rh isotopes

Properties of the odd-mass Rh isotopes are investigated in the framework of the interacting boson-fermion approximation (IBFA) model in which the odd proton movea in the $\text{1}\text{g}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}$ and $\text{2}\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}$ orbitals. Lifetimes of some high-spin positive-parity states in ⁹⁹Rh obtained by the recoil-distance method with the ⁸⁸Sr(¹⁴N, 3n) reaction are also reported. Calculated excitation energies and electromagnetic properties of the high-spin positive-parity states are compared with experiment and an acceptable agreement is obtained.     

Microscopic description of mixed-symmetry states in nearly spherical nuclei

We adopt the quasiparticle-phonon model to investigate the phonon content and the proton-neutron symmetry of low-lying states recently discovered in nuclei around shell closure. The results are in overall agreement with experiments and consistent with the interacting boson model.