Deuteron-equivalent and phase-equivalent interactions within light nuclei

Background: Phase-equivalent transformations (PETs) are well-known in quantum scattering and inverse scattering theory. PETs do not affect scattering phase shifts and bound state energies of two-body system but are conventionally supposed to modify two-body bound state observables such as the rms radius and electromagnetic moments. Purpose: In order to preserve all bound state observables, we propose a new particular case of PETs, a deuteron-equivalent transformation (DET-PET), which leaves unchanged not only scattering phase shifts and bound state (deuteron) binding energy but also the bound state wave function. Methods: The construction of DET-PET is discussed; equations defining the simplest DET-PETs are derived. We apply these simplest DET-PETs to the JISP16 $NN$ interaction and use the transformed $NN$ interactions in calculations of $^3$H and $^4$He binding energies in the No-core Full Configuration (NCFC) approach based on extrapolations of the No-core Shell Model (NCSM) basis space results to the infinite basis space. Results: We demonstrate the DET-PET modification of the $np$ scattering wave functions and study the DET-PET manifestation in the binding energies of $^3$H and $^4$He nuclei and their correlation (Tjon line). Conclusions: It is shown that some DET-PETs generate modifications of the central component while the others modify the tensor component of the $NN$ interaction. DET-PETs are able to modify significantly the $np$ scattering wave functions and hence the off-shell properties of the $NN$ interaction. DET-PETs give rise to significant changes in the binding energies of $^3$H (in the range of approximately 1.5 MeV) and $^4$He (in the range of more than 9 MeV) and are able to modify the correlation patterns of binding energies of these nuclei

Phenomenological theory of phase transitions in epitaxial BaxSr(1-x)TiO3 thin films

A phenomenological thermodynamic theory of BaxSr(1-x)TiO3 (BST-x) thin films epitaxially grown on cubic substrates is developed using the Landau-Devonshire approach. The eighth-order thermodynamic potential for BT single crystal and modified fourth-order potential for ST single crystal were used as starting potentials for the end-members of the solid solution with the aim to develop potential of BST-$x$ solid solution valid at high temperatures. Several coefficients of these potentials for BT were changed to obtain reasonable agreement between theory and experimental phase diagram for BST-x (x > 0.2) solid solutions. For low Ba content we constructed the specific phase diagram where five phases converge at the multiphase point (T_N2 = 47 K, x = 0.028) and all transitions are of the second order. The "concentration-misfit strain" phase diagrams for BST-x thin films at room temperature and "temperature-misfit strain" phase diagrams for particular concentrations are constructed and discussed. Near T_N2 coupling between polarization and structural order parameter in the epitaxial film is modified considerably and large number of new phases not present in the bulk materials appear on the phase diagram.Comment: 8 pages 5 figure

IBM: parameter symmetry, hidden symmetries and transformations of boson operators

A symmetry of the parameter space of interacting boson models IBM-1 and IBM-2 is studied. The symmetry is associated with linear canonical transformations of boson operators, or, equivalently, with the existence of different realizations of the symmetry algebras of the models. The relevance of the parameter symmetry to physical observables is discussed.Comment: LATEX, 11 pages including 1 eps figure and 1 table prepared as an eps figure; a talk given by A. M. Siirokov at XXII Symposium on Nuclear Physics, Oaxtepec, Morelos, M\'exico, 5--8 January, 1999; to be published in Revista Mex. Fi

Inverse scattering J-matrix approach to nucleon-nucleus scattering and the shell model

The $J$-matrix inverse scattering approach can be used as an alternative to a conventional $R$-matrix in analyzing scattering phase shifts and extracting resonance energies and widths from experimental data. A great advantage of the $J$-matrix is that it provides eigenstates directly related to the ones obtained in the shell model in a given model space and with a given value of the oscillator spacing $\hbar\Omega$. This relationship is of a particular interest in the cases when a many-body system does not have a resonant state or the resonance is broad and its energy can differ significantly from the shell model eigenstate. We discuss the $J$-matrix inverse scattering technique, extend it for the case of charged colliding particles and apply it to the analysis of $n\alpha$ and $p\alpha$ scattering. The results are compared with the No-core Shell Model calculations of $^5$He and $^5$Li.Comment: Some text is added following suggestions of a journal refere

Generalized compactness in linear spaces and its applications

The class of subsets of locally convex spaces called $\mu$-compact sets is considered. This class contains all compact sets as well as several noncompact sets widely used in applications. It is shown that many results well known for compact sets can be generalized to $\mu$-compact sets. Several examples are considered. The main result of the paper is a generalization to $\mu$-compact convex sets of the Vesterstrom-O'Brien theorem showing equivalence of the particular properties of a compact convex set (s.t. openness of the mixture map, openness of the barycenter map and of its restriction to maximal measures, continuity of a convex hull of any continuous function, continuity of a convex hull of any concave continuous function). It is shown that the Vesterstrom-O'Brien theorem does not hold for pointwise $\mu$-compact convex sets defined by the slight relaxing of the $\mu$-compactness condition. Applications of the obtained results to quantum information theory are considered.Comment: 27 pages, the minor corrections have been mad

On properties of the space of quantum states and their application to construction of entanglement monotones

We consider two properties of the set of quantum states as a convex topological space and some their implications concerning the notions of a convex hull and of a convex roof of a function defined on a subset of quantum states. By using these results we analyze two infinite-dimensional versions (discrete and continuous) of the convex roof construction of entanglement monotones, which is widely used in finite dimensions. It is shown that the discrete version may be 'false' in the sense that the resulting functions may not possess the main property of entanglement monotones while the continuous version can be considered as a 'true' generalized convex roof construction. We give several examples of entanglement monotones produced by this construction. In particular, we consider an infinite-dimensional generalization of the notion of Entanglement of Formation and study its properties.Comment: 34 pages, the minor corrections have been mad

Fine-Tuning Renormalization and Two-particle States in Nonrelativistic Four-fermion Model

Various exact solutions of two-particle eigenvalue problems for nonrelativistic contact four-fermion current-current interaction are obtained. Specifics of Goldstone mode is investigated. The connection between a renormalization procedure and construction of self-adjoint extensions is revealed.Comment: 13 pages, LaTex, no figures, to be published in IJMP