In the present paper we extend group theoretical analysis of a previous publication to obtain explicitly, as polynomical in sinγ, cosγ, function φλμlk(γ) required discussion quadrupole vibrations nucleus. The states appearing collective model 〈νλμLV〉=F1λ(β) ΣKφλμLK(γ) DL*MK(φi), l= (ν−λ)/2, are then defined, Fλl(β), DL*MK(φi) well known. All matrix elements nucleus related with expression (λμL;λ′μ′L′;λ″μ″L″= ∂π0ΣKK′K″ (LL′L″KK′K″) φλμLK(γ) φλ′μ′L′K′ (γ) φλ″μ″L″K″ (γ)sin 3γdγ, which is...

Over twenty years ago A. Bohr discussed the quantum mechanical problem of quadrupole vibrations in liquid drop model nucleus. States definite angular momentum L could not be obtained exactly except when L=0,3. In present paper we indicate how can determine states for arbitrary and number quanta ν terms polynomials creation operators characterized by irreducible representation (IR) chain groups U(5)⊃O(3). We furthermore characterize a IR λ O(5) replacing traceless ones. These are fully...

Recently Arima and Iachello proposed an interacting boson model of the nucleus involving six bosons, five in a d one s state. The most general interaction this can then be expressed terms Casimir operators following chains subgroups fundamental group U(6): U(6) ⊆U(5) ⊆O(5) ⊆O(3) ⊆O(2), ⊆O(6) ⊆SU(3) ⊆O(2). To determine matrix elements in, for example, basis characterized by irreducible representations first chain groups, we only need to evaluate O(6) SU(3) as others are already diagonal it....

The structure of the totally symmetric unit tensor operators (and their conjugates) in U(n) is examined from viewpoint pattern calculus and factorization lemma. geometrical properties arrow patterns fundamental projective (tensor) are demonstrated to be origin existence simple structural expressions for a class reduced matrix elements operators. An extension rules given whereby these can written out directly. This sufficient permit construction general operator. canonical splitting...

La vertiente de la industria petrolera actual se inclina a encontrar métodos eficaces y rentables hora realizar determinaciones parámetros clave como son las litologías edades formación rocas durante el proceso explotación un pozo. El análisis micropaleontológico proporciona no solamente información científica bioestratigráfica muy valiosa, sino también práctica (y logística) para estimar rendimientos extracción muestras canales exploración petrolera. Este trabajo describe brevemente alto...

Research Article| March 01, 2002 70 Ma nonmarine diatoms from northern Mexico Elizabeth Chacón-Baca; Chacón-Baca 1Instituto de Geología, Universidad Autónoma México, Circuito la Investigación Científica, México D.F. 04510, Search for other works by this author on: GSW Google Scholar H. Beraldi-Campesi; Beraldi-Campesi S.R.S. Cevallos-Ferriz; Cevallos-Ferriz A.H. Knoll; Knoll 2Botanical Museum, Harvard University, Cambridge, Massachusetts 02138, USA S. Golubic 3Department of Biology, Boston...

Holstein and Primakoff derived long ago the boson realization of a su(2) Lie algebra for an arbitrary irreducible representation (irrep) SU(2) group. The corresponding result su(1,1)≅sp(2) is also well known. This raises question whether it possible to obtain in explicit, analytic, closed form, any integer d, sp(2d) irrep Sp(2d) group, which problem considerable physical interest. case d=2 already illustrates its full generality thus this paper we concentrate on sp(4). Dyson known, passage...

An explicit algebraic expression [containing the minimal number (n − 1) sums] for general reduced Wigner coefficients associated with multiplicity free Kronecker product [h1 … hn] × [p0 0] of irreducible representations U(n), is determined. The calculation employs a combined use recursive relations derived coefficients, and matrix elements (with respect to Gel'fand basis states) generator U(n) raised an arbitrary power. We also give alternative procedure using techniques ``pattern...

A group-theoretical analysis of the states first-row atoms and their internal electrostatic interactions is developed. The Hamiltonian found to be completely expressible as a linear combination operators that are diagonal in $U(3)$, $O(4)$, both. This makes possible simple uniform treatment energy levels atoms. We use it here analyze configuration mixing between $2{s}^{2}2{p}^{x}$ $2{p}^{x+2}$ configurations, determine contribution configurations $O(4)$ $U(3)$ symmetry several types...

Rincon de Parangueo is a Quaternary maar that had perennial lake until the 1980s.The was gradually desiccated as consequence of drawdown in Salamanca-Valle Santiago regional aquifer and now functions playa-lake.In contrast with features observed other crater-lakes region (La Alberca, Cíntora, San Nicolás), which also dried up at same time, bottom Rincón crater displays clear evidence active deformation associated mass movement sediments towards depocenter inside crater.The most conspicuous...

Work done by many authors indicates that important tools for calculations in microscopic collective models are the matrix elements of generators symplectic group Sp(6) an Sp(6)⊇U(3) basis. Rosensteel has derived recursion relations these while Filippov determined them using generating function technique, but it would also be convenient to have explicit and analytic formulas them. This is what we do this paper case closed shells, i.e., when irreducible representation (irrep) characterized...

For several years the authors have been interested in determining complete sets of states for macroscopic nuclear collective models, such as Bohr–Mottelson one (BM) and interacting boson approximation (IBA), well their use structure calculations. In present paper we obtain a set microscopic models those Vanagas Filippov Smirnov. calculations these requires A nucleon system, appropriate coordinates which include ones related with degrees freedom. As is customary physics, derived more...

Since its start nuclear theory has lived with the dichotomy of viewing nucleus microscopically, as a system nucleons, or describing it macroscopically in terms collective coordinates. In last decade though, point transformation been introduced which single particle coordinates can be expressed ones plus others, opening possibility deriving microscopic model. present paper we confront macroscopic and models, first space two dimensions, find explicitly unitary representation quantum mechanics...

The main objective of this paper is to derive from a unified viewpoint particular one- and two-body radial matrix elements with respect oscillator Coulomb states. All the results have been obtained previosly using either generating functions Laguerre polynomials or group theoretical methods related realizations Lie algebras associated those We show, though, in how some proposed can be derived physical considerations. idea translate well-known realizations, Heisenberg picture, corresponding...

In a previous paper of this series we showed that nuclear collective behavior can be related to the symplectic geometry many-nucleon system, when introduce in it appropriate constraints. We full discussion many-body system requires—in space d dimensions—the basis for irreducible representations Sp(2d) group chain Sp(2d)⊇Sp(2)×𝒪(d), as well matrix elements generators basis. present implement program fully d=2, both because mathematical interest Sp(4)⊇Sp(2)×𝒪(2) and stepping stone...

In the present paper a program for collective symplectic model in two-dimensional space based on sp(4,R) Lie algebra is developed full. The problem only of conceptual interest but, as it admits complete analytic discussion, provides insights into more realistic nuclear models such interacting boson approximation (IBA) associated with u(6) and sp(6,R).

As was indicated in previous papers, general Hamiltonians for systems of n particles three-dimensional space can be formulated the enveloping algebra symplectic group Sp(6n). This admits, among others, subgroup Sp(6)×O(n) and, as has been noticed by many authors, collective Sp(6), so that their eigenstates characterized a definite irreducible representation (irrep) this group. The mathematical problem is then to determine matrix elements generators Sp(6) basis irreps well appropriate...