Gabriela Popa | Ohio University of Zanesville (original) (raw)

Papers by Gabriela Popa

Journal of stochastic analysis, Mar 7, 2023

For any random variable X, having finite moments of all orders, and any polynomial function f , i... more For any random variable X, having finite moments of all orders, and any polynomial function f , if N denotes the number operator of X, then f (N) can be written uniquely as an infinite series of terms of the form A k (X)D k , where A k is a polynomial of degree at most k and D denotes the differentiation operator. We study the random variables for which this infinite series, called the position-momentum decomposition of X, is a finite sum meaning that after a while all the position coefficients, A k (X), vanish. Thus, f (N) belongs to the Weyl algebra of X. A simple method, for recovering the probability distribution of X, from the given finite sum position-momentum decomposition of f (N) is presented first. We apply this method to the case when f is linear and f (N) is quadratic in D, recovering the Gaussian and Gamma distributions, and their Szegö-Jacobi parameters.

Journal of Stochastic Analysis

We describe the random variables, having finite moments of all orders, whose number operator sati... more We describe the random variables, having finite moments of all orders, whose number operator satisfies a quadratic equation whose positionmomentum decomposition is quadratic in the differentiation operator. We will see that the orthogonal polynomials generated by these random variables are the Jacobi polynomials.

Journal of Mathematical Physics, 2021

We present first a set of commutator relationships involving the joint quantum, semi-quantum, and... more We present first a set of commutator relationships involving the joint quantum, semi-quantum, and number operators generated by a finite family of random variables, having finite moments of all orders, and show how these commutators can be used to recover the joint quantum operators from the semi-quantum operators. We show that any linear operator defined on an algebra of polynomials or the polynomial random variables, generated by a finite family of random variables, having finite moments of all orders, can be written uniquely as an infinite sum of compositions of the multiplication operators, generated by these random variables, and the partial derivative operators. In the terms of this sum, each multiplication operator is placed to the left side of each partial derivative operator. We provide many examples concerning the decomposition of some classic operators.

Bulletin of the American Physical Society, 2014

Physical review, Nov 20, 2000

The pseudo-SU͑3͒ model is used to describe the low-energy spectra and electromagnetic transition ... more The pseudo-SU͑3͒ model is used to describe the low-energy spectra and electromagnetic transition strengths in 156 Gd, 158 Gd, and 160 Gd. The Hamiltonian includes spherical single-particle energies, the quadrupolequadrupole interaction, proton and neutron pairing interactions, plus four rotorlike terms. The quadrupolequadrupole and pairing interaction strengths are assigned the values ϭ23A Ϫ5/3 and G ϭ21/A, G ϭ17/A, respectively. The single-particle energies were taken from experiment but scaled to yield an overall best fit. For the other four rotorlike terms, which do not mix SU͑3͒ representations and induce only small changes in the spectra, a consistent set of parameters is given. The basis states are built as linear combinations of SU͑3͒ states which are the direct product of SU͑3͒ proton and neutron states with pseudospin zero. The results are in good agreement with experimental data, demonstrating the suitability of the model to describe heavy deformed nuclei.

Physical review, Jun 7, 2004

An empirical investigation of the trends in the properties of the nonyrast K =2 ␥ + and K =0 2 + ... more An empirical investigation of the trends in the properties of the nonyrast K =2 ␥ + and K =0 2 + bandhead configurations in nuclei that are related to one another through the addition or removal of ␣-particle-like structures, reveals their complex and changing behavior in contrast to the smooth behavior of the yrast states. A systematic application of the pseudo-SU(3) model for such a sequence of deformed nuclei from the rare earth region leads to an accurate and unified description of not only yrast, but nonyrast collective bands. The onset of deformation as manifested through the position of the excited bandheads in the spectra is understood and interpreted by using a realistic model Hamiltonian in conjunction with a microscopic distribution of the eigenstates across allowed proton and neutron strong-coupled SU(3) configurations.

Journal of Mathematical Physics

We show first how the joint semi-quantum and quantum operators of a finite family of random varia... more We show first how the joint semi-quantum and quantum operators of a finite family of random variables having finite moments of all orders can be recovered from their joint number operator. We then characterize the polynomially symmetric and polynomially factorizable random variables in terms of their joint number operator. Finally, we present the quantum decomposition of the number and quantum operators of the random variables whose orthogonal polynomials are the Gegenbauer polynomials.

Bulletin of the American Physical Society, Oct 30, 2020

interactions ('optical potentials') are needed as input to nuclear reaction calculations. In a mu... more interactions ('optical potentials') are needed as input to nuclear reaction calculations. In a multiple scattering expansion for nucleon-nucleus elastic scattering the leading order term requires integrating over nonlocal, translationally invariant one-body densities and off-shell nucleon-nucleon (NN) scattering amplitudes. For consistency the spin of the struck nucleon must be taken into account on the same footing as the spin of the projectile nucleon. In this talk, the first complete nucleon-nucleus ab initio leading order effective interactions will be used to calculate elastic scattering observables for light nuclei. These potentials are based on NCSM spin-dependent one-body densities together with NN amplitudes derived from the same NN interaction. We will focus on elastic scattering off the Helium isotope chain 4 He, 6 He, and 8 He in the energy regime between 71 and 200 MeV laboratory kinetic energy.

Revista Mexicana De Fisica, 2006

Bulletin of the American Physical Society, 2018

Revista Mexicana De Fisica, 2000

AIP Conference Proceedings, 2006

The recent 160Gd(p,t)158Gd experiment has raised again the question about the nature of the low-l... more The recent 160Gd(p,t)158Gd experiment has raised again the question about the nature of the low-lying excited 0+ states in deformed nuclei. New (p,t) experiments have resolved typically about ten low-lying excited 0+ states. Calculations using the IBA model, the projected shell model and the quasiparticle-phonon model have answered partially this question and showed the complicated nature of these states.We study

arXiv: Nuclear Theory, 2019

Constructing microscopic effective interactions (`optical potentials') for nucleon-nucleus (N... more Constructing microscopic effective interactions (`optical potentials') for nucleon-nucleus (NA) elastic scattering requires in first order off-shell nucleon-nucleon (NN) scattering amplitudes between the projectile and the struck target nucleon and nonlocal one-body density matrices. While the NN amplitudes and the {\it ab intio} no-core shell-model (NCSM) calculations always contain the full spin structure of the NN problem, one-body density matrices used in traditional microscopic folding potential neglect spin contributions inherent in the one-body density matrix. Here we derive and show the expectation values of the spin-orbit contribution of the struck nucleon with respect to the rest of the nucleus for 4^{4}4He, 6^{6}6He, 12^{12}12C, and 16^{16}16O and compare them with the scalar one-body density matrix.

Symmetries in Nuclear Structure, 2004

ABSTRACT Symmetries, articulated mathematically through group theory, play a central role in nucl... more ABSTRACT Symmetries, articulated mathematically through group theory, play a central role in nuclear physics. The Interacting Boson Model (IBM), introduced to our field by Franco Iachello, who's 60th birthday we honor through this symposium, is a clear and clever example of the use of group theory to model symmetries of atomic nuclei. While all present may not be IBM disciples, it is clear we are all at least IBM apostles and here to honor Franco and acknowledge his significant contributions to the field of nuclear physics and beyond. I will take the opportunity of this very special occasion to give a brief update on a complementary theory, the pseudo-SU(3) model, that builds on pseudo-spin symmetry in heavy nuclei, a theory that is applicable to deformed rare earth and actinide species.

Capture Gamma-Ray Spectroscopy and Related Topics, 2003

... Author(s): GABRIELA POPA Department of Physics, Rochester Institute of Technology, Rochester,... more ... Author(s): GABRIELA POPA Department of Physics, Rochester Institute of Technology, Rochester, NY 14623-5612, USA JORGE G. HIRSCH ... Postal 70-543 México 04510 DF, México JERRY P. DRAAYER Department of Physics and Astronomy, Louisiana State University, Baton ...

Computational and Group-Theoretical Methods in Nuclear Physics, 2004

The pseudo-SU(3) model has been extensively used to study normal parity bands in even-even and od... more The pseudo-SU(3) model has been extensively used to study normal parity bands in even-even and odd-mass heavy deformed nuclei. The use of a realistic Hamiltonian that mixes many SU(3) irreps has allowed for a successful description of energy spectra and electromagnetic transition strengths. While this model is powerful, there are situations in which the intruder states must be taken into account explicitly. The quasi-SU(3) symmetry is expected to complement the model, allowing for a description of nucleons occupying normal and intruder parity orbitals using a unified formalism.

ABSTRACT Recibido el 27 de marzo de 2003; aceptado el 27 de mayo de 2003 An update on the status ... more ABSTRACT Recibido el 27 de marzo de 2003; aceptado el 27 de mayo de 2003 An update on the status of pseudo-SU(3) shell-model calculations in strongly deformed nuclei in the rare earth region is presented. Represen-tative results for energy levels as well as E2 (quadrupole) and M1 (scissors) transitions strengths in 162 Dy (even-even) and 163 Dy (odd-mass) are given. The calculations use realistic single-particle energies and quadrupole-quadrupole and pairing interaction strengths fixed from systematics. The strengths of rotor-like terms included in the Hamiltonian – all small relative to the other terms in the interaction – were adjusted to give an overall best fit to the energy spectra. The results present a paradox: for even-even nuclei (integer angular momentum) non-zero pseudo-spin configurations seems to be unimportant while for the odd-mass systems (half-integer angular momentum) pseudo-spin mixing is essential as spin-flip couplings appear to dominate the M1 transition strengths. Keywords: Pseudo-SU(3) shell model; E2 and MI transition strengths; 162 Dy; 163 Dy. Se presenta una revisión actualizada de los cálculos del modelo de capas pseudo-SU(3) para núcleos fuertemente deformados en la región de las tierras raras. Se muestran resultados representativos de los niveles de energía y las intensidades de transición cuadrupolares (E2) y de tijera (M1) en los núcleos 162 Dy (masa par) y 163 Dy (masa impar). En los cálculos se emplean energías de partícula independiente realistas, y las intensidades de las interacciones de cuadrupolar y de apareamiento fueron fijadas usando análisis sistemáticos. Las intensidades de los términos de tipo rotor incluídos en el Hamiltoniano -todos ellos pequeños en relación con los primeros -fueron ajustadas para obtener el mejor ajuste global del espectro de energía. Los resultados obtenidos presentan una paradoja: para núcleos par-par, con momento angular entero, las configuraciones con pseudo-espín no nulo son de escasa importancia, mientras que para los sistemas de masa impar, con momento angular semientero, la mezcla de configuraciones con distinto pseudo-espín es esencial, pues domina las transiciones M1. Descriptores: Módelo de capas pseudo-SU(3); intensidad de las transiciones E2 y MI; 162 Dy; 163 Dy.

Energy levels of the four lowest bands in 160,162,164 Dy and 168 Er, B(E2) transition strengths b... more Energy levels of the four lowest bands in 160,162,164 Dy and 168 Er, B(E2) transition strengths between the levels, and the B(M1) strength distribution of the ground state, all calculated within the framework of pseudo-SU 3 model, are presented [9]. Realistic single-particle energies and quadrupolequadrupole and pairing interaction strengths fixed from systematics were used in the calculations [6]. The strengths of four rotor-like terms, all small relative to the other terms in the interaction, were adjusted to give an overall best fit to the energy spectra. The procedure yielded consistent parameter sets for the four nuclei.

Journal of Physics: Conference Series, 2017

The equivalence between the notions of "2-Meixner" and "classic Meixner" random variables is prov... more The equivalence between the notions of "2-Meixner" and "classic Meixner" random variables is proved first. A derivation of the classic Meixner random variables, using double commutators involving the semi-quantum operators, is presented next. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.