Irreducible Representations of the Semidirect‐Product Group Kn = An : Sn and the Harmonic‐Oscillator Shell Model

1968 ◽  
Vol 9 (4) ◽  
pp. 639-649 ◽  
Author(s):  
Peter Kramer
Keyword(s):  
Harmonic Oscillator ◽  
Shell Model ◽  
Semidirect Product ◽  
Irreducible Representations ◽  
Product Group ◽  
Oscillator Shell

THE RESPONSE FUNCTION OF THE 4He, 16O AND 40Ca NUCLEI IN THE HARMONIC OSCILLATOR SHELL MODEL AND THE IMPULSE APPROXIMATIONS

2013 ◽  
Vol 22 (02) ◽  
pp. 1350011
Author(s):  
M. MODARRES ◽  
Y. YOUNESIZADEH
Keyword(s):  
Harmonic Oscillator ◽  
Shell Model ◽  
Momentum Distribution ◽  
Impulse Approximation ◽  
Distribution Functions ◽  
Heavy Nuclei ◽  
Momentum Distribution Function ◽  
Oscillator Shell ◽  
Nucleus Scattering ◽  
The One

In this work, the response functions (RFs) of the 4 He , 16 O and 40 Ca nuclei are calculated in the harmonic oscillator shell model (HOSM) and the impulse approximation (IA). First, the one-body momentum distribution and the one-body spectral functions for these nuclei are written in the HOSM configuration. Then, their RFs are calculated, in the two frameworks, namely the spectral and the momentum distribution functions, within the IA. Unlike our previous work, no further assumption is made to reduce the analytical complications. For each nucleus, it is shown that the (RF) evaluated using the corresponding spectral function has a sizable shift, with respect to the one calculated in terms of the momentum distribution function. It is concluded that for the heavier nuclei, this shift increases and reaches nearly to a constant value (approximately 62 MeV), i.e., similar to that of nuclear matter. It is discussed that in the nuclei with the few nucleons, the above shift can approximately be ignored. This result reduces the theoretical complication for the explanation of the ongoing deep inelastic scattering (DIS) experiments of 3 H or 3 H nucleus target in the Jefferson Laboratory. On the other hand, it is observed that in the heavier nuclei, the RF heights (width) decrease (increase), i.e., the comparison between the theoretical and the experimental electron nucleus scattering cross-section is more sensible for heavy nuclei rather than the light ones.

scholarly journals The Chapman?Enskog Solution of the Boltzmann Equation: A Reformulation in Terms of Irreducible Tensors and Matrices

1967 ◽  
Vol 20 (3) ◽  
pp. 205 ◽  
Author(s):  
Kallash Kumar
Keyword(s):  
Boltzmann Equation ◽  
Kinetic Theory ◽  
Harmonic Oscillator ◽  
Shell Model ◽  
Nuclear Physics ◽  
Collision Integral ◽  
Polar Coordinates ◽  
Irreducible Tensors ◽  
The Boltzmann Equation ◽  
Oscillator Shell

The Chapman-Enskog method of solving the Boltzmann equation is presented in a simpler and more efficient form. For this purpose all the operations involving the usual polynomials are carried out in spherical polar coordinates, and the Racah-Wigner methods of dealing with irreducible tensors are used throughout. The expressions for the collision integral and the associated bracket expressions of kinetic theory are derived in terms of Talmi coefficients, which have been extensively studied in the harmonic oscillator shell model of nuclear physics.

On the Cortex of the Groups 𝕋n ⋉ ℍn

2020 ◽  
pp. 2150149
Author(s):  
Aymen Rahali
Keyword(s):  
Heisenberg Group ◽  
Semidirect Product ◽  
Representation Formula ◽  
Irreducible Representations ◽  
Coadjoint Orbits ◽  
Dimensional Torus ◽  
Product Group ◽  
Unitary Dual ◽  
Identity Representation

Let [Formula: see text] be the [Formula: see text]-dimensional Heisenberg group and let [Formula: see text] be the [Formula: see text]-dimensional torus acting on [Formula: see text] by automorphisms. We consider the semidirect product group [Formula: see text] The cortex, [Formula: see text] of [Formula: see text] is the set of all unitary irreducible representations [Formula: see text] in the unitary dual [Formula: see text] of [Formula: see text] that cannot be Hausdorff separated from the identity representation [Formula: see text] of [Formula: see text] In this paper, we describe explicitly the cortex ([Formula: see text]) of [Formula: see text] using the coadjoint orbits of the group.

Calculation of Coefficients of Fractional Parentage for Large-Basis Harmonic-Oscillator Shell Model

2002 ◽  
Vol 296 (2) ◽  
pp. 287-298 ◽  
Author(s):  
A. Deveikis ◽  
R.K. Kalinauskas ◽  
B.R. Barrett
Keyword(s):  
Harmonic Oscillator ◽  
Shell Model ◽  
Fractional Parentage ◽  
Oscillator Shell

Quantum Entropy for Nuclei

1997 ◽  
Vol 06 (03) ◽  
pp. 497-505 ◽  
Author(s):  
C. P. Panos ◽  
S. E. Massen
Keyword(s):  
Harmonic Oscillator ◽  
Shell Model ◽  
Momentum Space ◽  
Short Range ◽  
Functional Form ◽  
Oscillator Parameter ◽  
Nuclear Systems ◽  
Oscillator Shell ◽  
Short Range Correlations ◽  
Number Of Particles

The position- and momentum-space information entropies of nuclei are calculated in the framework of two models of the nucleus, i.e. the harmonic oscillator shell model and a correlated model which takes into account short range correlations. It is found that for every nucleus the sum of position and momentum entropies is independent of the oscillator parameter and increases slightly by introducing short range correlations. Finally it turns out that the same functional form S =aN + bN ln N for the entropy as function of the number of particles N (electrons or nucleons) holds approximately for atomic and nuclear systems.

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