DEFORMED SHELL CLOSURES FOR LIGHT ATOMIC CLUSTERS

The spheroidal shell model of the Nilsson type is used to describe the deformed states of atomic clusters. The Hamiltonian is analytically solved in cylindrical coordinates, where l2 term is treated as deformation-dependent. The usual asymptotic eigenfunctions are obtained for axially symmetric potentials without approximation, and the radial wave function usually employed for further computation is no longer needed. The energy levels obtained in such a way are used as input data for shell correction calculations. Minima due to shell effects are obtained as a function of the number of atoms in the atomic cluster as well as the δ-deformation-dependent. Calculations are performed for N up to 200, and spheroidally (oblate and prolate) deformed shell closures are predicted.

Download Full-text

Representations of the n-dimensional rotation group

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100035519 ◽

1961 ◽

Vol 57 (3) ◽

pp. 469-475 ◽

Cited By ~ 1

Author(s):

A. P. Stone

Keyword(s):

Bound States ◽

Differential Operators ◽

Energy Levels ◽

Radial Wave Function ◽

Rotation Group ◽

Wave Mechanics ◽

Radial Wave ◽

Shift Operators ◽

Branching Rule ◽

Infinitesimal Operators

ABSTRACTThe commutators of the infinitesimal operators of the n-dimensional rotation group Rn with vector operators under Rn are expressed in a vectorial notation. The infinitesimal operators for the representations (l 0…0) are treated in detail. Shift operators for l are constructed and are used to derive the branching rule for these representations. The energy levels and degeneracy of bound states of a particle under an inverse square force in n dimensions are found by wave mechanics and by expressing the Hamiltonian in terms of Casimir's operator for Rn+1. Differential operators which transform one radial wave function into another are obtained.

Download Full-text

Analytical solution of the Shredinger equation for the linear combination of the Manning-Rosen and the class of Yukawa potential

Izvestiya vysshikh uchebnykh zavedenii. Fizika ◽

10.17223/00213411/64/9/157 ◽

2021 ◽

pp. 157-169

Author(s):

G.A. Bayramova ◽

Keyword(s):

Analytical Solution ◽

Bound States ◽

Hypergeometric Functions ◽

Yukawa Potential ◽

Energy Levels ◽

Energy Eigenvalue ◽

Radial Wave ◽

Rosen Potential ◽

Analytical Expressions ◽

Potential Parameters

In the present work, an analytical solution for bound states of the modified Schrödinger equation is found for the new supposed combined Manning-Rosen potential plus the Yukawa class. To overcome the difficulties arising in the case l ≠ 0 in the centrifugal part of the Manning-Rosen potential plus the Yukawa class for bound states, we applied the developed approximation. Analytical expressions for the energy eigenvalue and the corresponding radial wave functions for an arbitrary value l ≠ 0 of the orbital quantum number are obtained. And also obtained eigenfunctions expressed in terms of hypergeometric functions. It is shown that energy levels and eigenfunctions are very sensitive to the choice of potential parameters.

Download Full-text

ECsim-CYL: Energy Conserving Semi-Implicit particle in cell simulation in axially symmetric cylindrical coordinates

Computer Physics Communications ◽

10.1016/j.cpc.2018.10.026 ◽

2019 ◽

Vol 236 ◽

pp. 153-163 ◽

Cited By ~ 2

Author(s):

Diego Gonzalez-Herrero ◽

Alfredo Micera ◽

Elisabetta Boella ◽

Jaeyoung Park ◽

Giovanni Lapenta

Keyword(s):

Axially Symmetric ◽

Cylindrical Coordinates ◽

Particle In Cell ◽

Energy Conserving ◽

Cell Simulation

Download Full-text

TEMPERATURE DEPENDENCE OF THE NUCLEAR ENERGY IN RELATIVISTIC MEAN-FIELD THEORY

International Journal of Modern Physics E ◽

10.1142/s021830130500334x ◽

2005 ◽

Vol 14 (03) ◽

pp. 505-511 ◽

Cited By ~ 5

Author(s):

B. NERLO-POMORSKA ◽

K. POMORSKI ◽

J. SYKUT ◽

J. BARTEL

Keyword(s):

Single Particle ◽

Level Density ◽

Mean Field Theory ◽

Mean Field ◽

Correction Method ◽

Shell Correction ◽

Shell Effects ◽

Relativistic Mean Field ◽

Single Particle Level ◽

Particle Level

Self-consistent relativistic mean-field (RMF) calculations with the NL3 parameter set were performed for 171 spherical even-even nuclei with 16≤A≤224 at temperatures in the range 0≤T≤4 MeV . For this sample of nuclei single-particle level densities are determined by analyzing the data obtained for various temperatures. A new shell-correction method is used to evaluate shell effects at all temperatures. The single-particle level density is expressed as function of mass number A and relative isospin I and compared with previous estimates.

Download Full-text

Approximate analytical solution of continuous states for the l-wave Schrödinger equation with a diatomic molecule potential

Open Physics ◽

10.2478/s11534-009-0108-7 ◽

2010 ◽

Vol 8 (4) ◽

Cited By ~ 10

Author(s):

Gao-Feng Wei ◽

Wen-Chao Qiang ◽

Wen-Li Chen

Keyword(s):

Schrödinger Equation ◽

Diatomic Molecule ◽

Schrodinger Equation ◽

Scattering Amplitude ◽

Energy Levels ◽

Bound State ◽

Radial Wave ◽

Continuous States ◽

Analytical Properties ◽

Function Potential

AbstractThe continuous states of the l-wave Schrödinger equation for the diatomic molecule represented by the hyperbolical function potential are carried out by a proper approximation scheme to the centrifugal term. The normalized analytical radial wave functions of the l-wave Schrödinger equation for the hyperbolical function potential are presented and the corresponding calculation formula of phase shifts is derived. Also, we interestingly obtain the corresponding bound state energy levels by analyzing analytical properties of scattering amplitude.

Download Full-text

EXACT SOLUTION OF THE CONTINUOUS STATES FOR GENERALIZED ASYMMETRICAL HARTMANN POTENTIALS UNDER THE CONDITION OF PSEUDOSPIN SYMMETRY

International Journal of Modern Physics A ◽

10.1142/s0217751x07037160 ◽

2007 ◽

Vol 22 (26) ◽

pp. 4825-4832 ◽

Cited By ~ 29

Author(s):

JIAN-YOU GUO ◽

FANG ZHOU ◽

FENG-LIANG GUO ◽

JIAN-HONG ZHOU

Keyword(s):

Exact Solution ◽

Bound States ◽

Continuation Method ◽

Radial Wave Function ◽

Pseudospin Symmetry ◽

Radial Wave ◽

Confluent Hypergeometric Functions ◽

Momentum Plane ◽

Scattering Phase ◽

Hartmann Potential

Under the condition of pseudospin symmetry, the exact solution of Dirac equation is studied and that no bound solutions are observed for generalized asymmetrical Hartmann potential, which is in agreement with that for Coulomb potential. With the analytic continuation method, the unbound solutions are presented by mapping the wave functions of bound states in the complex momentum plane. Furthermore, the scattering phase shifts are obtained from the radial wave function by analyzing the asymptotic behavior of the confluent hypergeometric functions.

Download Full-text

STUDY OF THE η-7Be INTERACTION NEAR THRESHOLD IN p-6Li FUSION

International Journal of Modern Physics E ◽

10.1142/s0218301309013609 ◽

2009 ◽

Vol 18 (05n06) ◽

pp. 1383-1388

Author(s):

N. J. UPADHYAY ◽

N. G. KELKAR ◽

K. P. KHEMCHANDANI ◽

B. K. JAIN

Keyword(s):

Wave Function ◽

Final State Interaction ◽

Radial Wave Function ◽

State Interaction ◽

Nuclear Medium ◽

Final State ◽

Radial Wave ◽

Near Threshold

We present a calculation for η production in the p-6Li fusion near threshold including the η-7Be final state interaction (FSI). We consider the 6Li and 7Be nuclei as α-d and α-3He clusters respectively. The calculations are done for the lowest states of 7 Be with [Formula: see text] resulting from the L = 1 radial wave function. The η-7Be interaction is incorporated through the η-7BeT–matrix, constructed from the medium modified matrices for the η-3He and η-α systems. These medium modified matrices are obtained by solving few body equations, where the scattering in nuclear medium is taken into account.

Download Full-text