Method of calculating matrix elements and cross sections with wave functions with definite angular momentum

1976 ◽  
Vol 26 (1) ◽  
pp. 26-30 ◽  
Author(s):  
V. S. Polikanov
Keyword(s):  
Angular Momentum ◽  
Cross Sections ◽  
Wave Functions ◽  
Matrix Elements ◽  
Definite Angular Momentum

Méthode du moment angulaire inversé. Partie I : La théorie MI

1975 ◽  
Vol 53 (5) ◽  
pp. 533-541 ◽  
Author(s):  
J-L. Féménias ◽  
C. Athénour
Keyword(s):  
Angular Momentum ◽  
Wave Functions ◽  
Matrix Elements ◽  
Intensity Factors ◽  
Normal Theory ◽  
Commutation Relations ◽  
Minus Sign ◽  
Mi Theory ◽  
Optimal Set ◽  
General Method

In order to present a general method of calculating wave functions, matrix elements, and intensity factors in molecular rotational problems, we deal here with a theory of reversed angular momentum (MI theory), i.e. momentum whose components obey commutation relations with an anomalous minus sign. This theory is built following the principal corresponding steps of the normal theory and a simple correspondence is established between both of them allowing us to perform calculations in the former and to give the results using the formalism of the latter.In particular we dwell here on the consistency of conventions and notations and on a rigorous presentation of spherical tensor operators in MI theory together with the choice of the optimal set of them leading to simplest calculations.

Low-lying collective bands in the even tungsten isotopes 180–186W

1989 ◽  
Vol 67 (5) ◽  
pp. 479-484 ◽  
Author(s):  
R. Sahu
Keyword(s):  
Wave Function ◽  
Angular Momentum ◽  
Quadrupole Interaction ◽  
Asymmetry Parameter ◽  
Degrees Of Freedom ◽  
Energy Levels ◽  
Wave Functions ◽  
Electromagnetic Properties ◽  
Matrix Elements ◽  
Rigid Model

The γ-rigid model has been used to study the energy levels and the electromagnetic properties of 180, 182, 184, 186W. In this model, the intrinsic wave functions are obtained using the pairing plus the quadrupole–quadrupole interaction Hamiltonian of Baranger and Kumar. Good angular momentum states are projected approximately from such a triaxially symmetric intrinsic wave function. This model assumes the nucleus to be γ rigid but soft in the β degrees of freedom. The asymmetry parameter γ for a given nucleus is extracted using the experimental energies of the first 2+ and second 2+ states within the framework of the Davydov–Filippov model. The symmetry parameter β for each J state is determined from the minimization of the projected energy. The calculated energy levels of the ground and the 7 band, the B(E2) values, the electromagnetic moments, the E2 and E4 matrix elements, and the B(E2) ratios agree quite well with experimental results.

THE STEREODYNAMICS STUDY OF THE C(3P) + OH (X2 Π) → CO(X1Σ+) + H(2S) REACTION

2010 ◽  
Vol 09 (05) ◽  
pp. 935-943 ◽  
Author(s):  
PENG SONG ◽  
YONG-HUA ZHU ◽  
JIAN-YONG LIU ◽  
FENG-CAI MA
Keyword(s):  
Angular Momentum ◽  
Cross Sections ◽  
Collision Energy ◽  
Energy Surface ◽  
Center Of Mass ◽  
Title Reaction ◽  
High Collision Energy ◽  
Dependency Relationship ◽  
Energy Dependency ◽  
Mass Frame

The stereodynamics of the title reaction on the ground electronic state X2A' potential energy surface (PES)1 has been studied using the quasiclassical trajectory (QCT) method. The commonly used polarization-dependent differential cross-sections (PDDCSs) of the product and the angular momentum alignment distribution, P(θr) and P(Φr), are generated in the center-of-mass frame using QCT method to gain insight of the alignment and orientation of the product molecules. Influence of collision energy on the stereodynamics is shown and discussed. The results reveal that the distribution of P(θr) and P(Φr) is sensitive to collision energy. The PDDCSs exhibit different collision energy dependency relationship at low and high collision energy ranges.

scholarly journals Fission cross sections as a probe of fusion dynamics at high angular momentum

2018 ◽  
Vol 98 (4) ◽  
Author(s):  
C. S. Palshetkar ◽  
D. J. Hinde ◽  
M. Dasgupta ◽  
E. Williams ◽  
K. Ramachandran ◽  
...  
Keyword(s):  
Angular Momentum ◽  
Cross Sections ◽  
High Angular Momentum

SYMMETRY DECOUPLING IN LINEAR ALGEBRAIC VARIATIONAL SCATTERING PROBLEMS

1995 ◽  
Vol 06 (01) ◽  
pp. 105-121
Author(s):  
MEISHAN ZHAO
Keyword(s):  
Angular Momentum ◽  
Variational Principle ◽  
Total Angular Momentum ◽  
Numerical Calculations ◽  
Quantum Mechanical ◽  
Matrix Elements ◽  
Scattering Problems ◽  
Identical Particles ◽  
Generalized Newton

This paper discusses the symmetry decoupling in quantum mechanical algebraic variational scattering calculations by the generalized Newton variational principle. Symmetry decoupling for collisions involving identical particles is briefly discussed. Detailed discussion is given to decoupling from evaluation of matrix elements with nonzero total angular momentum. Example numerical calculations are presented for BrH2 and DH2 systems to illustrate accuracy and efficiency.

A comparison of theory and experiment for photo-ionization cross-sections I. Neon and the elements from boron to neon

1951 ◽  
Vol 208 (1094) ◽  
pp. 408-418 ◽  
Keyword(s):  
Cross Sections ◽  
General Trend ◽  
Wave Functions ◽  
Ionization Cross ◽  
Hartree Fock ◽  
Quantal Theory ◽  
Ionization Cross Sections ◽  
Photo Ionization ◽  
Near Future ◽  
Dipole Length

The quantal theory of the continuous photo-electric absorption of radiation is briefly summarized, pàrticular attention being given to the alternative formulae available and to the accuracy to be expected in practical calculations. Detailed calculations are described for the photo-ionization cross-section of neon, a system for which it is understood that experimental data should be available in the near future. The calculation is made using Hartree-Fock wave functions and the two formulae of the dipole length and the dipole velocity. The corresponding cross-sections are found to be 5.8 and 4.4 x 10- 18 cm 2 . at the spectral head and to rise slowly with increasing frequency until a broad maximum is reached for an energy of the ejected electron of about 11 eV. A comparison is made with previous calculations on the elements from boron to neon ; the general trend of the results is discussed and improved estimates for boron and fluorine are given (10 x 10 -18 cm 2 . for boron and 4.3 x 10- 18 cm 2 . for fluorine at the spectral head).

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