scholarly journals Analytical formula for numerical evaluations of the Wigner rotation matrices at high spins

2015 ◽  
Vol 91 (1) ◽  
Author(s):  
Naoki Tajima
Keyword(s):  
Analytical Formula ◽  
Wigner Rotation ◽  
Rotation Matrices

Simplified derivation of the crossing relations using the substitution rule as a guide

1979 ◽  
Vol 57 (5) ◽  
pp. 706-716
Author(s):  
Richard A. Morrow
Keyword(s):  
Analytic Continuation ◽  
Weak Interaction ◽  
Rest Frame ◽  
Center Of Mass ◽  
Lorentz Transformations ◽  
Simple Derivation ◽  
Wigner Rotation ◽  
Substitution Rule ◽  
Rotation Matrices ◽  
Helicity Amplitudes

A simple derivation of the Trueman–Wick crossing relations for center of mass helicity amplitudes is presented. The method uses only Wigner rotation matrices and does not deal specifically with more general Lorentz transformations. Each particle is treated individually in turn in its own rest frame in order to discover how its helicity transforms under crossing and the substitution rule is used as a guide in determining the outcome of the analytic continuation. Crossing relations for different paths of analytic continuation in the s–t plane are discussed and it is shown that care must be exercised when dealing with weak interaction amplitudes. The method presented may be extended straightforwardly to multiparticle amplitudes.

Application of an analytical formula for UV Index reconstructions for two locations in Southwestern Spain

Tellus B ◽  
2011 ◽  
Vol 63 (5) ◽  
Author(s):  
M. Antón ◽  
A. Serrano ◽  
M. L. Cancillo ◽  
J. A. García ◽  
S. Madronich
Keyword(s):  
Analytical Formula ◽  
Uv Index

An alternative model of the vibronic coupling in octahedral complexes

1988 ◽  
Vol 53 (6) ◽  
pp. 1134-1140
Author(s):  
Martin Breza ◽  
Peter Pelikán
Keyword(s):  
Linear Regression ◽  
Alternative Model ◽  
Potential Surface ◽  
Analytical Formula ◽  
Coupling Model ◽  
Regression Method ◽  
Vibronic Coupling ◽  
Linear Regression Method ◽  
Active Systems ◽  
Jahn Teller

It is suggested that for some transition metal hexahalo complexes, the Eg-(a1g + eg) vibronic coupling model is better suited than the classical T2g-(a1g + eg) model. For the former, alternative model, the potential constants in the analytical formula are evaluated from the numerical map of the adiabatic potential surface by using the linear regression method. The numerical values for 29 hexahalo complexes of the 1st row transition metals are obtained by the CNDO/2 method. Some interesting trends of parameters of such Jahn-Teller-active systems are disclosed.

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