Recipes for Evaluation of Molecule-Fixed Angular Momentum Matrix Elements

2 Recipes for Evaluation of Molecule-Fixed Angular Momentum Matrix Elements 

The matrix elements of the J0 operator are calculated here as a first step toward those of R. Eigenvalues of the operator J2 do not appear in the list of quantum numbers which define the nJ LSQAY,Mj) basis. However, 

J2 is expressed in terms of operators for which the matrix elements axe easily evaluable. Further, L2, S2, and LZSZ have only diagonal matrix elements in the nJLSflA SMj) basis, whereas the L ST terms follow AA = —AE = 1, Afi = 0, A J = A L = AS = 0 selection rules  

AA = —AE = 1 off-diagonal matrix elements of J2 the only term in J2 that gives rise to AA = —AE = 1 matrix elements is L S=F thus the relevant matrix element is 

If L cannot be specified in the basis set, then the selection rules remain unchanged and L(L + 1), wherever it appears, must be replaced by an unknown constant. 

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