Quantum Numbers, Level Patterns, and the Effects of Terms Excluded from

2 Quantum Numbers, Level Patterns, and the Effects of Terms Excluded from.  

The energy-level pattern associated with the case (a) consists of groups 

That is, values of the off-diagonal matrix elements of the BJ S, S-uncoupling operator, within a 2S+1An multiplet state, must be much smaller than the energy separation between multiplet components that result from differences between diagonal matrix elements of Hso. Since matrix elements of the S-uncoupling operator are proportional to J, at sufficiently high-J case (a) ceases to be as good an approximation as case (b). 

The case (b) basis functions are defined as eigenfunctions of Hel and the I (N2 — N2) part of HROT. The part of HROT that is included in iR0) has only diagonal case (b) matrix elements, and the rotational energy is En = B[N(N +1) — A2] rather than B[J(J +1) — Q,2 + 5(5 +1) — E2]. Each TV-value is 25 + 1-fold degenerate, with J-values in the range N — S J N + S. This degeneracy is lifted by the spin-rotation term (Section 3.4.3), 

Neglecting HSR, from which the maximum resultant splitting of the. / components of a given iV-value is 

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