Assignments Based on Pattern-Forming Rotational Quantum Numbers

3 Assignments Based on Pattern-Forming Rotational Quantum Numbers 

When the electronic transition is between a known rotational level (N , e/f determined in a double resonance scheme) of a case (b) initial state and an unknown rotational level of a case (d) final state, the existence of pattern-forming rotational quantum numbers [[B N (N + 1) for case (b) and B+N+ (N+ +1) for case (d)] provides a basis for N+ — N rotational assignments. 

If S — 0 (or if S 0 but S is fully decoupled from the internuclear axis and the AN = A J propensity rule is rigorously obeyed), then for a given value of l in the nonpenetrating state, there are 21 + 3 possible values of N+ — N , from N+ = N — l — 1 to N+ = N + 1 + 1. These transitions are called A-form where X is the letter of the alphabet that corresponds to N+ — AT . A stacked plot of spectra recorded from consecutive values of N immediately reveals the value of N+ — N , based on the standard expression for rotational branches 

At low-Ar , the spacing of successive lines in a branch, dX/dN , is dominated by the term in X N ) linear in N . The stacked plot, in which the spectra for excitation of N , N +l, N +2. are plotted, without any shift of wavenumber axis, each one above the previous one, reveals the form of the rotational branch, m = N+ —N . For example, if B+ B , an iV-form branch (m = —3) appears on the stacked plot as a series of lines of slope —45. 

Once a value for N+ is established from the stacked plot, the three possibilities for IV7, e/f—symmetry, and Ir (Ir = N — N+ is the projection of the Rydberg orbital angular momentum, 1, on the axis of nuclear rotation, N+), N = N l,e// — N ,e/f and N1 = N ,f/e — N ,e/f, can be examined by careful search for an upper state term value match of the N+ level observed from the (N , e/f) lower level (lower state combination difference) in spectra recorded from the (N — 2, e/f), (N — 1, f/e), (N +1, f/e), and (IV + 2, e/f) lower levels. It is best to look at the lowest N+ levels, because the transition to case (d) will be least complete at low-lV+ and the normally weak rotational branch needed for an IV -determining combination difference may have sufficient intensity to be observable. Once the values of N, N+,Ir, and e/f symmetry are established, the (—1)1 1r reflection symmetry of the Ur) Rydberg orbital determines whether l is even or odd and the requirement that l lR puts a lower bound on l. 

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