# Radio-frequency spectrum of metastable N_{2}(A ^{3}Σ _{u}^{+}). II. Fine structure, magnetic hyperfine structure, and electric quadrupole constants in the lowest 13 vibrational levels

## Abstract

The hyperfine structure of the A 3 ΣU+ state of N2 has been measured at low magnetic fields (< 1 G) by means of the molecular beam magnetic resonance method. Resolved transitions between hyperfine levels with quantum numbers (v,N,J,F,MF) to levels (v,N,J,F-1, M'p = M F or M F ±1 ) have been ob served for states with quantum numbers (N,J,F) equal to (0,1,2), (1,2,4), (1,2,3), (2,1,2), and (3,2,4), within each of the vibrational levels, v = 0-12, and for various vibrational levels of the (3,2,3) and (3,2,2) states. Individual hyperfine frequencies have been measured to an accuracy of ±10 kHz. The theory needed to calculate and interpret the hyperfine structure in any 3 Σ state is developed in considerable detail. By using degenerate perturbation theory to remove various matrix elements connecting different electronic and vibrational states it is shown that the effective rotational-fine and hyperfine structure Hamiltonians for a particular vibrational level of the A 3 Σ state of N2 can be written, respectively, as H ve(RF-N 2)=Bṽ N2 + (2/3)1/2λ ṽ T2 (S,S) · T2 (n,n) + λṽ T1 (N) · T1 (S) and Hve(HF·N2)=aṽ T 1(IT)·T1(S)-(5/2)1/2 βṽ T1 (IT)·T 1 [T1 (S), T2(n)] +pṽ T 1 (N)·T1 (IT) + (3/8)1/2 φQ̃vT2 (Ia,Ia) ·T2 (n,n)+dvT2 (Ia,I b) · T2 (n,n). The parameters α ṽ,βṽ,Qṽ,p ṽ, and g v≡(2Bṽ- γṽ)/λṽ have been determined (independently for each level) from the observed molecular beam transitions. dv is calculated independently of the beam data and λv is obtained from gv by-4 assunyjig that B v and λv are known from optical data. The experimentally determined values for αv, βv, Qv, pv, and gv along with their experimental uncertainties are given. The parameters can be fit to within experimental error by quadratic power series in (v +1/2). Each v dependent parameter in the above effective Hamiltonian consists of a number of both first order (diagonal) and second order terms. It is concluded that in most cases second order terms (arising from matrix elements off diagonal in electronic and vibrational states) are not negligible compared to the present experimental error. However, for αṽ, βṽ, and Qṽ, such second order terms represent only a minor contribution.