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Astron. Astrophys. 322, L1-L4 (1997)

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3. Analysis

The electronic ground state of NH is [FORMULA], so that the rotational energy levels for [FORMULA] exhibit a fine structure leading to a triplet system in the observed spectrum. For the lowest pure rotational transition, this fine structure triplet is located at 946, 974, and 1000 GHz. Furthermore, the nonzero nuclear spins of nitrogen and hydrogen give rise to magnetic dipole hyperfine structure, which is further subdivided into Fermi contact ([FORMULA]), dipole-dipole (t), and nuclear spin-rotation ([FORMULA]) interactions. In addition, the 14 N nucleus has nuclear spin [FORMULA] and hence causes an electric quadrupole interaction governed by the parameter eQq. The Hamiltonian matrix elements needed to determine the energy levels were calculated according to the coupling scheme [FORMULA], [FORMULA], and [FORMULA]. Figure 2 shows the energy level diagram of the [FORMULA] transition.

[FIGURE] Fig. 2. Energy level diagram of the [FORMULA] and 1 states of NH. The energy scale for the fine structure splitting is enlarged 10 times and the scale for the hyperfine structure is enlarged 2000 times with respect to the rotational energy levels. Transitions with relative intensities of 2% or more are indicated as listed in Table 1 (frequencies increase from left to right).

We used the same computer program as previously employed by Saleck et al. (1994a ) and Klaus et al. (1994, 1996 ), where the explicit matrix elements can be found. The calculated spectral frequencies were varied in the standard manner to determine the best molecular constants. In the fitting procedure, the observed frequencies were weighted proportionally to the inverse square of their experimental uncertainties. For unresolved hyperfine splittings, the frequencies were calculated as the weighted average of the individual hyperfine components. The transitions already reported by van den Heuvel et al. (1982 ) were replaced by our remeasured frequencies, which were expected to be more reliable. The observed-minus-calculated (O-C) values given in Table 1 show that the experimental frequencies are reproduced very well within their uncertainties, the [FORMULA] value of the fit being 46 kHz.

In Table 2, the obtained constants are listed together with their 1 [FORMULA] uncertainties. In the analysis, [FORMULA], the centrifugal distortion constant, was fixed at 51.307 MHz. This value was derived from [FORMULA] of ND after measurement of its [FORMULA] transition in the 1 THz region (to be published). A value for [FORMULA] (N), the spin-rotation constant involving the nitrogen nucleus, was determined for the first time for NH by this study. The inclusion of [FORMULA] (H) yielded no significant improvement to the fit.


Table 2. Molecular constants for NH ([FORMULA]) in its vibrational ground state [FORMULA]

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© European Southern Observatory (ESO) 1997

Online publication: June 5, 1998