^{1}, G. Michalski

^{2,a)}and M. Thiemens

^{2}

### Abstract

We have measured the rovibronic densities of four symmetric and two asymmetric isotopologues of nitrogen dioxide just below their photodissociation threshold. At dissociation threshold and under jet conditions the laser-induced fluorescence abruptly disappears because the dissociation into is much faster than the radiative decay. As a consequence, in a narrow energy range below , the highest bound rovibronic energy levels of and can be observed and sorted. A statistical analysis of the corresponding rovibronic density, energy spacing, and rovibronic transition intensities has been made. The observed intensity distributions are in agreement with the Porter-Thomas distribution. This distribution allows one to estimate the number of missing levels, and therefore to determine and compare the rovibronic and the vibronic densities. The four symmetric isotopologues, , , , and , have, respectively, a sum of and rovibronic densities of , , , and , while for the two asymmetric isotopologues, and , the corresponding densities are and . The corresponding vibronic densities are in agreement only if we include both the merging of symmetry species (from those of to those of ) and the contribution of the long-range tail(s) of the potential-energysurface along the dissociation coordinate. The effects of isotopic substitution on dissociation rates and the possible relation to mass-independent isotopic fractionation are discussed.

I. INTRODUCTION AND OBJECTIVE

II. EXPERIMENT

III. RESULTS

A. Rovibronic level counting ( and ) for symmetric isotopologues

1. Intensity distributions

2. Next neighbor distribution (NND)

3. Rovibronic and vibronic densities of symmetric isotopologues

B. Asymmetric isotopologues

IV. COMPARISON OF VIBRONIC DENSITY BETWEEN SYMMETRIC AND ASYMMETRIC ISOTOPOLOGUES

V. DISCUSSION

VI. CONCLUSION

### Key Topics

- Dissociation
- 41.0
- Dissociation energies
- 18.0
- Laser induced fluorescence
- 14.0
- Ozone
- 11.0
- Photodissociation
- 11.0

## Figures

Stick spectra of the four symmetric isotopologues in their to energy range. The intensities are normalized to an average value of 1. A log scale is used for the intensities because they range over nearly to three orders of magnitude. The limit of detection (or detection threshold) of each isotopologue is represented.

Stick spectra of the four symmetric isotopologues in their to energy range. The intensities are normalized to an average value of 1. A log scale is used for the intensities because they range over nearly to three orders of magnitude. The limit of detection (or detection threshold) of each isotopologue is represented.

Histograms of the intensities in a standard log-log plot (Ref. 44). The widths of the bins are in a progression of . The continuous curve is the Porter-Thomas distribution (Ref. 44) (see text). For each isotopologue, we give the number of observed transitions and the number of transitions expected if the Porter-Thomas distribution remains valid for the (missing) weak transitions (see Table II).

Histograms of the intensities in a standard log-log plot (Ref. 44). The widths of the bins are in a progression of . The continuous curve is the Porter-Thomas distribution (Ref. 44) (see text). For each isotopologue, we give the number of observed transitions and the number of transitions expected if the Porter-Thomas distribution remains valid for the (missing) weak transitions (see Table II).

The next neighbor distribution (NND) for the four symmetric isotopologues. The smooth curve is a modified version of the Wigner distribution which apply for the random superposition of two subsets of weight and , which correspond to and and which obey individually to the Wigner distribution (see text). The standard deviation is expected to be 0.68 instead of 0.53 for a single set of level obeying a Wigner distribution. The experimental resolution, which corresponds to 0.07 average spacing for (646), is represented by a vertical dashed line in the first bin.

The next neighbor distribution (NND) for the four symmetric isotopologues. The smooth curve is a modified version of the Wigner distribution which apply for the random superposition of two subsets of weight and , which correspond to and and which obey individually to the Wigner distribution (see text). The standard deviation is expected to be 0.68 instead of 0.53 for a single set of level obeying a Wigner distribution. The experimental resolution, which corresponds to 0.07 average spacing for (646), is represented by a vertical dashed line in the first bin.

## Tables

and rovibronic symmetries for isotopologues of and symmetries. The levels observed by LIF are in bold. The missing levels are in brackets. This table does not include the contributions of the and electronic states which are assumed to be negligible. This is why the two columns corresponding to and are missing for the symmetry. For the symmetry, the column would have been omitted because all the rovibronic levels belong to electronic states which are the counterpart of the and electronic states observed for the (646) isotopologue.

and rovibronic symmetries for isotopologues of and symmetries. The levels observed by LIF are in bold. The missing levels are in brackets. This table does not include the contributions of the and electronic states which are assumed to be negligible. This is why the two columns corresponding to and are missing for the symmetry. For the symmetry, the column would have been omitted because all the rovibronic levels belong to electronic states which are the counterpart of the and electronic states observed for the (646) isotopologue.

Summary of the lines counting for the six isotopologues (see text).

Summary of the lines counting for the six isotopologues (see text).

Comparison of the sum of and rovibronic densities for six isotopologues of near .

Comparison of the sum of and rovibronic densities for six isotopologues of near .

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