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One or more of the Following Statements may affect this Document This document has been reproduced from the best copy furnished by the organizational source. It is being released in the interest of making available as much information as possible. This document may contain data, which exceeds the sheet parameters. It was furnished in this condition by the organizational source and is the best copy available. This document may contain tone-on-tone or color graphs, charts and/or pictures, which have been reproduced in black and white. This document is paginated as submitted by the original source. Portions of this document are not fully legible due to the historical nature of some of the material. However, it is the best reproduction available from the original submission. Produced by the NASA Center for Aerospace Information (CASI)

NASAfTechnical Memorandum 83869

Collisionall Excitation ofInterstellar Molecules: Amonia(NASA--Th- 63889) C6LLISIGIUL LXCITAT-UN CFN82-24954iNT2'LiSTLLLER MOLECULESAO.MCNIA (NASA)4b p HC AU318F A01CSCL 20H

Unc.1 a S

G3f72 2 U21

Sheldon Green

DECEMBER 1981

nil1 ^ Ni^`(1^`a2

National Aeronautics anda=1tECEIV ED

Space Administration gTt FP►CIUV

Goddard Space flight Center Greenbelt, Maryland 207715^^°^,,,,,,1k.r0 COLLISIONAL EXCITATION OF INTERSTELLAR MOLECULES; AMMONIA by

Sheldon Green

NASA Goddard Space Flight CenterInstitute for Space Studies2880 Broadway

New York, N.Y. 10025

x r 11

ABSTRACT

Theoretical rate constants are presented for excitation of NH3 by collisions with He. The lowest 22 levels of ortho-NH3 and the lowest 16 levels of para-NH 3 are considered at kinetic temperatures of 15 -- 300 K. 0 2

1. Introduction

Analysis of microwave and IA observations of interstellar ammonia requires knowledge of the rate constants for colaisional excitation among the observed rotation-inversion levels. It is not currently possible to obtain the required state-to- state rate constants for excitation by H2 and He experimentally. However, some related information is available; in particular, pressure broadening data provide a measure of the total rate of excitation out of the two spectral levels, and microwave double resonance data provide a measure of the relative rates among different levels. on the other hand, these collision rates can be obtained theoretically by solving the electronic Schrodirger equation for the intermolecular forces, followed by molecular scattering calculations to obtain collision cross sections. Such calculations can also predict pressure broadening and double resonance results so that comparisons with available experimental data provide some check on the theory. A theoretical study of NH3 excitation by collisions with He was recently presented.1 In that study the intermolecular forces were obtained by combining a previous Hartree-Fock calculation for the short-range forces with estimates for the long-range forces.. Scattering calculations were performed for para-NH3-He to obtain state-to-state cross sections and rate constants and also to predict pressure broadening and microwave double resonance results. Agreement with pressure io 3 broadening data was excellent. Agreement with double resonance data, however, was mixed. It was argued that the discrepancies here are due to an oversimplified analysis of the exper4mental, data and do not indicate a serious error in the theoretical calculations. Due to molecular symmetry and nuclear spin, ammonia molecules are either para-NH3 for rotation-inversion Levels with K=0,3, ... ,3n or ortho-NH3 for levels with K=1,2,4,5,...,

2n*l. These are interconverted only very slowly by radiation

or by non-reactive collisions and, for all practical purposes, can be considered as distinct species under the conditions in interstellar space. Ref. 1 presented calculations only for para-NH3. The present work extends these studies to obtain collision rates for ortho-NH3. For convenience, rates for para-NH3 are also tabulated here for more kinetic temper- atures than given in Ref. 1. Because the computational methods are essentially the same as those used previously, only a brief description will be given in the following Section. The accuracy of the resulting rate constants is addressed in Section III.

II, Computational Details

The interaction labeled "potential. 1" in Ref. 1 was used here. The short--range forces are from 1lartree-Fork calcula- tions for N133-He. To this are added estimates for the "'l 4 following long-range forces: a spherical, R-6 dispersion term, the quadrupole-induced-dipole interaction, and the anisotropy in the dispersion. As noted in Ref. 1, the value used for this last term is probably too large by about a factor of four, but it has only a minor effect on numerical results. Scattering calculations were done within the coupled states (CS) approximation. The accuracy of this approximation has been tested by comparisons with essentially exact close coupling calculations. 1r2 in general, CS results for the larger, more important cross sections are accurate to better than 10%; even for less probable transitions the error is rarely more than 50%. The NH3 rotational wavefunctions are taken as linear combinations of symmetric top functions with quantum numbers J and K:

JK e > = ! JK> + C I J-K> .

For K=O, only E=+1 is permitted; for K>Qc= (-1)J where the upper sign refers to the lower member of an inversion doublet and vice versa. Rotational energies were computed from the standard formula for symmetric tops with rotation constants A=B=9.9402 cm-1 and C=6.3044 cm-1. The separation between members of an inversion doublet (about 0.8 cm 1) was ignored in calculations for ortho-NH3. The effect of these splittings was considered in the earlier calculations for para-NH3 and found to be unimportant. i 5 Scattering calculations were done at several collision energies. .1ecause the astrophysical sources generally have low kinetic temperatures, special attention was given to energies near excitation thresholds. The collisional reduced mass was taken as 3.24 atomic mass units. Enough energetically closed channels and enough partial waves were included to assure convergence of inelastic cross sections to better than a few percent. In particularr, calculations were done including the 12 rotation-inversion levels with J=0-5 for nine energies from 25 to 145 cm-1including the 17 levels with J-0-6 for ten energies from 160 to 325 cm-1; including the 22 levels with J=0-7 for six energies from 360 to 600 cm-1; and Including the 27 levels with J=0-8 for energies of 800, 1000, and 1.200 - IcmResulting cross sections were integrated over Boltzmann distributions of collision velocity to obtain the rates presented in Table I. The cross sections obtained previously for para-NH3 have been integrated over Boltzmann distributions of collision energies to obtain the rates given in Table 2.

III. Accuracy of Results

As discussed in Ref. 1, pressure broadening ;.,.)rovides a measure of the total inelastic collision rate, and the calculations presented there agreed with microwave data to about 10%. in addition, broadening of the pure rotational 6 J,K w 4,0 - 1,0 infrared lire at about 20 cm-1 has been measured giving an attectivr, -ross section of 17 R2. The present calculation roe Lhis quantity of 18 ^2 is in goad agreement. Agreement of theory with microwave double resonance data for Para-NH3 was found to be mixed. Fewer data are available for ortho-NH3; however, comparison with the present theoretical results shows the same qualitative features found for para-NH3. As discussed in Ref. l this lack of accord is believed to reflect an oversimplification in the analysis of the data and not an inherent flaw in the theoretical collision rates.. The major source of error in the present results is undoubtedly due to uncertainties in the intermolecular forces. Ref. 1 considered the effect on collision cross sections of reasonable variations in the long--range interaction.. It was found that the larger cross sections were relatively insensitive to variations in the potential,, experlancinU changes of a factor of two or less, suggesting that the present results are at least this accurate. Thus, from comparison4i with pressure broadening data, the total excitation rate 0gut of a given level is likely to be predicted within 20% of the correct value in the present study. The absolute values of individual state-to-state rates are probably accurate to better than 50%, although 7 somewhat larger errors, especially in the smaller, less important rates, cannot be ruled out with complete confidence. Also, as discussed in Ref. 1, values for para-NH3 in Table 2 required extensive extrapolation in the high energy tail of the Boltzmann distribution for temperatures above about

200 K; however, this is not expected to introduce errors

larger than those due to uncertainty in the potential.. Excitation by collisions with cold H2 (in its lowest, J-=0 rotational, level) is expected to be similar to excitation by He, and this is supported by pressure broadening data." Owing to lower mass, at a given temperature H2 molecules have a 40% higher velocity than He atoms. To account for tl is and for the slightly large.T; observed pressure broadening cross sections, it is recommended that the rates in Tables

1 and 2 be increased by 50% for excitation by cold H2. if

the H2 molecules are in higher rotational levels (J>O) they are more effective in exciting NH3 due to the long-range quadrupole-dipole interaction. This enhances the rate of dipole allowed transitions in NH3, i.e., AJ=O transitions across an inversion doublet and AJ=l transitions from lower- to-lower and upper-to-upper members of inversion doublets. Although detailed calculations are not available for this system, enhancement is probably about a factor of two for these cases. This is in harmony with the observation that the total excitation rate, as measured by pressure broadening, is about 50% greater for H2(J>O) than for H2(J=0). k ;.t 8

TV. REFERENCES

1.S. Green, J. Chem. Phys. 73, 2740 (1980)

2.S. Green, J. Chem. Ptgs. 64, 3463 (1976) .

3.G. Bachet, J. Quant. Spectzosc. and Rad. Trans£. 13,

1305 (1972) .

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