Other
Scientific paper
Sep 1998
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1998apj...505..466w&link_type=abstract
The Astrophysical Journal, Volume 505, Issue 1, pp. 466-467.
Other
1
Scientific paper
In the paper ``Translational Band of Gaseous Hydrogen at Low Temperature'' by E. H. Wishnow, I. Ozier, H. P. Gush, & J. Schaefer (ApJ, 492, 843 [1998]), a correction should be made to the calculated ab initio absorption coefficients. In the computer coding, a recent optimization of the handling procedures for files containing the numerical scattering wave functions introduced frequent doubling of the contributions of these wave functions to the squares of the free-free dipole matrix elements. The remaining contributions to the spectrum were not affected. The error was discovered when the calculations were extended to the S(0) feature in the collision-induced spectrum; at these higher frequencies, obviously incorrect results were obtained with the optimized (but incorrect) coding. The revised theoretical spectra are compared to their experimental counterparts in Figures 2, 3, and 4, for T = 22.4, 25.7, and 36.0 K, respectively. The figure numbers here match those in the original paper. As can be seen from Figure 3, at the peak of the translational band, the theoretical spectrum is about 12% lower than its experimental counterpart, rather than being an almost exact match, as in the original paper. As before, in the high-frequency tail of the translational band, the theoretical curve is slightly stronger than the experimental spectrum, but the difference is now smaller. The changes in the theoretical curves due to the corrections are much the same at the different temperatures. For example, the peak intensity has decreased by a factor of 1.10 in each case. The three theoretical curves are still virtually coincident between 120 and 180 cm^-1, as was seen in the original calculation. As can be seen from Figure 4, at 36 K, the comparison between theory and experiment is very similar to that at 25.7 K. When the theoretical intensity is multiplied by a scale factor of 1.12 the match between theory and experiment is very good. (The same applies to the spectrum at 25.7 K.) As can be seen from Figure 2, at 22.4 K, the disagreement between theory and experiment at the peak of the translational band is only 5%. This difference was also about 5% in magnitude before the correction, but the sign was opposite. The nearly exact correspondence between theory and experiment in the original paper is no longer present. The differences between the theoretical and experimental spectra at 25.7 and 36.0 K are outside the experimental errors, which were estimated to be +/-5% of the peak of the absorption curves. For example, at 25.7 K, the experimental uncertainty is +/-0.24 x 10^-7 cm^-1 amagat^-2 across the entire spectrum. As can be seen from Figure 3, between 30 and 140 cm^-1, this uncertainty is less than the difference between the theoretical and experimental spectra. These differences cannot be accounted for by small changes in the temperature; see Figure 4. On the other hand, at each temperature, the difference in the integrated intensity alpha_1TR under the translational band is less than the experimental error. In units of 10^-32 cm^5 s^-1, the experimental/theoretical values of alpha_1TR are 2.127/1.979 at 22.4 K, 2.007/1.872 at 25.7 K, and 1.841/1.703 at 36.0 K. Each theoretical value is too small by about 7%. Since the experimental error across the entire band is 5% of the peak of the absorption, the error in the area is ~10%. There does not appear to be a clear explanation for the apparent discrepancy. On the experimental side, a drop of 10% is unlikely but cannot be ruled out. As was mentioned in the original paper, the low-frequency (LF) and high-frequency (HF) spectra were combined a posteriori to give a smooth spectrum over the entire range. If the weighting used between the LF and HF spectra is altered to give the lowest reasonable intensity, then the experimental curves would be lower by about 5%. The fact that the spectra at the three different temperatures are virtually coincident between 120 and 180 cm^-1 (as predicted theoretically) provides a check on many types of experimental error. On the theoretical side, the two sets of input data to the calculation are heavily constrained. First, the interaction potential has been adjusted to obtain an excellent match to a variety of other experimental data, including collision-induced absorption coefficients. Second, the dipole moment function cannot be scaled up by 6% to compensate for the factor 1.12 mentioned above. If this were done, the calculated spectrum in the S(0) region becomes unacceptably strong; the theoretical spectrum is already more intense by an amount somewhat larger than the experimental error as compared with the experimental data of J. Schaefer and A. R. W. McKellar (Z. Phys. D, 15, 51; erratum 17, 231 [1990]) and A. R. W. McKellar and J. Schaefer (J. Chem. Phys., 95, 3081 [1991]). The most reasonable explanation for the disagreement seems to be a combination of a few percent overestimate of the experimental intensity combined with a few percent adjustment in the dipole moment function. The revised theoretical results presented here must be similar to those mentioned in footnote 4 of G. Birnbaum, A. Borysow, and G. S. Orton (Icarus, 123, 4 [1996]). The anisotropy in the potential was included in the current work, but not by Birnbaum et al. (1996). This difference was originally thought to contribute a change of ~10% in the intensity of the translational band. Tests with the present corrected program show that changes this large do occur on the low-frequency side of the S(0) line of the para-H_2 spectrum at 77 K (with symmetry requirements obeyed). Corresponding relative changes in the translational band have not been calculated but seem to be much smaller.
Gush H. P.
Ozier Irving
Schaefer Joachim
Wishnow Edward H.
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