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SCIENTIFIC ABSTRACT We propose to observe the HD J=1-0 112 mu line in a dozen interstellar clouds to determine the deuterium abundance in the solar neighborhood, and to search for any possible gradients across the Galaxy. In two clouds, the HD J=2-1 56 mu line will be observed as well. The results will form important tests of cosmology and astration models. The total amount of time including overheads is 5.5 hours. The deuterium abundance is one of the most sensitive probes of the baryon density in the early Universe. However, attempts to measure the [D]/[H] ratio in stellar or interstellar sources have been plagued by a multitude of problems. Radio searches for the 92 cm line of D I in emission in interstellar clouds are still unsuccessful, whereas the recent possible detection of the line in absorption against Cas A has taken several months of integration time and is difficult to interpret. Observations of the Lyman lines of H and D toward early type stars suffer from confusion by stellar lines and possible stellar variability, whereas the use of deuterated molecules is hampered by chemical fractionation effects. The best estimates from the ultraviolet absorption line measurements give 5E-6<[D]/[H]<2E-5 in the solar neighborhood. This deuterium abundance requires the Universe to be open. Obviously, such an important conclusion warrants further confirmation. In molecular clouds, virtually all deuterium is expected to be in the form of HD. Thus, measurements of the HD abundance should provide direct limits on the [D]/[H] ratio, provided that the H2 column density is known. The HD J=1-0 line occurs at 112 mu, and cannot be observed from the ground or the airplane, but should be readily detectable by ISO. In contrast with absorption line studies, it is not limited to the Solar neighborhood, but should be observable all over the Galaxy, thus providing information on the [D]/[H] ratio as a function of galactocentric distance. We propose to search for the HD 112 mu line in about 10 sources with different distances R from the galactic Centre with the LWS Fabry Perot. Most of these sources are giant molecular clouds which have recently been used by Langer and Penzias (1990) to determine the 12C/13C ratio across the Galaxy from R=0 to 12 kpc. Their 13CO, C18O and 13C18O observations refer to nearly the same beam (100'') as that of the ISO LWS, which will greatly facilitate the analysis. To this list, we have added 4-5 molecular clouds that are located in the outer Galaxy up to R=30 kpc and that show strong 12CO emission (Wouterloot and Brand 1989). Because the proposal requires information with galactocentric radius, some of the positions will fall in one of the ISO holes. If the ``hole'' falls in the Galactic center, we will obviously loose information on the innermost part of the Galaxy. If the ``hole'' falls in Orion, on the other hand, it should be possible to obtain observations over the full range of galactocentric distances. Additional information on the HD abundance in the inner Galaxy and local neighborhood will be obtained from observations of Sgr A, SgrB2, Orion and other star-forming regions by Cox et al., Baluteau et al., Drapatz et al. and van Dishoeck et al. The investigators have direct contacts with all of these programs. These observations, however, form a less homogeneous set and are usually of lower quality. OBSERVATION SUMMARY We intend to search for the HD 112 mu line in 10 sources (for the autumn launch; 9 for the spring launch) with different distances from the Galactic Centre using the LWS Fabry Perot in the high resolution line mode (AOT LWS04). For 2 sources in each of the launch windows (W43 and W49 for autumn; DR21 (OH) and NGC2024 for spring), we will also search for the HD 56 mu line, again using the AOT LWS04. In all cases, we will take 4 res elements on either side of the line with 4 spectral samples per resolution element in the fast scanning mode. The integration times have been estimated as follows. For the sources with a strong continuum at 112 mu (>5000 Jy) (Autumn OSNs 1, 3, 4, and 5; Spring OSNs 1, 2 and 3), the line/continuum ratio is estimated to be about 0.03-0.05. Thus a high S/N>100 on the continuum is required for adequate discrimination of the line, resulting in an integration time of 600 seconds per source. For the weaker sources, the estimated line/continuum ratio is 0.05-0.1. For a S/N=30-60, this leads to integration times of 1000-2000 s. The expected strength of the HD line in the outer galaxy sources is particularly uncertain. For the 56 mu, a S/N on the continuum of 50-100 is needed to obtain a detection or a meaningful upper limit. This results in integration times per source ranging from 1200 to 4000 seconds.