The metal-deficient starburst galaxy I Zw 18 has been observed with the Fnr
Ultraviolet Spectroscopic Explorer (FUSE) in a search for H-2 molecules. T
he spectrum obtained with an aperture covering the full galaxy shows no abs
orption lines of diffuse H-2 at the radial velocity of the galaxy. The uppe
r limit for the diffuse H-2 column density is found to be very low, N(H-2)
less than or equal to 10(15) cm(-2) (10 sigma), unlike our Galaxy where H-2
is generally present for even low H I column densities. Although the H I c
olumn density here is as high as N(H I) approximate to 2 x 10(21) cm(-2) we
observe 2N(H-2)/N(H I) << 10(-6). We cannot exclude the possibility that s
ome H-2 could be in very dense, small, and discrete clumps that cannot be d
etected with the present observation. However, the remarkable absence of di
ffuse H, in this metal-poor galaxy can be explained by the low abundance of
dust grains (needed to form this molecule from H atoms), the high ultravio
let flux, and the low density of the H I cloud surrounding the star-forming
regions. Thus, having eliminated diffuse H-2 as a significant contributor
to the total mass, it appears that the gas of the galaxy is dominated by H
I and that the high dynamical mass is not composed of cold and diffuse bary
onic dark matter.