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The polytropic equation of state of an atomic hydrogen gas is examined forprimordial halos with baryonic masses of M_h~10^7-10^9 Mo. For roughlyisothermal collapse around 10^4 K, we find that line trapping of Lyman alpha(HI and HeII) photons causes the polytropic exponent to stiffen to valuessignificantly above unity. Under the assumptions of zero H2 abundance and verymodest pollution by metals (<10^-4 Solar), fragmentation is likely to beinhibited for such an equation of state. We argue on purely thermodynamicgrounds that a single black hole of ~0.02-0.003M_h can form at the center of ahalo for z=10-20 when the free-fall time is less than the time needed for aresonantly scattered Lyman alpha photon to escape from the halo. The absence ofH2 follows naturally from the high, 10^4 K, temperatures that are attained whenLyman alpha photons are trapped in the dense and massive halos that weconsider. An H2 dissociating UV background is needed if positive feedbackeffects on H2 formation from X-rays occur. The black hole to baryon massfraction is suggestively close to what is required for these intermediate massblack holes, of mass M_BH~10^4-10^6 Mo, to act as seeds for forming thesupermassive black holes of mass ~0.001M_spheroid found in galaxies today.Comment: Version accepted by ApJ: HeII effects now included, 8 page

Pregalactic Black Hole Formation with an Atomic Hydrogen Equation of State