  We have set ourselves the task of obtaining the probability distribution
function of the mass density of a self-gravitating isothermal compressible
turbulent fluid from its physics. We have done this in the context of a new
notion: the molecular clouds ensemble. We have applied a new approach that
takes into account the fractal nature of the fluid. Using the medium equations,
under the assumption of steady state, we show that the total energy per unit
mass is an invariant with respect to the fractal scales. As a next step we
obtain a nonlinear integral equation for the dimensionless scale Q which is the
third root of the integral of the probability distribution function. It is
solved approximately up to the leading-order term in the series expansion. We
obtain two solutions. They are power-law distributions with different slopes:
the first one is -1.5 at low densities, corresponding to a equilibrium between
all energies at a given scale, and the second one is -2 at high densities,
corresponding to a free fall at small scales.
