Density distribution function of a self-gravitating isothermal
  compressible turbulent fluid in the context of Molecular Clouds ensembles II:
  the contribution of the turbulent term and the potential of the outer shells
  In this paper we continue to investigate the energy conservation equation
obtained in our previous work. We set ourselves three new goals. The first one
is to rewrite the main equations in terms of density profile in order to give
more physical insight. The second one is to investigate the significance of two
new terms in the energy conservation equation. They originate from the gravity
of the outer shells of cloud and the masses outer to the cloud, respectively.
The third goal is to investigate the main equation in the case when the kinetic
turbulent term scales according to Larson's law and it is independent,
formally, of the accretion, in contrast to the previous work. The combination
of supersonic turbulence and spherical symmetry raises a caveat which is
commented in our conclusions. We obtained two solutions for the density
profile. They scale with slopes -2 and -3/2, respectively. The energy balance
for the second solution is the same as in the previous paper: this is a
free-fall. For the first solution there are two cases. The first one: if the
turbulent term does not scale, then it could be important for the energy
balance of the cloud. The second one: if the turbulent term does scale, then it
is not important for the energy balance of the cloud. The two new gravitational
terms don't affect the existence of the two solutions, but the gravitation of
the outer masses calibrate the energy balance for the first solution.
