Recent results from BATSE device onboard GRO observatory
have shown full isotropy of gamma-ray bursts locations upon the sky and
their unhomogeneous space density
) (Meegan et al. 1992),
where 
is the angle between the source and the galactic center,
b is the galactic latitude and 
signifies averaging upon
the whole sample. In the case of pure homogeneous isotropic distribution these
quantities would be, respectively, 1/2, 1/3, 0.
These observed statistical features of gamma-bursts
greatly reinforced interest
to the nature of its possible progenitors. An attractive hypothesis of their
being old galactic neutron stars begins loosing its credibility, especially
in view of negative results of searching for any specral feature in
gamma-burst spectra obtained by BATSE.
Some indications begins appearing that the gamma-ray bursts
can be devided at least into two types - the strong bursts having
hard spectra, with 
>1/2 and the weaker ones
with softer spectra and <1/2 (APEX
experiment results, Mitrofanov et al 1992; see also Lingenfelter & Higdon
1992). These results might indicate that
two populations of gamma-ray burst progenitors distinctive
by their space distributions actually
exist, viz. that producing weak bursts and lying outside galactic disc, and
that producing stronger bursts and hosting in the galactic disc.
Brainerd (1992) has shown that the BATSE results can
be reconciliated with the old neutron star paradigma if one considers
an extended ( 
kpc) halo made from old neutron stars. The question
arises is there any mechanism of natural populating such a halo by old
neutron stars?
Space distribution of old galactic neutron stars population as putative gamma-ray burst progenitors has been studied earlier (e.g. Paczynski 1990, Hartmann et al. 1990). By using direct integration of equations of motion they found distribution of old neutron star population, taking as an initial velocity that deduced from observations of radiopulsars. Essentially their results show that it seems difficult for a neutron star to run out too far away from the galactic plane (some kiloparsecs) unless very fast tail of their initial velocity distribution exists.
In this paper we consider another
method for obtaining such distributions based essentially on
searching for stationary solutions of Boltzmann kinetic equation
for the distribution fumction 
in 6-dimensional
phase space (here 
are 3-dimensional coordinate and velocity, respectively). As an initial
space position we take ordinary exponential distribution on r- and
z- coordinates, whereas as the intial
condition for neutron star velocities a distribution following from
contemporal binary star evolutionary scenario is taken.
We show that if one can use the ergodic hypothesis for motion in the galactic potential, then the population of old neutron stars can be extended very far from the galactic plane under reasonable initial conditions.