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SPIN EVOLUTION OF ISOLATED NEUTRON STARS:\\
 SPINDOWN THEOREM.\\
  V.M.Lipunov$^{1,2}$ and S.B.Popov$^{1}$\\
$^{1}$Department of Physics, Moscow University,\\
 119899, Moscow, Russia\\
 $^{2}$Sternberg Astronomical Institute, \\
Universitetsky pr. 13, Moscow, Russia\\

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\begin {abstract}

 In this article we give detail consideration of the possible scenario
of evolution of isolated neutron stars (INS's).

 The new points of our consideration:

--we give additional arguments for the short time scale of the Ejector
stage ( $ \approx 10^7-10^8 $ yrs ).

--we proposed specific SPINDOWN THEOREM and give some arguments for its
validity. Discovery of accreting INS's will means that
SPINDOWN THEOREM is true.

--we consider firstly evolution of spin period of a NS on the accretion stage
and predict that its period  $ \geq 5\cdot 10^2 $ sec and INS's can be observed
as pulsating X--ray sources.

--we consider new idea of stochastic acceleration of the very old NS's due to
accretion of turbulizated interstellar medium.

--last point means that INS can be spin up and spin down with equal probability.
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