  The analytical theory of diffusive cosmic ray acceleration at parallel
stationary shock waves with magnetostatic turbulence is generalized to
arbitrary shock speeds $V_s=\beta_1c$, including in particular relativistic
speeds. This is achieved by applying the diffusion approximation to the
relevant Fokker-Planck particle transport equation formulated in the mixed
comoving coordinate system. In this coordinate system the particle's momentum
coordinates $p$ and $\mu =p_{\parallel }/p$ are taken in the rest frame of the
streaming plasma, whereas the time and space coordinates are taken in the
observer's system. For magnetostatic slab turbulence the diffusion-convection
transport equation for the isotropic (in the rest frame of the streaming
plasma) part of the particle's phase space density is derived. For a step-wise
shock velocity profile the steady-state diffusion-convection transport equation
is solved. For a symmetric pitch-angle scattering Fokker-Planck coefficient
$D_{\mu \mu }(-\mu )=D_{\mu \mu }(\mu )$ the steady-state solution is
independent of the microphysical scattering details. For nonrelativistic
mono-momentum particle injection at the shock the differential number density
of accelerated particles is a Lorentzian-type distribution function which at
large momenta approaches a power law distribution function $N(p\ge p_c)\propto
p^{-\xi }$ with the spectral index $\xi (\beta_1)
=1+[3/(\Gamma_1\sqrt{r^2-\beta_1^2}-1)(1+3\beta_1^2)]$. For nonrelativistic
($\beta_1\ll 1$) shock speeds this spectral index agrees with the known result
$\xi (\beta_1\ll 1)\simeq (r+2)/(r-1)$, whereas for ultrarelativistic
($\Gamma_1\gg 1$) shock speeds the spectral index value is close to unity.
