The validity of Gor'kov's expansion in the small superconducting order para
meter near the upper critical field H-c2 of type II superconductors at low
temperatures is examined in the light of the accumulated experimental data
of the dHvA effect in the vortex state. Using a 2D electron gas model, it i
s shown that a small amount of thermal smearing is sufficient to ensure the
validity of the expansion within a significantly broad field range below H
-c2. The lowest order (i.e. quadratic) term in this expansion is insensitiv
e to the inhomogeneity of the pair potential in the vortex state and tends
to cancel the zeroth order (i.e. normal electrons) term. Higher order terms
are found, in the asymptotic limit, root E-F/(h) over bar omega(c) >> 1, t
o be much smaller than the corresponding terms in the random vortex lattice
model, thus reflecting weak 'scattering' of quasi-particles by the vortex
lattice. This picture seems to account qualitatively for a common feature o
bserved in almost all experiments so far, namely the crossover of the Dingl
e plot from a relatively large slope just below H-c2 to a smaller slope at
lower fields. (C) 1998 Elsevier Science Ltd. All rights reserved.