  In this paper, we show how the method of field theoretical renormalization
group may be used to analyze universal shape properties of long polymer chains
in porous environment. So far such analytical calculations were primarily
focussed on the scaling exponents that govern conformational properties of
polymer macromolecules. However, there are other observables that along with
the scaling exponents are universal (i.e. independent of the chemical structure
of macromolecules and of the solvent) and may be analyzed within the
renormalization group approach. Here, we address the question of shape which is
acquired by the long flexible polymer macromolecule when it is immersed in a
solvent in the presence of a porous environment. This question is of relevance
for understanding of the behavior of macromolecules in colloidal solutions,
near microporous membranes, and in cellular environment. To this end, we
consider a previously suggested model of polymers in d-dimensions [V.
Blavats'ka, C. von Ferber, Yu. Holovatch, Phys. Rev. E, 2001, 64, 041102] in an
environment with structural obstacles, characterized by a pair correlation
function h(r), that decays with distance r according to a power law: h(r) \sim
r-a. We apply the field-theoretical renormalization group approach and estimate
the size ratio <R_e^2>/<R_G^2 > and the asphericity ratio \hat{A}_d up to the
first order of a double \epsilon=4-d, \delta=4-a expansion.
