  An explicit expression is derived for the distribution function of end-to-end
vectors and for the mean square end-to-end distance of a flexible chain with
excluded-volume interactions. The Hamiltonian for a flexible chain with weak
intra-chain interactions is determined by two small parameters: the ratio
$\epsilon$ of the energy of interaction between segments (within a sphere whose
radius coincides with the cut-off length for the potential) to the thermal
energy, and the ratio $\delta$ of the cut-off length to the radius of gyration
for a Gaussian chain. Unlike conventional approaches grounded on the mean-field
evaluation of the end-to-end distance, the Green function is found explicitly
(in the first approximation with respect to $\epsilon$). It is demonstrated
that (i) the distribution function depends on $\epsilon$ in a regular way,
while its dependence on $\delta$ is singular, and (ii) the leading term in the
expression for the mean square end-to-end distance linearly grows with
$\epsilon$ and remains independent of $\delta$.
