  This paper deals with quantum fluctuations near the classical instanton
configuration. Feynman diagrams in the instanton background are used for the
calculation of the tunneling amplitude (the instanton density) in the
three-loop order for quartic double-well potential. The result for the
three-loop contribution coincides in six significant figures with one given
long ago by J.~Zinn-Justin. Unlike the two-loop contribution where all involved
Feynman integrals are rational numbers, in the three-loop case Feynman diagrams
can contain irrational contributions.
