  Using the Theory of Finite Fermi Systems, we obtained a non-magic nuclei
generalization of the old theoretical results by J. Speth for magic nuclei
dealing with the transitions between excited states and moment values of
excited state. Such an extension is quite necessary for microscopic
calculations of the gamma ray strength function. The comparison with the
standard QRPA has shown that the modern many-body approach gives some new
physics. The calculated value of the quadrupole moment of the excited state in
208Pb is agreed satisfactorily with the experiment. Some possible improvements
of the theory are briefly discussed.
