On the microscopic derivation of effective Hamiltonian for slow collective motions

Derivation of collective Hamiltonian using the method of generalized density matrix is suggested. At the first stage quantum hamiltonian describing collective dynamics well enough is plotted. At the second stage relation with other degrees of freedom resulting in fluctuating and dissipating phenomena in collective motion is taken into account. The developed-method permits to conduct coordinated calculations of the collective hamiltonian strictly observing requirements of rotational invariance. In this case potential and kinetic energy of collective motion as well as characteristics of rotational motion possible in the presence of slowly alternating deformation are determined simultaneously. Latest contributions are important both for description of low-lying quadrupole states and in the theory of nucleuss fission or fusion