A self-consistent approach to the description of collective states in
nuclei is developed. It is based on a new form of density functional a
nd quasiparticle RPA-type equations of the theory of finite Fermi syst
ems solved in coordinate representation with exact allowance for both
central and spin-orbit effective interactions. Within this approach th
e low-tying natural-parity states and octupole electric strength funct
ions for the O-16, Ca-40, 48Ca and Pb-208 nuclei are calculated. It is
shown that by incorporating the spin-orbit interaction self-consisten
tly the admixture of the isoscalar 1- spurious state is avoided and th
e agreement with experimental data on both excitation energies and red
uced probabilities of collective transitions is improved as a rule.