  The configuration interaction approach to nuclear structure uses the
effective Hamiltonian in a finite orbital space. The various parts of this
Hamiltonian and their interplay are responsible for specific features of
physics including the shape of the mean field and level density. This
interrelation is not sufficiently understood. We intend to study phase
transitions between spherical and deformed shapes driven by different parts of
the nuclear Hamiltonian and to establish the presence of the collective
enhancement of the nuclear level density by varying the shell-model matrix
elements. Varying the interaction matrix elements we define, for nuclei in the
sd and pf shells, the sectors with spherical and deformed shapes. Using the
moments method that does not require the full diagonalization we relate the
shape transitions with the corresponding level density. Enhancement of the
level density in the low-energy part of the spectrum is observed in clear
correlation with a deformation phase transition induced mainly by the matrix
elements of single-particle transfer. The single-particle transfer matrix
elements in the shell model nuclear Hamiltonian are indeed the carriers of
deformation, providing rotational observables and enhanced level densities.
