  The excitation spectra in the deformed nucleus 158Gd have been studied with
high energy resolution by means of the (p,t) reaction using the Q3D
spectrograph facility at the Munich Tandem accelerator. The angular
distributions of tritons were measured for more than 200 excited states seen in
the triton spectra up to 4.3 MeV. A number of 36 excited 0+ states (five
tentative), have been assigned by comparison of experimental angular
distributions with the calculated ones using the CHUCK code. Assignments for
levels with higher spins are the following: 95 for 2+ states, 64 for 4+ states,
14 for 6+ states and about 20 for negative parity states. Sequences of states
which can be treated as rotational bands are selected. The analysis of the
moments of inertia defined for these bands is carried out. This high number of
excited states in a deformed nucleus, close to a complete level scheme,
constitutes a very good ground to check models of nuclear structure. The large
ensembles of states with the same spin-parity offer unique opportunities for
statistical analysis. Such an analysis for the 0+, 2+ and 4+ states sequences,
for all K-values and for well-determined projections K of the angular momentum
is performed. The obtained data may indicate on a K symmetry breaking.
Experimental data are compared with interacting boson model (IBM) calculations
using the spdf version of the model. The energies of the low-lying levels, the
transition probabilities in the first bands and the distribution in transfer
intensity of the 0+ states are calculated and compared with experiment.
