  We present our results on the experiments with cold Rb Rydberg atoms in a
magneto-optical trap (MOT). Characteristic features of our experiment were the
excitation of Rydberg atoms in a small volume within the cold atom cloud and
sorting of the measured signals and spectra over the number of registered
Rydberg atoms. We have measured the effective lifetime of the Rydberg state
37P, as well as its polarizability in a weak electric field. The results are in
good agreement with the theoretical calculations. We have shown that
localization of the small excitation volume around the zero-magnetic-field
point makes possible to increase the spectral resolution and to obtain narrow
microwave resonances in Rydberg atoms without switching off the MOT quadrupole
magnetic field. We have measured the dependence of the amplitude of the
dipole-dipole interaction resonances on the number of Rydberg atoms, which has
a linear character and agrees with the theory for weak dipole-dipole
interaction.
