Collisional broadening of nS Rydberg states by K, Rb, and Cs atoms is studied using the adiabatic approach for the 'X quasimolecular state and impulse approximation for all other contributions to the collisional width. The calculations are based on the use of the low-energy phase shifts for electron scattering by alkali metals obtained from ab initio close-coupling calculations and their extrapolation according to the modified effective range theory. We obtain a good agreement for the magnitude of the width with experimental data and satisfactory agreement for the oscillatory part of the width as a function of the principal quantum number. We find that the theory overestimates the amplitude of the oscillations. In the case of Cs as a perturber, the agreement with experimental data is good if we assume the existence of the low-energy P resonance of Cs . However, recent ab initio bound-state and scattering calculations indicate the existence of the Cs ('P) bound state rather than the resonance.PACS number(s): 32.70.Jz, 34.60.+ z
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