  A study of the in-plane magnetic penetration depth \lambda_ab in a series of
the cuprate superconductors Ca_2-xNa_xCuO_2Cl_2 (Na-CCOC) with Na content
x=0.11, 0.12, 0.15, 0.18, and 0.19 is reported. The zero temperature values of
\lambda_ab(0) were obtained by means of the muon-spin rotation technique, as
well as from measurements of the intrinsic susceptibility \chi^int(0) by using
the procedure developed by Kanigel et al. [Phys.Rev.B 71, 224511 (2005)].
\lambda_ab at T=0K was found to increase with decreasing doping from
\lambda_ab(0)=316(19)nm for the x=0.19 sample to \lambda_ab(0)=430(26)nm for
the x=0.11 one. From a comparison of the present Na-CCOC data with those of
Bi2201 and La214 cuprate superconductors it is concluded that substitution of
the apical oxygen by chlorine decreases the coupling between the
superconducting CuO_2 planes, leading to an enhancement of the two-dimensional
properties of Na-CCOC.
