[en] The Josephson coupling between the particles, which results from tunneling of Cooper pairs, is inserted into a modified Ginzburg-Landau free energy. The local electronic properties, the effective gap δ and the order parameter relaxation rate Gamma, are calculated in the Hartree approximation of this coupling free energy. A general expression, valid for any number N of particles coupled in a closed chain, was derived for the effective gap. A method for deriving the spectrum of the order parameter correlation function for any N was developed and analytical expressions were obtained up to N = 8. The order parameter relaxation rate was determined as the halfwidth at half maximum of this spectrum. Extensive results for δ and Gamma were calculated for N = 8 coupled particles and the results were compared to the results for isolated particles. The overall effect of coupling was to increase the effective volume of the particles. This was most apparent for the smallest size particles. After demonstrating that the expresion for the nuclear spin lattice relaxation time T¹ for superconducting small particles in an applied magnetic field should not depend explicitly on the pair breaking energy, we calculated the nuclear spin lattice relaxation time using the results for δ and Gamma obtained for eight coupled particles. The significant result is that the effect of coupling and magnetic field nearly removes the size dependence of T¹ below T_c