Using current modulation theory for the transport of low-energy cosmic ray particles and the model of Fisk (1976a) for their acceleration by transit time damping large-scale field variations in the outer solar system, we construct a set of parameters which reproduce the quiet time spectra of He, O, N, and Ne as observed at 1 AU during the time period 1973--1975. With an analytic approximation for the acceleration and a numerical solution for the steady state spherical symmetric transport equation, both the observed spectral shapes and the relative intensities for He, O, N, and Ne can be fitted simultaneously remarkably well. For the fit, one set of parameters is used: the acceleration rate, the size of the heliosphere, and the total number of particles injected. To obtain this number, it is assumed that independent of the species, the same fraction of the particles, which are ionized inside the heliosphere (by UV radiation and charge exchange with solar wind particles), participate in the acceleration. For the calculation of the production rate of singly ionized ions the ionization rates provided by Siscoe and Mukherjee (1972) are used, and the solar system abundances of A. G. W. Cameron (unpublished manuscript, 1973) are assumed for the composition of the neutral wind.