  Low-mass X-ray binaries (LMXBs) with neutron stars show quite different
features which depend on the rate of mass transfer from the donor star. With a
high transfer rate the Z sources are in a persistent soft spectral state, with
a moderate rate the transient Atoll sources have outburst cycles like the black
hole X-ray binaries. The observations document very long outburst recurrence
times for quite a number of sources. We follow with our computations the
evolution of the accretion disc until the onset of the ionization instability.
For sources with a low mass transfer rate the accumulation of matter in the
disc is essentially reduced due to the continuous evaporation of matter from
the disc to the coronal flow. Different mass transfer rates result in nearly
the same amount of matter accumulated for the outburst which means the outburst
properties are similar for sources with short and sources with long outburst
cycles, contrary to some expectations. Then of systems with long recurrence
time less sources will be detected and the total population of LMXBs could be
larger than it appears. This would relieve the apparent problem that the
observed number of LMXBs as progenitors of millisecond pulsars (MSP) is too
small compared to the number of MSP. Concerning the few quasi-persistent
sources with year-long soft states we argue that these states are not
outbursts, but quasi-stationary hot states as in Z sources.
