We have studied the effect of X-rays from the accretion disc or corona
on the evolution of a Low Mass X-ray Binary (LMXB), via heating and b
lowing up the secondary. Hameury et al. (1993) concluded that the effe
ct of the X-ray heating is much smaller than earlier supposed to be: t
he heating blanket is so thin that only the outer radiative zone of th
e facing hemisphere is heated. Their result was that the star does not
expand and the evolution of a LMXB should not deviate much from that
of a CV. We included the form of a typical observed LMXB X-ray spectru
m into the computations. The absorption of the incident flux was compu
ted properly at all envelope layers, from the surface down to the conv
ective zone. For a large range of stellar masses and incident X-ray fl
uxes, about 10 per cent of the energy flux is absorbed in the deeper c
onvective part of the envelope. If the X-ray flux is occasionally very
hard, almost all of the heating penetrates into the adiabatic part of
the envelope. The luminosity released in the convective layer is dist
ributed in a short thermal time scale of the zone around the star. Thi
s time is short when compared to the evolutionary time scale. For this
reason, the use of the efficiency 10 per cent is well-justified (eta
= 0.1) with the assumption of a spherical heating. We computed two evo
lutionary sequences using eta = 0.1 and 0.001. The sequence with eta =
0.1 passed very close to the observed values of the eclipsing system
X1822-371 (P = 5.57 hr) explaining e.g. the value of its period increa
se. The sequence with eta = 0.001 penetrated into the 2-3h period gap
(while accreting) and might explain the many AM Her's found inside the
gap (compensating the lower X-ray luminosity by a higher efficiency a
nd the harder spectrum).