We present a modified scenario of gamma-ray emission from pulsars with
in the framework of polar cap models. Our model incorporates the possi
ble acceleration of electron-positron pairs created in magnetospheres,
and their subsequent contribution to the gamma-ray luminosity L-gamma
. It also reproduces the empirical trend in L gamma for seven pulsars
detected with Compton Gamma-Ray Observatory (CGRO) experiments. At the
same time it avoids basic difficulties faced by theoretical models wh
en confronted with observational constraints. We show that the classic
al and millisecond pulsars form two distinct branches in the L gamma -
L-sd diagram (where L-sd is the spin-down luminosity). In particular,
we explain why the millisecond pulsar J0437-4715 has not been detecte
d with any of the CGRO instruments despite its very high position in t
he ranking list of spin-down fluxes (i.e. L-sd/D-2, where D is a dista
nce). The gamma-ray luminosity predicted for this particular object is
about one order of magnitude below the upper limit set by EGRET.