Apparent number density enhancement of quasars near foreground galaxies due to gravitational lensing. I - Amplification cross sections. II - The amplification probability density distribution and results

Amplification cross-sections are presently calculated for extended sources, both for an isolated point mass lens and for a point mass imbedded in the gravitational field of a galaxy. It is found that these sensitively depend on the source's extent, as well as on the 'external shear' generated by the galaxy. In the second part of this work, the amplification probability distribution (APD) is determined for small amplifications by considering an ensemble of stars simultaneously acting on a light bundle, together with the galactic gravitational field. The probability distribution for the diffuse flux component is combined with strong and weak amplification results to yield the APD for all amplification factors greater than unity. The final ADP is used to obtain the number density enhancement of sources near foregroud galaxies. The application of these results to the observed quasar-galaxy associations indicates that the galactic shear is unimportant for isothermal galaxy models.