  We have used the density functional theory to study the effect of molecular
elongation on the isotropic-nematic, isotropic-smectic A and nematic-smectic A
phase transitions of a fluid of molecules interacting via the Gay-Berne
intermolecular potential. We have considered a range of length-to-width
parameter $3.0\leq x_0\leq 4.0$ in steps of 0.2 at different densities and
temperatures. Pair correlation functions needed as input information in density
functional theory are calculated using the Percus-Yevick integral equation
theory. Within the small range of elongation, the phase diagram shows
significant changes. The fluid at low temperature is found to freeze directly
from isotropic to smectic A phase for all the values of $x_0$ considered by us
on increasing the density while nematic phase stabilizes in between isotropic
and smectic A phases only at high temperatures and densities. Both
isotropic-nematic and nematic-smectic A transition density and pressure are
found to decrease as we increase $x_0$. The phase diagram obtained is compared
with computer simulation result of the same model potential and is found to be
in good qualitative agreement.
