  The Josephson oscillations between condensates in a double-well trap are
known theoretically to be strongly effected by the mean field interaction in
dilute atomic gases. The most important effect is that the amplitude of
oscillation in the relative population of the two wells is greatly suppressed
due to the mean field interaction, which can make it difficult to observe the
Josephson effect. Starting from the work of Raghavan, Smerzi, Fantoni, and
Shenoy, we calculate the maximum amplitude of oscillation in the relative
population as a function of various physical parameters, such as the trap
aspect ratio, the Gaussian barrier height and width, and the total number of
atoms in the condensate. We also compare results for ${}^{23}$Na and
${}^{87}$Rb. Our main new result is that the maximum amplitude of oscillation
depends strongly on the aspect ratio of the harmonic trap and can be maximized
in a ``pancake'' trap, as used in the experiment of Anderson and Kasevich.
