  When treating interactions in quantum dots within a RPA-like approach,
time-reversal symmetry plays an important role as higher-order terms -- the
Cooper series -- need to be included when this symmetry is present. Here we
consider model quantum dots in a magnetic field weak enough to leave the
dynamics of the dot chaotic, but strong enough to break time-reversal symmetry.
The ground state spin and addition energy for dots containing 120 to 200
electrons are found using local spin density functional theory, and we compare
the corresponding distributions with those derived from an RPA-like treatment
of the interactions. The agreement between the two approaches is very good,
significantly better than for analogous calculations in the presence of
time-reversal symmetry. This demonstrates that the discrepancies between the
two approaches in the time-reversal symmetric case indeed originate from the
Cooper channel, indicating that these higher-order terms might not be properly
taken into account in the spin density functional calculations.
