We have investigated whether many-body effects can induce significant level
fluctuations in a disorder-free quantum dot. The closed energy shell struc
tures and relaxation of the Hartree-Fock (HF) potentials are found to play
a significant role. The level degeneracy consistent with the rotational sym
metry of the confining potential determines the structure of the energy she
lls. A closed shell state of a dot can give rise to large fluctuations. Whe
n a strong magnetic field is present the shell structure is absent and fluc
tuations are significantly reduced.