Radiative and non-radiative exciton states of quantum dots with parabo
lic lateral potentials are calculated in an effective-mass approximati
on. Energy spectrum, radiative recombination rates and LA phonon scatt
ering rates of the different excitons are discussed in their dependenc
e on the lateral confinement potential. For sufficiently strong latera
l potentials the relaxation of excitons by LA phonon emission becomes
so weak that several excitonic levels should be observable in a photol
uminescence experiment even at low excitation intensity. The theoretic
al results are compared to microscopic photoluminescence data collecte
d from a series of single GaAs quantum dots fabricated by laser induce
d local interdiffusion.