  We present a detailed investigation of different excitonic states weakly
confined in single GaAs/AlGaAs quantum dots obtained by the Al droplet-etching
method. For our analysis we make use of temperature-, polarization- and
magnetic field-dependent $\mu$-photoluminescence measurements, which allow us
to identify different excited states of the quantum dot system. Besides that,
we present a comprehensive analysis of g-factors and diamagnetic coefficients
of charged and neutral excitonic states in Voigt and Faraday configuration.
Supported by theoretical calculations by the Configuration interaction method,
we show that the widely used single-particle Zeeman Hamiltonian cannot be used
to extract reliable values of the g-factors of the constituent particles from
excitonic transition measurements.
