  In $\mathrm{Cu_{2}O}$ parity is a good quantum number and thus the exciton
spectrum falls into two parts: The dipole-active exciton states of negative
parity and odd angular momentum, which can be observed in one-photon absorption
($\Gamma_4^-$ symmetry) and the exciton states of positive parity and even
angular momentum, which can be observed in two-photon absorption ($\Gamma_5^+$
symmetry). The unexpected observation of $D$ excitons in two-photon absorption
and of $F$ excitons in one-photon absorption has given evidence that the
dispersion properties of the $\Gamma_5^+$ orbital valence band is giving rise
to a coupling of the yellow and green exciton series. In this paper we show
that the even and odd parity exciton system can be consistently described
within the same theoretical approach. However, the Hamiltonian of the even
parity system needs, in comparison to the odd exciton case, modifications to
account for the very small radius of the $1S$ exciton. In the presented
treatment we take special care of the central-cell corrections, which comprise
a reduced screening of the Coulomb potential at distances comparable to the
polaron radius, the exchange interaction being responsible for the exciton
splitting into ortho and para states, and the inclusion of terms in the fourth
power of $p$ in the kinetic energy. Since the yellow $1S$ exciton state is
coupled to all other states of positive parity, we show how the central-cell
corrections affect the whole even exciton series. The close resonance of the
$1S$ green exciton with states of the yellow exciton series has a strong impact
on the energies and oscillator strengths of all implied states. The consistency
between theory and experiment with respect to energies and oscillator strengths
for the even and odd exciton system in $\mathrm{Cu_{2}O}$ is a convincing proof
for the validity of the applied theory.
