  By combining the local density approximation (LDA) with dynamical mean field
theory (DMFT), we report a systematic analysis of the spectral properties of
$\delta$-plutonium with varying $5f$ occupancy. The LDA Hamiltonian is
extracted from a tight-binding (TB) fit to full-potential linearized augmented
plane-wave (FP-LAPW) calculations. The DMFT equations are solved by the exact
quantum Monte Carlo (QMC) method and the Hubbard-I approximation. We have shown
for the first time the strong sensitivity of the spectral properties to the
$5f$ occupancy, which suggests using this occupancy as a fitting parameter in
addition to the Hubbard $U$. By comparing with PES data, we conclude that the
``open shell'' $5f^{5}$ configuration gives the best agreement, resolving the
controversy over $5f$ ``open shell'' versus ``close shell'' atomic
configurations in $\delta$-Pu.
