  Nanoparticles were predicted to exhibit unique physical properties due to
quantum size effects, but their identification remains difficult. According to
Kubo's theory, the gap size is inversely correlated with both the density of
states at the Fermi energy and the number of atoms in the particle. Previously,
we confirmed that the particle size and magnetic field dependence of NMR
anomaly temperature is consistent with the estimated "Kubo" gap. Here, we
investigated the density-of-states dependence in the Pt$_{1-x}$Cu$_{x}$
nanoparticles. While an enhancement of nuclear spin-lattice relaxation rate
$1/T_1$ at low temperatures was clearly observed for the Pt-rich nanoparticles,
such behavior was abruptly suppressed in the Cu-rich nanoparticles.
Furthermore, the NMR anomaly temperature is nearly unchanged with varying the
density of states. Our findings indicate that the quantum size effect contains
more profound physics than just the ones predicted by Kubo.
