  Collective plasmon excitations in solids that result from the process of
photoemission are an important area of fundamental research. In this study, we
identify a significant number ($n$) of multiple bulk plasmons ($n\omega_p$) in
the hard x-ray photoelectron spectra of the core levels and valence bands (VBs)
of two well-known, nearly free electron metals, aluminum (Al) and magnesium
(Mg). On the basis of earlier theoretical works, we estimate the contributions
of extrinsic, intrinsic, and interference processes to the intensities of 1$s$
to 2$s$ core level plasmons. The intrinsic contribution diminishes from 22% for
1$\omega_p$, to 4.4% for 2$\omega_p$, and becomes negligible thereafter (0.5%
for 3$\omega_p$). The extrinsic and intrinsic plasmon contributions do not vary
significantly across a broad range of photoelectron kinetic energies, and also
between the two metals (Al and Mg). The interference contribution varies from
negative to zero as $n$ increases. An asymmetric line shape is observed for the
bulk plasmons, which is most pronounced for 1$\omega_p$. Signature of the
surface plasmon is detected in normal emission, and it exhibits a significantly
increased intensity in the grazing emission. The VB spectra of Al and Mg, which
are dominated by $s$-like states, exhibit excellent agreement with the
calculated VB based on density functional theory. The VB exhibits four multiple
bulk plasmon peaks in the loss region, which are influenced by an intrinsic
process in addition to the extrinsic process. On a completely oxidized aluminum
surface, the relative intensity of the Al metal bulk plasmon remains nearly
unaltered, while the surface plasmon is completely attenuated.
