The generalized oscillator strengths (GOS) as a function of squared momentum transfer are calculated within the Bethe-Born approximation for the dipole
, quadrupole
, and octupole
transitions of the sodium atom under spherical confinement and quantum plasma conditions. These GOS values for multiple strengths (
) are computed using initial and final state wave functions obtained from the work of Bahar by solving the wave equation, including the more general plasma model potential (MGPM). Their results are reported for both spherical confinement with fixed radius
and different plasma conditions defined by a set of plasma shielding parameters
, two of which are fixed while the other is varied. The analysis elucidates that the competition between both interactions, due to the combined effect of these parameters, leads to various behaviors of the GOS for each multipole strength considered in the present work. According to the present calculations, additional GOS maxima emerge in the observed GOS curves, revealing the influence of the parameter
. We also note that, apart from a second maximum that appears near a small
region for some cases of
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