  The rich phenomenology of quantum many-body systems such as atomic nuclei is
complex to interpret. Often, the behaviour (e.g. evolution with the number of
constituents) of measurable/observable quantities such as binding or excitation
energies can be best understood on the basis of a simplified picture involving
auxiliary quantities that are not observable, i.e. whose values vary with
parameters that are internal to the theoretical construction (contrarily to
measurable/observable quantities). While being useful, the simplified
interpretation is thus theoretical-scheme-dependent. This applies, in
particular, to the so-called single-nucleon shell structure based on auxiliary
effective single-particle energies (ESPEs). In this context, the present work
aims at (i) recalling the way to compute ESPEs out of solutions of many-body
Schr\"odinger's equation, (ii) illustrating the use of ESPEs within the frame
of state-of-the-art ab initio calculations to interpret the outcome of a recent
nuclear experiment and (iii) demonstrating the impact of several alterations to
the computation of ESPEs. While the chosen alterations constitute
approximations within the ab initio scheme, they are built-in when employing
other theoretical constructs at play in nuclear physics. The present
considerations are thus meant to empirically illustrate variations that can be
expected between ESPEs computed within different (equally valid) theoretical
schemes.
