  Background: Effective interactions for elastic nucleon-nucleus scattering
from first principles require the use of the same nucleon-nucleon interaction
in the structure and reaction calculations, as well as a consistent treatment
of the relevant operators at each order.
  Purpose: Previous work using these interactions has shown good agreement with
available data. Here, we study the physical relevance of one of these
operators, which involves the spin of the struck nucleon, and examine the
interpretation of this quantity in a nuclear structure context.
  Methods: Using the framework of the spectator expansion and the underlying
framework of the no-core shell model, we calculate and examine spin-projected,
one-body momentum distributions required for effective nucleon-nucleus
interactions in $J=0$ nuclear states.
  Results: The calculated spin-projected, one-body momentum distributions for
$^4$He, $^6$He, and $^8$He display characteristic behavior based on the
occupation of protons and neutrons in single particle levels, with more
nucleons of one type yielding momentum distributions with larger values.
Additionally, we find this quantity is strongly correlated to the magnetic
moment of the $2^+$ excited state in the ground state rotational band for each
nucleus considered.
  Conclusions: We find that spin-projected, one-body momentum distributions can
probe the spin content of a $J=0$ wave function. This feature may allow future
\textit{ab initio} nucleon-nucleus scattering studies to inform spin properties
of the underlying nucleon-nucleon interactions. The observed correlation to the
magnetic moment of excited states illustrates a previously unknown connection
between reaction observables such as the analyzing power and structure
observables like the magnetic moment.
