  This work presents a theoretical approach for lineshapes of Rydberg
excitations. In particular, we introduce the quasi-static lineshape theory,
leading to a methodic and general approach, and its validity is studied. Next,
using $^{84}$Sr as a prototypical scenario, we discuss the role of the thermal
atoms and core-perturber interactions, generally disregarded in Rydberg
physics. Finally, we present a characterization of the role of Ryderg-core
perturber interactions based on the density and principal quantum number that,
beyond affecting the lineshape, could potentially apply to chemi-ionization
reactions responsible for the decay or Rydberg atoms in high density media.
