  In this study, we investigate gravitational lensing within the framework of
more realistic dark matter halo models, transcending the limitations of
spherical-collapse approximations. Through analytical computations utilizing
diverse mass functions, we address critical factors typically overlooked in the
standard Press-Schechter formalism, including ellipsoidal-collapse conditions,
angular momentum dynamics, dynamical friction, and the cosmological constant.
Our analysis incorporates two widely recognized halo density profiles, the
Navarro-Frenk-White and Einasto profiles, considering both spherical and
ellipsoidal-collapse scenarios. We present relevant calculations of pivotal
gravitational lensing observables, such as Einstein radii, lensing optical
depths, and time delays, spanning a wide range of redshifts and masses across
two distinct lensing models: the point mass and singular isothermal sphere
(SIS) lens models. Our findings illuminate that adopting more realistic dark
matter halo models leads to heightened lensing effects compared to their
spherical-collapse counterparts. Furthermore, our analyses of lensing optical
depths and time delays reveal distinct characteristics between point mass and
SIS lens models. These outcomes highlight the need for more realistic halo
descriptions instead of simple approximations when modeling gravitational
lensing, as this approach can potentially better reveal the complex structures
of dark matter.
