Adiabatic theory of strong-field photoelectron momentum distributions near a backward rescattering caustic

We present a comprehensive treatise on the derivation of the factorization formula describing strong-field photoelectron momentum distributions near the outermost backward rescattering caustic within the adiabatic theory and its validation by calculations. The formula derived holds for ionization by linearly polarized laser pulses of sufficiently low frequency and becomes exact as the frequency tends to zero for a fixed pulse amplitude. The convergence of the results obtained from the formula to accurate photoelectron momentum distributions obtained by solving the time-dependent Schr\"odinger equation is demonstrated. The formula is shown to work quantitatively in both tunneling and over-the-barrier regimes of ionization for finite-range potentials as well as potentials with a Coulomb tail. This paves the way for future applications of the present theory in strong-field physics. In particular, the explicit analytical form of the returning photoelectron wave packet given here enables one to extract differential cross sections for elastic scattering of a photoelectron on the parent ion from experimental photoelectron momentum distributions.