We derive an off-energy-shell generalization of the two-potential formula by using a coordinate-space approach and apply the formalism to construct algorithms for studying spatial behaviour of the fully off-shellT matrix. We also suggest some future applications of the proposed theory.

Collisional absorption of laser light in an under-dense plasma is studied by particle-in-cell (PIC) simulation with Monte Carlo binary Coulomb collisions between charge particles. For a given plasma thickness of a few times the wavelength of 800 nm laser, fractional absorption ($\alpha$) of the laser light due to Coulomb collisions (mainly between electrons and ions) is calculated at different electron temperature $T_{e}$ with a total velocity $v = (v^{2}_{th} + v^{2}_{0}/2)^{1/2}$ dependent Coulomb logarithm ln $\Lambda(v)$, where $v_{th}$ and $v_{0}$ are thermal and ponderomotive velocity of an electron. In the low-temperature regime ($Te \lesssim 15 eV$), it is found that $\alpha$ increases with increasing laser intensity $I_{0}$ up to a maximum corresponding to an intensity $I_{c}$, and then it drops (approximately) obeying the conventional scaling of $\alpha \varpropto I^{−3/2}_{0}$ when $I_{0}$ > $I_{c}$. Such a non-conventional increase of $\alpha$ with $I_{0}$ in the low intensity regime was demonstrated earlier in experiments, and recently explained by classical and quantum models [Phys. Plasmas 21, 13302 (2014); Phys. Rev. E 91, 043102 (2015)]. Here, for the first time, we report this non-conventional collisional laser absorption by PIC simulation, thus bridging the gap between models, simulations, and experimental findings. Moreover, electron energy distributions naturally emanating during the laser interaction(in PIC simulations) are found to be anisotropic and non-Maxwellian in nature, leading to some deviations from the earlier analytical predictions.