Abstract We are considering the quadrature formulas of “practical type” (with five knots) for approximate computation of integral [xxx] where w(·) denotes (even) Tchebychev weight function. We prove that algebraic degree of exactness of those formulas can not be greater than five. We also determined some admissible nodes and compared proposed formula with some other quadrature formulas.
Laser-induced electron detachment or ionization of atoms and negative ions is considered. In the context of the saddle-point evaluation of the strong-field approximation (SFA), the velocity maps of the direct electrons (those that do not undergo rescattering) exhibit a characteristic structure due to the constructive and destructive interference of electrons liberated from their parent atoms/ions within certain windows of time. This structure is defined by the above-threshold ionization rings at fixed electron energy and by two sets of curves in momentum space on which destructive interference occurs. The spectra obtained with the SFA are compared with those obtained by numerical solution of the time-dependent Schrödinger equation. For detachment, the agreement is excellent. For ionization, the effect of the Coulomb field is most pronounced for electrons emitted in a direction close to laser polarization, while for near-perpendicular emission the qualitative appearance of the spectrum is unaffected.
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