A generalized Schr¨odinger approximation,due to Ikhdair & Sever,of the semi-relativistic two-body problem with a rectangular barrier in(1+1) dimensions is compared with exact computations.Exact and approximat...A generalized Schr¨odinger approximation,due to Ikhdair & Sever,of the semi-relativistic two-body problem with a rectangular barrier in(1+1) dimensions is compared with exact computations.Exact and approximate transmission and reflection coefficients are obtained in terms of local wave numbers.The approximate transmission and reflection coefficients turn out to be surprisingly accurate in an energy range |∈-V0| < 2μc^2,where μ is the reduced mass,∈ the scattering energy,and V_0 the barrier top energy.The approximate wave numbers are less accurate.展开更多
Non-relativistic phase shifts for a generalized Yukawa potential V(r) =-V_0( e^(-αr)/r)-V_1( e^(-2αr)/r^2) are studied by the amplitude-phase method and by a frequently used analytic method based on a Pekeris-type a...Non-relativistic phase shifts for a generalized Yukawa potential V(r) =-V_0( e^(-αr)/r)-V_1( e^(-2αr)/r^2) are studied by the amplitude-phase method and by a frequently used analytic method based on a Pekeris-type approximation of power-law potential terms.Small variations of V_1 seem to have marginal effects on the effective potential and on exact phase shifts.However,as pointed out in this study,a Pekeris-type approximation in scattering applications often implies serious distortions of both effective potentials and phase shifts.The Pekeris-type based analytic approximation in this study seems to give low-quality scattering results for this model potential at low energies.展开更多
文摘A generalized Schr¨odinger approximation,due to Ikhdair & Sever,of the semi-relativistic two-body problem with a rectangular barrier in(1+1) dimensions is compared with exact computations.Exact and approximate transmission and reflection coefficients are obtained in terms of local wave numbers.The approximate transmission and reflection coefficients turn out to be surprisingly accurate in an energy range |∈-V0| < 2μc^2,where μ is the reduced mass,∈ the scattering energy,and V_0 the barrier top energy.The approximate wave numbers are less accurate.
文摘Non-relativistic phase shifts for a generalized Yukawa potential V(r) =-V_0( e^(-αr)/r)-V_1( e^(-2αr)/r^2) are studied by the amplitude-phase method and by a frequently used analytic method based on a Pekeris-type approximation of power-law potential terms.Small variations of V_1 seem to have marginal effects on the effective potential and on exact phase shifts.However,as pointed out in this study,a Pekeris-type approximation in scattering applications often implies serious distortions of both effective potentials and phase shifts.The Pekeris-type based analytic approximation in this study seems to give low-quality scattering results for this model potential at low energies.
