Transmission and scattering problems involving complex potentials are important in physics, in particular in describing nuclear collisions. We describe many pedagogical features of transmission in one dimension and scattering and absorption cross sections in three dimensions for a rectangular absorptive potential and compare the results with scattering from real barriers and a hard sphere. For a given energy in one dimension we show that the absorption reaches a maximum for a critical value of the absorption strength and then monotonically decreases with an increase in the absorption strength. An infinitely absorptive well becomes almost fully reflective and thus is similar to an infinitely high barrier. Similar results are found in three dimensions. We show that the absorption cross section in three dimensions diverges at a threshold energy, which is of critical importance for exothermic reactions. © 2007 American Association of Physics Teachers.
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Dr. Umamaheswari A., Dr. Mahadevan S., Prema, Pa, Shastry, C. Sa, and Agarwalla, S. Kb, “Transmission and scattering by an absorptive potential”, American Journal of Physics, vol. 75, pp. 245-253, 2007.