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Optical Transition Rates in a Cylindrical Quantum Wire with an Inverse Parabolic
Potential

Electron transition rates due to interaction with circularly polarized light incident along the axis of a free-standing
solid cylindrical nanowire are evaluated in the dipole approximation. In this case, the allowed optical transitions
are only those for which the azimuthal quantum numbers of the initial and final states differ by unity. The envisaged
electric potential of the quantum wire is modeled as inversely parabolic in the radial distance and such that it assumes
a value of zero at the surface of the nanostructure. The investigations here are on the influence of this form of the
confining potential on the transition rates involving some few electrons’ states of higher radial quantum numbers,
nonetheless limited to transitions only between a pair of the electron’s energy sub bands. It is found that a sweep
of the strength of the potential gives rise to modulations of the optical transition rates for higher radial quantum
numbers. Furthermore, an increase of the strength of this potential reduces the transition energies thus such an
increase redshifts peaks of the corresponding transitions rates.