Size effects on excitons in nano-rings
  The size effects of an exciton in a nano-ring are investigated theoretically by using an effective-mass Hamiltonian which can be separated in terms of the center-of-mass and relative coordinates. The binding energy and oscillator strength of the ground state are calculated for two different ring radii as a function of the ring width. The resulting linear optical susceptibility of the low-lying exciton states is also discussed. 
Hui Hu, Dai-Jun Li, Jia-Lin Zhu, and Jia-Jiong Xiong