Nonextensive statistical mechanics approach to electron trapping in degenerate plasmas

•The electron trapping in a degenerate plasma is reformulated by incorporating the nonextensive entropy prescription.•The qq-deformed Fermi–Dirac distribution function including the quantum as well as the nonextensive statistical effects is used.•A new generalized electron density is obtained.•The modifications arising in the propagation of ion-acoustic solitary waves are analyzed.

The electron trapping in a weakly nondegenerate plasma is reformulated and re-examined by incorporating the nonextensive entropy prescription. Using the qq-deformed Fermi–Dirac distribution function including the quantum as well as the nonextensive statistical effects, we derive a new generalized electron density with a new contribution proportional to the electron temperature TT, which may dominate the usual thermal correction (∼T2∼T2) at very low temperatures. To make the physics behind the effect of this new contribution more transparent, we analyze the modifications arising in the propagation of ion-acoustic solitary waves. Interestingly, we find that due to the nonextensive correction, our plasma model allows the possibility of existence of quantum ion-acoustic solitons with velocity higher than the Fermi ion-sound velocity. Moreover, as the nonextensive parameter qq increases, the critical temperature TcTc beyond which coexistence of compressive and rarefactive solitons sets in, is shifted towards higher values.