  In this work, we investigate reconfigurable intelligent surfaces
(RIS)-assisted cooperative non-orthogonal multiple access (C-NOMA) consisting
of two paired users, where the phases of RIS are configured to boost the
cell-center device. The cell-center device is designated to act as a
full-duplex (FD) relay to assist the cell-edge device. The cell-center device
does not use its battery energy to cooperate but harvests energy using
simultaneous wireless information power transfer (SWIPT). A more practical
non-linear energy harvesting model is considered. Expressions for outage
probability (OP) and ergodic rate (ER) are devised, assuming that all users'
links undergo Nakagami-$m$ channel fading. We first approximate the harvested
power as Gamma random variables via the moments matching technique. This allows
us to derive analytical OP/ER expressions that are simple to compute yet
accurate for a wide range of RIS passive elements configurations, energy
harvesting (EH) coefficients, and residual self-interference (SI) levels, being
extensively validated by numerical simulations. The OP expressions reveal how
paramount is to mitigate the SI in the FD relay mode since for reasonable
values of residual SI coefficient ($\omega \geq -20$dB), it is notable its
detrimental effect on the system performance. Also, numerical results reveal
that increasing the number of RIS elements can benefit the cooperative system
more than the non-cooperative one.
