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Models of static wormholes are investigated in the framework of$f(\textit{R}, \textit{T})$ gravity ($\textit{R}$ being the curvature scalar,and $\textit{T}$ the trace of the energy momentum tensor). An attempt to linkthe energy density of the matter component to the Ricci scalar is made, whichfor the Morris and Thorne wormhole metric, with constant redshift function,yields $R(r) = 2b^{\prime}(r)/r^{2}$. Exact wormhole solutions are obtained forthree particular cases: $\rho(r) = \alpha R(r) + \beta R^{\prime}(r)$, $\rho(r)= \alpha R^{2}(r) + \beta R^{\prime}(r)$, and $\rho(r) = \alpha R(r) + \betaR^{2}(r)$, when $f(\textit{R}, \textit{T}) = R + 2 \lambda T$. For the twofirst ones, traversable wormhole models are obtained. When the matter energydensity is of the 3rd type, only solutions with constant shape may correspondto traversable wormholes. Exact wormhole solutions with same properties can beconstructed for $\rho = \alpha R(r) + \beta R^{-2}(r)$, $\rho = \alpha R(r) +\beta r R^{2}(r)$, $\rho = \alpha R(r) + \beta r^{-1} R^{2}(r)$, $\rho = \alphaR(r) + \beta r ^{2} R^{2}(r)$, $\rho = \alpha R(r) + \beta r^{3} R^{2}(r)$ and$\rho = \alpha r^m R(r) \log (\beta R(r))$, as well. On the other hand, for$f(\textit{R}, \textit{T}) = R + \gamma R^{2} + 2 \lambda T$ gravity, twowormhole models are constructed, assuming that the energy density of thewormhole matter is $\rho(r) = \alpha R(r) + \beta R^{2}(r)$ and $\rho(r) =\alpha R(r) + \beta r^{3} R^{2}(r)$, respectively. In this case, the functionalform of the shape function is taken to be $b(r) = \sqrt{\hat{r}_{0} r}$ andpossible existence of appropriate static traversable wormhole configurations isproven. These results can be viewed as an initial step towards using specificproperties of the new exact wormhole solutions, in order to propose newfunctional forms for describing the matter content of the wormhole.

Wormholes with $\rho(R,R^{\prime})$ matter in $f(\textit{R}, \textit{T})$ gravity