Nuclear recoil corrections to the $2p_\frac{3}{2}$ state energy of hydrogen-like and high $Z$ lithium like atoms in all orders in $αZ$

The relativistic nuclear recoil corrections to the energy of the $2p_{\frac{3}{2}}$ state of hydrogen-like and the $(1s)^{2}2p_{\frac{3}{2}}$ state of high $Z$ lithium-like atoms in all orders in $\alpha Z$ are calculated. The calculations are carried out using the B-spline method for the Dirac equation. For low $Z$ the results of the calculation are in good agreement with the $\alpha Z$ -expansion results. It is found that the total nuclear recoil contribution to the energy of the $(1s)^{2}2p_{\frac{3}{2}}- (1s)^{2}2s$ transition in lithium-like uranium constitutes $-0.09\,eV$.