Recoil correction to the decay rate of $2p$ states in hydrogenlike atoms

An approach is developed for high-accuracy calculations of the $2p$ state decay width in the hydrogenlike atoms. The relativistic recoil correction to the $2p$ state decay width of the relative order ${\left(Z\alpha \right)}^{2}m/M$, which is responsible for the uncertainty of the total width calculation, is obtained in the frame of the two-body formalism. Numerical results for total widths of the $2p$ state of some medium-$Z$ muonic atoms are presented. As additional applications of the developed technique, the relativistic recoil correction to the electric dipole matrix element for the $2p-1s$ transition is obtained and that for the bound $g$ factor of $ns$ states is reproduced.