Higher-order recoil corrections for triplet states of the helium atom

Nuclear recoil corrections of order ${\alpha }^6{m}^2/M$ are calculated for the lowest-lying triplet states of the helium atom. It improves the theoretical prediction for the isotope shift of the $2{}^{3}S-2{}^{3}P$ transition energy and influences the determination of the ${}^3\mathrm{He}-{}^4\mathrm{He}$ nuclear charge radii difference. This calculation is a step forward on the way towards the direct determination of the charge radius of the helium nucleus from spectroscopic measurements.