  With this work we start a project of calculating the QED contribution of
order $\alpha^7m$ to the $2^3P$-$2^3S$ transition energy in helium, aiming for
an accurate determination of the nuclear charge radius $r_E$ from measurements
of the corresponding transition frequency. Together with the complementary
determination of $r_E$ from muonic helium, this project will provide a
stringent test of universality of electromagnetic interactions of leptons in
the Standard Model. We report a calculation of the relativistic corrections to
the Bethe logarithm for the $2^3S$ and $2^3P$ states, which is the most
numerically demanding part of the project.
