We describe a nonperturbative (in Zα) numerical evaluation of the one-photon electron self-energy for 3P1∕2, 3P3∕2, 4P1∕2, and 4P3∕2 states in hydrogenlike atomic systems with charge numbers $Z=1$ to 5. The numerical results are found to be in agreement with known terms in the expansion of the self-energy in powers of Zα and lead to improved theoretical predictions for the self-energy shift of these states.
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