A systematic calculation of the hyperfine structure of 2 P-3 levels of
heliumlike ions is presented. Reduced matrix elements of the magnetic
-dipole hyperfine operator between substates of the 2 P-1,P-3 states a
re evaluated using relativistic configuration-interaction wave functio
ns that account for both Coulomb and Breit interactions. These matrix
elements, together with the energy intervals Delta E(10)=E(2(3)P(1))-E
(2 P-3(0)), Delta E(20)=E(2 P-3(2))-E(2 P-3(0)), and Delta E(st)=E(2 P
-1(1))-E(2 P-3(0)), are tabulated for ions with nuclear charges in the
range Z=2-100. For Z=2, the matrix elements are in close agreement wi
th precise nonrelativistic variational calculations, but as Z increase
s from 2 to 10, the present values deviate smoothly from the variation
al values owing to relativistic corrections. Applications are given to
determine the hyperfine structure of He-3, Li-6,7(+), Be-9(2+), and F
-19(7+). Hyperfine quenching rates of 2 P-3(0) states are calculated u
sing a radiation-damping formalism for all stable isotopes in the rang
e Z=6-92. Quenching rates of 2 P-3(2) states are also calculated for s
elected ions. For Z=9-29, the 2 P-3(0) quenching rates are in good agr
eement with relativistic 1/Z calculations. For Z>40, the diagonal hype
rfine matrix elements disagree in sign with previously published multi
configuration Dirac-Fock values. In view of these differences, the pre
sent matrix elements are used to reevaluate the fine-structure interva
ls Delta E(10) inferred from hyperfine quenching experiments for the i
ons Ni26+, Ag45+, and Gd62+.