Isotope shifts and energies of the 1s 2p states in helium

Abstract

The specific mass shift (SMS) and energies of the (1s2p)1, 3P states in helium are evaluated using wave functions expressed in terms of radial “pair functions” which are obtained by numerical solution of inhomogeneous two-particle differential equations. The results obtained when including successively higher angular symmetries in the wave function indicate that the SMS converges asl max −3 for the singlet state and betweenl max −5 andl max −6 for the triplet state. These convergence rates are considerably slower than thel max −5 andl max −7 behaviours found for the singlet and triplet energies. The total energies,E(21P)=−2.123835 a.u. andE(23P)=−2.133155 a.u., are about 0.00001 a.u. above the “exact” non-relativistic results obtained with perimetric coordinates and also the SMS between3He and4He, SMS(21P)=0.4533 cm−1 and SMS(23P)=−0.6356 cm−1, are very close to the “exact” results.