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

Abstract

The specific mass shift (SMS) and energies of the (1s2p)^{1, 3} P 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 ⁻³_max for the singlet state and betweenl ⁻⁵_max andl ⁻⁶_max for the triplet state. These convergence rates are considerably slower than thel ⁻⁵_max andl ⁻⁷_max behaviours found for the singlet and triplet energies. The total energies,E(2¹ P)=−2.123835 a.u. andE(2³ P)=−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(2¹ P)=0.4533 cm⁻¹ and SMS(2³ P)=−0.6356 cm⁻¹, are very close to the “exact” results.