Lamb Shift in the Metastable States of the Helium Atom

K. S. Suh, M. H. Zaidi
1966 Proceedings of the Royal Society A  
The rad iativ e corrections of order a 3 ry d b erg s are ev a lu a te d for th e ionization energy o f th e m etastab le sta te s 21-3S, o f th e helium ato m . I n th e calculation of th e average e x c ita tio n energy Jc0, th e m ain co n trib u tio n comes from th e tra n sitio n to a n d (ms, ep) sta te s. T he oscillator stren g th s for tran sitio n s to (Is, ep), (2s, ep) a n d (3s, ep) sta te s a re e v a lu a te d b y using six-param eter w avefunction for th e m eta sta b le sta te
more » ... a n d a p ro d u c t o f a hydrogenic w avefunction w ith Z = 2 fo r th e s electron a n d a w av efu n ctio n analogous to t w avefunction for th e ex cited p electron. M aking use of these oscillator stre n g th s a n d a m eth o d used b y P ekeris, th e values o f th e average ex citatio n energies for th e singlet a n d trip le t sta te s are fo u n d to be 77-09+ 1-6 a n d 79-84+ TO rydb erg s respectively. W ith th ese values of th e average ex cita tio n energies, th e L am b shift corrections, including th e e stim ate o f a 4 R y o rd er corrections, to th e io n izatio n energies of th e singlet a n d trip le t sta te s becom e -0-106 + 0-018 cm -1 a n d -0-129 + 0-013 c m -1 respectively. W hen th e y are a d d e d to th e th eo retical values o f th e ion izatio n energies o b ta in e d b y Pekeris, th e values of th e ionization energies becom e 32033-212 + 0-018 a n d 38454-698 + 0-013 cm -1 com pared w ith H erzb erg 's ex p erim en tal v alu es o f 32033-24 + 0-05 a n d 38454-73 + 0-05 cm -1 for th e singlet a n d trip le t sta te s respectively. 1. I n t r o d u c t i o n Recent experimental measurements of the ionization potentials of the metastable states (Is, 2s)1*3S of helium atom by Herzberg have stimulated the interest in the evaluation of the radiative corrections to the metastable states. The experimental values of the ionization potentials of the metastable states of the helium atom estimated by Herzberg are 7expt. = 38 454-73 + 0-05 cm-1 for triplet,! = 32 033-24 + 0-05 cm-1 for singlet, j ^ Â ccording to Pekeris (1959) the non-relativistic ionization potentials for the m eta stable states of helium atom are In T = 38 453-129 cm-1 for triplet,! = 32 033-204 cm-1 for singlet.J T he relativistic corrections of order a 2 Ry and the mass polarization correction have been evaluated by Pekeris (1962) who gives the values A/r = 1-698 cm-1 for triplet, = 0-114 cm-1 for singlet. Thus the theoretical values of the ionization potentials up to order a 2 Ry are In r + A/r. = 38 454-827 cm-1 for triplet, 1 = 32 033-318 cm-1 for singlet. J [ 94 ]
doi:10.1098/rspa.1966.0081 fatcat:q6am6f55kvgjfp4fcir7mip72q