Oscillator strengths forS-PandP-Dtransitions in heliumlike ions

Abstract

states, with n (7, of the two-electron ions from He through Ne +. The variational energies are the best available for 180 of the 261 states. Electron-nuclear and electron-electron cusp checks are used to test the wave functions. For each ion, dipole oscillator strengths are calculated for 55 S-P and 40 P-D transitions. Our oscillator strengths are more accurate than previous values for 739 of the 855 transitions considered. Some coefficients for the 1/Z expansions of the energies and oscillator strengths have been estimated as an aid to extrapolating our results to higher nuclear charges.PACS number(s): 32.70.Cs, 31. 20.Tz X k( -12) I e P(~krl~kr2 Ykr12) k=1 X YL 0( 0 ] ) Yo o ( Q~) in which Xis the number of terms, P]p is the permutation operator, the plus and minus signs refer to the singlet and triplet states, respectively, L is the total orbital angular in which r;=(r;, Q;) is the position vector of electron i for i = 1,2, r, z is the interelectronic distance, and Z is the nuclear charge. Schiff, Pekeris, and Accad [l], Kono and Hattori [2,3), and Sanders and Knight [4] all used Hylleraas-type [5] wave functions containing several hundred and, in some cases, a few thousand terms. We have previously [6 -8] shown that use of exponential correlation factors [5,9] can lead to compact wave functions of similar accuracy. Although our original work was restricted to low-lying states [6,7], the success of our ansatz for obtaining pseudospectra [8] encouraged us to expect that it would do well for more highly excited states as well. Thus, for the S and P states, we use spin free wave functions of the form [6 -8] 46 5397

Relativistic Calculations of Transition Amplitudes in the Helium Isoelectronic Sequence

“…These benchmark calculations were confirmed and extended by Kono and Hattori [22] and by Sandars and Knight [23]. Most recently, Cann and Thakkar [24] have carried out high-precision variational calculations of oscillator strengths for S − P and P − D transitions for ions in the range Z = 2 − 10. The nonrelativistic oscillator strengths from Ref.…”

“…(23,24), have no effect on the magnetic-multipole potentials, but they do modify electric-multipole potentials. In particular, a gauge transformation of the transverse-gauge potentials using the gauge function,…”

“…The source of these errors is the use of nonrelativistic energies and wave functions in the calculations of Ref. [24].…”

“…The nonrelativistic oscillator strengths from Ref. [24] are rounded to five digits and compared with the present calculations in Table 7. The present results for the triplet transitions are obtained by summing the oscillator strengths of the three fine-structure components to give a composite relativistic oscillator strength.…”

Accurate Atomic Transition Probabilities for Hydrogen, Helium, and Lithium

“…Cann and Thakkar 47 and Chen 48 made precise calculations similar to Drake but on a less extensive and slightly less sophisticated basis. Where they overlap, the results are identical within the first four digits.…”