Singlet-Triplet Mixing in Excited Helium Atoms

Abstract

Experiments in collisional transfer of excitation, as well as theoretical considerations, have shown that singlet-triplet mixing occurs for nE states of helium. In this work the helium fine structure has been calculated using polarized orbitals to determine the amount of mixing and its dependence on the state {n)) of the excited electron, and on the polarization of the orbital of the inner electron. Results are presented for n=3-10 and )=2{n -1). All P statesgave poor results because of a large exchange effec', involving the polarization term in the wave function. However, the 3 D and 4 D levels showed improved agreement with experiment for the fine structure. The singlet-triplet mixing is essentially zero for l =2, is significant for l =3, and is virtually complete for l~4 . It is also found that the mixing decreases slightly with increasing n.

Fine-structure and tensor polarizabilities of 1snd 3 D levels of He I (n=3 to 7)

“…Finally a comment must be made with regard to the influence of singlet-triplet mixing on the polarizability of the n3D levels. The strongest singlet-triplet mixing is expected for the 33D level [9,10]. According to van den Eynde et al [9] this mixing coefficient is co =0.937 %.…”

“…But even here a more direct measurement of the small level splitting A E2a is desirable. It is this level splitting which depends most sensitively on singlet-triplet mixing coefficients for which theoretical predictions [9,10] are rather doubtful. The fine-structure splittings of the n3D levels with n= 5, 6, 7 can be deduced from the beam-foil investigations [6,7] and from the early measurements of Descoubes [3].…”

Strong-Field Excitation of Helium: Bound State Distribution and Spin Effects

“…However, they are only forbidden as long as low angular momentum states with l < 3 are involved. For higher / states the LS coupling scheme breaks down and with respect to the LS coupled basis the two spin components are nearly equally mixed [31]. As a conse quence, one might expect excitation of triplet states with equal probability to singlet state excitation for states with l > 2.…”

Coherent excitation of the singlet-triplet mixed1s4fstate of helium

“…Table VIII of Ref. [18]. van Raan and Heideman [24] made a considerable simplification to the wave functions for these states and gave them in the following form: For calculations in relation to the angular and polarization correlations of the radiation field emitted by the excited atom, it is most convenient to use the statemultipole description defined as [5] (T( A further symmetry (16) In addition, the interaction of the electron-atom collision possesses reAection invariance in the scattering p1ane and thus the scattering amplitudes defined in the collision frame must satisfy the condition [25] f((LS)Jmzm, m, p) =( - 1) Xf((LS)J -mJ -m, -m, o) .…”

“…Parish and Mires [18] calculated the mixing coefficients for various states of helium using the Breit-Pauli Hamiltonian, which takes into account the Coulomb interaction, spin-orbit, spin-other-orbit, and spin-spin interactions between the two electrons. More sophisticated descriptions, which include relativistic and masspolarization effects, were given by Cok and Lundeen [19,20] and Sims and Martin [21].…”