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Physical Review A

Observation of singlet-triplet anticrossing in He

Terry A. Miller, Robert S. Freund, Foch Tsai, Thomas J. Cook, Bernard R. Zegarski

Published Jun 1, 1974• 32 citations

Abstract

Two independent anticrossings have been observed between singlet and triplet levels in the He atom, one between the $7^{1}D$ and $7^{3}D$ states, the other between the $8^{1}D$ and $8^{3}D$ states. The states are excited by electron bombardment. Compensatory changes in the luminosity of the singlet and triplet states are detected as the levels are tuned through the anticrossing points by a magnetic field. The positions of the anticrossings have been analyzed to provide new values for these singlet-triplet separations accurate to \ensuremath{\sim}0.03 GHz. These results show the previous best optical determinations for the separations to be in error by over a GHz. The widths of the anticrossings are analyzed to provide the most direct measures of the spin-orbit coupling constant between a singlet and a triplet state yet obtained for any system. The measured values of these coupling constants are found to be several times larger than their corresponding diagonal value in the $7^{3}D$ and $8^{3}D$ states.

DOI: 10.1103/physreva.9.2474

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Two independent anticrossings have been observed between singlet and triplet levels in the He atom, one between the

7^{1}D

and

7^{3}D

states, the other between the

8^{1}D

and

8^{3}D

states. The states are excited by electron bombardment. Compensatory changes in the luminosity of the singlet and triplet states are detected as the levels are tuned through the anticrossing points by a magnetic field. The positions of the anticrossings have been analyzed to provide new values for these singlet-triplet separations accurate to \ensuremath{\sim}0.03 GHz. These results show the previous best optical determinations for the separations to be in error by over a GHz. The widths of the anticrossings are analyzed to provide the most direct measures of the spin-orbit coupling constant between a singlet and a triplet state yet obtained for any system. The measured values of these coupling constants are found to be several times larger than their corresponding diagonal value in the

7^{3}D

and

8^{3}D

states.

The method of singlet-triplet level anticrossing has been extended to the

n=6^{1,3}D

levels of He. Measurement of this anticrossing gives a highly accurate determination of the zero-field singlet-triplet separation and a less accurate determination of the antisymmetric part of the spin-orbit coupling perturbation between the

n=6^{1,3}D

states. The zero-field separation for

n=6

, although considerably more accurate, is in essential agreement with previous optical results, confirming the accuracy of the intercombination line measurements. The singlettriplet intervals calculated by many-body perturbation theory are also found to be in very good agreement with the experimental results.

The anticrossing spectra of the $n=6,7,8 ^{1}D\ensuremath{-}^{3}D$ states of

^{3}\mathrm{He}

have been observed. From these measurements precise values of the electrostatic singlet-triplet separation of these states have been obtained and are found to differ systematically from the accepted values of the

^{4}\mathrm{He}

singlet-triplet separation by approximately 34 MHz. We have investigated mass-dependent contributions to both the energy-level structure and the magnetic-tuning characteristics of the states of interest. We have found no mechanism that can explain such a large difference in the electrostatic-energy separation of the singlet and triplet

^{3}\mathrm{He}

states between the two helium isotopes.

Singlet-triplet anticrossings of 1s3d Stark sublevels of He I were investigated by inducing resonance transitions from the 1s2p 3 P level to the 1s3d Stark states at electric fields 80 kV cm -1 <F z <100 kV cm -1 . The measurements were performed using a beam of metastable helium atoms perpendicular to a 588 nm laser beam from a tunable dye laser. From the energy separations of closest approach of four anticrossings we deduced the radial integrals h off 3p =(3660+or-200) MHz and h off 3d (652.6+or-1.0) MHz of the singlet-triplet off-diagonal matrix elements of the spin-orbit coupling for the 1s3p and 1s3d configurations. They agree with recently calculated values.

The energy separations of closest approach were measured for the 1s n ℓ 1 Λ× 3 Λ anticrossings of singlet and triplet Stark states of the 1s4d, 1s5d and 1s5f configurations of He I. Using a fast atomic He beam, a selective population of the upper state of the anticrossing was accomplished by starting with an initial selective excitation of singlet states by 12 keV He-He collisions followed by an adiabatic transit to the electric field of the anticrossing, where radiofrequency transitions were induced. From the resonance signals the energy separations of three 1s4d, four 1s5d and three 1s5f anticrossings were determined. We evaluated the off-diagonal matrix elements of the spin-orbit coupling for the 1s4ℓ and 1s5ℓ configurations from the measured energy separations. The experimental results are compared with the calculated values.