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A quantum defect model for the s, p, d, and f Rydberg series of CaF
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10.1063/1.3565967
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Affiliations:
1 Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
2 Laboratoire Aimé Cotton du CNRS, Université de Paris Sud, Bâtiment 505, F-91405 Orsay, France
3 Department of Physics and Astronomy, University College London, London WC1E 6BT, United Kingdom
a) Author to whom correspondence should be addressed. Electronic mail: rwfield@mit.edu.
J. Chem. Phys. 134, 114313 (2011)
/content/aip/journal/jcp/134/11/10.1063/1.3565967
http://aip.metastore.ingenta.com/content/aip/journal/jcp/134/11/10.1063/1.3565967

## Figures

FIG. 1.

Comparison of selected observed and calculated energy levels near = 5.0, where vibronic states tend to be well-separated. For visual clarity, the reduced energy + ( + 1) is plotted against ( + 1) for each energy level. Filled circles indicate calculated energy levels and connected open circles indicate observed energy levels. Many levels with < 6.0 are fitted to within 1 cm−1, and most to within 5 cm−1.

FIG. 2.

Comparison of selected observed and calculated energy levels for vibrationally excited levels with low . For visual clarity, the reduced energy + ( + 1) is plotted against ( + 1) for each energy level. Many levels with < 6.0 are fitted to within 1 cm−1, and most to within 5 cm−1.

FIG. 3.

Comparison of selected observed and calculated energy levels in the vicinity of = 7.0. For visual clarity, the reduced energy + ( + 1) is plotted against ( + 1) for each energy level. Vibronic states at this energy are interleaved. Here, the classical period of electronic motion [proportional to ()3] is approximately equal to the classical period of vibrational motion. Vibronic perturbations are frequent.

FIG. 4.

Example of a strong vibronic (homogeneous) perturbation. In the absence of the perturbation, the 7.36 “” Π v = 0 and 6.36 “” Π v = 1 levels are nearly degenerate. The perturbation causes a ∼45 cm−1 splitting of the levels and complete mixing of the two zero-order wavefunctions.

FIG. 5.

Comparison of selected observed and calculated energy levels in the vicinity of * = 14.0. At this energy, the electronic energy level spacing is much smaller than the vibrational spacing, but still larger than the rotational spacing of the ion-core energy levels. Vibronic perturbations are uncommon, but rotational (inhomogeneous) perturbations become increasingly frequent.

FIG. 6.

Quality of fit in the 14 complex. A rotational perturbation between the 14 Π and 14.14 “” Δ states gives rise to the avoided crossing at the top of the figure.

FIG. 7.

Quality of fit in the = 16.5 – 17.5 region. Above ∼ 16, rotational interactions are ubiquitous and quite strong, causing the disappearance of regular patterns which is evident here.

FIG. 8.

-dependence of MQDT-fitted and -matrix calculated eigenquantum defects for (a) Σ and (b) Π series with = -0.020 Ry ( ≈ 7.0) and = −0.012 Ry ( ≈ 9.0), respectively. = 3.54 a, is the equilibrium internuclear separation of the ion core.

FIG. 9.

Energy dependence of MQDT-fitted and -matrix calculated Σ and Π series eigenquantum defects at the equilibrium internuclear separation, = 3.54 a. Energy is in Rydberg units.

FIG. 10.

Comparison of energy dependence of Σ series MQDT-fitted and -matrix calculated matrix elements, at the equilibrium internuclear separation, = 3.54 a. Energy is in Rydberg units. The calculated matrix elements have been adjusted as discussed in Appendix to allow direct comparison with the fitted matrix elements.

FIG. 11.

-dependence of MQDT-fitted and -matrix calculated matrix elements for Σ series, = –0.02 Ry ( ≈ 7.0). Trends with show some differences from the experimental result away from the equilibrium . (Also see Appendix .) The calculated matrix elements have been adjusted as discussed in Appendix to allow direct comparison with the fitted matrix elements.

FIG. 12.

Comparison of -dependence of MQDT-fitted and -matrix calculated matrix elements for Π series, = –0.012 Ry ( ≈ 7.0). Trends with show some differences from the experimental values away from . (Also see Appendix .) The calculated matrix elements have been adjusted as discussed in Appendix to allow direct comparison with the fitted matrix elements.

FIG. 13.

Calculated -dependence of higher- mixing in Σ and Π states of dominant character, at = –0.02 Ry. The calculation predicts mixing outside of the experimentally fitted , , , block dominantly to character, but also to . These mixings enhance experimental access to non-penetrating states, as reported in Kay (Ref. ).

## Tables

Table I.

quantum defect matrix element values and derivatives obtained from fits to CaF Σ, Π, Δ, and Φ states. Uncertainties are indicated in parentheses. If no numerical value is given, the parameter has been held fixed at zero.

Table II.

( = 3.54a) matrix for Σ symmetry.

Table III.

( = 3.54a) matrix for Π symmetry.

/content/aip/journal/jcp/134/11/10.1063/1.3565967
2011-03-18
2014-04-19

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