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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
/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

Image of FIG. 1.
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.

Image of FIG. 2.
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.

Image of FIG. 3.
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.

Image of FIG. 4.
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.

Image of FIG. 5.
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.

Image of FIG. 6.
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.

Image of FIG. 7.
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.

Image of FIG. 8.
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.

Image of FIG. 9.
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.

Image of FIG. 10.
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 C to allow direct comparison with the fitted matrix elements.

Image of FIG. 11.
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 C .) The calculated matrix elements have been adjusted as discussed in Appendix C to allow direct comparison with the fitted matrix elements.

Image of FIG. 12.
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 C .) The calculated matrix elements have been adjusted as discussed in Appendix C to allow direct comparison with the fitted matrix elements.

Image of FIG. 13.
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. 31 ).

Tables

Generic image for table
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.

Generic image for table
Table II.

( = 3.54a) matrix for Σ symmetry.

Generic image for table
Table III.

( = 3.54a) matrix for Π symmetry.

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/content/aip/journal/jcp/134/11/10.1063/1.3565967
2011-03-18
2014-04-19
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: A quantum defect model for the s, p, d, and f Rydberg series of CaF
http://aip.metastore.ingenta.com/content/aip/journal/jcp/134/11/10.1063/1.3565967
10.1063/1.3565967
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