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Theory of vibronic interactions in D2 and H2: A comparison between multichannel-quantum-defect and coupled-equation approaches
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10.1063/1.3593274
/content/aip/journal/jcp/134/20/10.1063/1.3593274
http://aip.metastore.ingenta.com/content/aip/journal/jcp/134/20/10.1063/1.3593274

Figures

Image of FIG. 1.
FIG. 1.

Experimental N = 1 levels of the state of D2 from various authors, plotted as function of the vibrational quantum number v. The differences of the levels with respect to a CE reference calculation are plotted: Filled squares (red) connected by full lines: present data. Filled triangles (green): Monfils (Ref. 22). Filled circles (black): Dabrowski and Herzberg (Ref. 33). Open circles (blue): Freund et al. (Ref. 36). Open stars (purple): Hinnen et al. (Ref. 2). Inset: enlarged section corresponding to small v.

Image of FIG. 2.
FIG. 2.

Histograms representing the deviations of the present energy levels for D2, compared to those determined in previous experiments. (a) 2pπC state: present—Hinnen et al. (Ref. 2). (b) 3pπD state: Roudjane et al. (Ref. 14)—Freund et al. (Ref. 36). (c) 2pπC state: present—Refs. 30 and 35. (d) 4pπD′ state: Roudjane et al. (Ref. 14)—Takezwa and Tanaka (Ref. 34). Full curves: Gaussian curves fitting the distributions.

Image of FIG. 3.
FIG. 3.

Histograms representing the residuals observed-calculated (fully ab initio) for D2: Left: MQDT calculations. Right: CE calculations, for the 2pπC, 3pπD, and 4pπD1 excited states, respectively.

Image of FIG. 4.
FIG. 4.

Histograms representing the residuals observed-calculated (fully ab initio) for H2: Left: MQDT calculations. Right: CE calculations, for the 2pπC, 3pπD, and 4pπD1 excited states, respectively.

Image of FIG. 5.
FIG. 5.

Residuals obs.-calc. (in cm−1) for the state of D2 for different N values, plotted as functions of the vibrational quantum number v. Full symbols connected by full lines: MQDT evaluation. Open symbols connected by broken lines: CE evaluation. (a) N = 1 − 6 (b) N = 7 − 10. (Color coding as indicated.)

Image of FIG. 6.
FIG. 6.

Residuals obs.-calc. (in cm−1) for H2 for N = 1 − 5, plotted as functions of the vibrational quantum number v. (a) state. (b) state. (c) state. (Symbols and color coding as in Fig. 5.)

Image of FIG. 7.
FIG. 7.

Residuals obs.-calc. (in cm−1) for the state of D2 for different N values, plotted as functions of the vibrational quantum number v. Full symbols connected by full lines: MQDT evaluation. Open symbols connected by broken lines: CE evaluation (Ref. 14). (a) N = 1 − 6, (b) N = 7 − 10. (Symbols and color coding as in Fig. 5.)

Image of FIG. 8.
FIG. 8.

Residuals obs.-calc. (in cm−1) for the state of D2 for different N values, plotted as functions of the vibrational quantum number v. Full symbols connected by full lines: MQDT evaluation. Open symbols connected by broken lines: CE evaluation (Ref. 14). (a) N = 1 − 5, (b) N = 6 − 10. (Symbols and color coding as in Fig. 5.)

Image of FIG. 9.
FIG. 9.

Calculated “complex” resonance arising from the vibronic interaction between the low-n 6pπ(v = 3, N = 1) level and the high-n Rydberg series of levels converging towards the v + = 1, N + = 1 ion threshold. Each vertical line represents a narrow autoionization resonance, the integrated intensity of which is given by the position of the filled square. The latter represents the (hypothetical) Einstein coefficient for emission to the v′ = 0 level of the ground state.

Image of FIG. 10.
FIG. 10.

Ratios of theoretical Einstein emission coefficients for Q(N) lines obtained in the MQDT and CE calculations. (a) 2pπC(v′) → X(v′′ = 0) transitions. (b) 3pπD(v′) → X(v′′ = 0) transitions. (c) 4pπD′(v′) → X(v′′ = 0) transitions. The left hand side of the figure displays these ratios plotted as functions of the upper state vibrational quantum number for various values of the rotational quantum number N′. On the right hand side histograms illustrate the statistical distributions of these ratios. (Symbols and color coding as in Fig. 5.)

Image of FIG. 11.
FIG. 11.

Intensity perturbation due to vibronic interaction between the 3pπD(v′ = 8) and 4pπD′(v′ = 4) levels in D2. Top: The Einstein emission coefficients calculated by MQDT for the Q(N′) optical transitions from the interacting upper states to the v′′ = 0 ground state level are plotted as a function of the rotational quantum number N′. Bottom: Corresponding ratios between Einstein coefficients evaluated by MQDT and in the adiabatic approximation.

Image of FIG. 12.
FIG. 12.

Residuals observed-calculated for the N = 1 levels of the H2 state as functions of the vibrational quantum number v, calculated in various approximations. Full circles (red) and full squares (blue) connected by full lines: MQDT and CE results, respectively, as reported in Fig. 6. Open squares (blue) connected by full lines: standard adiabatic approximation for the molecule in the state. Open diamonds (blue) connected by dashed lines: adiabatic approximation, with the non-adiabatic correction of each ion level v + added to the corresponding adiabatic molecular level v. Open diamonds (red) connected with dotted lines: MQDT calculation with ionization limits calculated in the adiabatic approximation (cf. the text for more details).

Image of FIG. 13.
FIG. 13.

Extrapolation of residuals for H2 and D2 in the 2pπC state to infinite mass. Upper panel: Residuals plotted for each vibrational level as function of the energy below the H(1s)+H(n = 2) dissociation energy. (Symbols and color coding as in Fig. 5.) Lower panel: Residuals plotted versus 1/μ, the inverse of the nuclear mass, for 10 points chosen on the abscissa of the upper graph. Inset: Histogram showing the distribution of the values for 1/μ = 0 obtained by linear extrapolation.

Tables

Generic image for table
Table I.

Experimentally determined rotation-vibration levels of the state of D2.

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/content/aip/journal/jcp/134/20/10.1063/1.3593274
2011-05-26
2014-04-17
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Theory of vibronic interactions in D2 and H2: A comparison between multichannel-quantum-defect and coupled-equation approaches
http://aip.metastore.ingenta.com/content/aip/journal/jcp/134/20/10.1063/1.3593274
10.1063/1.3593274
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