Band-head energies

Figure 13. Action spectrum of the linear He I Cl complex near the He + I Cl(By = 2) dissociation limit obtained by scanning the excitation laser through the ICl B—X, 2-0 region and monitoring the l Cl E—>X fluorescence induced by the temporally delayed probe laser, which was fixed on the l Cl E—B, 11-2 band head, (a). The transition energy is plotted relative to the I Cl B—X, 2-0 band origin, 17,664.08 cm . Panels (b), (c), and (d) are the rotational product state spectra obtained when fixing the excitation laser on the lines denoted with the corresponding panel letter. The probe laser was scanned through the ICl B—X, 11-2 region. Modified with permission from Ref. [51].

From his first paper (Mulliken 1925a), Mulliken understood that the band heads did not represent a transition from a non-rotating initial state to non-rotating final state. Yet, he used the band heads to study the vibrational isotope effect since he could measure the band heads more easily and since the rotational energy differences are very small compared to the vibrational energy difference. From the theory, the terms linear in n and n" (ain and bin") arise from the harmonic approximation with the coefficients ai and bi corresponding to the harmonic vibrational frequencies in the... 

Table 4. Comparison of variationally calculated excitation energies (cm ) for H2O with the spectroscopic band heads.

Figure 59. Emission spectra resulting from 0+-H2 collisions at various relative energies. Band heads for A—>X transitions of OH and OH+ are indicated.12b...

While there is little doubt about the rotational properties of the band which is based upon the 495 keV state, the nature of the levels below the band head and of those which are only populated in the 13 decay of 8Sr is not clear. These levels do not show a membership to bands and it is probable that most of them are not of rotational character. In particular, although the energy of 119 keV of the first excited state is similar to the... 

D14.3 A band head is the convergence of the frequencies of electronic transitions with increasing rotational quantum number, J. They result from the rotational structure superimposed on the vibrational structure of the electronic energy levels of the diatomic molecule. See Figs 14.8 and 14.11. To understand how a band head arises, one must examine the equations describing the transition frequencies (eqns 14.5). As seen from the analysis in Section 14.1 (e). convergence can only arise when terms in both (S — B) and (S + B) occur in the equation. Since only a term in (fl — B) occurs for the Q branch, no band head can arise for that branch. 

The following free parameters were introduced (1) energy of the band head, (2) absolute intensity of the band, and (3) rotational parameter of the band. The last parameter was kept identical for all of the groups, i.e., the 5.28, 5.37 and 5.47 MeV groups. A fit to the measured spectrum was performed with the above parameters using the least squares method. The nonresonant part of the fission probability was taken into account as an exponential background. ... 

The energies of the band heads, the absolute intensities of the bands, and an inertia parameter were fitted to the experimental data. The obtained inertia parameter is... 

To make quantitative statements about the product internal distribution a computer program is utilized to simulate the observed excitation spectrum [10]. As input for the calculations we estimate the relative vibrational and rotational populations. Each line is weighted by the population of the initial (v, J ) level, by the Franck-Condon factor and the rotational line strength of the pump transition. At each frequency, the program convolutes the lines with the laser bandwidth and power to produce a simulated spectrum such spectra are compared visually with the observed spectra and new estimates are made for the (v ,J") populations. Iteration of this process leads to the "best fit" as shown in the lower part of Fig. 3. For this calculated spectrum all vibrational states v" = 0...35 are equally populated as is shown in the insertion. The rotation, on the other hand, is described by a Boltzmann distribution with a "temperature" of 1200 K. With such low rotational energy no band heads are formed for v" < 5 in the Av = 0 sequence and for nearly all v" in the Av = +1 sequence (near 5550 A). 

The peaks representing the R branch get closer and closer together as / increases, a. Use equation 14.41 to estimate at what rotational state the rovibrational lines will cease to be separated from each other, and will start moving to lower energy. (This point is called the band head of the series of absorptions.) To simplify the problem, neglect the centrifugal distortion term. Use Bq = 10.44 cm and = 10.14 cm h... 

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