Band-head

Units are cm throughout. Measurements are of band heads, formed by the rotational stmcture, not band origins. Figures in parentheses are differences variations in differences (e.g. between the first two columns) are a result of uncertainties in experimental measurements. 

Band-feder, /. flat spring, -fdrderer, m. belt conveyor, -kante, /. edge of a band, band head, -mass, n. tape measure, -stabl, m. band steel, strip steel, bandstreifig, a. banded, streaked, striped. Band-trockuer, m. belt drier, -wunn, m. tapeworm. 

Figure 7. Action spectra recorded by fixing the probe laser on the rotational band head of the E—B, 1-11 transition and scanning the excitation laser through (a) the Br2 B—A, 12-0,...

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].

Fig. 1. Model Spectra re-binned to CRIRES Resolution To demonstrate the potential for precise isotopic abundance determination two representative sample absorption spectra, normalized to unity, are shown. They result from a radiative transfer calculation using a hydrostatic MARCS model atmosphere for 3400 K. MARCS stands for Model Atmosphere in a Radiative Convective Scheme the methodology is described in detail e.g. in [1] and references therein. The models are calculated with a spectral bin size corresponding to a Doppler velocity of 1 They are re-binned to the nominal CRIRES resolution (3 p), which even for the slowest rotators is sufficient to resolve absorption lines. The spectral range covers ss of the CRIRES detector-array and has been centered at the band-head of a 29 Si16 O overtone transition at 4029 nm. In both spectra the band-head is clearly visible between the forest of well-separated low- and high-j transitions of the common isotope. The lower spectrum is based on the telluric ratio of the isotopes 28Si/29Si/30Si (92.23 4.67 3.10) whereas the upper spectrum, offset by 0.4 in y-direction, has been calculated for a ratio of 96.00 2.00 2.00.

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... 

It should be noted in passing that Mulliken also examined the isotope effect on the quadratic terms in the equations for the band heads. These ratios should theoretically show an isotope effect proportional to the reduced masses of the diatomic molecules (rather than the square root of the reduced masses). While Mulliken concludes that these ratios also confirm that the molecule is BO rather than BN, the four experimental ratios show a fairly large scatter so that the case for identifying the molecule is not as strong as that from the experimental a and b ratios. He also measured some of the rotational lines in the spectra of BO and considered the measured and theoretical isotope effects. Here one experimental isotope ratio checks the theoretically calculated ratio quite well, but for the other two the result was unsatisfactory. However, Mulliken judged the error to be within the experimental uncertainty. 

The last discovery of an isotope of an element in the second row of the periodic table was that of 15N. This is credited to R. Naude (1929). In the band spectrum of NO, he observed band heads for not only lsNieO but also 14N180 and 14N1tO on the basis of the expected isotope effect on the reduced mass of the molecule. 

As a quantitative test of the potential the vibrational eigenvalues have been calculated by a variational method using the program of Whitehead wA Handy (139). Table 4 shows the calculated fundamental frequency and one overtone. They are compared with values calculated directly from the Taylor - expanded potential using the same method, and with experimental band heads. The improvement of the Murrell-Sorbie potential over the Taylor expansion is striking. The results on H2O give some cause for optimism about a procedure in which other polyatomic surfaces are deduced largely from spectroscopic data. The procedure has been applied to other triatomics, notably O3 and SO2 with similar success (140). 

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

In IR spectra, the term quadratic in J is small [Eq. (4.118)] because Be is the same for the upper and lower levels of the transition. In electronic transitions, the dimensions of the molecule change substantially, and B e and Bf are generally quite different. For example, note the difference in Re and Be for the two states of CO listed in Table 4.1. The effect of the quadratic term is thus quite significant, and we get band-head formation for reasonably low values of J in electronic spectra band heads are a highly characteristic feature of such spectra. In the majority of cases, the... 

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...

Figure 60. Comet-tail CO+(A1l —>X2 2+) spectra from (a, c) luminescent ion-molecule reaction C++02- C0+ + 0 at lab = 5 eV (b,d), charge-transfer reaction Ar+ +CO->CO+ + Ar at lab=1000 eV. Experimental spectra (a, b) were obtained with 2-nm spectral resolution. Tabulated band heads for CO+ (A— BX) system are indicated. Spectral lines designated as Ar(II) and C(I) do not belong to CO+ emission. Dashed portion of curves was not actually measured. Spectra simulated by computer calculations are given in diagrams (c and d). Rotational distributions assumed in simulation calculations were thermal with T= 45,000°K (c) and 1000°K (

The distinction between a truly continuous absorption spectrum and a banded absorption spectrum for diatomic molecules may be made by instruments of relatively low resolving power. Even though individual rotational lines are not resolved, a discrete spectrum will have sharp band heads and the appearance will in no way resemble the appearance of a continuum. 

Table 6 summarizes the characteristics of the modeled and experimental level sets for the nuclei that we have studied so far the modeled sets provided by Hoff are designated as Set A. Note, as an example, that the available experimental level information for Np consists of only 5 levels (including 3 rotational bands) up to 0.22 MeV in nuclear excitation, whereas the modeled Set A consists of 998 levels in the first 1.48 MeV and includes 94 rotational bands. Sets B through D were obtained by truncating the 998-level set just below selected band heads. In Fig. 7(a), curve A shows our calculated g/m ratio for 236Np production... 

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... 

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