Abstract
The spectra of substances may, in a general way, be assigned to one of three categories, namely; the continuous spectra, the bright line spectra and the band spectra. The first of these occur only in emission and are produced by bodies heated to incandescence and are incapable of resolution into lines regardless of the resolving power of the available instruments. The second type are the spectra of atoms. They may be produced as bright line emission spectra by suitable excitation of the atoms, as for example by placing them in the crater of an arc or by passing an electric discharge through their vapors. When radiation from an incandescent source is allowed to pass through an atomic vapor and is examined with a spectroscope the spectra occur in absorption as dark line spectra against a continuous bright background.
Literature references are not given in footnotes, but in a bibliography at the end of this article.
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Abbreviations
- X, Y, Z:
-
space-fixed coordinate system
- X0, Y0, Z0 :
-
coordinates of center of mass in space-fixed coordinate system
- Xi, Yi, Zi :
-
coordinates of nuclei relative to center of mass in space-fixed coordinate system
- x, y, z:
-
body-fixed coordinate system
- ϑ, φ, ψ:
-
Eulerian angles relating x, y, z and X, Y, Z axes
- α (β, γ):
-
symbol to denote x, y, or z
- α’i, α’j :
-
coordinates of nuclei and electrons, respectively, relative to center of mass in body-fixed system
- αi, αj :
-
\(M_i^{\frac{1} {2}} \alpha '_i = \alpha _i ,m^{\frac{1} {2}} \alpha '_j = \alpha _j ,\), M i , and m being, respectively, the masses of the i-th nucleus and of an electron
- α0 i :
-
equilibrium value of α i .
- Iαα :
-
moment of inertia about α-axis
- Iαβ :
-
product of inertia
- I’αα :
-
effective moment of inertia about α axis. See Eq. (12.19)
- I’αβ :
-
effective product of inertia. See Eq. (12.19)
- ωα :
-
angular velocity about α-axis
- Qsσ, qsσ :
-
normal coordinates. \( {Q_{s\sigma }} = {\left( {{{{\hbar ^2}} \mathord{\left/ {\vphantom {{{\hbar ^2}} {{\lambda _s}}}} \right. \kern-\nulldelimiterspace} {{\lambda _s}}}} \right)^{\frac{1}{4}}}{q_{s\sigma }};{\lambda _s} = {\left( {2\pi c{\omega _s}} \right)^2} \)
- ωs :
-
normal vibration frequency in cm-1
- lisσ :
-
transformation coefficients relating δα i to normal coordinatesQ s σ
- psσ :
-
linear momentum conjugate to q s σ
- rt, χt, ϑt :
-
polar coordinates used to describe degenerate vibrations. (Note difference between ϑand ϑt.)
- Prt, Pχt, Pϑt :
-
momenta conjugate to r t , x t , and ϑt
- pΞ, PH, Pz :
-
linear momenta conjugate to coordinates of center of mass \( \Xi = {\left( {\sum\limits_i {{M_i} + Nm} } \right)^{\frac{1}{2}}}{X_0} \), etc
- pα :
-
component of internal angular momentum of nuclei directed along α-axis
- πα :
-
component of angular momentum of electrons directed along α-axis
- Πα :
-
Π α = Π α + p α
- sX, sY, sZ :
-
components of spin angular momentum directed along space-fixed X, Y, Z axes
- sx, sy, sz :
-
components of spin angular momentum directed along body-fixed x, y, z axes
- \( {S_\alpha } = \sum\limits_j {{S_{j\alpha }}} \) :
-
a component of total spin angular momentum directed along the α-axis
- Mα :
-
Mα = Π α + S α total internal angular momentum directed along the α-axis
- Pα :
-
component of total angular momentum directed along the α-axis
- smn :
-
distance between two atomic nuclei m and n
- s 0mn :
-
equilibrium value of s mn (s mn - s 0 mn = δs mn )
- A (αβ)sσsσ ,a (αβ)sσ :
-
etc., see definitions (18.24)
- ζ (α)sσs’σ’ :
-
Coriolis coupling factor. See definition (18.24)
- vs :
-
total vibration quantum number for a harmonic oscillator
- ls :
-
quantum number of total vibrational angular momentum associated with a two- or three-fold degenerate vibration
- ms :
-
component of vibrational angular momentum associated with a three-fold degenerate oscillator directed along an axis fixed in the molecule
- J:
-
quantum number of angular momentum of a molecule exclusive of spin
- F:
-
quantum number of angular momentum of a molecule inclusive of spin
- K:
-
quantum number associated with the component of J directed along the z-axis
- M:
-
the magnetic quantum number of rotation of a molecule
- Λ:
-
quantum number of electronic angular momentum directed along z axis of a linear molecule
- Σ:
-
quantum number of spin angular momentum directed along z axis of a molecule
- L:
-
angular momentum of the molecular framework directed along the z axis (not quantized)
- gs :
-
weight factor assuming the values 1, 2, or 3, respectively, as ω s is one-, two-, or threefold degenerate
- xss’, xlsls,:
-
etc. anharmonic constants (corresponding to ω e x e in diatomic molecules)
- DJ, DJK, DJL :
-
etc. centrifugal stretching coefficients. See definitions (34.15) and (34.16)
- B (αα)e :
-
reciprocal of inertia (h/8 π 2 I (e)αα c)
- B (αβ)v :
-
effective reciprocal of inertia or reciprocal product of inertia
- λαB :
-
direction cosines relating body-fixed axes to space-fixed axes
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Nielsen, H.H. (1959). The Vibration-rotation Energies of Molecules and their Spectra in the Infra-red. In: Atoms III — Molecules I / Atome III — Moleküle I. Encyclopedia of Physics / Handbuch der Physik, vol 7 / 37 / 1. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45917-7_2
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