Angular momentum quantum number. See

Figure 9. Lowest adiabatic channel potential curves [33] for the interaction of electronic ground state O2 with ions (q = ionic charge, Q = O2 quadrupole moment N,J,M= free-rotor quantum numbers M, k, v = harmonic oscillator quantum numbers N = electronic angular momentum quantum number see Ref. 33).

Coriolis zeta constant angular momentum quantum numbers see additional information below 1... 

Table 6.2 Explicit list of angular momentum quantum numbers (see also Table 6.1).

The second quantum number describes an orbital s shape, and is a positive integer that ranges in value from 0 to (n - 1). Chemists use a variety of names for the second quantum number. For example, you may see it referred to as the angular momentum quantum number, the azimuthal quantum number, the secondary quantum number, or the orbital-shape quantum number. 

Quantum mechanical considerations show that, like many other atomic quantities, this angular momentum is quantized and depends on I, which is the angular momentum quantum number, commonly referred to as nuclear spin. The nuclear spins of / = 0, 1/2, 1, 3/2, 2. .. up to 6 have been observed (see also Table 1). Neither the values of I nor those of L (see below) can yet be predicted from theory. 

The y>Ee(R) are the radial free-state wavefunctions (see Chapter 5 for details). The free state energies E are positive and the bound state energies E(v,S) are negative v and ( are vibrational and rotational dimer quantum numbers t is also the angular momentum quantum number of the fth partial wave. The g( are nuclear weights. We will occasionally refer to a third partition sum, that of pre-dissociating (sometimes called metastable ) dimer states,... 

We now consider many-electron atoms. We will assume Russell-Saunders coupling, so that an atomic state can be characterized by total electronic orbital and spin angular-momentum quantum numbers L and S, and total electronic angular-momentum quantum numbers J and Mj. (See Section 1.17.) The electric-dipole selection rules for L, J, and Mj can be shown to be (Bethe and Jackiw, p. 224)... 

The appearance of a vibration-rotation band is shown in Fig. 4.9. Because A/=0 is forbidden, we have a gap at the wave number of the band origin o0. (We are considering only diatomic molecules in 2 electronic states for electronic states in which the electronic orbital angular-momentum quantum number A is nonzero, transitions with AJ=0 are allowed, giving a Q branch in each band. An example is NO, which has a 2n electronic ground term, -branch transitions also occur for vibration-rotation bands of polyatomic molecules see Chapter 6.) Under low resolution, an infrared band of a diatomic molecule looks like Fig. 4.10. 

The selection rules state that the total angular momentum quantum number may change by 1 or 0. Thus an element with several isotopes each with its own nuclear spin will present a line spectrum with a very complex and, under most experimental conditions, unresolved hyperfine structure. Nevertheless, as we shall see later, the overlap between the hyperfine components of a spectrum line is sufficiently incomplete to permit preferential excitation of one isotope in a mixture of isotopes by radiation from a lamp containing that same isotope. 

To see how an octahedral crystal field reduces the (2L+l)-fold degeneracy of a spectroscopic term, we first need to determine the character of a rotation operating on an atomic state defined by the orbital angular momentum quantum number L. It can be shown that the character / for a rotation of angle a about the z axis is simply... 

As a model case for discussing optical alignment and orientation of molecules possessing low values of the angular momentum quantum number one may consider the transition (J" = 1) — (J = 1). With such a choice of transition the values of the quantum numbers are the smallest ones at which both orientation (K, k = 1) and alignment (K, k — 2) can exist on both levels, since K < 2J = 2, k < 2J" = 2 see (5.17). A... 

What do quantum numbers mean As we shall see in Sections 3.5, the three spatial quantum numbers (n, l, m ) for the H atom identify the allowed eigenstates for the solution of the Schrodinger89 equation, with certain characteristic energies and spatial features (e.g., the angular momentum quantum number describes how much angular momentum the atom has). But then, what is the meaning of the "electron spin" quantum number ... 

For each value of n, the angular momentum quantum number ( ) for an electron can have integral values from zero to ( — 1) it cannot be as large as n. The angular momentum quantum number has a small role in determining the energy of the electron, and it determines the shape of the volume of space that the electron can occupy (see Section 4.6). 

Another selection rule allows only transitions between states having the same spin. This is relaxed somewhat through spin orbit (SO) coupling see Coupling). In a free atom/ion, this means that the spin and orbital angular momenta (represented respectively by S and L for a state labeled L) are combined so that the state is spUt into 2S + 1 levels, classified according to their total angular momentum quantum number J = L + S,L + S—, — S. For example, the... 

---