Total angular momentum quantum number applications, 826

The operator Tang contains the cross-terms that give rise to the Coriolis coupling that mixes states with different fl (the projection of the total angular momentum quantum number J onto the intermolecular axis). This term contains first derivative operators in y. On application of Eq. (22), these operators change the matrix elements over ring according to... 

Here p, is the reduced mass, and are the Hamiltonians defined in Equation 11.1 for each atom, and Vint is the effective interaction potential depending on the relative position of the atoms, r. For many applications, such as the description of broad scattering resonances and their associated Feshbach molecules, it is sufficient to include in Vint only the rotationally symmetric singlet and triplet Born-Oppenheimer potentials, Vs=o and V5=i, respectively. Their labels 5 = 0 and 5=1 refer to the possible values of the angular-momentum quantum number associated with the total spin of the two atomic valence electrons, S = si -E S2. In this approximation, the interaction part of Equation 11.4 can be represented by [8,29]... 

This method is equally applicable to atoms 26) and to molecules 22). In molecules the Zeeman splitting depends on the quantum number / of the total angular momentum and therefore the fluorescence from a single rotational level (v, f) need be observed. Because of this necessarily selective excitation, these molecular level-crossing experiments can be performed much more easily with lasers than with conventional light sources and have been sucessfully performed with Naj 2 > and NaK 29). 

Application of the symmetry correlation scheme to reaction (12) is summarized in Table 4 where N is the Himd s coupling case (b) rotational quantum number for O2 and - 5 is the difference of the Hund s coupling case (a) quantum numbers of total angular momentum and electron spin (5 = 1/2) angular momentum, respectively. To consider the high-symmetry isotopomer system first, the results in Table 4 indicate that only odd / collisions - 5 = odd) with 2 can lead... 

Scattering theory concerns a collision of two bodies, that may change the state of one or both of the bodies. In our application one body (the projectile) is an electron, whose internal state is specified by its spin-projection quantum number v. The other body (the target) is an atom or an atomic ion, whose internal bound state is specified by the principal quantum number n and quantum numbers j, m and / for the total angular momentum, its projection and the parity respectively. We... 

Therefore we find that Yj is an eigenfunction of with the eigenvalue mh. The z component of the angular momentum is therefore quantized the quantum number is m = 0, + 1, 2, . Again, precise values of the z component of angular momentum are permitted since the angle 0 is totally unspecifiable. Repeating the application of on Eq. (21.75), we obtain... 

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