Hund coupling

Here and below we follow the usual spectroscopic notations for molecular terms [8, 9], In the case of the Hund coupling scheme a the notation a +1Aw refers to a molecular term with total electron spin S, the projection A (A > 0) of electronic orbital angular momentum on the molecular axis, and parity w. 

Under this condition a collision practically does not induce intramultiplet mixing, but during a collision there is an appreciable distortion of atomic functions. The mere fact of the existence of the molecular term A2ni/2 described by the Hund coupling scheme a means that the electronic spin follows rotation of the molecular axis. To this approximation there will be depolarization of the P1/2 state although the relevant molecular term... 

We now write down the possible interaction potential in the quasimolcculc under consideration. In contrast to the Hund coupling scheme (Table 1), we separate various interactions of cui ion and atom at Uu ge distances in the form... 

Comparing this with the data in Table 1, the real situation is found to be between the cases " a and " c of Hund coupling, but case (6) docs not correspond exactly to any one of the Hund cases. Now we evaluate the exchange ion-atom interaction potential A(i ) on the basis of the formula for the resonant charge exchange cross section (Te,r ill the case of the transition of s—electron [4, 14, 15]... 

Here is the wave function of the (juctsimolcculc when a valence electron is located near the first core (an electron is connected with the first nucleus), and 5 2 corresponds to electron location near the second nucleus, H is the Hamiltonian of electrons. Note that for an accurate evaluation of this interaction it is necessary to use the accurate wave functions of the quasimolcculc which take into account interaction of a valence elertron located between the cores with both cores simultaneously. We assume this to be fulfilled within the framework of the cisymptotic theory. Using a genei cd method of calculation of the exchange interaction potential A(i ) by analogt with that for the case a of Hund coupling [3, 17, 20, 21], we... 

Let us summarize the Hund coupling scheme [5, 6, 7] that is given in Table 1 together with the quantum numbers of the quasimolecule for each case of Hund coupling. We denote by L the total electron angular momentum of the molecule, S is the total electron spin, J is the total electron momentum of the molecule, n is the unit vector along the molecular axis, K is the rotation momentum of nuclei, A is the projection of the angular momentum of electrons onto the molecular axis, H is the projection of the total electron momentum J onto the molecular axis, 5 is the projection of the electron spin onto the molecular axis, Lyv, Si, Jn are projections of these momenta onto the direction of the nuclear rotation momentum N. Below we will take this scheme as a basis. 

In formula (21) is the onc-clcctron exchange interaction potential that respects the case when a valence electron with (luanturn numbers is located in the field of two structureless cores and has the same asymptotic wave function as in real atoms. As a result, we obtain by analogy with the case "a" of Hund coupling [3, 9, 17, 20, 21]... 

TABLE 5. Tho average eross sections for the halogen atom and ion in tho ground clectroiuc states X( P) + X P) in at indicated collision energies e in the laboratory frame of reference for the hierarchy (6) of interactions and for case "a" of Hund coupling[19, 21] (in parentheses). 

In contrast to the case a of Hund coupling, in the halogen and oxygen cases the resonant diargc exchange process is not entangled with transitions between fine states of colliding particles and rotaion of the molecular axis. This increases... 

Though many of the semi-classical ideas entering the concept of vector-coupling no longer are useful, it may be just to define the Hund coupling of two quantum numbers 2, and Q2 as the manifold of resulting values of the quantum number Q... 

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