Nuclear orbital angular momentum

When the molecule is not in a S state there is an interaction between the rotation of the molecule and S and/or L, and the details of coupling the angular momenta are involved. Most nonsinglet molecules with electronic orbital angular momentum A = 0 obey Hund s case (b) coupling. In Case (b), the electronic orbital angular momentum combines with the nuclear orbital angular... 

The Stern-Gerlach experiment demonstrated that electrons have an intrinsic angular momentum in addition to their orbital angular momentum, and the unfortunate term electron spin was coined to describe this pure quantum-mechanical phenomenon. Many nuclei also possess an internal angular momentum, referred to as nuclear spin. As in classical mechanics, there is a relationship between the angular momentum and the magnetic moment. For electrons, we write... 

For typical lepton energies of a few MeV, the de Broglie wavelength is of order 100 times the nuclear radius and when orbital angular momentum is zero, one can use the allowed approximation for their wave functions... 

Figure 1. Cartoon depicting symmetry considerations of the asymptotic wavefunction that influences which potential energy surface is accessed. Representative angular momentum quantum numbers relevant to the process are the total molecular angular momentum exclusive of nuclear spin (f) and the relative orbital angular momentum (/).

For the electro-nuclear model, it is the charge the only homogeneous element between electron and nuclear states. The electronic part corresponds to fermion states, each one represented by a 2-spinor and a space part. Thus, it has always been natural to use the Coulomb Hamiltonian Hc(q,Q) as an entity to work with. The operator includes the electronic kinetic energy (Ke) and all electrostatic interaction operators (Vee + VeN + Vnn)- In fact this is a key operator for describing molecular physics events [1-3]. Let us consider the electronic space problem first exact solutions exist for this problem the wavefunctions are defined as /(q) do not mix up these functions with the previous electro-nuclear wavefunctions. At this level. He and S (total electronic spin operator) commute the spin operator appears in the kinematic operator V and H commute with the total angular momentum J=L+S in the I-ffame L is the total orbital angular momentum, the system is referred to a unique origin. 

Quantitative theories for the chemical shift and nuclear spin-spin interaction were developed by Ramsey (113) soon after the experimental discoveries of the effects. Unfortunately the complete treatments of these effects involve rather detailed knowledge of the electronic structures of molecules and require evaluation of matrix elements of the orbital angular momentum between ground and excited electronic states. These matrix elements depend sensitively on the behavior of the wave function near... 

Recall that linear molecules have Ah as the absolute value of the axial component of electronic orbital angular momentum the electronic wave functions are classified as 2,n,A,, ... according to whether A is 0,1,2,3,. Similarly, nuclear vibrational wave functions are classified as... 

For 2 molecules, we used J as the rotational angular-momentum quantum number since 2 molecules have no electronic spin or orbital angular momentum, J is also the total angular-momentum quantum number, exclusive of nuclear spin, for such molecules. Recall that for atoms J is also used as the total angular-momentum quantum number apart from nuclear spin.) The rotational energy in case (a) is given approximately by... 

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