Nuclear Angular-Momenta

Gases-Optical properties. 4. Angular momentum (Nuclear physics). 5. Polarization (Light). I. Ferber, Ruvin II. Title. 

Electron orbital angular momentum Electron spin angular momentum Resultant of orbital and spin momenta Molecular rotational angular momentum Nuclear spin angular momentum... 

Initially, we neglect tenns depending on the electron spin and the nuclear spin / in the molecular Hamiltonian //. In this approximation, we can take the total angular momentum to be N(see (equation Al.4.1)) which results from the rotational motion of the nuclei and the orbital motion of the electrons. The components of. m the (X, Y, Z) axis system are given by ... 

The quantum numbers tliat are appropriate to describe tire vibrational levels of a quasilinear complex such as Ar-HCl are tluis tire monomer vibrational quantum number v, an intennolecular stretching quantum number n and two quantum numbers j and K to describe tire hindered rotational motion. For more rigid complexes, it becomes appropriate to replace j and K witli nonnal-mode vibrational quantum numbers, tliough tliere is an awkw ard intennediate regime in which neitlier description is satisfactory see [3] for a discussion of tire transition between tire two cases. In addition, tliere is always a quantum number J for tire total angular momentum (excluding nuclear spin). The total parity (symmetry under space-fixed inversion of all coordinates) is also a conserved quantity tliat is spectroscopically important. 

The permutational symmetry of the rotational wave function is determined by the rotational angular momentum J, which is the resultant of the electronic spin S, elecbonic orbital L, and nuclear orbital N angular momenta. We will now examine the permutational symmetry of the rotational wave functions. Two important remarks should first be made. The first refers to the 7 = 0 rotational... 

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... 

Nuclear spin 1 = Total angular momentum quantum number 7 = 0,1,2,., ... 

Electron spin and nuclear spin angular momentum... 

Similarly, the magnitude of the angular momentum Pj due to nuclear spin is given by... 

Figure 5.12 shows the J= — 0 transition of the linear molecule cyanodiacetylene (H—C=C—C=C—C=N) observed in emission in Sagittarius B2 (Figure 5.4 shows part of the absorption spectrum in the laboratory). The three hyperfine components into which the transition is split are due to interaction between the rotational angular momentum and the nuclear spin of the nucleus for which 1= 1 (see Table 1.3). The vertical scale is a measure of the change of the temperature of the antenna due to the received signal. 

Equation (1.48) shows that, for I =, space quantization of nuclear spin angular momentum results in the quantum number Mj taking the values 5 or — 5. The nuclear spin wave function J/ is usually written as a or /i, corresponding to Mj equal to 5 or —5,... 

The phrase total angular momentum is commonly used to refer to a number of different quantities. Here it implies orbital plus electron spin but it is also used to imply orbital plus electron spin plus nuclear spin when the symbol F is used. 

---