Nuclear spin angular momentum

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

The nuclei of many isotopes possess an angular momentum, called spin, whose magnitude is described by the spin quantum number / (also called the nuclear spin). This quantity, which is characteristic of the nucleus, may have integral or halfvalues thus / = 0, 5, 1, f,. . . The isotopes C and 0 both have / = 0 hence, they have no magnetic properties. H, C, F, and P are important nuclei having / = 5, whereas and N have / = 1. 

When great accuracy is desired, and in certain cases when only ordinary accuracy is required, it is necessary to consider the coupling between electronic and nuclear motions, and especially between the electronic angular momentum (either spin or orbital) and the rotation of the molecule. We shall not discuss these questions,1 but shall treat only the simplest problems in the complex field of molecular structure and molecular spectra in the following sections. Some further discussion is also given in Chapter XII and in Section 48 of Chapter XIV. 

The V represents the antineutrino v is the neutrino. Neutrino and antineutrino emissions serve to balance the energy and rotation before and after decay. Neutrinos have no charge and little mass as a result, they interact to a vanishingly small degree with matter and are difficult to detect without elaborate apparatus. The neutrino (or antineutrino) must be included in the decay equation to conserve energy, angular momentum, and spin. The neutron, proton, beta particle, and neutrino all have a nuclear spin of 1 /2. A fuller discussion of this topic is in nuclear chemistry texts such as Choppin et al. (1995). 

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... 

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

---