I, nuclear spin angular momentum

I nuclear spin angular momentum, moment of inertia, inversion operator (f), radiation intensity j one-electron angular momentum... 

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,... 

Similarly, a nucleus of nuclear spin angular momentum quantum number I and vector I has spin angular momentum L ... 

In addition there will often be nuclear spin angular momentum (I), which is coupled to the electronic orbital and spin angular momenta these coupling cases are described in section 6.7.8. 

In order to understand the selection rules, it is useful to identify three quantum numbers that stay good even after the levels are badly mixed they are J, the parity +, and the total nuclear spin angular momentum I I = + l + /j). These... 

Nuclei can also possess spin. Whereas every electron has a spin of half, nuclei can have nuclear spin angular momentum quantum number, I, equal to zero or other integer factors of1/2. 

Hie total magnetic moment m of an atom contains contributions from the magnetic moments m5, and m/ associated with the total electronic orbital angular momentum L, the total electronic spin angular momentum S, and the nuclear spin angular momentum I. (a) For an atom with L, S, and I all nonzero, which one of these three contributions to m is by far the smallest (b) For the Rb ground electronic state (used in the Bose-Einstein condensation experiment of Section 10.S), which one of these three contributions is zero ... 

The nuclear magnets are ordered into 2/ - -1 states determined by the nuclear spin quantum number I. The spin angular momentum is quantized in units of h and the change in the z component is detected in the NMR experiment. For many common NMR nuclei 1= 1/2 (iR, Si, ip) and there are two... 

The total magnetic moment m of an atom contains contributions from the magnetic moments m , m, and m/ associated with the total electronic orbital angular momentum L, the total electronic spin angular momentum S, and the nuclear spin angular momentum I. (a) For an... 

Principles and Characteristics An interaction that is never directly seen in liquid spectra but that, if present, always dominates solid-state spectra is quadrupole interaction. Nuclei with I > Vi have an electric quadrupole moment Q that is a measure of the deviation of the nuclear charge distribution from spherical symmetry. Nuclei with 7 = 0, Vi do not care about electric field gradients their charge distribution is spherical. Some 74% of all NMR-active nuclei have I > V2, as listed elsewhere [763]. The nuclear electric quadrupole moment, 2, of an 7 > 1 nucleus can interact with the electronic environment near that nucleus to affect the nuclear spin angular momentum energy levels, even in zero magnetic field. Quadrupole interactions can... 

Protons and neutrons have an intrinsic spin and an intrinsic magnetic moment. Experiments have revealed that there are just two possible orientations of their spin vectors with respect to a z-axis defined by an external field. This means that their intrinsic spin quantum number is 1/2 they are fermions. Whereas the letter S is commonly used for the electron spin quantum number, the letter I is commonly used for nuclear spin quantum numbers. Thus, I = 1/2 for a proton, and the allowed values for the quantum number giving the nuclear spin angular momentum projection on the z-axis, Mj, are + 1/2 and -1/2. 

In Eq. (2) the summations are taken over all the nuclei in the molecular species. The new symbols in Eq. (2) are defined as follows g is the nuclear g factor, which is dimensionless is the nuclear magneton, having units of joules per gauss or per tesla the nuclear spin angular momentum operator I the electron-nucleus hyperfine tensor A the quadrupole interaction tensor Q and Planck s constant h. 

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

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