Total nuclear spin

Total Nuclear Spin Rovibronic Vibronic Electronic" Rotational Vibrational... 

Total Nuclear Spin s Rovibronic Rotational Pseudorotational... 

Equation (2.3) describes line positions correctly for spectra with small hyperfine coupling to two or more nuclei provided that the nuclei are not magnetically equivalent. When two or more nuclei are completely equivalent, i.e., both instantaneously equivalent and equivalent over a time average, then the nuclear spins should be described in terms of the total nuclear spin quantum numbers I and mT rather than the individual /, and mn. In this coupled representation , the degeneracies of some multiplet lines are lifted when second-order shifts are included. This can lead to extra lines and/or asymmetric line shapes. The effect was first observed in the spectrum of the methyl radical, CH3, produced by... 

Total Nuclear Spin Rovibronic Rotational6 Pseudorotational... 

In contrast to ESR spectroscopy, which can only be used to study species with unpaired electrons, NMR spectroscopy is applicable to the investigation of all polymer samples. Nuclei with non-zero total nuclear spin (e.g., 1H, l3C, 19F, 14N) will have a magnetic moment which will interact with an external magnetic field resulting in quantized energy levels. Transitions between these energy levels form the basis of NMR spectroscopy. 1H and 13C... 

It is a fundamental property of atomic particles, such as electrons, protons, and neutrons, to have spins. Spins can be classified as + or spin. For example, a deuterium atom, H, has one unpaired electron, one unpaired proton, and one unpaired neutron. The total nuclear spin = j (from the proton) + j (from the neutron) = 1. Hence, the nuclear spins are paired and result in no net spin for the nucleus. For atoms such as H,... 

Write down the nine nuclear spin functions of D2. Show that the three antisymmetric spin functions are eigenfunctions of the operator for the square of the magnitude of the total nuclear spin with the eigenvalue 2ft2. Find the corresponding eigenvalues for the symmetric spin functions. 

This has been discussed above for several specific instances. In the absence of -anisotropy, hyperfine anisotropy increases for individual lines in a spectrum on going from the centre outwards. Thus a central line often corresponds to a state where the total nuclear spin is zero so that there is no anisotropy and a narrow line results. This situation is exemplified by the spectrum of trapped ethyl radicals (Section V) and also by the effect of cooling on the spectrum of the radical NH3+ (Hyde and Freeman, 1961). 

It turns out that the most significant contribution to the total nuclear spin—spin interaction in most cases is the contact term H3. Since the first-order perturbation energy due to H3 is zero,9 the energy of interaction between nuclei A and X, namely AX, is represented by the second-order perturbation energy... 

Figure 1-11. Theoretical and experimental relative integral cross sections for Ar-CH4. The experimental data are displayed in red, the results displayed in blue and green were generated from the SAPT and empirical potentials, respectively. The labels A, E, and F refer to the total nuclear spin states of methane. The empirical potential was fitted to the total differential cross sections...

These represent the nuclear spin Zeeman interaction, the rotational Zeeman interaction, the nuclear spin-rotation interaction, the nuclear spin-nuclear spin dipolar interaction, and the diamagnetic interactions. Using irreducible tensor methods we examine the matrix elements of each of these five terms in turn, working first in the decoupled basis set rj J, Mj /, Mi), where rj specifies all other electronic and vibrational quantum numbers this is the basis which is most appropriate for high magnetic field studies. In due course we will also calculate the matrix elements and energy levels in a ry, J, I, F, Mf) coupled basis which is appropriate for low field investigations. Most of the experimental studies involved ortho-H2 in its lowest rotational level, J = 1. If the proton nuclear spins are denoted I and /2, each with value 1 /2, ortho-H2 has total nuclear spin / equal to 1. Para-H2 has a total nuclear spin / equal to 0. 

We turn now to the corresponding studies of the isotopic species D2 and HD. The deuterium nucleus has spin Id equal to 1, so that the two equivalent deuterium nuclei in D2 have their spins coupled to give total nuclear spin / equal to 2, 1 or 0. The states with / equal to 2 or 0 correspond to ortho-D2, whilst that with / equal to 1 is known as para-T>2. The molecular beam magnetic resonance studies have been performed on para-D2, in the. 1 = 1 rotational level. Formally, therefore, the effective Hamiltonian is the same as that described above for experimental studies of ortho-H2, also in the J = 1 rotational level. There is one extremely important difference, however, in that the... 

The nuclear spins 7) and I2 may be coupled to form the total nuclear spin /, which in turn is coupled to J to form F In this coupled basis set the matrix elements of 3 q are given by... 

The radiofrequency resonances observed arise from transitions between the nuclear hyperftne components of the J" = 28 rotational level. The 23Na nuclei have spin I =h = 3/2, so that the total nuclear spin / can take the values 3, 2, 1 and 0. A rotational level with J even combines with 1 = 2 and 0, so that for 1 = 2, the total angular momentum F takes all integral values from 26 to 30 when I = 0 we have F =... 

In order to understand the observed spectra it is first necessary to consider the importance of nuclear spin in determining the nature of the allowed rotational levels. Each 14N nucleus has spin 7=1, and in the homonuclear N2 system the individual spins are coupled to form a total nuclear spin IT of 2, 1 or 0. The most appropriate basis system for 3 + N2 is Hund s case (b) coupling ... 

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