Consequences of Nuclear Spin

Observation of the NMR signal requires a sample containing atoms of a specific atomic number and isotope, i.e., a specific nuclide such as 

Nuclide Element-isotope Spin Natural abundance (%) Frequency relative to H 

Spin state. Syn. spin angular momentum quantum number.The projection of the magnetic moment of a spin onto the z-axis. The orientation of a component of the magnetic moment of a spin relative to the applied field axis (for a spin-V2 nucleus, this can be -cy2 or -1/2). 

Magnetic moment A vector quantity expressed in units of angular momentum that relates the torque felt by the particle to the magnitude and direction of an externally applied magnetic field. The magnetic field associated with a circulating charge. 

Nuclear spin. The circular motion of the positive charge of a nucleus. 

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Un speaking about NMK, the words profou- and hydrogen are often used interchangeably.> Let s see what the consequences of nuclear spin are and how we can use the results. 

The inversion of Bcff for the low-frequency line takes place at a = 2 vn = 2 Ng B0. As a consequence the nuclear spin states belonging to ms = 1/2 change their precession direction from l.h. (ais0 < a J) to r.h. (aiso > aj J). For ms = -1/2, ENDOR transitions are only observed with a l.h. rotating field. 

The first-order treatment which is applicable when A gives the number of nuclear spin states of equivalent sets of nuclei as 2/ + 1 where I is the total spin of the equivalent set. The spin for a fluorine atom is Therefore, for the SF4 molecule, observation of triplet fine structure establishes that I = 1 for an equivalent set and, consequently, that each equivalent, set contains two fluorine atoms. 

Let us therefore re-examine the lowest-order terms in (3.140) containing the magnetic vector potential, including the effects of nuclear spin and an apphed magnetic field, but excluding A whose consequences were investigated hilly in chapter 3. The important terms are... 

Interaction between the magnetic field of the electrons and the nuclear spin is the basis for various techniques that are broadly applied in chemistry, atomic physics, nuclear physics and solid-state physics. The magnetic field of the electrons is due to their spin and orbital angular momentum and much larger than the magnetic field of the nucleus. Consequently, the nuclear spin is oriented in relation to the field produced by the electron shell. This leads to hyperfine spectra which can be resolved by means of optical spectrometers of very high resolution. 

Fig. 1. Cartoon depicting the spin-cooling effect of optical polarization on an ensemble of nuclear spins (assuming /= 1/2 and positive gyromagnetic ratio). Normally (at thermal equihbrium), the numbers of spins aligned parallel and antiparallel to the magnetic field (Bq) are nearly equal, yielding a low net spin polarization - and consequently, a tiny detectable magnetization, Mq. However, optical polarization can provide the means to drive the population distribution far away from equilibrium, thereby increasing M by several orders of magnitude. In the spin-temperature model, such polarization can often result in nuclear spin ensembles with miUi-Kelvin effective temperatures. (After Ref [110].)...

The detection of NMR signals is based on the perturbation of spin systems that obey the laws of quantum mechanics. The effect of a single hard pulse or a selective pulse on an individual spin or the basic understanding of relaxation can be illustrated using a classical approach based on the Bloch equations. However as soon as scalar coupling and coherence transfer processes become part of the pulse sequence this simple approach is invalid and fails. Consequently most pulse experiments and techniques cannot be described satisfactorily using a classical or even semi-classical description and it is necessary to use the density matrix approach to describe the quantum physics of nuclear spins. The density matrix is the basis of the more practicable product operator formalism. 

As is illustrated by the example of nuclear spin-spin couphng constants, it is possible to estimate the consequences of correlation effects on the values of physical properties computed from IPM wave functions by mixing the perturbations due to electron correlation and external fields... 

GHz. This line was measured towards the cold, dark cloud L673 (2) and the molecular cloud M17-NW. The nitrogen nucleus has a spin of 1(N) = 1 / is the quantum number defining nuclear spin. An important spectroscopic effect of nuclear spin is quadrupole hyperfme structure. Consequently, the spectrum of the J= 1 -> 0 transition is split into three hyperfine components, indicated by the quantum number F F = J + I), which provides a spectral fingerprint for HCN. In order of increasing frequency, these transitions are labeled F= ->, F= —> 2, and F = 1 0. The intrinsic, or fundamental, intensity of the three... 

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