Spin number Nuclear spins

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. 

This equation is fully equivalent to the time-independent Schrodinger equation and its roots give the exact energies. Since the set (2.50) generally has an infinite number of functions, the secular determinant generally is of infinite order. In certain cases, however, one need only deal with a finite-order secular determinant. For example, in electron-spin (and nuclear-spin) problems, the number of basis spin functions is finite. Applications will be found in later chapters. 

H 1 1/2+ <-Chemical symbol, mass number nuclear spin I, nuclear parity... 

Symbol, mass number nuclear spin I, nuclear parity -Half-life (s = seconds, ps = microseconds, d = days, m = months, or y = years) -Decay mode (emission), and energy (MeV( if to ground state)), separated by / if several modes if in parentheses, mode produces a shortlived daughter, or occurs <10% Emissions a = alpha = 2He4++ P"= electron ... 

The spin-Hamiltonian operator can be written as the sum of a large number of terms for example, see Equation (A3) in Appendix 3. As may be seen therein, the convention for the two Zeeman terms (electron spin and nuclear spin) is that their signs differ, due to the difference in charge of the two most basic particles to be dealt with the electron and the proton. Hence the g values of these particles are taken to be both positive. 

Many nuclei possess a property described as spin. The nuclear spin (nuclear angular momentum) is quantized and is described by the spin quantum number I which can have values of 0, 1, 2, etc. If the value of I for a nucleus is... 

Nuclear magnetic resctnance involves the transitions between energy levels of the fourth quantum number, the spin quantum number, and only certain nuclei whose spin is not zero can be studied by this technique. Atoms having both an even number of protons and neutrons have a zero spin for example, carbon 12, oxygen 16 and silicon 28. 

The interaction of the electron spin s magnetic dipole moment with the magnetic dipole moments of nearby nuclear spins provides another contribution to the state energies and the number of energy levels, between which transitions may occur. This gives rise to the hyperfme structure in the EPR spectrum. The so-called hyperfme interaction (HFI) is described by the Hamiltonian... 

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. 

As was shown in the preceding discussion (see also Sections Vin and IX), the rovibronic wave functions for a homonuclear diatomic molecule under the permutation of identical nuclei are symmetric for even J rotational quantum numbers in and E electronic states antisymmeUic for odd J values in and E elecbonic states symmetric for odd J values in E and E electronic states and antisymmeteic for even J values in Ej and E+ electeonic states. Note that the vibrational ground state is symmetric under pemrutation of the two nuclei. The most restrictive result arises therefore when the nuclear spin quantum number of the individual nuclei is 0. In this case, the nuclear spin function is always symmetric with respect to interchange of the identical nuclei, and hence only totally symmeUic rovibronic states are allowed since the total wave function must be symmetric for bosonic systems. For example, the nucleus has zero nuclear spin, and hence the rotational levels with odd values of J do not exist for the ground electronic state f EJ") of Cr. 

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

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