Nuclear magnetic moments, stable isotopes

While the early optical measurements suffered from limited resolution, the development of atomic beam methods provided a useful tool in the study of atomic and nuclear magnetic moments [ 12,13] (for a review see [ 14]) and it became possible to measure the nuclear magnetic moments (and nuclear spins) in a direct way for both stable and radioactive isotopes, by using a variety of methods ] 15]. The study of optical IS was, however, limited to Doppler-limited optical spectroscopy until the invention of the laser and the development of suitable high-resolution optical methods (a review can be found in [16]). It is also possible to obtain information on the nuclear charge distribution by electron scattering experiments and from muonic X-ray transitions and electron K X-ray IS [17], perhaps even with a higher accuracy than with optical spectroscopy. 

For the vast majority of stable nuclei the nuclear magnetic moments have been determined most accurately using nuclear magnetic resonance (NMR). This includes nuclei of the various transition groups with d-eleclrons, where compounds can be prepared with no unpaired electrons. For the 4f group only those ions with an empty shell (La " ) or a full shell (Yb, Lu ) have been measured in this way. The reason is that for all the other ions (except Eu, discussed in section 9.3), the existence of unpaired electrons in the 4f-shell produces hyperfine fields at the nucleus of order 100-800 T. The presence of this large internal field makes it necessary to use the triple resonance atomic beam method (section 1.4) for atoms, or ENDOR (section 3) for ions in the solid state to measure the nuclear moments. With few exceptions, the values in table 1 have all been obtained by such methods, and the corresponding nuclear resonance frequencies for the stable isotopes are listed in table 12. 

Values of the nuclear spin I and of the magnetic resonance frequency in MHz per tesla for the stable isotopes of the lanthanide ions. Based on the best values of the nuclear magnetic moments in table I, without the correction for diamagnetic shielding, with rounded errors, calculated from the relation y/2n = 7.62253(2)p,/f. 

Figure 8.9 TbPc2-based single ion magnets (SIMs) [90] (a) Schematic representation molecular localization of the three spin-systems characteristics of the [TbPc2]° complex J = 6, the uniaxial magnetic moment of the 4f configuration / = 3/2 nuclear spin of the only stable and naturally occurring 159Tb isotope S = 1/2 organic radical delocalized over the two Pc ligands. The radical...

Before the advent of magnetic resonance spectroscopy, nuclear spins and moments were determined almost entirely by optical spectroscopy. When a hyperfine multiplet is observed with good resolution, the value of the nuclear spin / is obtained immediately from the multiplicity, provided that / < J. In practice, the resolution has proved to be adequate for the stable isotopes of odd Z, that are all odd-proton isotopes Tb, Ho and Tm (each 100% abundant) La,... 

Selected best values of nuclear spins and moments from Table of Isotopes (Lederer and Shirley 1978) with some later data. In most cases the method identified applies only to measurements of magnetic moments (corrected for diamagnetic shielding). Values of the nuclear resonance frequency in MHz per tesla for the stable isotopes, uncorrected for diamagnetic shielding, are given in table 12. 

The nuclear moments p,i and Qs can be extracted from A and B using empirical or theoretical values for the magnetic hyperfine field HdO) and the electric field gradient hyperfine anomaly corrections He(0) is usually known from direct g,-factor measurements (g = iii/.IfiM) on the stable isotopes. semi-empirical or theoretical analyses, unless precise values are available from the hfs of muonic atoms. 

In an NMR experiment, transitions are induced between these levels with radio frequency fields applied at or near the resonant frequency a o (Abragam, 1961 Slichter, 1990). The alkali metals are good candidates for NMR experiments because there are a number of abundant, stable nuclear isotopes, Li, Li, Na, Rb, Rb, and Cs. The exception is potassium the isotope possesses only a weak magnetic moment and occurs with low natural abundance. 

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