Properties of Nuclei

The spin quantum number / is a physical property of the nucleus, which is made up of protons and neutrons. From observations of the nnclear spins of known nuclei, some empirical rules for 

Mass (P + N) (Atomic Weight) Charge (P) (Atomic Number) Spin Quantum Number (/) 

Eor on the other hand, the atomic weight is 13 (i.e., P + N = 13), an odd number, and the atomic number is 6, an even number. From Table 3.1, we predict that I for C is therefore a half integer like H, has / = 1/2. So NMR can detect C, and although C represents only 1.1% of the total C present in an organic molecule, NMR spectra are very valuable in elucidating the structure of organic molecules. 

The physical properties predict whether the spin number is equal to zero, a half integer, or a whole integer, but the actual spin number—for example, 1/2 or 3/2 or 1 or 2— must be determined experimentally. All elements in the first six rows of the periodic table have at least one stable isotope with a nonzero spin quantum number, except Ar, Tc, Ce, Pm, Bi, and Po. It can be seen from Table 3.1 and Appendix lO.A that many of the most abundant isotopes of conunon elements in the periodic table cannot be measured by NMR, notably those of C, O, Si, and S, which are very important components of many organic molecules of interest in biology, the pharmaceutical industry, the polymer industry, and the chemical manufacturing industry. Some of the more important elements that can be determined by NMR and their spin quantum numbers are shown in Table 3.2. The two nuclei of most importance to organic chemists and biochemists, C and H, both have a spin qnan-tum number = 1/2. 

The number of orientations or number of magnetic quantum states is a function of the physical properties of the nucleus and is numerically equal to 2/ h- 1  

When a nucleus is placed in a very strong, uniform external magnetic field Bq, the nucleus tends to become lined up in definite directions relative to the direction of the magnetic 

So we have nuclei, in this case, protons, with two discrete energy levels. In a large sample of nuclei, more of the protons will be in the lower energy state. The basis of the NMR experiment is to cause a transition between these two states by absorption of radiation. It can be seen from Fig. 3.1 that a transition between these two energy states can be brought about by absorption of radiation with a frequency that is equal to AE according to the relationship AE = hv. 

The first concepts of nuclear forces and nuclear radii were developed by Rutherford in 1911 on the basis of the scattering of a particles in metal foils. The experiments showed that the positive charge of the atoms is concentrated in a very small part of the atom, the nucleus. The scattering of the a particles could be explained by the Coulomb interaction with the nuclei, whereas the electrons did not influence the path of the a particles. The radius of an atomic nucleus can be described by the formula 

The layer of decreasing density is about 2.5 fm, independently of the atomic number. The distribution of the neutrons is assumed to be approximately the same as that of the protons. Then the mass distribution in the nucleus is also the same as the charge distribution, and it follows from eq. (3.1) that the density of nuclear matter in the interior of the nuclei is given by 

3 Physical Properties of Atomic Nuclei and Elementary Particles 

The Coulomb repulsion energy Ec between two protons is given by E 

Type of interaction Mediating particle Relative force constant 

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We will now explain the meaning of the word identical used above. Physically, it is meant for particles that possess the same intrinsic attributes, namely, static mass, charge, and spin. If such particles possess the same intrinsic attributes (as many as we know so far), then we refer to them as physically identical. There is also another kind of identity, which is commonly refeiTed to as chemical identity [56]. As discussed in the next paragraph, this is an important concept that must be steessed when discussing the permutational properties of nuclei in molecules. 

I have found that the assumption that in atomic nuclei the nucleons are in large part aggregated into clusters arranged in closest packing leads to simple explanations of many properties of nuclei. Some aspects of the closest-packing theory of nuclear structure are presented in the following paragraphs.1... 

Nuclear magnetic resonance spectroscopy is a technique that, based on the magnetic properties of nuclei, reveals information on the position of specific atoms within molecules. Other spectroscopic methods are based on the detection of fluorescence and phosphorescence (forms of light emission due to the selective excitation of atoms by previously absorbed electromagnetic radiation, rather than to the temperature of the emitter) to unveil information about the nature and the relative amount specific atoms in matter. 

The NMR signal arises from a quantum mechanical property of nuclei called spin . In the text here, we will use the example of the hydrogen nucleus (proton) as this is the nucleus that we will be dealing with mostly. Protons have a spin quantum number of V . In this case, when they are placed in a magnetic field, there are two possible spin states that the nucleus can adopt and there is an energy difference between them (Figure 1.1). 

Physical Constants, Conversion Factors, and Properties of Nuclei (Tables A1.1—A1.4)... 

G. Baym, H. Monien and C. J. Pethick, In Hirschegg 1988, Proceedings, Gross properties of nuclei and nuclear excitations 128-132 C. J. Pethick, G. Baym and H. Monien, Nucl. Phys. A 498, 313C (1989). 

The NMR phenomenon is based on the magnetic properties of nuclei and their interactions with applied magnetic fields either from static fields or alfemaling RF fields. Quanfum mechanically subatomic particles (protons and neutrons) have spin. In some nuclei these spins are paired and cancel each other out so that the nucleus of the atom has no overall spin that is, when the number of protons and neutrons is equal. However, in many cases the sum of the number of protons and neutrons is an odd number, giving rise to... 

Nuclear relaxation rates, iron-sulfur proteins, 47 267-268 Nuclear resonance boron hydrides and, 1 131-138 fluorescence, 6 438-445 Nuclear spin levels, 13 140-145 Magnetic properties of nuclei, 13 141-145 Nuclear testing... 

Martin, J.A., W. Greiner Potential Energy Surface Model of Collective States, in High-Angular Momentum Property of Nuclei (N.R Johnson, Ed.) Harwood Academic Publishers, New York, NJ, 1983. 

These questions lie in the field of nuclear astrophysics, an area concerned with the connection of fundamental information on the properties of nuclei and their reactions to the perceived properties of astrological objects and processes that occur in space. The universe is composed of a large variety of massive objects distributed in an enormous volume. Most of the volume is very empty (< 1 x 10 18 kg/m3) and very cold ( 3 K). On the other hand, the massive objects, stars, and such are very dense (sun s core 2 x 105 kg/m3) and very hot (sun s core 16 x 106 K). These temperatures and densities are such that the light elements are ionized and have... 

Symmetry Properties of Nuclei, Proceedings of the Fifteenth Conference on Physics at the University of Brussells, 28 September to 3 October 1970, Gordon and Beach, New York, 1974. 

The IBM calculations use only two nuclear constituents, identical S and D bosons, or in the IBM-2, proton collective motion in a single formalism. Thus one might hope to be able to use the IBM to extrapolate from known properties of nuclei near the stability line to nuclei far from stability. The parameters are the total numbers of tt and v bosons, and Nv, and their one and two boson interactions. The usefulness of this theory for extrapolation depends on these parameters being Independent of N and Z, or known functions of N,Z. 

LEA83] G.A. Leander, S. Frauendorf and F.R. May, Proc. Conf. on High Angular Momentum Properties of Nuclei, Vol. 4, Nuclear Science Research Conf. Series, ed. by N.R. Johnson (Harwood Academic Publishers, New York, 1983) p. 281. 

Momentum Properties of Nuclei, Oak Ridge (1982), p. 281 [MUL78] M. Muller-Veggian et al., Nucl. Phys. A304 1 (1978)... 

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