Abstract
Nuclear medicine exists because of the instability of some atomic nuclei which result in the emission of photons or particulate radiations. Later chapters consider the microscopic theories of these radioactive decays and how, in practice, they can be quantified. This chapter reviews the fundamental properties of atomic nuclei, through phenomenology and consideration of the Fermi nuclear gas, the nuclear liquid drop and the nuclear shell models, and how changes in these properties result in the radioactive instability necessary for nuclear medicine.
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Notes
- 1.
The vector must have high specificity for its intended target and, either directly or through metabolism, results in a clearance of the radioactive isotope from nontarget tissues in order to increase the target-to-background ratio of the image and to reduce that absorbed dose to uninvolved tissues.
- 2.
Such as Auger/Coster–Kronig and conversion electrons and which are discussed in Chap. 6.
- 3.
Fermions are particles with half-integral spin and subject to Fermi–Dirac statistics.
- 4.
Throughout this book, gravity is ignored and reference will be made to the remaining three forces only.
- 5.
The descriptive mesos was selected as a result of Yukawa’s prediction of the mass of the boson exchanged between protons and neutrons to be 130 MeV, intermediate between those of the electron and the neutron and proton.
- 6.
Bosons are those particles with zero or integral spin and subject to Bose–Einstein statistics.
- 7.
Experimental evidence for the existence of a quantum number of color is provided by the existence of the Δ33 resonance which has a mass of about 1,232 Mev, an intrinsic spin of 3/2, isospin of 3/2, and an electric charge of +2e (Close 1979). This combination of spin, isospin and electric charge indicates that the Δ33 is made up of three up quarks which have coupled to provide spin 3/2 and isospin of 3/2. In the absence of an additional quantum number, the Pauli exclusion principle would not allow for the existence of such a particle. Hence, for this principle for fermions to remain valid, an additional quantum number distinguishing the three quarks is required. This additional quantum number is color.
- 8.
Historically, the term “strong interaction” referred to the residual strong force between hadrons as mediated by mesons. With the development of QCD in describing color interactions between hadrons, “strong interactions” became synonymous with these color interactions, thus requiring a differentiation between “strong nuclear” and “strong color” interactions. Throughout the remainder of this book, unless otherwise noted, we will use “strong interaction” to mean “strong nuclear interaction” exclusively.
- 9.
The converse is not possible for a free proton. However, it is possible for a nuclear proton to be transformed to a neutron, as in β+ decay, where the energy required is gained from the Fermi momentum of the proton.
- 10.
The name comes from the Greek iso = same; topos = place as the variants would all be at the same position in the periodic table of elements. Anecdotally, the term was suggested by Margaret Todd, a Scottish physician, to Frederick Soddy who had discovered atoms with identical chemical properties but with different atomic masses.
- 11.
The rest-masses of the neutron, proton, and electron are (to three decimal places) 939.565, 938.272, and 0.511 MeV, respectively. For simplicity in some of the following discussions, both nucleon rest-masses will be approximated by the value of 940 MeV.
- 12.
There would also be a small effect due to the difference between proton and neutron masses, but we will neglect this.
- 13.
Consider a spherical nucleus of charge Ze and radius R. The charge density is a constant, \( {\rho_e} = 3Ze/4\pi {R^3} \) and the total work required to assemble the nucleus from differential shells containing charge dq = 4πr2ρe dr from infinity to the position of the nucleus is \( \frac{{\alpha \hbar c}}{{{e^2}}}\int\limits_0^{Ze} {dq\frac{q}{r}} \) which, noting that \( q(r) = {\raise0.7ex\hbox{${4\pi }$} \!\mathord{\left/{\vphantom {{4\pi } 3}}\right.}\!\lower0.7ex\hbox{$3$}}{\rho_e}\,{r^3} \), gives the Coulomb repulsion energy as \( \left( {{\raise0.7ex\hbox{$3$} \!\mathord{\left/{\vphantom {3 5}}\right.}\!\lower0.7ex\hbox{$5$}}} \right)\alpha \it \hbar c\frac{{{Z^2}}}{R} \).
- 14.
The pion can be produced by, for example, proton bombardment of targets such as beryllium, carbon, and copper.
- 15.
The formation of muonic atoms was predicted by Fermi and Teller (1947).
- 16.
While neutron scattering can also be used to infer the nucleon spatial distribution, we will restrict ourselves to the problem of elastic Coulomb scatter from nuclei, which will be more relevant to nuclear medicine.
- 17.
This statement implicitly assumes that the de Broglie wavelength of the incident electron is of the order of nucleon dimensions. At higher electron momenta, this wavelength becomes of the order of subnucleon dimensions allowing mapping of the electrical distributions of quarks within the nucleons.
- 18.
A collision with a nucleus is strictly elastic if no energy is transferred to any internal energy absorption channels. Even ignoring these energy absorption channels, the simultaneous conservation of energy and momentum requires that the projectile lose a small amount of energy which is transferred to the recoil kinetic energy of the atom. This energy transfer will be of the order of the product of the incident kinetic energy and the ratio of the projectile to target atom rest masses. Clearly, for electron and positron projectiles, the target recoil kinetic energy can be neglected (the ratio of projectile to target electron mass being no smaller than 5 × 10−4). This may not be the case if the projectile was an energetic alpha particle and the target atom had a comparable atomic mass which would be typical of elements of biological interest (e.g., carbon and oxygen).
- 19.
As the electron and positron are the particles of greatest interest to nuclear medicine dosimetery, derivations of their Coulomb scatter cross sections will be necessary for later descriptions of radiation transport in tissue.
- 20.
Some authors use a normalisation in which the volume integral of the charge density is equal to Ze, which would require the removal of Z from (3.93).
- 21.
As the derivation of the Mott cross section neglected both the recoil and the angular momentum of the target nucleus, this formula is applicable strictly to only J = 0 nuclei with sufficient mass that the recoil kinetic energy can be neglected.
- 22.
Also known as the Fermi–Dirac distribution in statistical mechanics and solid-state physics.
- 23.
The nomenclature used in this book takes a slight diversion here (in order to maintain consistency with that used elsewhere) as the energy level, denoted by E, is equal to the kinetic energy only which would normally be denoted by T. Here, E does not denote the total energy (i.e., the sum of kinetic and rest mass energies).
- 24.
Some authors have included the 9 − excited state of 180Ta as stable odd-Z even-A nucleus; however it is unstable with a half life of 1.8 × 1013 years.
- 25.
While the excited states of 99Sr, 99Y, and 99Zr can decay via single neutron emission and excited states of 99Ag can decay via proton emission, the probabilities of such exotic decays are extremely small and are neglected here.
- 26.
Strictly speaking, the calculated levels are for the neutron as the Coulomb potential was not accounted for. In practice, this would mean that the proton levels would be slightly higher due to the Coulomb repulsion, but the relative spacing would be the same.
- 27.
Consider a full shell from which a nucleon is removed; the resulting angular momentum is that of the unpaired nucleon remaining in the shell, which is also that of the remnant hole.
- 28.
Consider a particle of mass m in an orbit of radius r with a constant angular velocity ω. The tangential velocity is equal to ωr and the kinetic (rotational) energy is \( {\raise0.7ex\hbox{${m{\omega^2}{r^2}}$} \!\mathord{\left/{\vphantom {{m{\omega^2}{r^2}} 2}}\right.}\!\lower0.7ex\hbox{$2$}} \). This energy can also be written as \( {\raise0.7ex\hbox{${{\rm I}{\omega^2}}$} \!\mathord{\left/{\vphantom {{{\rm I}{\omega^2}} 2}}\right.}\!\lower0.7ex\hbox{$2$}} \) where I is defined as the moment-of-inertia, mr2, for the orbiting particle.
- 29.
In the literature, this ratio is often simply (and confusingly) written as Q.
- 30.
Internal conversion is a radiation-less transition for an excited nucleus to a lower-energy state via the transfer of energy directly to an atomic electron which is ejected.
References
Belkić DŽ (2004) Principles of quantum scattering theory. Institute of Physics, Philadelphia
Bjorken JD, Drell SD (1964) Relativistic quantum mechanics. McGraw-Hill, New York
Blatt JM, Weisskopf VF (1979) Theoretical nuclear physics. Dover, New York
Chadwick J, Goldhaber M (1934) A ‘nuclear photo-effect' – disintegration of the diplon by gamma-rays. Nature 134:237–238
Close FE (1979) An introduction to quarks and partons. Academic, London
Dyson F (2007) Advanced quantum mechanics. World Scientific, Singapore
Ehrenfest P, Oppenheimer JR (1931) Note on the statistics of nuclei. Phys Rev 37:333–338
Fermi E, Teller E (1947) The capture of negative mesotrons in matter. Phys Rev 72:399–408
Goldberger ML, Watson KM (1964) Collision theory. Wiley, New York
Grotz K, Klapdor HV (1990) The weak interaction in nuclear, particle and astrophysics. Institute of Physics, Bristol
Haxel O, Jensen JHD, Suess HE (1949) On the “magic numbers” in nuclear structure. Phys Rev 75:1766
Koide Y (1983) New view of quark and lepton mass hierarchy. Phys Rev D 28:252–254
Mayer MG (1949) On closed shells in nuclei II. Phys Rev 75:1969–1970
Mayer MG (1950) Nuclear configurations in the spin-orbit coupling modelI. Empirical evidence. Phys Rev 78:16–21
Messiah A (1958) Quantum mechanics. Wiley, New York
Mott NF (1929) Scattering of fast electrons by atomic nuclei. Proc Roy Soc A124:425–442
Pauli W (1973) Pauli lectures on physics: selected topics in field quantization. Massachusetts Institute of Technology Press, Cambridge
Preston MA, Bhaduri RK (1975) Structure of the nucleus. Addison-Wesley, Reading
Rivero A, Gjsponer A (2005) The strange formula of Dr Koide. arXiv:hep-ph/0505220v1
Seaborg GT, Segrè E (1939) Nuclear isomerism in element 43. Phys Rev 55:808–814
Segrè E (1977) Nuclei and particles, 2nd edn. Benjamin/Cummings, Reading
Sick I (1974) Model-independent nuclear charge densities from elastic electron scattering. Nucl Phys A 218:509–541
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McParland, B.J. (2010). Nuclear Properties, Structure, and Stability. In: Nuclear Medicine Radiation Dosimetry. Springer, London. https://doi.org/10.1007/978-1-84882-126-2_3
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