Abstract
This chapter provides an historical overview of non-radiative interactions of charged particles with matter.
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- 1.
An excellent review of the development of experiment and theory leading to the Standard Model can be found in the compilation of lectures, given at a 1985 symposium held at Fermilab, provided by Brown et al. (1989).
- 2.
And also referred to as ‘beauty’.
- 3.
They are also all subject to the gravitational force, but, as demonstrated by Table 1.1, this force is inconsequential and will be neglected.
- 4.
To the ‘outside world’, a composite of quarks does not exhibit colour. This is achieved, in the case of the meson which is made up of two quarks, by a colour/anti-colour pair and, in the case of the baryon made up of three quarks, by quarks with red, green and blue colour.
- 5.
The ‘W’ refers to the ‘weak force’ and the ‘Z’ refers to ‘zero’ charge. The W ± and Z 0 bosons have masses of about 80 GeV and 91 GeV, respectively, and hence, the weak force has an extremely short range. In contrast, the photon has zero mass leading to the electromagnetic force having infinite range.
- 6.
The neutral pion decays predominantly through the electromagnetic process π 0 → 2γ and, less frequently, through π 0 → γ + e + + e −.
- 7.
Isotopic spin (or ‘isospin’) was proposed as a new quantum number by Heisenberg in 1932 due to the near equality of the rest masses of the proton and neutron, allowing consideration of them as being two quantum states of the same particle, the nucleon. It is an additive quantum number and is conserved in strong interactions. It is not conserved in weak interactions as shown in the β-decay of the neutron of Fig. 1.3.
- 8.
On its own, this would not be a conclusive argument for the existence of the colour quantum number. However, measurements of high-energy electron–positron annihilations demonstrate that the ratio of the cross section at which these annihilations produce hadrons to that at which they produce muon pairs is consistent with the existence of the colour quantum number with three states. Similar confirmation is obtained from measurements of the decay of the neutral pion to two photons.
- 9.
The particle’s minimum energy will in fact equalise to the thermal energy at equilibrium which will be greater than zero.
- 10.
As these moved in the direction opposite to the cathode rays, we now recognise that these have a positive electric charge. While Goldstein was unable to observe a deflection of these canal rays by a magnetic field, Wien was subsequently able to do so by using a very strong magnetic field and thus demonstrated their positive charge. Further, using combined electrostatic and magnetic fields, he concluded that some of these canal rays had a mass comparable to that of hydrogen; hence, this was one of the first pieces of experimental evidence of the existence of the proton in motion. Being what we now know as positive ions, canal rays had a far more complex composition than the cathode rays which we now know as electrons (Thomson 1913).
- 11.
This was a refutation of the hypothesis that the cathode ray (or electron) was a wave in the aether, not the de Broglie wave–particle duality hypothesis.
- 12.
- 13.
Whereas in our previous discussion of Thomson’s discovery of the electron we had used e as the symbol of the electric charge of the entity discussed – and which was entirely appropriate as that is the electric charge carried by the electron – we will now use q as the generic symbol for electric charge. In our nomenclature of the interactions of charged particles with matter, the projectile will have an electric charge ze where z is an integer equal to 1 or greater and the target will be assigned an electric charge Ze where, again, Z is an integer equal to 1 or greater.
- 14.
That this is the case demonstrated by the existence of transitions between nuclear states with zero angular momentum (0 → 0) resulting in IC, whereas electromagnetic (0 → 0) transitions without the involvement of an electron are impossible since there are no multipoles with zero angular momentum in the radiation field. See Section 4.4.3 of McParland (2010) for a proof of this derived using perturbation theory.
- 15.
This was not the only time that Meitner had been supplanted or excluded in a major physics discovery, as will be discussed later in the synopsis of the discovery of nuclear fission.
- 16.
For convenience, we will group Auger, Coster–Krönig and super Coster–Krönig non-radiative transitions as Auger transitions in later discussions.
- 17.
Refer to Chapter 3 of McParland (2010) for the derivation of the mass parabolae and the β±-decays that reach the stable nucleus at the minimum of the parabola.
- 18.
Being an Austrian Jew, Meitner had been forced to leave Germany for Sweden following the Anschluss in 1938. She continued to collaborate with Hahn and Strassmann and during Christmas of 1938, with her nephew Otto Frisch, modelled fission on the basis of Bohr’s liquid-drop model of the nucleus and accurately calculated that the resulting fission fragments would carry a net kinetic energy of about 200 MeV due to both mass defect and Coulomb repulsion. Hahn received the 1945 Nobel Prize in Chemistry for the discovery, but Meitner did not. Controversy over that decision remains.
- 19.
Frisch was staying at the Bohr Institute when he performed these measurements there. Also staying there was an American biologist, William A Arnold, who was approached by Frisch to describe the division of cell. Arnold replied that this was ‘binary fission’ and Frisch adopted the term ‘fission’ to describe the process he had just measured.
- 20.
The Crookes tube is a partially evacuated tube in which electrons are created through the ionisation of residual air by a high-tension supply. These are accelerated by this potential between that cathode and anode.
- 21.
This is a step-up transformer in which the primary coil is connected to an interruptible DC voltage. The change in the primary voltage causes a voltage in the secondary coil through induction.
- 22.
There has been a suggestion that Nikola Tesla may have detected x-rays prior to Röntgen (Hrabak et al. 2008).
- 23.
The primary beam being the α-particles incident to the beryllium and the secondary beam being the neutral radiation incident to the medium.
- 24.
Experiment does, however, play a role in determining parameters used in modifications to the theoretical derivation.
- 25.
The notion of electrons ‘orbiting’ the nucleus only became considered with the development by Bohr of his model of the atom.
- 26.
The Born series is derived in Chap. 2 as a means of solving the Lippmann–Schwinger equation.
- 27.
- 28.
Upon reflection, this is a rather profound judgment on Bethe’s part considering his having been awarded the 1967 Nobel Prize in Physics for his discovery of the stellar energy production mechanism, his significance in the development of nuclear weaponry and his later political challenges to their use and his deep and wide work in nuclear physics.
- 29.
The current Internet sites for these codes are:
- 30.
In such a case, the electron beam current within the accelerator must be reduced for patient safety from that used for x-ray therapy by a factor of about 103, as the latter current is higher due to the low efficiency of bremsstrahlung production at electron energies used for radiotherapy.
- 31.
Details of the roles of RBE and OER can be found in Chapters 6 and 7 of Hall and Giaccia (2006).
- 32.
One solution is the mounting of the cyclotron on the rotating gantry. In practice, this would require the cyclotron to have an especially intense magnetic field in order to reduce its size and, hence, the use of superconducting magnetic coils.
- 33.
In this case, the pion (or its wavefunction) entering the nucleus is ‘real’ and the effects of its rest mass are cogent. Pions mediating the strong nuclear force within the nucleus are ‘virtual’ and do not contribute to the same result.
- 34.
‘Fast’ neutrons are defined as those with an energy of the order of 1 MeV. These are moderated as they pass through a hydrogenous medium (such as tissue) through (n,p) elastic scatters until they ‘thermalise’.
- 35.
The Lawrences, mother had been diagnosed with a pelvic tumour with the prognosis of a 3-month survival. Following the neutron therapy, she survived for sixteen years.
- 36.
The mean free path length is derived in Chap. 6.
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Haug E, Nakel W. The elementary process of bremsstrahlung. Singapore: World Scientific Publishing Co; 2004.
Heitler W. The quantum theory of radiation. 3rd ed. Oxford: Clarendon Press; 1954.
Heilbron JL. The scattering of α and β particles and Rutherford’s atom. Arch Hist Exact Sci. 1967;17:247–307.
Moore R. Niels Bohr. Cambridge, MA: The MIT Press; 1985.
Rhodes R. The making of the atomic bomb. New York: Simon and Schuster; 1988.
Segrè E. Enrico Fermi – Physicist. Chicago: University of Chicago Press; 1970.
Sigmund P. Particle penetration and radiation effects. Berlin: Springer; 2008.
Sime RL. Lise Meitner – a life in physics. Berkeley: University of California Press; 1996.
Thomson JJ, Thomson GP. Conduction of electricity through gases, vol II: Ionisation by collision and the gaseous discharge. 3rd ed. Cambridge: University Press; 1933.
Wilson D. Rutherford – simple genius. London: Hodder and Stoughton; 1983.
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McParland, B.J. (2014). Introduction. In: Medical Radiation Dosimetry. Springer, London. https://doi.org/10.1007/978-1-4471-5403-7_1
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