Handbook of radiotherapy physics

The neutrons have no electric charge. Their rest mass is very close to the proton mass. The number of neutrons in a nucleus is close to the number of protons. Outside the nucleus, neutrons are unstable, dividing into protons, electrons and antineutrinos.

The mass of the nucleus is slightly smaller than the sum of the masses of the Z protons and N neutrons, due to their nuclear bonding energy corresponding, according to Einstein, to the use of a tiny proportion of the nuclear mass, called the mass defect see Section 1.

The Z peripheral electrons revolve about the nucleus in well defined orbits, called electronic K, L, M, N,. According to the principles of the atomic model, the number of electrons present in a given shell is limited.

The innermost shell, called the K shell, has the rank of 1. Any shell with a rank n has a maximum allowed number of electrons of 2n2. Hydrogen is the simplest atom, consisting of one electron revolving about one proton on the K shell Figure 1. The next simplest atom, helium, has two electrons, saturating the K shell, and spinning in opposite directions.

The next atom, lithium, has 3 electrons and the additional electron is alone on the L shell. The same evolution can be observed from carbon to neon atoms, the latter presenting a saturated L shell.

The most peripheral electrons, those belonging to the outermost shell valence electrons , are directly linked to the chemical properties of atoms and molecules, and so determine the chemical elements or nuclides reported in the Mendeleyev table.

Helium and neon atoms, presenting a saturated outer shell, are remarkably chemically stable. It ranges from 1 hydrogen to more than for the heaviest nuclei. Atomic Mass: As seen previously, the mass of a given atom is close to the sum of the masses of the nucleons and the electrons. Remember that the mass of an electron is about times smaller than the mass of a nuclear particle. The actual mass of an atom X, m X , expressed in terms of kilograms, the international unit of mass, is very small and not of much practical use.

Consequently, another approach is often used, by defining a special unit of atomic mass a. The international unit of atomic mass is approximately the mass of a nuclear particle, permitting the atomic mass of an atom to be expressed with numbers close to the mass number.

Because the mass number of a carbon atom is exactly 12, its atomic mass is also 12 u. However, for oxygen 16, for example, 1 atom corresponds to Atomic masses range from 1 u hydrogen to more than u for the heaviest nuclei.

Another definition of atomic mass is used in chemistry, with the same symbol A, but in this case, it refers to the so-called atomic weights. The difference from the definition above is that, for a given element, this definition takes the naturally occurring mixture of nuclides into account with the isotopes so the value of A may be different from the mass number.

Furthermore, in addition to the classical parameters qualifying the behaviour of a particle mass, 3D coordinates and speed components an intrinsic angular momentum, the spin, is added.

When the mole is used, the elementary entities must be specified, and may be atoms, molecules, ions, electrons, other particles or specified groups of such particles. As stated above, n can have the values 1, 2, 3. This allows us to derive the maximum number of electrons in a given shell. Only 2 electrons can reside in the K shell.

The same rule leads to 8 possibilities for the L shell, 18 for the M shell, etc. The liquid drop model assumes that the nucleus is made up of closely packed nucleons in constant motion. This model is compatible with the explanation of interactions of heavy particles with the nucleus, but is not compatible with the explanation for discrete nuclear energy states revealed in interactions with light particles.

Because of this, a shell model of the nucleus has been proposed, which is similar to the shell model for the peripheral electrons. More elaborate models have been proposed in order to fit better with the latest experimental data, but they will not be considered here. Isotopes are atoms that have the same number of protons Z with different number of neutrons. They are therefore different versions of the same element.

Many elements are made of a mixture of several isotopes, with a fairly stable composition. The atomic mass A for such elements may then be calculated and is not necessarily an integer. Isobars are atoms that have the same number of nucleons value of A. For the so-called natural nuclides, A ranges from 1 to 92 U.

The fundamental laws of physics include the conservation of the total energy of a given system, whatever the transformations in it. The energy unit, in the International System of Units is the joule J , but because this quantity is too large when applied to particle energies, the electron volt eV is often used instead. This unit, representing the energy acquired by an electron accelerated through a potential difference of 1 V, is such that: 1 eV z! Considering the frequency v of the electromagnetic wave associated with a given photon behaving as a particle in the energy range of radiotherapyi.

When a particle is moving, its total energy is the sum of the energy corresponding to its rest mass, and of the translation kinetic energy. So, the total energy of the particle becomes EZmc2, according to Einstein, in such a way that mc2Zm0 c2CT, where T is the translation kinetic energy, i. When the particle velocity becomes small, the above equation becomes close to the classical value of T Z 12 mv 2.

This theory shows that, for instance, in the energy range of the electrons considered in medical radiological physics, their very small rest mass can nevertheless allow large kinetic energies obtained with large velocities approaching the light velocity in vacuo Table 1.

The nature of these forces is not yet fully understood. Four kinds of interactions have been considered to explain such remote interactions, involving quantum energy exchanges between elementary particles: gravity, electromagnetic interactions, weak interactions and strong interactions.

For example, in the nucleus, the strong interactions are believed to be between the elementary particles called quarks; nucleons are believed to be made up of three quarks.

The quantum exchanged in such interactions is called the gluon, which has no mass. The rest of this Chapter will deal with atomic and molecular structures. The structure of the nucleus will be considered in Chapter 2. The bonds associated with different matter structures can be quantified with the definition of binding energy: the energy required to dissociate a given structure or substructure. It is usually denoted by W. Table 1. So, the total mass of the system is smaller than the sum of the masses of its individual components.

This is called the mass defect and is about 7 MeV per nucleon in the helium atom. Obviously, the outer shells are less dependent on the Z number of the atoms, due to increasing values of b. Consequently the outer shells correspond to a binding energy ranging from 1 to 16 eV, whatever the value of Z. This corresponds to the first ionisation energy of the atoms.

Note that the value of n is related to the principal energy level of a given shell usually nZ1 means the K shell, nZ2 the L shell etc. The binding energies of sublevels are close to the binding energy of the principal energy level, but cannot be calculated with the empirical Moseley formula. TABLE 1. This state also corresponds to the minimum internal energy. Consequently, the binding energies of such electrons are changed.

The magnitude of the changes depends on the molecules, and on the chemical species considered. The binding energies of electrons belonging to inner shells are less affected, or may remain unchanged. In crystals, the situation is different, as the number of electrons shared is usually large, depending on the crystal structure and the atom. Consequently, electrons can be found at many different energy levels, in an energy range comparable to an energy band, called the valence band.

If, in the fundamental state, the crystal absorbs external energy, electrons can reach a higher energy level an excited state , and behave as they do in conductors of electricity. The corresponding energy band is then the conduction band. When the conduction band overlaps the valence band, the crystal is a conductor of electricity. If the bands do not overlap, a forbidden band of a few eV between the two bands ensures that the crystal behaves as an insulating material.

This corresponds to a higher level of internal energy. The atom is then said to be excited. If the energy given to the atom, increasing its internal energy, is defined as positive, then the binding energies should be considered as negative. For instance, for Tungsten: WL ZK11 eV and WM ZK2 eV So : DW ZK2 C 11 Z 8 eV: As in the fundamental state all inner shell electron positions are occupied, the electron transitions are most often observed between outer shells, involving the peripheral electrons, which are also responsible for the chemical characteristics of the atom.

As such, peripheral electrons have a weak binding energy, and excitations can be produced with low energy photons UV or visible. Conversely, excitations linked to internal shells require higher energy photons. For a given electron to be removed from the atom, the energy transfer must be higher than the binding energy of this electron. The excess of energy is, in principle, shared between the ionised atom and the electron as kinetic energy. Since particle momentum is conserved, most of the kinetic energy is given to the electron, because of the very large difference in masses.

This recovery of the fundamental state is associated with re-emission of energy. In the fluorescence process, the energy re-emission is made through prompt emission of one or several photons after a delay of the order of 10K6 s. The mechanism of this process is described as follows: after excitation or ionisation, vacancies or holes appear in electron shells, and are promptly filled by electrons cascading from energy levels corresponding to shells farther from the nucleus.

As the vacancies are filled, energy is released for instance through photon emission and the internal energy of the atom is reduced. A single photon is emitted if the original event is a single ionisation and if the position of the electron removed from the atom is re-occupied by an external free electron. The photon energy is then equal to the binding energy of the electron removed by ionisation W.

Several photons are emitted if the return to the fundamental state is made through successive transitions of different electrons, from the inner part of the atom to the peripheral shell, where a free external electron can be captured.

The global energy emitted through the photons is still equal to W, the binding energy of the electron initially removed by the ionisation. If the original event is an excitation, the energy available is the difference in the binding energies corresponding to the shells involved in the electron transition Figure 1.

The energy of the emitted fluorescence photons is closely related to the mechanism of their production. This energy is therefore characteristic of the energy structure of the atoms and molecules involved in the production process and the emitted photons are called characteristic x-rays.

The fluorescence spectrum is made up of lines allowing the characteristic radiation to be identified and associated with a specific atom. Fluorescence emission is usually described according to the destination of the cascading electron, as, for instance, K characteristic radiation, or K fluorescence. K shell is a general name for a family of sub-shells with close energy levels, in such a way that the K characteristic radiation is made of a number of lines with close energies, with subfamilies described as Ka, Kb.

Depending on the energy levels in the atoms, the fluorescence photons can belong to the infrared, visible, UV or x-ray part of the electromagnetic spectrum. This ejected electron is called an Auger electron. Like fluorescence photons, Auger electrons have well-defined energies, depending on whether the energy is effectively transferred to more external electrons or whether the emission of the Auger electron is due to a free electron filling the initial vacancy Figure 1.

The probability of the Auger effect is higher for low-Z biological media than the probability of fluorescence, close to 1 for Z! From Dutreix, J. The M fluorescence has an energy of a few keV and is usually not visible in the spectra from x-ray tubes, b Spectral distributions of fluorescence lines for tungsten atoms: Families of lines can be shown as a function of energy or of wavelength.

This could appear paradoxical because the nucleus is made up of a mixture of protons and neutrons despite the repulsive electrostatic forces between protons. It is supposed to be effective when the distance between nucleons is smaller than the diameter of the nucleus, and it is associated with the exchange of gluons between the quarks constituting the nucleons. Its strength is much smaller than the strength of the nuclear force 10K2 to 10K6 , and it is believed to be associated with the exchange of photons.

It is associated with the exchange of bosons so called W and Z particles which have large mass but cannot be observed directly. The binding energy of nucleons can be considered similarly to the principles presented for the peripheral electrons.

The major difference is the magnitude of this binding energy that is of the order of 1 MeV per nucleon, i. This binding energy is obviously linked to the content of the nucleus, and it is the result of the combination of the different forces described above.

Figure 2. It appears that the maximum binding energy per nucleon about 9 MeV per nucleon occurs for values of A around 60 to 70 Fe, Ni, Co, Ca, etc. Due to the broad range of topics covered and the clear, concise explanations, this text would be ideal for anyone wishing to study or refresh their knowledge of any central area of radiotherapy physics.

IPEM Part 1 trainees in the UK and any other trainee following a similar training programme elsewhere in particular should take note Part 2 trainees will also benefit, especially in exploring the excellent source of referenced material.

In comparison to other reference texts, the Handbook of Radiotherapy Physics is clear and also filled with many knowledgeable and useful observations and notes. It is an excellent reference text and sits nicely on the shelf alongside your old copy of Williams and Thwaites.

With contributions from renowned specialists, this book provides essential theoretical and practical knowledge to deliver safe and effective radiotherapy. Convert currency. Add to Basket. Book Description Hardback. Condition: New.

Language: English. Brand new Book. Seller Inventory ROD More information about this seller Contact this seller. Book Description Condition: New. Seller Inventory ON OFF. We use cookies to understand how customers use our services so we can make improvements.

We use cookies to serve you certain types of ads, including ads relevant to your interests on Book Depository and to work with approved third parties in the process of delivering ad content, including ads relevant to your interests, to measure the effectiveness of their ads, and to perform services on behalf of Book Depository.

Cancel Save settings. Home Contact us Help Free delivery worldwide. Free delivery worldwide. Bestselling Series. Harry Potter. Books By Language. Books in Spanish. Handbook of Radiotherapy Physics : Theory and Practice. C Rosenwald. Expected delivery to Germany in business days. Not ordering to Germany? Click here. Description From background physics and biological models to the latest imaging and treatment modalities, the Handbook of Radiotherapy Physics: Theory and Practice covers all theoretical and practical aspects of radiotherapy physics.

In this comprehensive reference, each part focuses on a major area of radiotherapy, beginning with an introduction by the editors and then subdividing into self-contained chapters. The first three parts present the fundamentals of the underlying physics, radiobiology, and technology involved.