# Introduction to Physical Science/Excerpts from sources

This is the final chapter of a wikibook entitled Basics Physics of Nuclear Medicine, written originally by Kieran Maher in 1997.

## Chapter Review: Atomic & Nuclear Structure

* The atom consists of two components - a nucleus (positively charged) and an electron cloud (negatively charged);
* The radius of the nucleus is about 10,000 times smaller than that of the nucleus;
* The nucleus can have two component particles - neutrons (no charge) and protons (positively charged) - collectively called nucleons;
* The mass of a proton is about equal to that of a neutron - and is about 1,840 times that of an electron;
* The number of protons equals the number of electrons in an isolated atom;
* The Atomic Number specifies the number of protons in a nucleus;
* The Mass Number specifies the number of nucleons in a nucleus;
* Isotopes of elements have the same atomic number but different mass numbers;
* Isotopes are classified by specifying the element's chemical symbol preceded by a superscript giving the mass number and a subscript giving the atomic number;
* The atomic mass unit is defined as 1/12th the mass of the stable, most commonly occurring isotope of carbon (i.e. C-12);
* Binding energy is the energy which holds the nucleons together in a nucleus and is measured in electron volts (eV);
* To combat the effect of the increase in electrostatic repulsion as the number of protons increases, the number of neutrons increases more rapidly - giving rise to the Nuclear Stability Curve;
* There are ~2450 isotopes of ~100 elements and the unstable isotopes lie above or below the Nuclear Stability Curve;
* Unstable isotopes attempt to reach the stability curve by splitting into fragments (fission) or by emitting particles/energy (radioactivity);
* Unstable isotopes <=> radioactive isotopes <=> radioisotopes <=> radionuclides;
* ~300 of the ~2450 isotopes are found in nature - the rest are produced artificially.

## Chapter Review: Radioactive Decay

* Fission: Some heavy nuclei decay by splitting into 2 or 3 fragments plus some neutrons. These fragments form new nuclei which are usually radioactive;
* Alpha Decay: Two protons and two neutrons leave the nucleus together in an assembly known as an alpha-particle;
* An alpha-particle is a He-4 nucleus;
* Beta Decay - Electron Emission: Certain nuclei with an excess of neutrons may reach stability by converting a neutron into a proton with the emission of a beta-minus particle;
* A beta-minus particle is an electron;
* Beta Decay - Positron Emission: When the number of protons in a nucleus is in excess, the nucleus may reach stability by converting a proton into a neutron with the emission of a beta-plus particle;
* A beta-plus particle is a positron;
* Positrons annihilate with electrons to produce two back-to-back gamma-rays;
* Beta Decay - Electron Capture: An inner orbital electron is attracted into the nucleus where it combines with a proton to form a neutron;
* Electron capture is also known as K-capture;
* Following electron capture, the excited nucleus may give off some gamma-rays. In addition, as the vacant electron site is filled, an X-ray is emitted;
* Gamma Decay - Isomeric Transition: A nucleus in an excited state may reach its ground state by the emission of a gamma-ray;
* A gamma-ray is an electromagnetic photon of high energy;
* Gamma Decay - Internal Conversion: the excitation energy of an excited nucleus is given to an atomic electron.

## Chapter Review: The Radioactive Decay Law

* The radioactive decay law in equation form;
* Radioactivity is the number of radioactive decays per unit time;
* The decay constant is defined as the fraction of the initial number of radioactive nuclei which decay in unit time;
* Half Life: The time taken for the number of radioactive nuclei in the sample to reduce by a factor of two;
* Half Life = (0.693)/(Decay Constant);
* The SI Unit of radioactivity is the becquerel (Bq)
* 1 Bq = one radioactive decay per second;
* The traditional unit of radioactivity is the curie (Ci);
* 1 Ci = 3.7 x 10$^{10}$ radioactive decays per second.

## Chapter Review: Units of Radiation Measurement

* Exposure expresses the intensity of an X- or gamma-ray beam;
* The SI unit of exposure is the coulomb per kilogram (C/kg);
* 1 C/kg = The quantity of X- or gamma-rays such that the associated electrons emitted per kg of air at STP produce in air ions carrying 1 coulomb of electric charge;
* The traditional unit of exposure is the roentgen (R);
* 1 R = The quantity of X- or gamma-rays such that the associated electrons emitted per kg of air at STP produce in air ions carrying 2.58 x 10$^{-4}$ coulombs of electric charge;
* The exposure rate is the exposure per unit time, e.g. C/kg/s;
* Absorbed dose is the radiation energy absorbed per unit mass of absorbing material;
* The SI unit of absorbed dose is the gray (Gy);
* 1 Gy = The absorption of 1 joule of radiation energy per kilogram of material;
* The traditional unit of absorbed dose is the rad;
* 1 rad = The absorption of 10$^{-2}$ joules of radiation energy per kilogram of material;
* The Specific Gamma-Ray Constant expresses the exposure rate produced by the gamma-rays from a radioisotope;
* The Specific Gamma-Ray Constant is expressed in SI units in C/kg/s/Bq at 1 m;
* Exposure from an X- or gamma-ray source follows the Inverse Square Law and decreases with the square of the distance from the source.

## Chapter Review: Interaction of Radiation with Matter

* Alpha-Particles:
** exert considerable electrostatic attraction on the outer orbital electrons of atoms near which they pass and cause ionisations;
** travel in straight lines - except for rare direct collisions with nuclei of atoms in their path;
** energy is always discrete.
* Beta-Minus Particles:
** attracted by nuclei and repelled by electron clouds as they pass through matter and cause ionisations;
** have a tortuous path;
** have a range of energies;
** range of energies results because two particles are emitted - a beta-particle and a neutrino.
* Gamma-Rays:
** energy is always discrete;
** have many modes of interaction with matter;
** important interactions for nuclear medicine imaging (and radiography) are the Photoelectric Effect and the Compton Effect.
* Photoelectric Effect:
** when a gamma-ray collides with an orbital electron, it may transfer all its energy to the electron and cease to exist;
** the electron can leave the atom with a kinetic energy equal to the energy of the gamma-ray less the orbital binding energy;
** a positive ion is formed when the electron leaves the atom;
** the electron is called a photoelectron;
** the photoelectron can cause further ionisations;
** subsequent X-ray emission as the orbital vacancy is filled.
* Compton Effect:
** A gamma-ray may transfer only part of its energy to a valence electron which is essentially free; ** gives rise to a scattered gamma-ray;
** is sometimes called Compton Scatter;
** a positive ion results;
* Attenuation is term used to describe both absorption and scattering of radiation.

## Chapter Review: Attenuation of Gamma-Rays

* Attenuation of a narrow-beam of gamma-rays increases as the thickness, the density and the atomic number of the absorber increases;
* Attenuation of a narrow-beam of gamma-rays decreases as the energy of the gamma-rays increases;
* Attenuation of a narrow beam is described by an equation;
* the Linear Attenuation Coefficient is defined as the fraction of the incident intensity absorbed in a unit distance of the absorber;
* Linear attenuation coefficients are usually expressed in units of cm$^{-1}$;
* the Half Value Layer is the thickness of absorber required to reduce the intensity of a radiation beam by a factor of 2;
* Half Value Layer = (0.693)/(Linear Attenuation Coefficient);
* the Mass Attenuation Coefficient is given by the linear attenuation coefficient divided by the density of the absorber;
* Mass attenuation coefficients are usually expressed in units of cm$^2$ g$^{-1}$.

## Chapter Review: Gas-Filled Detectors

* Gas-filled detectors include the ionisation chamber, the proportional counter and the Geiger counter;
* They operate on the basis of ionisation of gas atoms by the incident radiation, where the positive ions and electrons produced are collected by electrodes;
* An ion pair is the term used to describe a positive ion and an electron;
* The operation of gas-filled detectors is critically dependent on the magnitude of the applied dc voltage;
* The output voltage of an ionisation chamber can be calculated on the basis of the capacitance of the chamber;
* A very sensitive amplifier is required to measure voltage pulses produced by an ionisation chamber;
* The gas in ionisation chambers is usually air;
* Ionisation chambers are typically used to measure radiation exposure (in a device called an Exposure Meter) and radioactivity (in a device called an Isotope Calibrator);
* The total charge collected in a proportional counter may be up to 1000 times the charge produced initially by the radiation;
* The initial ionisation triggers a complete gas breakdown in a Geiger counter;
* The gas in a Geiger counter is usually an inert gas;
* The gas breakdown must be stopped in order to prepare the Geiger counter for a new event by a process called quenching;
* Two types of quenching are possible: electronic quenching and the use of a quenching gas;
* Geiger counters suffer from dead time, a small period of time following the gas breakdown when the counter is inoperative;
* The true count rate can be determined from the actual count rate and the dead time using an equation;
* The value of the applied dc voltage in a Geiger counter is critical, but high stability is not required.

## Chapter Review: Scintillation Detectors

* NaI(Tl) is a scintillation crystal widely used in nuclear medicine;
* The crystal is coupled to a photomultiplier tube to generate a voltage pulse representing the energy deposited in the crystal by the radiation;
* A very sensitive amplifier is needed to measure such voltage pulses;
* The voltages pulses range in amplitude depending on how the radiation interacts with the crystal, i.e. the pulses form a spectrum whose shape depends on the interaction mechanisms involved, e.g. for medium-energy gamma-rays used in in-vivo nuclear medicine: the Compton effect and the Photoelectric effect;
* A Gamma-Ray Energy Spectrum for a medium-energy, monoenergetic gamma-ray emitter consists (simply) of a Compton Smear and a Photopeak;
* Pulse Height Analysis is used to discriminate the amplitude of voltage pulses;
* A pulse height analyser (PHA) consists of a lower level discriminator (which passes voltage pulses which are than its setting) and an upper level discriminator (which passes voltage pulses lower than its setting);
* The result is a variable width window which can be placed anywhere along a spectrum, or used to scan a spectrum;
* A single channel analyser (SCA) consists of a single PHA with a scaler and a ratemeter;
* A multi-channel analyser (MCA) is a computer-controlled device which can acquire data from many windows simultaneously.

## Chapter Review: Nuclear Medicine Imaging Systems

* A gamma camera consists of a large diameter (25-40 cm) NaI(Tl) crystal, ~1 cm thick;
* The crystal is viewed by an array of 37-91 PM tubes;
* PM tubes signals are processed by a position circuit which generates +/- X and +/- Y signals;
* These position signals are summed to form a Z signal which is fed to a pulse height analyser;
* The +/- X, +/- Y and discriminated Z signals are sent to a computer for digital image processing;
* A collimator is used to improve the spatial resolution of a gamma-camera;
* Collimators typically consist of a Pb plate containing a large number of small holes;
* The most common type is a parallel multi-hole collimator;
* The most resolvable area is directly in front of a collimator;
* Parallel-hole collimators vary in terms of the number of holes, the hole diameter, the length of each hole and the septum thickness - the combination of which affect the sensitivity and spatial resolution of the imaging system;
* Other types include the diverging-hole collimator (which generates minified images), the converging-hole collimator (which generates magnified images) and the pin-hole collimator (which generates magnified inverted images);
* Conventional imaging with a gamma camera is referred to as Planar Imaging, i.e. a 2D image portraying a 3D object giving superimposed details and no depth information;
* Single Photon Emission Computed Tomography (SPECT) produces images of slices through the body;
* SPECT uses a gamma camera to record images at a series of angles around the patient;
* The resultant data can be processed using a Filtered Back Projection method;
* SPECT gamma-cameras can have one, two or three camera heads;
* Positron Emission Tomography (PET) also produces images of slices through the body;
* PET exploits the positron annihilation process where two 0.51 MeV back-to-back gamma-rays are produced;
* If these gamma-rays are detected, their origin will lie on a line joining two of the detectors of the ring of detectors which encircles the patient;
* A Time-of-Flight method can be used to localise their origin;
* PET systems require on-site or nearby cyclotron to produce short-lived radioisotopes, such as C-11, N-13, O-15 and F-18.

## Chapter Review: Production of Radioisotopes

* Naturally-occurring radioisotopes generally have long half lives and belong to relatively heavy elements - and are therefore unsuitable for medical diagnostic applications;
* Medical diagnostic radioisotopes are generally produced artificially;
* The fission process can be exploited so that radioisotopes of interest can be separated chemically from fission products;
* A cyclotron can be used to accelerate charged particles up to high energies so that they to collide into a target of the material to be activated;
* A radioisotope generator is generally used in hospitals to produce short-lived radioisotopes;
* A technetium-99m generator consists of an alumina column containing Mo-99, which decays into Tc-99m;
* Saline is passed through the generator to elute the Tc-99m - the resulting solution is called sodium pertechnetate;
* Both positive pressure and negative pressure generators are in use;
* An isotope calibrator is needed when a Tc-99m generator is used in order to determine the activity for preparation of patient doses and to test whether any Mo-99 is present in the collected solution.