Module 03 followed photons through attenuation and showed that μ_tr and μ_en track how much of each interaction's energy goes to electrons. This module takes the next step. Multiply the energy fluence by μ_tr/ρ and you get kerma. Ask when kerma equals dose and you get charged particle equilibrium. Put a small air cavity in the medium and ask what dose the air receives and you get cavity theory, which is how every ion chamber calibration works.

Three answers carry the whole module:

1. Under charged particle equilibrium, absorbed dose equals collision kerma. That lets you calculate dose from the photon beam alone.
2. One coulomb of ionization in air corresponds to 33.97 joules deposited. That number, W/e, converts charge to dose in air.
3. A small cavity converts with stopping power ratios; a large one with μ_en ratios. The size is judged against the range of the electrons, not against the patient.

Before you can say how much energy a beam deposits, you need a way to say how much beam there is at a point. Picture a small sphere centred on the point. Count the photons that cross it, from any direction, and divide by the sphere's cross-sectional area. That is the particle fluence, Φ, in photons per square metre (usually quoted per cm²). Using a sphere rather than a flat plate means a photon counts once whatever direction it travels, which matters inside a patient where scattered photons come from everywhere.

Weight each photon by its energy and you have the energy fluence, Ψ, in joules per square metre. For a single photon energy the two are related simply. For a real beam you sum over the spectrum. The rates, fluence per unit time, are the fluence rate and energy fluence rate.

Worked number: 1.0 × 10¹⁰ photons/cm² of 1.25 MeV carry Ψ = 1.0 × 10¹⁰ × 1.25 MeV × 1.602 × 10⁻¹³ J/MeV = 2.0 × 10⁻³ J/cm².

When a photon interacts, some of its energy becomes kinetic energy of electrons (the Compton electron, the photoelectron, the electron and positron from pair production). The rest leaves as a scattered photon, a characteristic x-ray, or annihilation radiation. Kerma (kinetic energy released per unit mass) counts only the kinetic energy given to charged particles in a small mass, at the place where the photon interacted. Its unit is the gray, J/kg, the same as dose.

Kerma has the shape it has because it is the product of how much energy passes the point (Ψ) and what fraction of that energy is transferred to electrons per unit mass of the medium (μ_tr/ρ). More photons, or a medium that takes a bigger share of each photon's energy, means more kerma.

Worked number: continuing from section 02, Ψ = 2.0 × 10⁻³ J/cm² of 1.25 MeV photons in water, μ_en/ρ = 0.0296 cm²/g. K_col = 2.0 × 10⁻³ × 0.0296 = 5.9 × 10⁻⁵ J/g = 0.059 J/kg = 5.9 cGy.

Kerma tells you where electrons were launched. Absorbed dose tells you where their energy ended up. It is the mean energy imparted by all ionizing radiation to a small mass, divided by that mass. Energy imparted is everything that comes in (photons and electrons) minus everything that goes out, so electrons launched upstream that stop inside the mass count, and electrons launched inside that leave do not.

Dose applies to any ionizing radiation, directly or indirectly ionizing, in any medium. It is what biology responds to and what you prescribe.

For protection, ICRP 103 assigns w_R = 1 for photons and electrons, 2 for protons, 20 for alpha particles, and an energy-dependent value for neutrons. Effective dose then weights organs by tissue factors. These are risk quantities for populations and belong to Module 21; never use them for a patient's treatment dose.

Take a small volume in a uniform photon beam. Electrons are launched inside it and some carry energy out. Electrons launched upstream carry energy in. If, for every electron that leaves with some energy, another of the same energy enters, the volume keeps exactly the energy that was transferred inside it, minus the bremsstrahlung that escapes. That balance is charged particle equilibrium (CPE), and under it:

CPE needs the photon fluence to be uniform over a region at least as large as the maximum electron range around the point, in a uniform medium. In a real megavoltage beam that is never quite true, because the photons are attenuated over the distance the electrons travel. The electrons arriving at a point were launched upstream, where the photon fluence was slightly higher. So beyond the buildup region, dose is a little larger than the local collision kerma, by a nearly constant factor β. Physicists call this transient charged particle equilibrium (TCPE).

Before anyone could measure energy deposited directly, they could measure charge. Exposure, X, is the total charge of one sign produced in a small mass of air when all the electrons liberated by photons in that mass are stopped completely in air. It is the ionization equivalent of collision kerma in air. Its SI unit is C/kg; the old unit, the roentgen, is 1 R = 2.58 × 10⁻⁴ C/kg.

To turn charge into energy you need the average energy spent per ion pair formed in dry air, W. Divided by the electron charge, W/e = 33.97 J/C (equivalently 33.97 eV per ion pair). ICRU Report 90 kept this value and widened its uncertainty to about 0.35 percent. Multiply exposure by W/e and you have collision kerma in air.

To get dose in another medium placed at the same point, under CPE, scale by how much more energy per gram that medium absorbs from the same photon fluence: the ratio of mass energy absorption coefficients. The combination is the f-factor, in cGy per R.

An ion chamber measures dose to the air in its cavity. You want dose to the water around it. Cavity theory connects the two.

Suppose the cavity is so small that photons essentially never interact in it. Every bit of dose in the air then comes from electrons launched in the surrounding water that cross the cavity. If the cavity is also too small to change the number or energy of those electrons, the same electron fluence crosses the air as would have crossed the water it replaced. Dose from an electron fluence is fluence times mass collision stopping power, energy lost per unit path per unit density. The ratio of doses is therefore the ratio of stopping powers.

The two Bragg-Gray conditions are worth stating exactly, because exams ask for them:

1. The cavity does not perturb the charged particle fluence in the medium (it is small compared with electron ranges).
2. The dose in the cavity is deposited entirely by charged particles crossing it; photon interactions in the cavity itself are negligible.

CPE is not one of the conditions. Bragg-Gray works in regions without CPE, which is why it holds for electron beams and why chambers work at depth in megavoltage beams.

Worked number: a cavity collects charge that gives D_air = 0.959 Gy in a Co-60 beam. With s̄_water,air = 1.133, D_water = 0.959 × 1.133 ≈ 1.09 Gy, before perturbation corrections.

Spencer-Attix: the delta-ray fix

Bragg-Gray treats every electron as losing energy continuously along its track. Real electrons occasionally knock out a fast secondary electron, a delta ray, that may itself cross the cavity or escape it. Spencer and Attix split electrons at a cutoff energy Δ, the energy an electron needs to just cross the cavity (about 10 keV for a typical chamber). Energy losses that create electrons below Δ are counted as local; electrons above Δ are counted as part of the fluence. The ratio uses restricted stopping powers, L_Δ/ρ, plus a track-end term for electrons that fall below Δ.

Large cavities: back to μ_en

Now make the detector large compared with electron ranges, for example a thick LiF chip in a kilovoltage beam, or any detector thick enough to set up its own CPE. Electrons from the surrounding medium deposit their energy in a thin rim; almost all the dose in the detector comes from photons interacting in the detector material itself. Under CPE in both media, each dose is K_col = Ψ·μ_en/ρ, and the photon fluence is common, so the ratio is the μ_en ratio.

Follow one chamber reading all the way to dose to water. Change the room temperature and pressure and watch the air mass, and therefore the dose, move. Then compare the Bragg-Gray answer with what you would get from the wrong (μ_en) ratio.

Work each one on paper first. The constants are given in the problem, as they are on the exam.

You will never compute a Spencer-Attix ratio in clinic. You will hear these ideas every time a plan is reported in dose to medium, a detector is chosen for skin dose, or a chamber reading is turned into a calibration.

Ballpark numbers to carry in your head

Dose to water or dose to medium

Monte Carlo and grid-based Boltzmann solvers (Acuros XB) compute dose in the actual tissue, D_m. Convolution algorithms and every clinical trial before them report dose to water, D_w. Converting one to the other is a cavity theory problem: a small water cavity in bone is Bragg-Gray, so D_w = D_m × s̄_w,m. In soft tissue the difference is about 1 to 2 percent; in cortical bone it is around 10 percent. A spine SBRT plan or a mandible constraint can therefore look different with no change in the delivered beam, only in what is being reported.

Detectors where CPE fails

Skin and buildup-region dose cannot be measured with a detector that needs CPE. Extrapolation chambers and thin-window parallel-plate chambers are the reference tools; OSLDs, TLDs and diodes used in vivo need either buildup caps, which measure dose at d_max rather than at the skin, or calibration under the same conditions as the measurement.

Sources

1. American Board of Radiology. Study Guide for Medical Physics for Radiation Oncology (2023 domain ranges; domain II.A, radiation quantities and units).
2. Attix FH. Introduction to Radiological Physics and Radiation Dosimetry. Wiley, 1986. Chapters on kerma, CPE and cavity theory.
3. Khan FM, Gibbons JP. The Physics of Radiation Therapy, 5th ed. Chapters on measurement of ionizing radiation and quantification of absorbed dose.
4. Podgorsak EB, ed. Radiation Oncology Physics: A Handbook for Teachers and Students. IAEA, 2005. Chapters 1 to 3.
5. ICRU Report 85. Fundamental Quantities and Units for Ionizing Radiation. J ICRU 2011;11(1).
6. ICRU Report 90. Key Data for Ionizing-Radiation Dosimetry: Measurement Standards and Applications. J ICRU 2014;14(1). W_air = 33.97 eV, uncertainty 0.35%.
7. Almond PR et al. AAPM TG-51 protocol for clinical reference dosimetry of high-energy photon and electron beams. Med Phys 1999;26:1847.
8. IAEA Technical Reports Series 398. Absorbed Dose Determination in External Beam Radiotherapy. Vienna, 2000.
9. ICRP Publication 103. The 2007 Recommendations of the International Commission on Radiological Protection. Ann ICRP 2007;37.

The buildup panel uses a two-exponential teaching model and the cavity bench applies bare Bragg-Gray without perturbation factors. Both teach direction and magnitude. Clinical numbers come from your physicist's calibration and your machine's commissioning data.