Keywords

1 Introduction

Current requirements for releases of radioactive substances into the environment are so strict that under normal circumstances, when regulations are observed, any excessive radioactive contamination is expected and thus the contribution to the total average exposure of the population due to these discharges is trivial and much lower than the natural background exposure. Just for a comparison and a realistic perception aimed at the assessment how much is too much, Fig. 1 illustrates the typical contributions of specific components to the total average exposure of individual members of the public worldwide (UNSCEAR 2011) and in the USA (NCRP 2009; UNSCEAR 2011). Similar situations can also be found in some other developed countries, and it is presumed that many other countries all over the word will soon be in a similar position. The exposure is given in terms of effective dose in mSv, which is directly related to radiation stochastic health effects. In any case, there has obviously been an enormous recent increase in exposure from the medical field.

Fig. 1
figure 1

Individual contributions to the overall average annual population exposure worldwide (UNSCEAR 2010) and in the USA (NCRP 2009)

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This, however, does not mean that we do not need to pay appropriate attention to controlling exposure from man-made activities, where the radioactive releases and contamination of the environment should be minimized and optimized.

Currently, excessive radioactive contamination of the environment may occur as a result of incidents and accidents, causing uncontrollable contamination of the air, water and soil or the surface contamination of the terrain and other surfaces surrounding the place of radioactive releases, including those far away from the source of contamination since the air containing radioactive dust may transport radioactivity to very remote locations. In fact, the major portion of any radioactive contamination of the air will sooner or later be deposited on the surface of the earth somewhere. In all these cases the assessment of the magnitude of the exposure of persons affected requires the use of internationally accepted quantification which should be preferably consistent with quantities and units recommended by the ICRP (International Commission on Radiological Protection) (ICRP 2007) and ICRU (International Commission on Radiation Units and Measurements) (ICRU 2011).

Radiological compliance criteria for determining acceptable remediation actions at radioactively contaminated sites should also be expressed in the internationally recognized quantities and units. Any remediation should be justified taking into account that such intervention should result in the radiation exposure situation of the contaminated territory doing more good than harm. In another words, the remediation actions have to be optimized so that they would result in the likelihood of incurring exposures, the number of people exposed and the magnitude of their individual doses all being kept as low as reasonably achievable, taking into account economic and social factors (Voigt and Fesenko 2009).

Site characterisation based on the monitoring of radiation level and radioactive contamination, as the first necessary stage in the remediation of any contaminated environment, as well as all criteria in relevant regulations should be expressed in quantities and units which are unambiguously understood so that all interpret them in the same way and the data could be compared for the reliable evaluation of the results and the effectiveness of remediation actions. This is why a sound introduction of an appropriate system of quantities and units applicable to the evaluation of radioactive contamination and its impact on the exposure of persons is so important.

2 Quantification of Radioactive Sources and Radiation Fields

2.1 Radioactive Sources

All radioactive sources consist of one or more radionuclides, each of which is characterized by some unique properties such as the type of decay, type and energy of particles emitted, activity and half-life. It is well-known that a radioactive atom contains an unstable nucleus which is spontaneously disintegrating (decaying) into other atoms, releasing energy by the emission of ionizing radiation.

Although the amount of radioactive material can be expressed in its mass, a more appropriate measure of its ability to emit ionizing radiation is the activity (A) of radionuclides present. The activity of a radionuclide is related to the rate at which it decays i.e.

$$ A=-\frac{dN}{dt}=\lambda\ N\cong \frac{\varDelta N}{\varDelta t} $$
(1)

where dN is the expectation value of the number of spontaneous nuclear transformations from the given energy state in the time interval dt and λ is the decay constant. The negative sign is needed here because N decreases as the time t increases. In practical use, the definition of this quantity, as well as in the definition of other similar quantities, the infinitesimal values dN and dt can be approximated by the finite delta values Δt (sufficiently small) and corresponding ΔN. A more detailed treatment of the activity and other radiation protection quantities and units can be found in a number of relevant publications, e.g. (Sabol and Weng 1995; Martin 2000; Martin et al. 2012).

The activity SI unit is Bq (becquerel) corresponding to one decay per second (s−1). The old unit is Ci (curie) equals 37 GBq (1 GBq = 1012 Bq).

Radioactive sources may be represented formally in the form of point sources (where their size is very small so that they can be essentially considered negligible in relation to their surroundings) or the radioactive material may be distributed throughout a certain volume of the material or on its surface. In these cases, it may be useful to introduce such additional quantities as an activity concentration corresponding to the activity per unit of mass or volume containing certain radionuclides, or the activity may be related to the unit of an area on the surface of the contaminated material or ground.

Consequently, for the volume activity concentration (a v ) , mass activity concentration (a m ) and surface activity concentration (a s ) the following relationships can be written

$$ {a}_v=\frac{dA}{dV},{a}_v=\frac{dA}{dV},{a}_v=\frac{dA}{dV}, $$
(2)

where dA is the activity in the volume element of dV, in the mass element dm and on the surface of dS, respectively. The basic units of these quantities are Bq/m3 (or Bq l−1), Bq kg−1 and Bq/m2.

The activity as a function of time can be expressed in the form

$$ A(t)={A}_0\ {e}^{-\lambda\ t}={A}_0\ {e}^{-{T}_{1/2}} $$
(3)

where A(t) is the activity A at the time t, A 0 is the activity at the beginning (at the time t 0 ) and T 1/2 is the half-life, i.e. the time during which the original activity falls to one-half of its value. The half-life of some commonly used radionuclides is shown in Table 1.

Table 1 The half-life T1/2 of some of the radionuclides
Full size table

Radioactive decay is a random process , and therefore the measurement of radioactivity must be treated with statistical methods. We have to observe a sufficient number of events (counts) with detectors to achieve an acceptable level of fluctuations (standard deviation) of the mean rate (counts/time). If the activity in the sample is low, we have to measure it for a longer time, increase the size of the sample, or use a more sensitive detector system to achieve satisfactory count statistics .

The emission of radiation from a radionuclide is isotropic, which means that particles or photons are emitted in all directions with the same probability. However, this may not always be the case for all radiation sources, where sometimes the quantity emission rate (N r ) is more appropriate. This quantity is defined as

$$ {N}_r=\frac{d{N}_e}{dt} $$
(4)

where dN e is a number of particles or photons emitted by the source during the interval dt in all directions (into the 4π space). The unit of emission rate is s−1 equivalent to the number of particles emitted by the source 1 s−1. Sometimes, it is useful to relate the emission to a selected direction, which is important for the characterization of radiation sources the emission of which is not homogenous .

2.2 Radiation Field

Around any radiation source, a radiation field is formed. A complete description of a radiation field requires the (particle) fluence distribution as a function of particle type, e.g. electrons, photons, neutrons, and their energy. The field can be characterized by such quantities as the fluence, fluence rate, energy fluence and energy fluence rate.

The fluence (Φ) is defined as the quotient of the number of particles dN incident on a sphere of cross-sectional area da

$$ \varPhi =\frac{dN}{da\ } $$
(5)

where dN is the number of particles incident on a sphere of cross-sectional area da. The use of a sphere expresses the fact that one considers the area perpendicular to the direction of each particle. By using a sphere, the area perpendicular to the direction of each particle is accounted for so that all particles passing through this volume of space are included. The basic unit of the fluence is m−2 (number of particle per square meter).

The energy fluence (Ψ) is defined as the energy dE of particles incident on a sphere of cross-sectional area da. If you have a fluence Φ of particles all of energy E, then the energy fluence is Ψ = Φ E. The SI unit of energy fluence is J/m2 or eV/m2 (keV/m2, MeV/m2 etc.).

Both (particle) fluence and energy fluence can be related to the unit of time, thus defining two useful quantities, namely the fluence rate (φ) and energy fluence rate (ψ) introduced as

$$ \varphi =\frac{d\varPhi}{d a},\psi =\frac{d\varPhi}{d a} $$
(6)

The SI units of these field quantities are (m−2 s−1) and J/(m2 s1), respectively. In practice, instead of J, a conventional energy unit eV (and its multiples) is often used, where the approximate conversion between eV and J is 1 eV = 1.6 × 10−19 J.

3 Interaction of Radiation with Matter

The interaction of radiation with matter is the most essential part of radiation physics, which is particularly important for the understanding of dosimetry, radiation protection, the biological effects of radiation, and also the interpretation of results obtained from detectors and monitors in terms of relevant quantities.

Radiation emitted by any radionuclide or radioactively contaminated material always forms a radiation field around such a source. If the nearby space is filled with a substance consisting of specific nuclides present, radiation will interact with their atoms and molecules. The processes will result in the absorption of radiation energy, causing ionization of the medium.

There is a substantial difference between the interaction of uncharged particles (indirectly ionizing radiation) and charged particles (directly ionizing radiation). While the fluence of indirectly ionizing radiation lies with the thickness of the absorber going down exponentially, on the other hand, the charged particles are losing their energy in small portions along their path and, eventually, at the end of the range they lose their entire energy. Because of these characteristic phenomena, in the case of indirectly ionizing radiation one can only refer to its attenuation , or the reduction in terms of number of individual uncharged particles or photons depending on the thickness of the absorber. This is schematically illustrated in Fig. 2, where μ is the linear attenuation coefficient for gamma radiation depending on the energy of the photons and the composition of the absorbing material.

Fig. 2
figure 2

Principal difference between the interaction of gamma photons as a typical representative of indirectly ionizing radiation (exponential decrease of their fluence) and alpha particles characterized by their definite range

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Any single uncharged particle or photon may interact with atoms and nuclei of the matter by several different major processes, each of which is characterized by a certain probability. Generally, on a certain distance a particle may not interact at all or it can be absorbed or scattered. In this case, one cannot predict the behavior of any individual particle which, in principle, may be absorbed at a very short distance in the material or it may travel some long distance without any interactions. This is why in the case of uncharged particles we cannot refer to their definite range but we can only specify the attenuation of a sufficient number of such particles.

X-ray and gamma radiations interact with matter through a variety of alternative mechanisms, the three most important of which are the photoelectric effect, Compton scattering and pair production.

In the photoelectric effect , all the energy of a photon is transferred to an atomic electron located on the one of the atomic shells. The energy of the ejected electron, which then begins to pass through the surrounding matter, is sooner or later absorbed in the medium. Since the interaction creates a vacancy in one of the electron shells, typically the K or L, an electron moves down to fill it. The drop in energy of the filling electron produces a characteristic x-ray photon .

Conversely, when Compton scattering occurs, only part of the energy of the photon is transferred to an atomic electron, which then ionizes the medium around it. The scattered photon then continues with reduced energy. This photon leaves the site of the interaction in a direction different from that of the original photon .

If the energy of the incident photons is higher than the so-called threshold energy of 1.02 MeV, a positron-electron pair is produced in the intense electric field close to a nucleus. Any energy above the threshold energy is, according to the conservation law, split between the kinetic energy of these two particles. The positron is the anti-particle of the electron, so when a positron comes to rest, it interacts with another electron, resulting in the annihilation of both particles; this process is associated with the emission of two oppositely directed 0.511 MeV photons. The probability of pair production increases approximately with the square of atomic number Z of the absorber and increases with photon energy.

The result of these interactions is the transfer of the entire or a substantial portion of the energy of the incident photon to an electron and the scatter of the original photons. In other words, one cannot completely stop all photons in the beam; one can only reduce their number and this depends on the energy of the photons as well as on the type and thickness of the absorbing materials where a specific quantity, the half-value layer ( HVL) , is a useful characteristic parameter of the properties of the material in terms of its ability to attenuate a photon beam. The half-value layer corresponds to such thickness of the material which will reduce the number of original photons to the half of their number. It can be expressed as

$$ HVL=\frac{\lg 2}{\mu}\cong \frac{0.693}{\mu } $$
(7)

where HVL is in m (meter) when the linear attenuation coefficient μ is given in m−1.

A similar situation is also found with other commonly encountered indirectly ionizing radiation. Neutrons, which essentially interact only with the atomic nucleus, may undergo a variety of processes; the probability (cross-section) of each process occurring depends on the neutron energy and the composition of the material. In one of these interactions a new radioactive nucleus is produced by the absorption of a neutron by a stable nucleus of the material. Many man-made radionuclides are produced by the neutron activation of a suitable sample of relevant material.

Interaction coefficients for indirectly ionizing radiation , in addition to the linear attenuation coefficient μ, include also the mass attenuation coefficient (μ/ρ) , mass energy transfer coefficient (μ tr /ρ) , mass energy transfer coefficients (μ tr /ρ) and mass energy absorption coefficients (μ en /ρ) which are mainly used for photons, while for neutrons the cross section (σ) is usually used. The values of these coefficients depend on the type and energy of radiation, and on the composition of the material in which the interactions take place.

The above mentioned interaction coefficients are given by the following relationships

$$ \frac{\mu }{\rho }=\frac{1}{\rho\ dl}\ \frac{dN}{N},\kern0.5em \frac{\upmu_{tr}}{\rho }=\frac{1}{\rho }\ \frac{d{R}_{tr}}{R},\kern0.5em \frac{\mu_{en}}{\rho }=\frac{1}{\rho }\ \frac{d{R}_{tr}}{R}\ \left(1-g\right),\upsigma\ \frac{P}{\varPhi } $$
(8)

where dN/N is the fraction of particles that experience interactions in traversing a distance dl in the material of density ρ, dR tr /R is the fraction of incident radiant energy that is transferred as kinetic energy of charged particles by interactions in traversing a distance dl in a material of density ρ, g is the fraction of the energy of liberated charged particles that is lost in radiative processes in the material, and P is the probability of a particular interaction for a single target entity when subjected to the particle fluence Φ.

The SI unit of the first three interaction coefficients stated above is m2 kg−1, while the cross section is given in the unit m2.

High-energy photons transfer their energy to matter in complex interactions with atoms, nuclei, and electrons. For practical purposes, however, these interactions can be viewed as simple collisions between a photon and a target atom, nucleus, or electron.

Charged particles , as directly ionizing radiation (electrons, positrons, protons, heavy ions), ionize the matter directly by removing outer electrons from originally neutral atoms, which then become positive ions. In contrast to charged particles, uncharged particles or photons can ionize the matter only indirectly through the secondary charged particles formed as a result of the interaction processes of this radiation with matter.

In the case of directly ionizing radiation , the main interaction coefficients are linear stopping power (S l ) , mass stopping power (S m ) , linear energy transfer (L) and mean energy expended in a gas per ion pair production (W i ). These quantities are defined by the following equations

$$ {S}_l=-\frac{d{E}_k}{dl},{S}_m=\frac{S_l}{\rho },{W}_{\acute{\mathrm{1}}}=\frac{E_c}{N_i} $$
(9)

where dE k is the kinetic energy lost by the charged particle on the distance dl (i.e. S l is the energy loss per unit path length of the charged particle), ρ is the density of the material, E c is the initial energy of the particle and N i is the number of ion pairs produced by this particle.

In the assessment of the biological effects of ionizing radiation, the quantity linear energy transfer ( LET) of charged particles in a medium plays an important role. This quantity corresponds to the quotient dE/dl, where dE is the average energy locally imparted to the medium by a charged particle of specified energy in traversing a distance of dl. One has to distinguish between the LET and the linear stopping power (formally defined in a similar way): Stopping power is closely related to LET except that LET does not include radiative losses of energy (which are lost to the medium and so not absorbed) since the LET is related to biological damage. The severities of biological changes are directly related to the local rate of energy deposition along the particle track.

Charged particles (alphas, betas, positrons and heavy ions) interact with the electrons of atoms by transferring gradually some small portion of their kinetic energy to these electrons. If charged particles possess sufficient energy they may also transfer enough energy to an electron (generally one in an outer shell) to eject the electron from the atom, which is in this way ionized. When radiation causes the ejection of an electron from an atom of an absorber, the resulting positively charged atom and free negatively charged electron are called an ion pair. The process is known as ionization . The amount of energy transferred per ion pair created, Wi, is characteristic of the materials in the absorber. For example, approximately 33 eV (25–40 eV) is transferred to the absorber for each ion pair created in air or water.

It is often convenient to refer to the number of ion pairs created per unit distance the radiation travels as its specific ionization . Heavier particles with more charge (alpha particles) have a higher specific ionization than lighter particles with less charge (electrons). Linear energy transfer is related to specific ionization: alpha particles are classified as high-LET radiation, and beta particles and photons as low-LET radiation.

In traversing an absorber, an electron loses its energy at each interaction with the atoms of the absorber. The energy loss per interaction is variable. Therefore, the total distance travelled by electrons of the same energy can vary by as much as 3–4%. This variation in range is called the straggling of the range. The heavier alpha particles are not affected to a significant degree and demonstrate very little straggling of range.

Both alpha and beta particles lose energy mainly through interactions with atomic electrons in the absorbing medium. The energy transferred to the electrons causes them either to be excited to a higher energy level (excitation) or separated entirely from the parent atom (ionization). Another important effect is that when charged particles are slowed down very rapidly, they emit energy in the form of x-rays. This is known as bremsstrahlung (braking radiation) and is of practical importance only in the case of beta radiation.

As has already been mentioned, the range of a charged particle is the distance it travels before coming to rest. It is assumed that the particle loses its energy in a continuous way and at a rate equal to the linear stopping power S l . Since the stopping power is the energy loss of the particle per unit path, the range can be calculated by

$$ R\left({E}_i\right)=\underset{E_0}{\overset{E_i}{\int }}\frac{dE}{S_l\ (E)} $$
(10)

where E i is the initial energy of the charged particle, E 0 is the energy where the particle is effectively absorbed. The range is the path length travelled by the particle. Since the particle’s path is usually not straight due to scattering, its actual range is always longer than the projected range, which is the distance between the point where the particle enters the stopping medium and the point where the particle is absorbed (or comes to rest), projected onto the original direction of travel. The ranges of electrons, positrons and alpha particles in air under standard temperature and pressure are illustrated in Fig. 3.

Fig. 3
figure 3

Ranges in cm of electrons, protons and alpha particles in air

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4 Dosimetric Quantities and Units

At the beginning of the radiation era, for the assessment of biological consequences of radiation exposure, some simple physical quantities were used. These quantities were successfully evolved into more sophisticated physical dosimetric quantities which were gradually modified using various appropriate factors and converted into what we now know as radiation protection quantities . These current quantities more accurately approximate the biological effects of ionizing radiation at lower levels, where only stochastic effects occur.

4.1 Exposure

The unit roentgen (R) was the first unit introduced in 1928. The original definition has changed several times before coming to the present concept of the quantity exposure , the unit of which is now C kg−1 instead of R (roentgen).

The current definition of the exposure (X), the exposure rate (dX/dt) and the relationship of the exposure with the quantities characterizing the photon radiation field (Ψ) and the interaction of photon radiation (including x-radiation, γ-radiation or annihilation radiation) with the air is as follows

$$ X=\frac{dQ}{dm},\kern0.75em \dot{X}=\frac{dX}{dm},\kern0.75em X=\varPsi\ {\left(\frac{\mu_{en}}{\rho}\right)}_{air}\ \frac{e}{W_{i, air}} $$
(11)

where dQ is the absolute value of the total charge of the ions of one sign produced in air when all the electrons and positrons liberated or created by photons in air of mass dm are completely stopped in air, Ψ is the energy fluence, μ en /ρ is the mass energy absorption coefficient, W i,air is the average energy required to produce an ion pair in air and e is the electronic charge.

The SI unit of exposure and exposure rate is C kg−1 and W kg−1, respectively. The old (traditional) unit of the exposure is related to the SI unit as 1 R = 2.54 × 10−4 C kg−1.

4.2 Absorbed Dose

The term dose of radiation was initially used in a pharmacological sense that means it is analogous to its meaning when used in prescribing a dose of medicine . Radiation dosimetry is a now a pure physical science.

The quantity of the absorbed dose (D), often only dose, is the most universal dosimetry quantity; it can be used for any radiation and any material or substance. The quantities absorbed dose (or sometimes referred to as only the dose), the dose rate (dD/dt) and the expression of the dose at the point of interest for indirectly ionizing radiation (D i ) and directly ionizing radiation (D d ) can be written in the following forms

$$ \boldsymbol{D}=\frac{\boldsymbol{d}\overline{\boldsymbol{\varepsilon}}}{\boldsymbol{d}\boldsymbol{m}},\kern0.75em \dot{\boldsymbol{D}}=\frac{\boldsymbol{d}\overline{\boldsymbol{\varepsilon}}}{\boldsymbol{d}\boldsymbol{m}},\kern0.5em {\boldsymbol{D}}_{\boldsymbol{i}}=\varPsi\ {\left(\frac{\mu_{en}}{\rho}\right)}_m,\kern0.75em {D}_d=\varPhi\ E\ {\left(\frac{S}{\rho}\right)}_m $$
(12)

where \( d\overline{\upvarepsilon} \) is the mean energy imparted to the matter of mass dm. The SI units of the dose and the dose rate are gray (Gy) and gray per hour (Gy h−1). In practice, units as mGy, μGy and mGy h−1 or μGy h−1 are also used quite often. The relationship of the main SI unit to the old unit of the dose is 1 Gy = 100 rad.

It should be emphasized that in the definition of the dose the energy imparted is not necessarily only the energy absorbed since the energy ε is the sum of all energy deposits in the volume considered. The energy imparted and energy deposit can be expressed in the form

$$ \varepsilon =\sum \limits_i{\varepsilon}_i,\kern1.25em {\varepsilon}_i={\varepsilon}_{in}-{\varepsilon}_{out}+{Q}_r $$
(13)

where ε i is the energy deposit in a single interaction i, ε i is the energy of the incident ionizing particle (excluding rest energy), ε out is the sum of the energies of all ionizing particles leaving the interaction (excluding rest energy), Q r is the change in the rest energies of the nucleus and of all particles involved in the interaction (Q r  > 0, decrease of rest energy, and Q r  < 0, increase of rest energy).

For a differential fluence Φ(E) of identical charged particles the dose D is given by

$$ D=\int \frac{S_l(E)}{\rho }\ \varPhi (E)\ dE $$
(14)

where S l (E)/ρ) is the tabulated mass stopping power of the charged particle as a function of energy E for the considered material .

4.3 Kerma

This quantity kerma , which is the acronym for Kinetic Energy Released per unit Mass, can only be used for indirectly ionizing radiation in any matter. The kerma (K) is defined as the following quotient

$$ K=\frac{d{E}_{tr}}{dm} $$
(15)

where dE tr is the sum of the initial kinetic energies of all the charged particles liberated by uncharged particles in a mass dm of material. The medium should always be specified. There are various primary standards to realise K for various particle types and energies.

The special name for the unit of kerma is gray (Gy); the unit for the kerma and dose is the same, namely gray (Gy). The older unit which is no longer supposed to be used was rad, where 1 Gy = 100 rad.

For a fluence Φ(E) of uncharged particles of energy E, the kerma (K) in a specified material and the relationship between the kerma in air (K air ) and the exposure (X) are given by

$$ K=\int \varPhi (E)\ E\ \frac{\mu_{tr}(E)}{\rho }\ dE,\kern0.75em {K}_{air}=\frac{W_{i, air}}{e\ \left(1-g\right)}\ X $$
(16)

The average fraction of the energy transferred to electrons that is lost through radiative processes is represented by a factor referred to as the radiative fraction g. Analogically one can derive a formula expressing the dose D m in a given material m at a point where the air kerma is K air .

The air kerma rate constant is often used to characterize gamma emitting radioactive sources in terms of their ability to produce the kerma rate at a distance of 1 m from a point source related to its unit activity.

The kerma is usually expressed in terms of the distribution Φ(E) of the uncharged particle fluence with respect to energy. The kerma K is then given by

$$ K=\int \left(\frac{\mu_{tr}}{\rho}\right)\ \Phi \left(\mathrm{E}\right)\mathrm{EdE} $$
(17)

where (μ tr /ρ) is the tabulated mass energy transfer coefficient of the material for uncharged particles of energy E.

As the mass of a sample decreases in general, the energy per unit mass will become more random (stochastic). The energy imparted per unit mass can still be defined in region z, but the definition of absorbed dose implies an averaging to give D (a non-stochastic quantity).

All above-mentioned quantities can be related to the unit of time, dX/dt, dK/dt and dD/dt, which are then called the exposure rate , kerma rate and dose rate with the units of A.kg−1 and Gy.s−1, respectively.

5 Radiation Protection Quantities

The main aim of radiation protection is to ensure adequate protection of persons including radiation workers, patients and members of the public as well as satisfactory protection of the environment. Recently, due attention is also being paid to the security of high activity radioactive sources which may be misused for radiological terrorism.

The ICRP in its latest general recommendations (ICRP 2007) redefined or modified some quantities which had been previously recommended for specification in terms of the limits on exposure to external radiation and to intakes of radionuclides. In addition, the ICRU (ICRU 2011) has defined a set of operational dose equivalent quantities to be used in radiation protection measurements of external radiation.

5.1 Dose Equivalent and Dose Equivalent Rate

The dose equivalent (H) represents one of the initial quantities in radiation protection. It is the point quantity obtained by multiplying the dose (D) at a point in tissue by the quality factor (Q). The modifying factor Q depends on the unrestricted linear energy transfer (L) in water of the charged particles responsible for the dose. The dose equivalent and dose equivalent rate at a point are defined by the relationships

$$ H={\int}_LQ(L)D(L) dL,\kern1em \dot{H}=\frac{dH}{dt} $$
(18)

where Q(L) and D(L) are the quality factor and the dose as a function of L, respectively. The unit of the dose equivalent is sievert (Sv) which corresponds to J kg−1 (multiplied by Q). In a simplified manner the definition of the dose equivalent can be written as

$$ H=D\ Q $$
(19)

where D is the absorbed dose and Q is the mean value of the quality factor for the specific radiation at this point .

5.2 Equivalent Dose and Committed Equivalent Dose

The equivalent dose (H T ) is specified as the summation of doses (D T,R ) averaged over a tissue or organ T due to radiations of type R incident on the body or emitted by radionuclides in the body and weighted by radiation weighting factors (w R ).

The committed equivalent dose H T (τ) is the time integral of the equivalent dose rate in a particular tissue or organ that will be received by an individual following intake of radioactive material into the body by a Reference Person (an idealized person for whom the organ or tissue equivalent doses are calculated), where τ is the integration time in years (50 years for adults or 70 years in the case of children). This quantity reflects the contribution of the internal exposure to the total equivalent dose.

The equivalent dose H T , mean dose D T and committed equivalent dose H T (τ) are given by

$$ {H}_T=\sum \limits_R{w}_R\ {D}_{T,R},\kern0.75em {D}_T=\frac{1}{m_T}\ {\int}_{m_T}D\ dm,\kern1em {H}_T\left(\tau \right)=\underset{t_0}{\overset{t_0+\tau }{\int }}\frac{d\ {H}_T}{dt}\ dt $$
(20)

where m T is the mass of the tissue or organ and D is the dose in the mass element dm. In fact, the dose D T equals the ratio of the energy imparted ε T to the tissue or organ and the mass of this tissue or organ m T . The integration time τ follows the intake at time t 0 .

Since the radiation weighting factor is considered to be a dimensionless factor, the unit of both the equivalent dose and committed equivalent dose is Sv (provided the dose is in Gy).

5.3 Effective Dose and Committed Effective Dose

The effective dose (E) is the main quantity in radiation protection for the assessment of biological effects at low doses. It has been defined only for stochastic effects. The effective dose is defined as:

$$ E={\sum}_T{w}_T\ {\sum}_R{w}_R{D}_{T,R} $$
(21)

The contribution to the total effective dose due to intakes of radionuclides is quantified by the committed effective dose (E(τ)) which is defined as the sum of the products of the committed equivalent doses and the appropriate tissue weighting factors w T . The basic unit for both the above-mentioned quantities is Sv. The values of weighting factors w R and w T are given in the latest recommendations of the ICRP (Table 2).

Table 2 Recommended radiation weighting factors (wR) and tissue weighting factors (wT)
Full size table

5.4 Assessment of External Exposure

The body-related radiation protection quantities such as the equivalent dose and effective dose are, due to their nature, not directly measurable and so they cannot be used directly as quantities in radiation monitoring. This is why so-called operational quantities have been introduced by the ICRU.

The purpose of these quantities is to provide an estimate or upper limit for the value of the protection quantities related to an exposure, or potential exposure of persons under most irradiation conditions. Operational quantities are often used in practical regulations or guidance aimed at controlling external exposures. Individual operational quantities (which are point quantities) can be defined as follows:

The ambient dose equivalent H*(10), at a point in a radiation field, is numerically equal to the dose equivalent that would be produced by the corresponding expanded and aligned field a 30 cm tissue-equivalent ICRU sphere at a depth of 10 mm on a radius vector opposing the direction of the aligned field. It should be understood/noted that the ambient dose equivalent is now the only quantity to be applied for the measurement of external radiation.

The directional dose equivalent H′(0.07, Ω), which is intended for the assessment of low-penetrating radiation, is the dose equivalent that would be produced by the corresponding radiation field in the ICRU sphere at a depth 0.07 mm on a radius in a specified direction Ω.

The personal dose equivalent H p (d) is the dose equivalent in soft tissue at an appropriate depth d below a specified point on the body. For strongly penetrating radiation a depth of 10 mm is usually used while for weakly penetrating radiation a depth of 0.07 mm is normally employed.

The basic unit of all operational quantities is Sv, which also serves as a unit for some other radiation protection quantities .

5.5 Assessment of Internal Exposure

While the contribution of external radiation to the total effective dose is related to the period during which a person is exposed, in case of internal exposure its contribution may be spread over a much longer period of time following intakes by inhalation or ingestion. Moreover, there are no operational quantities for the direct assessment of internal exposure. Any assessment due to the intake of radionuclides relies first on the evaluation of the intake of a radionuclide, based typically either on direct measurement of the radioactivity of the body (e.g., by a whole-body counter or external detectors measuring the radioactivity of specific organs and tissues) or indirect measurements (e.g., measuring the activity of radionuclides in urine, faeces, air or other environmental samples).

Once the intake is known, the effective dose is calculated using reference dose coefficients recommended by the ICRP; these coefficients have been adopted by the EU (Basic Safety Standards Directive) and IAEA (International Basic Safety Standards).

5.6 Radiation Source as a Cause of the Exposure of Persons

Many attempts have been made to define a universal quantity to quantify the exposure to a person in order to assess the probability of detriment regardless of the type of radiation (or irradiation conditions), including nonhomogeneous exposure of individual organs. The quantity of the effective dose has been adopted for this noble purpose and extensive effort has been made to associate its value with whole-body stochastic effects. In principle, this has been achieved by the introduction of relevant weighting factors – the radiation weighting factor and the tissue weighting factor, which convert a physical quantity - the absorbed dose - into a bio-physical quantity expressed in Sv. These factors, based largely on epidemiological studies, have often been changed (and presumably this process will continue also in the future) in order to match the value of the effective dose with the impact of the exposure in terms of stochastic effects based on the latest scientific findings. A similar concept, relying on the quantity of equivalent dose, has also been adopted for the stochastic effects occurring in an individual organ or tissue exposed to ionizing radiation.

In principle, the stochastic dose has to consider both components, namely from external and internal exposure (Fig. 4).

Fig. 4
figure 4

Illustration of ionizing radiation sources and the resulting exposure in terms of the effective dose reflecting the total stochastic effects due to external and internal exposure

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The present system has been developed through many phases reflecting available information and scientific knowledge at that time. The primary aim of the system was based on the effort to fully assess harmful stochastic effects. Obviously one had to have considered some important biological factors related to the harm caused by different types of ionizing radiations in individual tissues or organs. Consequently, the quantity, which would adequately represent stochastic effects, would no longer be a physical quantity, but rather a bio-physical quantity, which apparently could not be assessed using only pure physical principles. This is why the effective dose as well as the equivalent dose cannot be measured directly. These quantities can only be approximated using specifically defined operational quantities. Even here one experiences some problems in measuring or monitoring operational quantities directly.

6 Dose Limits for Workers and the Public

The adequate protection of radiation workers (professionally exposed) and members of the public is ensured by keeping radiation exposures not only below recommended dose limits but at the same time reducing the exposure to a very minimum in accordance with one of basic principles of radiation protection – ALARA (As Low As Reasonably Achievable). The latest dose limits proposed by the ICRP and recommended by the IAEA, EU and other international organizations are given in Table 3.

Table 3 Recommended dose limits in planned exposure situations
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All professionals in radiation protection, including the users of radiation sources, should be familiar with the average values of the exposure to natural sources, dose limits, and at least be approximately aware of the exposure due to most important man-made sources and their applications. They are supposed to make use of this information when dealing and communicating with the public. In order to establish a good communication atmosphere, no complex technical or scientific terminology should be used. Under normal conditions, in accordance with the basic radiation protection requirements, the exposure is not supposed to exceed the above-mentioned dose limits. On the contrary, everything possible has to be done to keep actual exposures at the lowest achievable level well below those limits. However, in the case of an accident, some guidance levels have been recommended in order to restrict the exposure of emergency workers. In such situations the guidance values for restricting exposure to external penetrating radiation of emergency workers, who are engaged in life saving actions or actions to prevent severe deterministic effects and actions to prevent the development of catastrophic conditions that could significantly affect people and the environment, can reach up to 500 mSv.

7 Biological Effects of Radiation Exposure

It is well known that when radiation undergoes an interaction processes, it can deposit some energy in the material either directly (by charged particles) or indirectly (by secondary charged particles produced by uncharged particles). This energy usually results in ionization and excitation of atoms and molecules. If living organs or tissues are exposed to radiation, some specific biological effects may appear which, at low exposure levels, may induce cancer (with a certain probability proportional to the amount of exposure), or some biological damage as long as the exposure is above a certain threshold level. The first type of biological effects is referred to as stochastic effects (they may appear in an exposed individual or not), while the second type of effects are called deterministic effects (they will surely develop in an individual who has received high exposure).

At low exposure levels, no visible or clinical effects can be recognized following the exposure of a person. However, deterministic effects (known now as harmful tissue reactions) occur when sufficient cells are killed or changed following high exposure above a certain dose, the so-called threshold level, i.e. a level below which a visible health effect is absent, but above which the effect is expected with certainty. This means that a person exposed to such high doses will be directly affected and the severity will increase with increasing doses.

It has been recognized that high-LET radiations, e.g., alpha particles, heavy ions and also neutrons, produce greater damage per unit of absorbed dose than radiations characterized by low LET, namely photons and electrons or positrons. For the quantification of low-LET radiations the dose is completely adequate but for high-LET radiations an RBE-weighted dose has been proposed. This quantity, proposed by the ICRP and adopted by the IAEA for the evaluation of emergency exposure, is defined as the product of the averaged absorbed dose D T,R due to the radiation of type R in an organ or tissue T and the relative biological effectiveness RBE T,R related to the tissue or organ T and radiation R. In order to differentiate the unit of the dose (Gy) from that associated with the RBE-weighted dose, a unit equivalent/gray (Eq-Gy) has been attributed to this quantity.

The IAEA has developed an International Nuclear and Radiological Event Scale (INES) (IAEA 2009) for ease in comparing various nuclear accidents, taking into account many factors reflecting the impact of such accidents (Fig. 5). As with most things, it is not perfect but it serves the purpose at least partially of meeting the needs of public awareness in a broad sense. The difficulties in using this scale became apparent following the Fukushima accident (Thielen 2012), where there was some hesitation concerning classifying it in accordance with the INES . Formally, it should fall into category 7, but everything suggests that the Fukushima impact was much lower than that of Chernobyl (Balonov 2012, 2013), which was classified as an event at the same level 7 (no higher ranking).

Fig. 5
figure 5

An illustration of individual levels of the IAEA categorization of nuclear and radiation incidents and accidents in accordance with the INES

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The public would welcome something as simple and illustrative as the Richter scale, which reflects the magnitude of earthquakes with its non-linear representation of the massiveness of the event rather than its consequences. In the case of nuclear accidents, the public would prefer a scale reflecting the number of immediate and potential casualties as well as the impact on the environment and thus the influence on future generations.

8 Radiation Measurements and Monitoring

The interactions of various types of ionizing radiation with matter form a basis for measuring the amount of radiation present and emitted by a source or absorbed in a particular material. Radiation instruments include portable survey instruments that are designed to detect radiation and measure exposure or absorbed dose and laboratory instruments that allow precise quantitation and identification of the radiation source. Various detectors are used in them, and these can be roughly divided into two categories: gas-filled chambers and crystalline materials. The operation of each of these various devices is based on the liberation of electrons in a medium and the collection and processing of the ions by electronic means.

In addition to the detection and monitoring instruments using an active detector (sensor) which produces an electrical signal and must be powered by a source of electricity, there are other types of radiation sensors – passive dosimeters. These sensors accumulate the information about the measured quantity (usually the dose) and after the measurement they have to be read using specific processes and a reader. An example of these types of radiation monitors are film badges or thermoluminescent dosimeters (TLDs) to measure the radiation dose received by persons over a period of time, usually a month or a quarter. For short-term monitoring of work, a pocket ion chamber dosimeter is worn or an electronic dosimeter. Electronic dosimeters can be useful for this purpose because they can be set to indicate an alert or warning level of exposure.

For field measurements and surveys a variety of instruments based on specific detectors are widely used. However, one has to be aware of their limitations since none of the monitors can be universally used in all cases. Table 4 (Voigt and Fesenko 2009) shows an overview of survey instruments and their properties from which we can see the potential for their applications.

Table 4 Main features of the survey instruments relying on specific detectors as sensors of radiation
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9 Main Principles of Radiation Protection

The main task of radiation protection is aimed at avoiding the occurrence of any deterministic effects and minimizing the risk due to stochastic effects to acceptable levels. Consequently, the principal objectives of radiation protection may be formulated as follows:

  1. (a)

    To prevent deterministic effects by keeping the dose below levels approaching the threshold level, and

  2. (b)

    To ensure adequate protection under normal or planned situations by implementing effective protective actions and other measures to reasonably reduce the risk of stochastic effects by keeping the dose below levels approaching the generic criteria, namely the dose limits and dose constraints set by regulatory authorities.

The precept of justification postulates that any decision which may alter the radiation exposure situation should do more good than harm. The optimization of protection consists in adopting such measures that the likelihood of incurring exposures, the number of people exposed, and the magnitude of their individual doses should all be kept as low as reasonably achievable, taking into account economic and societal factors. The limitation means that the total dose to any individual from authorized sources in planned exposure situations other than the medical exposure of patients is not supposed to exceed the dose limits set by the regulatory authority.

The regulatory body is responsible for the planning, implementation and verification of remedial actions including

  • approval of the remedial action plan and granting of any necessary authorisation;

  • establishment of criteria and methods for assessing safety;

  • review of work procedures, monitoring programmes and records;

  • review and approval of significant changes in procedures or equipment that may have an environmental impact or may alter the exposure conditions of remediation workers or of members of the public;

  • receipt and assessment of reports of abnormal occurrences;

  • performance of regular inspections and, where necessary, any enforcement actions;

  • verification of compliance with the legal and regulatory requirements, including criteria for waste management and discharges established for the remediation programme; and

  • where necessary, establishment of regulatory requirements for post-remediation control measures (Voigt and Fesenko 2009; IAEA 2007, 2016).

The overall aims and objectives of implementing remedial measures in a radioactively contaminated ecosystem is to improve the radiological situation for the affected populations where compliance with the criteria related to the exposure of people and impact on the environment should be unambiguously defined using the relevant quantities and units. In achieving this, the main goal consists in reducing the adverse radiological impact imposed by the remaining radioactive contamination.

In accordance with the international standards, the main objectives of remediation actions should be aimed at

  • the reduction of the doses to individuals or groups of individuals who may be exposed;

  • the averting of doses to individuals or groups of individuals who are likely to get exposed in the future; and

  • the prevention or reduction of environmental consequences due to the radionuclides present in the contaminated area.

The reductions in the exposure to individuals as well as environmental impacts should be to be achieved by means of interventions focusing on removing the existing sources of contamination, modifying the pathways of exposure, and/ or reducing the numbers of individuals exposed to radiation from the source.

10 Conclusion

Nuclear science and technology offer many beneficial peaceful uses, including the generation of energy and the production of radionuclides for use in medical examinations and cancer treatment. All radioactive sources and nuclear materials as well as facilities housing them have to be carefully disposed at the end of their useful lives. At present, before embarking on any new programmes involving the use of radioactive material, preliminary plans for the eventual decommissioning, the safe disposal of radioactive material and necessary remediation are developed. However, this was not always the case since at the time when many radiation, nuclear and mining facilities were built and operated, there were no such strict safety and security requirements as we have today. Many countries are now implementing or devising plans for decommissioning such facilities and for remediation of radioactively contaminated sites. The IAEA helps them to do so, bringing its international expertise (Amano 2016). An essential component of planning for decommissioning and environmental remediation is knowledge sharing. This requires using of unified terminology where the correct understanding and interpretation of use of quantities and units in radiation protection plays an important role.