Neutron Dosimetry in Radiotherapy:
Multicenter Comparison of Neutron Detectors
Relatore:
Dott. Alessandro Tofani
Lucio Alticozzi
Presentata da:
electrons and photons, which induces photoneutron creation through (γ, n) reactions. As energy increases, the photoneutron contribution to the total dose becomes less and less negligible. These photoneutrons originated mainly in the head of the linac, in the sur-rounding structures and in the air.
The aim of this work was to compare and realign the responses of dierent rem counters used in the north-west area of Tuscany by exposing them to neutrons produced by radia-tion of dierent qualities, including neutrons from Am-Be sources (typically also used for the calibration of such instruments) and photoneutrons produced by linacs operating in the hospitals of Lucca, Livorno and Massa Carrara. The operating dosimetric quantity used for the inter-comparison was the ambient equivalent dose H∗(10).
Graphs showing the deviation of dierent instruments from a reference one (provided by INFN Pisa and recently calibrated) were obtained for all radiation qualities.
The gamma-ray emission induced by neutron activation was also measured inside several treatment rooms.
The availability of a calibrated rem counter made it possible to realign the answers of the other instruments and therefore have the possibility of correcting and unambiguously comparing the measurements carried out at dierent centers.
The LUPIN (Long-interval, Ultra-wide dynamic, PIle-up free, Neutron REM counter), made available by the Politecnico of Milan and particularly suitable for measurements in high intensity pulsed elds, was also compared to other rem counters in some measure-ment sessions.
1 Neutron Physics and Radiobiology 5
1.1 Neutron sources . . . 6
1.1.1 Spontaneous ssion . . . 6
1.1.2 Radioisotope (α, n) sources . . . 8
1.2 Neutron detection . . . 11
1.2.1 Nuclear reactions of interest in neutron detection . . . 11
1.2.2 Detectors based on the boron reaction . . . 15
1.2.3 The 3He proportional counter . . . . 19
1.2.4 Fast neutron detection . . . 22
1.3 Neutron dosimetry . . . 27
1.3.1 High LET radiation . . . 30
1.3.2 Operational dose quantities . . . 33
1.4 Neutron emission in clinical facilities . . . 38
1.4.1 Linac neutron emission . . . 38
1.4.2 Neutron activation . . . 41
2 Material and Methods 45 2.1 Rem counter calibration . . . 46
2.1.1 Angular energy response . . . 46
2.2 Rem counter comparison . . . 46
2.2.1 Experimental set-up . . . 48
2.2.2 LUPIN . . . 49
2.3 Neutron activation . . . 51
3 Results 53
Modern radiotherapy linear accelerators (linacs) used in medicine generate electrons and X-rays with energies up to over 20 MeV. Such energies are enough to induce nuclear reactions inside materials itercepted by the therapeutic beam where neutrons and ra-dioisotopes are produced[38].
These particles represent a not desire contribution to patient and sta dose.
Neutron detection is not an easy task because of their neutral nature which prevents direct detection. The so called rem counters are the most commonly used detectors in radiotherapy facilities.
For this work, 5 rem counters - plus LUPIN, particularly suitable for measurements in high intensity pulsed elds - were used to detect neutrons and estimate the ambient equiv-alent dose H∗(10).
In chapter 1 we see physical and radiobiological aspects of neutron elds, we get closer to the neutron detection and the high LET radiaton properties[1][2][3]. The operational quantities used in the neutron dosimetry will be introduced and some considerations will be made about neutron activation in a treatment room[38].
In chapter 2 we will enter into detail talking about the material and methods. The rem counters will be introduced, the linacs used in this work and the experimental set-up will be described.
In chapter 3 we will enter in the heart of the work showing the results. The plots show the detectors responses both for calibration and inter-comparison for dierent experimental conditions (beam quality, eld size, linac model...etc). In addition to those plots there are also those about neutron activation in each treatment room. Furthermore some plots are about theoretical calculations and comparison with the LUPIN detector. In the last part, some considerations that must be taken into account will be evaluated.
1
Neutron Physics and Radiobiology
Neutrons and protons are the building blocks of atomic nuclei. The neutron is made up of three quarks namely up, down, down and thus is a baryon, g. 1.1. It has a relatively big mass, like the proton (mn= 939.57MeV/c
2, m
p = 938.28MeV/c
2). Neutrons are not
stable outside the nucleus. They β decay into a proton, electron and anti-neutrino with a mean life time of τn= 886.7 ± 1.9 seconds:
n −→ p + e−+ ¯νe
Neutrons are subject to all four fundamental interactions.
Nuclear reactions and scattering at the nucleus potential are both strong interactions. The β-decay of a neutron is a weak interaction. Neutrons are uncharged particles and therefore are unaected by the Coulomb potential of the electrons. The electron magnetic interaction of the neutrons is only due to its spin coupling (spin − 1
2) with the magnetic
moment. The magnetic moment of neutrons is given by: µn = −1.91 · µK where µK = 2me·¯hp = 5.05 · 10−27 Joule Tesla denotes the moment of one nucleon.
Neutrons can be divided into 4 dierent groups depending on their kinetic energies (K): Fast neutrons (K > 1 MeV): they are usually produced in nuclear reactions. In this process, the binding energy is converted into kinetic energy of the neutron. The binding energy is in the range 7-8 MeV per nucleon.
Epithermal neutrons (1 MeV ≤ K < 0.025 eV): they are produced in a moderating material through inelastic collisions.
Figure 1.1: Neutron structure.
Thermal neutrons (K ∼ 0.025 eV): they have a velocity of 2200 m/s and are in thermal equilibrium with moderator atoms at room temperature (∼ 300K) and so their energies follow a Maxwellian distribution.
Slow or Cold neutrons (K << 0.025 eV): they are in thermal equilibrium with a very cold environment (e.g. liquid Deuterium about ∼ 25K).
According to de Broglie relatioship the neautron wavelength is: λ = h
pn
(1.1) . where pn is the linear momentum of the neutron.
1.1 Neutron sources
Although nuclei created with excitation energy greater than the neutron binding energy can decay by neutron emission, these highly excited sates are not produced as a result of any convenient radioactive decay process. Consequently, practical isotope sources of neutrons does not exist as it happens with gamma-ray sources. The possible choices for radioisotope neutron sources are much more limited and are based on either spontaneous ssion or nuclear reactions for which the incident particle is the product of a conventional decay process.
1.1.1 Spontaneous ssion
Many of the transuranic heavy nuclides have an appreciable spontaneous ssion decay probability. Several fast neutrons are promptly emitted in each ssion event, so a sample of such a radionuclide can be a simple and convenient isotopic neutron source. Other products of the ssion process are the heavy ssion nuclei, prompt ssion gamma rays and induced beta and gamma activity. When used as a neutron source, the isotope is generally encapsulated in a su ciently thick container so that only fast neutrons and
Figure 1.2: Measured neutron energy spectrum from the spontaneous ssion of252Cf [8].
gamma rays emerge from the source.
The most common spontaneous ssion source is 252Cf. Its half-life of 2.65 years is long
enough to be reasonably convenient, and the isotope is one of the most widely produced of all the transuranics. The dominant decay mechanism is alpha decay, and the alpha emission rate is about 32 times that for spontaneous ssion. The neutron yield is 0.116 n/s per Bq, where the activity is the sum of both alpha and spontaneous ssion decay rates. On a unit mass basis, 2, 3 · 106 n/s are produced per microgram of the sample.
Compared with the other isotopic neutron sources described below,252Cf sources involve
very small amounts of active material (normally of the order of micrograms) and can therefore be made in very small sizes dictated only by the encapsulation requirements. The energy spectrum of the emitted neutrons is plotted in Fig. 1.2. The spectrum is peaked between 0.5 and 1 MeV, although a signi cant yield of neutrons extends to as high as 8-10 MeV. The shape of a typical ssion spectrum is approximately given by the expression: dN dE = E 1 2 e− E T (1.2)
where, for the spontaneous ssion of 252Cf, the constant T has a value of 1.3 MeV[42].
Each ssion yields approximately ∼ 3.8 neutrons and 9.7 gamma photons. Most (> 85%) of the latter are relatively high-energy prompt gamma rays that are emitted within the rst nanoseconds following the ssion event.
Figure 1.3: Thick target neutron yield for alpha particles on beryllium[4].
1.1.2 Radioisotope (α, n) sources
Because energetic alpha particles are available from the direct decay of a number of convenient radionuclides, it is possible to manufacture a small self-contained neutron source by mixing an alpha-emitting isotope with a suitable target material. Several dierent target materials can lead to (α, n) reactions for the alpha particle energies that are readily available in radioactive decay. The maximum neutron yield is obtained when beryllium is chosen as the target, and neutrons are produced through the reaction
4
2α + 94Be −→ 126 C + 10n
which has a Q-value of 5.71 MeV.
The neutron yield from this reaction when a beam of alpha particles strikes a target that is thick compared with their range is plotted in Fig. 1.3. Most of the alpha particles are stopped in the target, and only 1 in about 104 reacts with a beryllium nucleus.
Virtually the same yield can be obtained from an intimate mixture of the alpha particle emitter and beryllium, provided the alpha emitter is homogeneously distributed through-out the beryllium in a small relative concentration. All the alpha emitters of practical interest are actinides, and investigations have shown that a stable alloy can be formed between the actinide metal (M) and beryllium to the form MBe13. Most of the sources
described below therefore are metallurgically prepared in the form of this alloy, and each alpha particle has a chance to interact with beryllium nuclei without any intermediate energy loss.
sources are listed in Table 1.1. Several of these isotopes, notably 222Ra and 227Ac, lead
to long chains of daughter products that, although adding to the alpha particle yield, also contribute to a larger gamma-ray background. These sources are therefore inappro-priate for some applications in which the intense gamma-ray background interferes with the measurement. Also, these Ra-Be and Ac-Be sources require more elaborate handling procedures because of the additional gamma radiation hazard. The remaining radioiso-topes in Table 1.6 involve simpler alpha decays and the gamma-ray background is much lower. The choice between these alternatives is made primarily on the basis of availabil-ity, cost, and half-life. Because the physical size of the sources is no longer negligible, one would like the half-life to be as short as possible, consistent with the application, so that the speci c activity of the emitter is high. The 239Pu source is probably the most
Source Half life Eα [MeV]
Neutron yield per 106 Percent yield primary alpha particles with En < 1.5 MeV
Calculated Experimental Calculated Experimental
239Pu/Be 24000 y 5.14 65 57 11 9-33 210Po/Be 138 d 5.30 73 69 13 12 238Pu/Be 87.4 y 5.48 79a - - -241Am/Be 433 y 5.48 82 70 14 15-23 244Cm/Be 18 y 5.79 100b - 18 29 242Cm/Be 162 d 6.10 118 106 22 26 226Ra/Be 1602 y Multiple 502 - 26 33-38 + daughters 227Ac/Be 21.6 y Multiple 702 - 28 38 + daughters
aFrom Anderson and Hertz[4]. All other data as calculated or cited in Geiger and Van der Zwan[27].
bDoes not include a 4% contribution from spontaneous ssion of 244Cm.
Table 1.1: Characteristics of Be(α, n) neutron sources.
widely used of the (α, n) isotopic neutron sources. However, because about 16 g of the material are required for 1 Ci (3.7 · 1010 Bq) of activity, sources of this type of a few
centimeters in dimension are limited to about 107 n/s. In order to increase the neutron
yield without increasing the physical source size, alpha emitters with higher speci c ac-tivities must be employed. Therefore, sources incorporating 241Am (t
1/2 = 433 y) and 238Pu (t
1/2 = 87.4 y) are also widely used if high neutron yields are needed. Sources
utilizing 244Cm (t
1/2 = 18 y) represent a near ideal compromise between speci c activity
and source lifetime, but this isotope is not easily available.
The neutron energy spectra from all such α/Be sources are similar, and any dierences re- ect only the small variations in the primary alpha energies. A plot of the spectrum from a 239Pu/Be source is shown in Fig. 1.4. The various maxima and minima in this energy
Figure 1.4: Measured energy spectra of neutrons from a 80 g239Pu/Be source (Anderson
and Ne[5]).
distribution can be analyzed in terms of the excitation state in which the 12C daughter
nucleus is left. The alpha particles lose a variable amount of energy before reacting with a beryllium nucleus, however, and their continuous energy distribution washes out much of the structure that would be observed if the alpha particles were monoenergetic. For sources that contain only a few grams of material, the spectrum of neutrons that emerges from the source surface is essentially the same as that created in the (α, n) reactions. For larger sources, the secondary processes of neutron scattering within the source1 make the
spectrum shape dependent on source size[5].
Because larger activities of the actinide isotope are involved in these neutron sources, spe-cial precautions must be taken in their fabrication to ensure that the material remains safely encapsulated. The actinide-beryllium alloys are usually sealed within two indi-vidually welded stainless steel cylinders. Some expansion space must be allowed within the inner cylinder to accommodate the slow evolution of 3He gas formed when the alpha
particles are stopped and neutralized.
When applied to the e ciency calibration of detectors, some caution must be used in assuming that the neutron yield from these sources decays exactly as the half-life of the principal actinide alpha emitter. Small amounts of contaminanting alpha activity, present in either the original radioisotope sample or produced through the decay of a precursor, can in uence the overall neutron yield. For example, many 239Pu/Be sources have been
prepared from plutonium containing small amounts of other plutonium isotopes. The iso-tope241Pu is particularly signi cant, because it β-decays (t
1/2 = 13.2 y) into 241Am. The
neutron yield of these sources can therefore gradually increase with time as the 241Am
accumulates in the source. An original 241Pu isotopic fraction of 0.7% will result in an
initial growth rate of the neutron yield of 2% per year[6].
A number of other alpha-particle-induced reactions have occasionally been employed as neutron sources, but all have a substantially lower neutron yield per unit alpha activity compared with the beryllium reaction. Some of potentially useful reactions are listed in Table 1.2. Because all the Q-values of these reactions are less than that of the beryllium reaction, the resulting neutron spectra shown in Fig 1.5 have a somewhat lower average energy. In particular, the 7Li (α, n) reaction with its highly negative Q-value leads to a
neutron spectrum with a lower (0.5 MeV) average energy that is especially useful in some applications.
Target Reaction Q-Value [MeV] per 10Neutron yield6 alpha particles
Natural B 10B(α, n) +1.07 13 for 241Am alpha particles 11B(α, n) +0.158
F 19F(α, n) -1.93 4.1 for 241Am alpha particles
Isotopically separated 13C(α, n) +2.2 11 for 238Pu alpha particles
Natural Li 7Li(α, n) -2.79
Be (for comparison) 9Be(α, n) +5.71 70 for 241Am alpha particles Data from Lorch and Geiger and Van der Zwan.
Table 1.2: Various (α, n) isotopic neutron sources.
1.2 Neutron detection
Neutrons are elementary particles without electrical charge. Because of this they cannot directly produce ionization in a detector, and therefore cannot be directly detected. This means that neutron detectors must rely upon a conversion process where an incident neutron interacts with a nucleus to produce a secondary charged particle. These charged particles are then directly detected and presence of neutrons is inferred from them. Because the cross sections for neutron interactions in most materials strongly depend on neutron energy, rather dierent techniques have been developed for neutron detection in dierent energy ranges.
1.2.1 Nuclear reactions of interest in neutron detection
In searching for nuclear reactions that might be useful in neutron detection, several factors must be considered. First, the cross section for the reaction must be as large as possible so that e cient detectors can be built with small dimensions.This is particularly important for detectors in which the target material is incorporated as a gas. For the same reason, the target nuclide should either be of high isotopic abundance in the natural element, or
Figure 1.5: Neutron energy spectra from various (α, n) sources (7Li data from Geiger
and Van der Zwan[28], remainder from Lorch[42]).
alternatively, an economic source of arti cially enriched samples should be available for detector fabrication. In many applications, intense elds of gamma rays are also found with neutrons and the choice of reaction bears on the ability to discriminate against these gamma rays in the detection process. Of principal importance here is the Q-value of the reaction that determines the energy liberated in the reaction following neutron capture. The higher the Q-value, the greater is the energy given to the reaction products, and the easier is the task of discriminating against gamma-ray events using simple amplitude discrimination.
It is important to point out that all the common reactions used to detect slow neutrons result in heavy charged particles. Possible reaction products are listed below:
target nucleus + neutron −→ recoil nucleus proton alpha particle ssion fragments
All the conversion reactions are su ciently exothermic so that the kinetic energy of the reaction products is determined solely by the Q-value of the reaction and does not re ect the very small incoming energy of the slow neutron.
The distance traveled by the reaction products following their formation also has impor-tant consequences in detector design. If we are to capture the full kinetic energy of these products, the detector must be designed with an active volume that is large enough to fully stop the particles. If the detection medium is a solid, this requirement is easily
achieved because the range of any of the reaction products shown does not exceed a few tenths of a millimeter in any solid material. If the detection medium is a gas, however, ranges of the reaction products (typically several centimeters) can be signi cantly com-pared with detector dimensions and some may not deposit all their energy. If the detector is large enough so that these losses can be neglected, the response function will be very simple, consisting only of a single full-energy peak as shown in the sketch below.
Under these circumstances the detector would exhibit a very at counting plateau, and the ability to discriminate against low-amplitude events (such as gamma-ray-induced processes) would be maximized. If, on the other hand, a signi cant number of neutron-induced events do not deposit the full energy, a low-energy continuum is added to the pulse height distribution and the detector performance with respect to these criteria will worsen.
The 10B(n, α) reaction
Probably the most popular reaction for the conversion of slow neutrons into directly detectable particles is the 10B(n, α)reaction. The reaction may be written
10
5 B + 10n −→
(
7
3Li + 42α Q = 2.792MeV (ground state) 7
3Li ∗
+ 4
2α Q = 2.310MeV (excited state)
where the branching indicates that the reaction product 7Li may be left either in its
ground state or in its rst excited state. When thermal neutrons (0.025 eV) are used to induce the reaction, about 94% of all reactions lead to the excited state and only 6% directly to the ground state. In either case, the Q-value of the reaction is very large (2.310 or 2.792 MeV) compared with the incoming energy of the slow neutron, so that the energy imparted to the reaction products (7Li and α) is essentially just the Q-value
itself. Thus, the incoming kinetic energy of the neutron is overwhelmed by the much larger reaction energy, and it is impossible to extract any information about its original value. Also, because the incoming linear momentum is very small, the reaction products must also show a net momentum of near zero. Consequently, the two reaction products must be emitted in exactly opposite directions, and the energy of the reaction will always be shared in the same manner between them. Individual energies of the alpha particle
Figure 1.6: Cross section versus neutron energy for some reactions of interest in neutron detection.
and lithium nucleus can be calculated simply by conservation of energy and momentum as follows: ELi+ Eα = Q = 2.31MeV mLivLi = mαvα p 2mLiELi = p 2mαEα (1.3)
Solving Eqs. 1.3 simultaneously:
ELi=0.84 MeV and Eα=1.47 MeV
where the calculation has been carried out for the case of populating the excited state of
7Li.
Figure 1.6 is a plot of cross sections versus neutron energy for a number of nuclear reactions of interest in neutron detection. The thermal neutron cross section for the
10B(n, α) reaction is 3840 barns. The cross-section value drops rapidly with increasing
neutron energy and is proportional to 1/v (the reciprocal of the neutron velocity) over much of the range. The utility of this reaction stems from its rather large and structureless cross section and from the fact that boron, highly enriched in its 10B concentration, is
The 6Li(n, α) reaction
Another popular reaction for the detection of slow neutrons is the (n, α) reaction in 6Li.
Here the reaction proceeds only to the ground state of the product and is simply written as:
6
3Li + 10n −→ 31H + 10α Q = 4.78MeV
Calculation of the reaction product energies for negligible incoming neutron energy yields the following:
E3H = 2.73 MeV and Eα = 2.05 MeV
The alpha particle and triton produced in the reaction must be oppositely directed when the incoming neutron energy is low.
The thermal neutron cross section for this reaction is 940 barns. Figure 1.6 shows that the cross section remains below that for the 10B reaction up to the resonance region (>
100 keV). The lower cross section is generally a disadvantage but is partially oset by the higher Q-value and resulting greater energy given to the reaction products. 6Li occurs
with a natural isotopic abundance of 7.40% and is also widely available in separated form. The 3He(n, p) reaction
The gas3He is also widely used as a detection medium for neutrons through the reaction 3
2He + 10n −→ 31H + 10p Q = 0.764 MeV
For reactions induced by slow neutrons, the Q-value of 764 keV leads to oppositely directed reaction products with energies
Ep = 0.573 MeV and E3H = 0.191 MeV
The thermal neutron cross section for this reaction is 5330 barns, signi cantly higher than that for the boron reaction, and its value also falls o with a 1/v energy dependence (see Fig. 1.6).
Although3He is commercially available, its relatively high cost is a detrimental factor in
some applications.
1.2.2 Detectors based on the boron reaction
A widely used detector for slow neutrons is the BF3 proportional tube. In this device,
boron tri uoride serves both as the target for slow neutron conversion into secondary particles as well as a proportional gas. A number of other boron-containing gases have been evaluated, but BF3 is the near-universal choice because of its superior properties as
a proportional gas, as well as its high concentration of boron. In nearly all commercial detectors, the gas is highly enriched in 10B, resulting in an e ciency about ve times
greater than that within naturally occurring boron. Because the performance of BF3 as
a proportional gas is poor when operated at higher pressures, its absolute pressure in typical tubes is limited to about 0.5-1.0 atm.
BF3 Tube construction
The neutron detection e ciency can be increased and the wall eect suppressed by mak-ing the tube dimension larger. Similar improvements can be achieved by raismak-ing the pressure of the BF3 ll gas. Fowler[26] has reported the successful construction and
oper-ation of BF3 tubes with diameter up to 15 cm and 180 cm long. Filling pressure ranged
from 100 to 600 torr (approximately 13-80 kPa). Pressures in the range 200-300 torr (approximately 27-40 kPa) gave the best resolution in this work, whereas the full-energy peaks in the spectrum broadened considerably at higher pressure due to recombination and negative ion formation. In many counting situations, the poorer resolution is of no real consequence, and tubes with the higher gas pressure would be quite acceptable as long as a distinct counting plateau is maintained. Small-diameter tubes lled to several atmospheres pressure are commercially available, although pressures in the range 500-600 torr (approximately 67-80 kPa) are much more common.
In common with most proportional counters, BF3 tubes are universally constructed using
cylindrical outer cathodes and small-diameter central wire anodes. Aluminum is often the material of choice for the cathodes because of its low neutron interaction cross section. For low background applications, other materials such as stainless steel are preferred be-cause aluminum normally shows a small amount of low-level alpha activity. With typical anode diameters of 0.1 mm or less, operating voltages tend to be about 2000-3000 V. Larger-diameter anode wires and/or higher ll gas pressures require higher applied volt-ages. Typical gas multiplication at operating voltage is on the order of 100-500.
BF3 tubes of typical construction are normally limited to operating temperatures up to
about 100°C, but tubes of special design can extend the operating range to as high as 150°C. However, the pulse amplitude decreases and the pulse height resolution decreases sharply[51] when operated well above room temperature. These changes may be related to the possible desorption of impurities from the counter wall or other components at elevated temperatures.
Because of the relatively high operating voltages, BF3 tubes share some behavioral
qual-ities with other proportional counters. Spurious pulses of about the same size as signal pulses can sometimes arise from uctuations in leakage currents through insulators, es-pecially under conditions of high humidity. Spurious counts can also arise in applications in which the counter is subject to vibration or shock[49]. These eects are attributed to detector microphonics and the in uence of small particles of lint or dirt within the counter.
In common with other proportional counters, BF3 tubes show signi cant eects of aging.
In some cases[50] signi cant degradation in the performance is observed after operation of 1010-1011 registered counts. This degradation is likely related to the contamination of
the anode wire and cathode wall by molecular disassociation products produced in the avalanches. The same study indicates that 3He tubes described later are more resistant
Gamma-Ray discrimination
A very important consideration in many applications of BF3 tubes is their ability to
discriminate against gamma rays, which often are found together with the neutron ux to be measured. Gamma rays interact primarily in the wall of the counter and create secondary electrons that may produce ionization in the gas. Because the stopping power for electrons in gases is quite low, a typical electron will deposit only a small fraction of its initial energy within the gas before reaching the opposite wall of the counter. Simple amplitude discrimination can then easily eliminate these gamma rays without sacri cing neutron detection e ciency.
If the gamma-ray ux is su ciently high, however, several complications can reduce the eectiveness of this amplitude discrimination. At high rates, pulse pile-up can result in apparent peak amplitudes for gamma rays which are considerably larger than any indivi-ual pulse. Brown[15] discusses the compromise that must then be struck in choosing the pulse-shaping time constant in the detector electronics. Short time constants are desir-able to reduce the gamma-ray pile-up but may lead to reduction in the neutron-induced pulse amplitude due to incomplete charge integration. At very high gamma rates, there is evidence that chemical changes occur in the BF3 gas caused by molecular
disassocia-tion, leading to degraded pulse height spectra from neutron-induced events[58]. If this degradation is su ciently severe, it may no longer be possible to separate gamma- and neutron-induced events[20]. In extreme cases, the radiation-induced chemical changes can result in permanent damage to the tube. Verghese et a1.[59] report successful dis-crimination against gamma rays at exposure rates as high as 12 R/h (10.6 mGy/h in air) using a conventional BF3 tube. Developmental tubes that employ activated charcoal
within the tube to act as an absorbing agent for contaminants have been reported[55]. These tubes exhibit good operating characteristics in gamma-ray uxes up to 1000 R/h (∼ 1 Gy/h).
Detection e ciency of a BF3 tube
The detection e ciency for neutrons incident along the axis of a BF3 tube is given
approximately by
(E) = 1 − e−Σa(E)L (1.4)
where
Σa(E) = macroscopic absorption cross section of10B at neutron energy E
L = active length of the tube
Using Eq. 1.4, we nd that the calculated e ciency for a 30-cm long BF3 tube (96%
enriched in 10B) lled to 600 torr (80 kPa) is 91.5% at thermal neutron energies (0.025
eV) but drops to 3.8% at 100 eV. Thus, a BF3 tube exposed to neutrons with mixed
energies will respond principally to the slow neutron component. Equation 1.4 slightly overestimates the neutron counting e ciency because there usually are regions near the
end of the tube in which charge collection is ine cient, resulting in reduced neutron response. The in uence of these dead spaces is most severe for detectors whose length is small and has been the subject of experimental investigations that lead to a more precise prediction of detector e ciency[53]. End window designs are common in which the dead space and structural materials at one end of the tube are minimized.
Most practical BF3 counters are lled with pure boron tri uoride enriched to about
96% in 10B. However, because BF
3 is not ideal as a proportional counter gas, counters
are sometimes manufactured using BF3 with an admixture of a more suitable gas such
as argon. This dilution causes a decrease in detection e ciency, but the pulse height spectrum from the tube generally shows sharper peaks and consequently a more stable counting plateau than tubes lled with pure BF3.
Boron-lined proportional counters
An alternate approach is to introduce the boron in the form of a solid coating on the interior walls of an otherwise conventional proportional tube. This con guration has the advantage that a more suitable proportional gas than BF3 can now be used. Some
applications, particularly those in which fast timing is important, are better served by introducing one of the common proportional gases. Also, the chemical degradation prob-lems in BF3 when exposed to high gamma ray uxes can be greatly reduced by using
alternative ll gases.
Because the maximum range of the alpha particles from the boron reaction is on the order of 1 mg/cm2, the e ciency of boron-lined counters will improve only as the coating
thickness is increased to about this value. Making the deposit thicker will simply create layers in the coating that are too far from the lling gas to permit any reaction products to reach the gas, and the e ciency will actually begin to decrease slightly because of the added attenuation of the incident neutrons. Eorts have been made to increase the surface area available for coating by introducing boron-coated plates or ba es within cylindrical tubes, but these con gurations have not achieved widespread popularity. The pulse height spectrum to be expected from a boron-lined proportional chamber with a thick boron layer is sketched in Fig. 1.7. Because the interactions are now taking place in the wall of the chamber and the reaction products are oppositely directed, only one reaction product can be expected per interaction. If the alpha particle is directed toward the interior of the tube, the maximum energy it can deposit is its initial kinetic energy of 1.47 MeV. The actual alpha particle energy deposited in the gas will vary from this value down to zero as the possible location of the neutron interaction varies from the surface of the boron coating through those locations that are more than an alpha range away from the counter gas. Because all these locations are almost equally probable, the expected energy deposition distribution for alpha particles will be approximately rectangular in shape with a maximum at 1.47 MeV. This distribution is sketched in Fig. 1.7a as a dashed rectangle. A similar argument can be made for the lithium recoil nucleus, with its maximum possible deposited energy equal to 0.84 MeV. The sum of these two individual rectangular distributions is shown as the solid line in Fig. 1.7b and is a somewhat
ideal-ized indication of the expected pulse height spectrum from a boron-lined chamber with a thick (greater than 1 mg/cm2) boron lining. A dierential pulse height spectrum without
a "valley" structure does not lead to a counting plateau. Thus, it would be expected that boron-lined chambers would be less satisfactory than BF3 tubes in terms of long-term
counting stability. Because the average energy deposited for neutron interaction is also considerably less than for BF3tubes, the gamma-ray discrimination ability of boron-lined
chambers will be inferior to that of BF3 tubes.
1.2.3 The
3He proportional counter
With a cross section even higher than that of the boron reaction, the 3He(n, p) reaction
is an attractive alternative for slow neutron detection. Unfortunately, because 3He is
a noble gas, no solid compounds can be fabricated and the material must be used in gaseous form. 3He of su cient purity will act as an acceptable proportional gas, and
detectors based on this approach have come into common use. General properties of 3He
proportional tubes are reviewed in Ref. [48]. In a large detector, one would expect each thermal neutron reaction to deposit 764 keV in the form of kinetic energy of the triton and proton reaction products. Because the range of these reaction products is not always small compared with the dimensions of the proportional tube, however, the wall eect discussed earlier for a BF3 tube can also be important for3He proportional counters. The
expected pulse height spectrum for a tube of typical size is illustrated in Fig. 1.8. Only a single full-energy peak should be expected for neutron energies that are small compared with 764 keV.
The continuum in the pulse height spectrum due to the wall eect is detrimental from several standpoints. The voltage range over which an acceptable counting plateau will be observed is reduced, and the smaller pulse height for some neutron events will reduce the separation expected from low-amplitude, gamma-induced pulses. Consequently, consid-eration is often given in the design of3He tubes to minimize the wall eect. One obvious
step is to build the counter with a diameter as large as possible so that most neutron interactions occur far away from the wall. Another is to increase the pressure of the 3He
gas to reduce the range of the charged particle reaction products. Because of the low atomic mass of 3He, the ranges of the reaction products are unusually long and the wall
eect is considerably more signi cant than for a BF3 tube of the same size and ll gas
pressure. One method of reducing the charged particle ranges is to add a small amount of a heavier gas to the 3He to provide an enhanced stopping power. A detailed analysis
of the wall eect in 3He counters can be found in Ref. [54].
The rise time of the output pulse observed from either a BF3 tube or a 3He tube will
depend both on the position of the neutron interaction and the orientation of the charged particle tracks with respect to the tube axis. Since both of these quantities are ran-domly variable, substantial dierences are observed in the rise time of the pulses. In the example[21] shown in Fig. 1.9, the time to reach about 80% of nal amplitude ranged from 0.3 to 1.6 µs. These variations are the result of dierences in the drift times of the electrons from their formation along the particle tracks to the anode. The signi cant
(a)
(b)
Figure 1.7: Idealized pulse height spectra from a boron-lined proportional tube. (a) Separate contributions of alpha particles and lithium recoil nuclei, which add to give the spectrum shown in plot (b).
Figure 1.8: Expected pulse height spectrum from a 3He tube in which the wall eect is
signi cant.
Figure 1.9: Variation in the digitized pulse leading edge from a 3He tube due to
dier-ences in the orientation of the proton-triton tracks with respect to the anode wire (Dietz and Sosaat[21]).
charges that give rise to the output pulse are produced only in the avalanches around the anode wire. If the electrons all have the same drift time, then the avalanches are triggered at nearly the same time. If the electron arrivals are staggered because of dierent drift times, however, the avalanches are spread out in time and the pulse rise time is slower. In the same study, it was found that the full amplitude of the pulse was not realized until after about 50 µs. This slow component of the rise comes about because of the slow motion of the positive ions after they leave the immediate vicinity of the anode wire. In practical circumstances, a much shorter shaping time must be used to prevent pulse pile-up, and therefore conditions prevail in which there is a relatively large ballistic de cit. If the shaping times are chosen to be too small, the variability of the pulse rise time will also contribute to the ballistic de cit and will begin to broaden the peaks observed in the pulse height spectrum. If su ciently extreme, these changes will reduce the length of the counting plateau and diminish the ability to discriminate against gamma rays. Compared with BF3 tubes, 3He counters can be operated at much higher pressures with
acceptable gas multiplication behavior and are therefore preferred for those applications in which maximum detection e ciency is important. The lower Q-value of the3He reaction,
however, makes gamma-ray discrimination more di cult than for an equivalent BF3tube.
When the gamma irradiation rate is high, the pile-up of the resulting pulses can raise their amplitudes to the point that a clean separation from the neutron-induced pulses is no longer possible. To minimize the gamma-ray pile-up, the choice of a gas additive such as CO2 or Ar that speeds up the electron drift will allow the use of shorter shaping
times in the pulse processing electronics. Other factors that in uence the behavior of3He
tubes in high gamma-ray environments include the choice of wall material and/or the use of an activated carbon coating on the inner tube wall to adsorb gas impurities[9]. The acceptable operating temperature for3He tubes has been shown[51][29] to extend as high
as 200-250°C. In general, the pulse amplitude increases and the pulse height resolution decreases with increasing temperature, while the pulse rise time shows little temperature dependence.
As with all proportional counters, purity of the gas is critical, and the most typical cause of failure is leakage of air into the tube over long periods of time. Another factor is the buildup of electronegative poisons in the gas with use. As in BF3 tubes, a layer of
acti-vated charcoal within the tube has been shown to be eective in removing these poisons and can extend the useful lifetime of a3He detector[24].
1.2.4 Fast neutron detection
Conventional BF3 tubes have an extremely low detection e ciency for fast neutrons and
consequently are almost never used for this purpose. The BF3 proportional counter is
useful both for thermal neutron detection and for fast neutron spectroscopy. As a rule, however, fast neutron devices must employ a modi ed or completely dierent detection scheme to yield an instrument with acceptable detection e ciency.
The most important additional conversion process useful for fast neutrons is elastic neu-tron scattering. In this interaction an incident neuneu-tron transfers a portion of its kinetic
energy to the scattering nucleus, giving rise to a recoil nucleus. The energy that can be transferred from a slow neutron is therefore very small, and the resulting recoil nuclei are too low in energy to generate a usable detector signal. Once the neutron energy reaches the keV range, however, recoil nuclei can be detected directly and assume a large importance for fast neutron detection. By far the most popular target nucleus is hydro-gen. The cross section for neutron elastic scattering from hydrogen is quite large and its energy dependence is accurately known. More important, however, is the fact that an incident neutron can transfer up to its entire energy in a single collision with a hydrogen nucleus, whereas only a small fraction can be transferred in collisions with heavy nuclei. Therefore, the resulting recoil protons are relatively easy to detect and serve as the basis for a wide variety of fast neutron detectors.
An important distinction in the application of fast neutron detectors is whether an at-tempt is made to measure the energy of the incoming neutron. For all the slow neu-tron detection methods discussed, the information on initial neuneu-tron kinetic energy is hopelessly lost in the conversion process, because the neutron energy is extremely small compared with the energy liberated in the conversion reaction itself (the Q-value). Once the incoming neutron energy is no longer negligible compared with the reaction Q-value (that means at least 10-100 keV for most of the reactions discussed), the energy of the reaction products begins to change appreciably with changes in the neutron energy. An accurate measurement of the reaction product energies can then, in principle, be used to deduce the incoming neutron energy by simply subtracting the reaction Q-value. In elastic scattering the reaction Q-value is zero, so that neutron energies can begin to be measured by this technique at the point at which the resulting recoils have measurable kinetic energy. The collection of instruments and techniques applied to the measurement of fast neutron energy is conventionally included in the category of fast neutron spec-troscopy.
In some instances, however, the purpose of the measurement is simply to record the pres-ence of fast neutrons without a corresponding measurement of their energy. Such fast neutron counters can employ any of the methods discussed to convert neutrons to charged particles, and then simply record all pulses from the detector. Fast neutron counters of this type will have a severe variation in e ciency with neutron energy, but if the incident neutron energy is not likely to change greatly between measurements, they can provide useful information on the relative intensity of a fast neutron ux. Other applications in which the fast neutron spectrum may change considerably between measurements bene t from counters tailored to the application.
Counters based on neutron moderation
The inherently low detection e ciency for fast neutrons of any slow neutron detector can be somewhat improved by surrounding the detector with a few centimeters of hydrogen containing moderating material. The incident fast neutron can then lose a fraction of its initial kinetic energy in the moderator before reaching the detector as a lower-energy neutron, for which the detector e ciency is generally higher. By making the moderator
thickness greater, the number of collisions in the moderator will tend to increase, leading to a lower value of the most probable energy when the neutron reaches the detector. One would therefore expect the detection e ciency to increase with moderator thick-ness if that were the only factor under consideration. A second factor, however, tends to decrease the e ciency with increasing moderator thickness: The probability that an incident fast neutron ever reaches the detector will inevitably decrease as the moderator is made thicker.
Several eects are at work here, as illustrated in Fig. 1.10. As the detector becomes a smaller and smaller fraction of the total volume of the system, there will be a lower prob-ability that a typical neutron path will intersect the detector before escaping from the surface of the moderator. Furthermore, a neutron may be absorbed within the moderator before it has a chance of reaching the detector. The absorption probability will increase rapidly with increasing moderator thickness because absorption cross sections generally are larger at lower neutron energies.
As a result of all these factors, the e ciency of a moderated slow neutron detector when used with a monoenergetic fast neutron source will show a maximum at a speci c mod-erator thickness. Assuming that the modmod-erator is the usual choice of a hydrogenous material such as polyethylene or para n, we nd that the optimum thickness will range from a few centimeters for keV neutrons up to several tens of centimeters for neutrons in the MeV energy range.
If the thickness of the moderator is xed at a fairly large value, the overall counting e ciency of the system versus incident neutron energy will also tend to show a maxi-mum. Low-energy neutrons will not penetrate far enough into the moderator before they are likely to be captured in the moderator itself, whereas high-energy neutrons will not be adequately moderated for e cient detection. By careful choice of the diameter and composition of the moderator-detector system, its overall e ciency versus energy curve can often be shaped and tailored to suit a speci c application.
The spherical moderator systems are generally known as Bonner spheres after one of the authors (T. W. Bonner) of the original paper describing its experimental investigation. More recent work[33][47] has reexamined the response of spherical moderators used in combination with several dierent thermal neutron detectors, both experimentally and by neutron transport calculational techniques.
Hankins[30][31] rst chose to study the response of a 10-in. diameter (25.40 cm) sphere used with a 4 × 4 mm2 lithium iodide scintillator.The moderator size was selected as that
likely to give the closest t between the e ciency and the dose equivalent per incident neutron over a wide range of neutron energy. Figure 1.11 shows the estimated response of the 10-in. sphere detector together with the dose per neutron curve. Obviously, the match is quite good over several decades of neutron energy. Below 100 keV, direct mea-surements of the detector e ciency are di cult. A neutron transport code can be applied to calculate the detector response over this energy range, and these results are included in Fig. 1.12. The calculations con rm the good match between the two curves above 100 keV and at thermal energy but show a sizable deviation in the intermediate energy range
Figure 1.10: Schematic representation of neutron histories in moderated detectors. The small thermal neutron detector at the center is shown surrounded by two dierent thick-nesses of moderator material. Histories labeled 1 represent incident fast neutrons that are successfully moderated and detected. Those labeled 2 are partially or fully moderated but escape without reaching the detector. History 3 represents those neutrons that are parasitically captured by the moderator. Larger moderators will tend to enhance process 3 while reducing process 2.
Figure 1.11: Sensitivity of a 10 in. (25.4 cm) diameter moderating sphere surrounding a 4 × 4 mm2 LiI scintillator. Also shown is the relative dose per neutron labeled "inverse
of RPG curve." (From Hankins[30]).
Figure 1.12: Calculated sensitivity of a 10-in. (25.4 cm) diameter moderating sphere, together with the relative dose per neutron (inverse of RPG curve). (From Hankins[30])
between 0.1 eV and 100 keV. The deviation is such as to lead to an overestimate of the neutron dose if the spectrum contains a signi cant component over this energy range. Although the deviation at 10 keV is as much as a factor of 5, measurements made when the neutron spectrum covers a broad range in energies will show a considerably lower average deviation.
An alternate version of the spherical neutron dosimeter developed by Leake[40] is shown in Fig. 1.13. This design has come to be widely implemented as the Harwell type 95/0075 neutron survey meter. A spherical3He proportional counter is substituted for the lithium
iodide scintillator as the slow neutron detector. This substitution is made to minimize the response of the detector to gamma rays, and Leake reports application of the dosimeter in gamma-ray elds as high as 20 R/h. Used with a simple 20.8-cm diameter polyethy-lene moderator, the energy response of the system to thermal and epithermal neutrons is higher than ideal. Therefore, a spherical cadmium absorber, perforated with holes, is placed around the 3He detector to shape the response curve. Although the instrument
still overresponds to neutrons in the keV energy range (by a factor of 4.9 at 10 keV), the response to broad neutron spectra typical of shielded ssion sources does not deviate by more than ±40% for a very wide range of experimental and calculated spectra[32][41]. The response at high neutron energies drops o somewhat; the instrument underestimates the dose from 14 MeV neutrons shielded by concrete by about a factor of 2[32].
There have been continuing eorts to develop new designs of spherical or cylindrical neu-tron dosimeters[11][37] whose sensitivity more closely matches the dose per neuneu-tron curve over a wide energy range. Some of the challenge comes about because of evolving stan-dards for quality factors that are necessary inputs in calculating the desired curve shape. The incorporation of lead or other high-Z elements as heterogeneous components[13][35] increases the relative response to high-energy neutrons, where the response of a pure moderator tends to fall o. Secondary neutrons produced in (n, 2n) and other multiply-ing reactions in these heavy elements at high energies can extend the useful sensitivity to several hundred MeV.
1.3 Neutron dosimetry
When in a certain region of space radiation of any kind propagate, it is said that this region is the seat of a radiation eld, described by eld quantities. A simple way to describe the radiation eld consists in counting the number of particles that pass through a sphere of maximum section dA in a nite time interval. We de ne uence of the radiation eld the number of particles dN crossing the sphere during the measurement time: Φ = dN dA particle cm (1.5) The uence rate is the time derivative of the uence:
φ = dΦ dt particle cm s (1.6)
Figure 1.13: A spherical neutron dosimeter based on a 3He neutron detector (From
Leake[40]).
Another important quantity is the stopping power, which is the rate at which a particle loses kinetic energy per unit path lenght when attraversing a medium:
S = −dE dx M eV cm (1.7) frequently used is the mass stopping power:
S ρ = − dE ρdx M eV g/cm2 (1.8) which does not depend on the density of the medium.
The purpose of dosimetry is to identify and measure physical quantities that correlate with biological eects of ionizing radiation.
The oldest dosimetric quantity is the exposure, and it was introduced to describe the ability of electromagnetic radiation to produce ionization in air
X = dQ
dm (1.9)
where dQ is the absolute value of the total charge of the ions, produced in the air when all the charges (positive ions and electrons) released by the photons in the element of volume of mass dm are completely stopped in the air. The unit of exposure in the International Sistem of Units (SI) is the C kg−1. For historical reasons, the most widely used exposure
unit is still the old special unit, the roentgen (R), where 1R = 2.58 × 10−4Ckg−1.
We de ne the absorbed dose as:
D = d¯
where d¯ is the mean energy imparted2 by ionizing radiation to a volume element of mass
dm.
In the same manner we can de ne the kerma as: K = dtr
dm (1.11)
where dtr is the sum of the initial kinetic energy of all the charged ionizing particles
liberated by uncharged ionizing particles within dm.
For purposes of radiation protection it is useful to de ne a mean absorbed dose to tissue or organ, called organ dose
DT =
dT
dm (1.12)
Where T is the total energy imparted in a tissue or organ and mT is the mass of that
tissue or organ. The unit of measurement of dose is the gray (1 Gy = 1 J/kg).
L∞(keV · µm−1) Q(L)
L < 10 1
10 ≤ L ≤ 100 0.32L − 2.2 L < 100 300L−1/2
Table 1.3
The probability of stochastic eects3 depends not only on the absorbed dose, but also
on the type and energy of radiation. This fact is taken into account by weighting the absorbed dose by a factor related to the quality of radiation. In the past this factor has been applied to the absorbed dose in a point and was called quality factor (Q) related to radiation LET (see section 1.3.1 and table 1.3)(ICRP 26). This factor is now called weighting factor of radiation wR and depends on the type and energy of radiation (ICRP
60). We de ne the equivalent dose: HT =
X
R
wRDT,R (1.13)
where DT ,R is the absorbed dose averaged over tissue or organ T, due to radiation R. The
value of the radiation weighting factor is indicative of the relative biological eectiveness value of that radiation to induce stochastic eects at rrelatively low doses. The unit of measurement of equivalent dose is the sievert (Sv), whose dimensions are the same as the gray.
2The energy ¯ imparted to a medium is the energy spent to produce ionizations and excitations within
that medium
3The stochastic eects of ionizing radiations consist of mutations in the exposed cells which may lead
Type and energy range Weighting factor
Photons of all energies 1
Electrons and muons of all energies 1 Neutrons, of energy < 10 keV 5 Neutrons, of energy from 10 keV to 100 keV 10 Neutrons, of energy from 100 keV to 2 MeV 20 Neutrons, of energy from 2 MeV to 20 MeV 10 Neutrons, of energy > 20 MeV 5 Alpha particles, ssion fragments, heavy nuclei 20
Protons, of energy > 2 MeV 5
Table 1.4: All values are related to the incident radiation on body or, for inside sources, emitted from the source.
The relationship between the probability of stochastic eects and the equivalent dose also depends on the organ or the tissue irradiated. The equivalent dose in tissue or organ T is then weighed with the tissue weighting factor, wT, representing the contribution of that
organ or tissue to the total detriment resulting from uniform irradiation of the whole body. Then we can de ne eective dose as the sum of the weighted equivalent doses in all the relevant tissues and organs of the body:
E =X
T
wTHT (1.14)
where HT is the equivalent dose in tissue or organ T and wT is the weighting factor for
the tissue T. The values of wT are chosen so that a equivalent uniform dose over the
entire body gives an eective dose numerically equal to the equivalent uniform dose. The sum of the weighting factors is therefore equal to 1 (see table 1.5).
1.3.1 High LET radiation
Although all ionizing radiations interact with living matter in a similar manner, dierent types of radiation dier in their eectiveness, or ability to cause harm in a biological system. The various radiations, in fact, interact with matter in a dierent way depending to the amount of energy deposited along their path.
The transfer of energy of the radiation is de ned by the LET (linear energy transfer) and denoted by the symbol L∆
L∆= dE dl ∆ (1.15) where dE is the local energy loss due to collisions of charged particles along a track seg-ment of length dl, considering only collisions involving transfer of energy less than ∆. L∆
Organ or tissue Weighting factor
Gonads 0.20
Red bone marrow 0.12
Colon 0.12 Lung 0.12 Stomach 0.12 Bladder 0.05 Breasts 0.05 Liver 0.05 Esophagus 0.05 Thyroid 0.05 Skin 0.01 Bone surface 0.01
Remaining organs and tissues 0.05
Table 1.5: The values were derived from a reference population, comprising an equal number of individuals of both sexes and a wide range of ages. The values apply to workers, to population and to both sexes.
High LET means high speci c ionization per unit path length. A particle can have a low LET at high energy and a high LET at low energy.
Low-LET radiations have tracks with primary events (collisions) well separated in space; it is the case of X-rays, which are said to be sparsely ionizing.
High-LET radiations have tracks with primary events not well separated in space, a dense ion-ization column is produced; it is the case of ions and heavy particles, which are said to be densely ionizing.
Figure 1.14: The LET at wich the RBE reaches a peak is much the same (about 100 keV /µm) for a wide range of mammalian cells; as the LET increases, the RBE increases slowly at rst, and then more rapidly as the LET increases beyond 10 keV/µm. Beyond 100 keV/µm, the RBE falls again to lower values. In the case of sparsely ionizing X-rays the probability of a single track causing a DSB is low, thus X-rays have a low RBE. At the other extreme, densely ionizing radiation (ex. LET of 200 keV/µm) readily produce DSB, but energy is "wasted" because the ionizing events are too close together; thus, RBE is lower than optimal LET radiation.
Densely ionizing radiations have a high probability to induce double strands break (DSB) in the DNA double helix. With respect to a single strand break (SSB), this kind of dam-age, which interests two close and separated strands of DNA, is more di cult to repair, and repair itself is prone to errors, giving rise to genetic mutations.
Therefore, for a given absorbed dose radiation with dierent LET lead to dierent bio-logical eects and to take account of this fact the relative biobio-logical eectiveness (RBE) has been introduced. The intent is to quantify the eects, at the same absorbed dose, of a radiation r with respect to a reference radiation, which is assumed to be that of X-rays at 250 kV. By this de nition, the reference radiation has RBE equal to 1. In this way, RBE quanti es the increment of biological eects of highly ionizing radiations with respect to X-rays at the same absorbed dose.
Accordingly, the RBE of some test radiation r compared with X-rays is de ned as the ratio:
RBE = D250
Dr (1.16)
where D250 and Dr are respectively, the doses of X-rays of 250 kV, and the test radiation
required for equal biological eect. The higher the LET, the higher the biological eec-tiveness (RBE), as it is shown in Fig. 1.14 for radiations of dierent LET.
Although neutrons are uncharged particles, they are considered highly penetrating and are classi ed as high LET radiation.
Figure 1.15: Neutron weighting factors in function of energy for ICRP 60 and ICRP 103 (recommended).
Neutron weighting factors
The values of the weighting factors introduced by the ICRP 60 are reported in table 1.4. For neutrons ICRP 60 suggests the stepwise function of gure 1.15 which can be tted by the analytical relationship:
wR= 5 + 17 e−
[ln(2E)]2
6 (1.17)
where E is the neutron energy.
In 2007 the ICRP, in its publication 103, partially revised the neutron weighitng factor according the following equation:
wR= 2.5 + 18.2 e−[ln(E)]26 if E < 1 MeV
5 + 17 e−[ln(2E)]26 if 1 MeV ≤ E ≤ 50 MeV
2.5 + 3.25 e−[ln(0.04E)]26 if E > 50 MeV
(1.18)
The most signi cant change concerns the decrease of the wR coe cient at low energy
range and for energy values above 100 MeV.
1.3.2 Operational dose quantities
Both HT and E are not measurable quantities. Therefore, strictly speaking, they are
not physical quantities. One can give an estimate of HT, and hence of E, only through
and E for a given individual can never be measured. The result of this simulation are conversion coe cients that allow to convert measurable quantities ( air kerma, dose-area product..etc) into dosimetric quantities. But this only holds for the reference person represented by this particular phantoms.
Operational dose quantities were introduced to convert a measurable eld quantity into a surrogate of eective dose. This quantities must ful ll the following requirements[2]
1. be measurable and applicable for any kind of radiation and without the request to specify the type of radiation, when the value is provided;
2. be de ned with reference to measurement conditions well speci ed (speci cation of the measurement point in a given reference medium) both in the calibration phase and in the operational measure;
3. provide directly a precautionary estimate, but not an excessive overestimation, of the protection reference quantity (HT or E).
A group of operational dosimetric quantities characterized by these properties has been elaborated (and accepted internationaly) by the International Commission on Radiation Units and Measurements (ICRU) for two types of measurement: area monitoring and individual monitoring. In particular, the ambient dose equivalent, H∗(10), and the
di-rectional dose equivalent, H0(d), are the operational dose quantities for area monitoring,
while for individual monitoring the operational dose quantity is the personal dose equiva-lent Hp(d). The advantage of these operating quantities lies in the fact that they satisfy
the above mentioned 1), 2) and 3) requirements and that they can be correlated to eld and dosimetric quantities, such as uence and air kerma. Such correlation is important since the basic dose quantities are the only ones to have primary measurement standards and this is an essential requirement to be able to calibrate the measuring instruments of the operative dose quantities.
The operational dose quantities must have the same dependence on variables like inci-dence angle and radiation energy as HT and E in the dierent irradiation conditions (i.e.
antero-posterior, lateral, isotropic...etc). The values of HT and of E in fact depend on the
orientation of the exposed phantom in the radiation eld and the penetrating character of radiation. The requirement of measurability and the need of calibrating instrument of such quantities implies that operational dose quantities at a given point in a medium are therefore associated with average value in a volume.
Ambient equivalent dose
The ambient equivalent dose, H∗(d), is the operational dose quantity that is used to
estimate eective dose in area monitoring with strongly penetrating radiation. Neutrons, photons with energy greater than 15 keV and beta radiation with energy greater than 2 MeV are typically considered strongly penetrating radiations[2].
Figure 1.16: The ICRU sphere is exposed to an aligned and expanded radiation eld. The point at which the environmental dose equivalent H∗(d) is determined is found at
the depth d in the sphere along the radius of the sphere opposite to the eld alignment direction. The aligned and expanded eld is a unidirectional eld having the same uence and the same energy distribution that has the real eld at the point at which H∗(d) is
referred to (the point where the detector with which one performs the measure is placed).
Ambient equivalent dose H∗(d) at a point in a radiation eld is the dose equivalent that
would be produced by the corresponding expanded and aligned eld in the ICRU sphere at a depth, d, on the radius opposing the direction of the aligned eld4.
The meaning of H∗(d)is illustrated in gure 1.16. The recommended depth value d is 10
mm. So for area monitoring the quantity used for strongly penetrating radiation is the ambient dose equivalent H∗(10).
Since by its de nition H∗(10)does not depend on the direction of the incident radiation,
the instruments used for the measurement of this quantity must also have an answer as independent as possible from the orientation in the radiation eld. The greater is the ra-diation energy, the more isotropic is the detector response. Therefore the use of H∗(10)is
limited to strongly penetrating radiation. The expansion and alignment of the radiation eld are not necessary in real measurement conditions. This is a condition required only on a theoretical level, to de ne the quantity H∗(10) and when one wants to calculate the
values of H∗(10) in the point of interest in the ICRU sphere, as a function of the energy
of a given type of radiation. These values provide the conversion factors to be used when calibrating the instrument. Of course, even during calibration it is important that the radiation beams used are as "aligned" and "expanded" as possible.
The ambient equivalent dose is a quantity that provides a reasonable estimate of the eective dose, the quantity which expresses the radioprotection dose limits. This esti-mate is more or less accurate depending on the type and energy of the radiation and the irradiation conditions (in particular the radiation angle of incidence).
In practice, ambient radiation does not have a privileged direction, nor does the individual in the radiation eld possess it. In most of the irradiation conditions the ambient
Figure 1.17: Ambient equivalent dose H∗(10) (full line) and eective dose E (dotted
line) dependence from photon energy in a typical irradiation condition (incident radiation in front of the whole body). The values of H∗(10) and of E are normalized to air kerma
Ka of photons. In the photon energy range of greatest interest in radioprotection (below
1 MeV), the ambient equivalent dose overestimates the eective dose, but has the same trend as a function of energy (see ICRU 1998).
lent dose H∗(10)overestimates the eective dose E, as shown in gure 1.17 concerning an
irradiation situation with photons. The few exceptions in which H∗(10) underestimate
E mainly relate to neutron exposures (Fig. 1.18). In approximating the eective dose it is generally preferable to overestimate rather than underestimate. An overestimation is indeed more precautionary from a protectionist point of view as it leads to implemen-tation of precautions (such as shielding) that are more eective than would actually be necessary.
Figure 1.18: Ambient equivalent dose H∗(10) (full line) and eective dose E (dotted
line) dependence from neutron energy in a typical irradiation condition (incident radiation in front of the whole body). The values of H∗(10) and E are normalized to the neutron
uence Φ. In the neutron interval of energy between 0.01 eV and 1 eV, the ambient equivalent dose overestimates the eective dose, but has the same trend as a function of energy. The ambient equivalent dose underestimates instead the eective dose in the energy range between 1 eV and 100 keV and in the range between ∼ 1 MeV and 40 MeV (see ICRU 1998).
