Neutron Detection

Abstract

A neutron has no electric charge and therefore leaves no trace in matter except when it undergoes a nuclear interaction. All detection of neutrons is therefore based on letting the neutron interact and observing the charged reaction products. The detection of high-energy neutrons was discussed in Sect. 6.6. The present chapter deals with the detection of neutrons at nuclear energies, i.e. neutrons with a kinetic energy less than a few 10 MeV. Because the neutron interaction cross sections in most materials are very strongly dependent on the energy, different methods are used for neutrons of different energies. In many applications, the neutrons have to be detected in the presence of a large gamma ray background. The issue therefore often is distinguishing the neutrons from the gamma rays.

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A neutron has no electric charge and therefore leaves no trace in matter except when it undergoes a nuclear interaction. All detection of neutrons is therefore based on letting the neutron interact and observing the charged reaction products. The detection of high-energy neutrons was discussed in Sect. 6.6. The present chapter deals with the detection of neutrons at nuclear energies, i.e. neutrons with a kinetic energy less than a few 10 MeV. Because the neutron interaction cross sections in most materials are very strongly dependent on the energy, different methods are used for neutrons of different energies. In many applications, the neutrons have to be detected in the presence of a large gamma ray background. The issue therefore often is distinguishing the neutrons from the gamma rays.

The present chapter is for a large part based on [1] in Chap. 1 where a more extensive discussion of the subject can be found.

7.1 Slow Neutron Detection

The term ‘slow neutrons’ refers to neutrons with a kinetic energy of less than 0.5 eV. In this energy range, a very important reaction is the neutron capture. Some isotopes have very large neutron absorption cross sections and all slow neutron detection will be based on using one of these isotopes. The most important isotopes for this purpose are

Boron-10. The neutron absorption reaction is

$$\begin{array}{l@{\quad}l} {{}_5^{10} {\rm{B}} + {}_0^1 {\rm{n}} \to {}_3^7 {\rm{Li}} + {}_2^4 \alpha } & {Q = 2.792\,{\rm MeV}} \\ {{}_5^{10} {\rm{B}} + {}_0^1 {\rm{n}} \to {}_3^7 {\rm{Li^*}} + {}_2^4 \alpha } & {Q = 2.310\,{\rm MeV}} \\\end{array}$$

The symbol Q stands for the difference in mass between the particles in the initial and the final state and therefore for the total energy liberated in the reaction. The exited state ⁷Li^* decays with emission of a gamma ray with a lifetime of ≈10⁻³ s. Usually, this gamma ray escapes unobserved from the detector. For thermal neutrons, the second reaction has a branching fraction of 96%.

Energy-momentum conservation applied to the reaction above requires

$$\begin{array}{l} E_{Li} + E_\alpha = Q \\ m_{Li} \nu _{Li} = m_\alpha \nu _\alpha \\ \end{array}$$

From this we readily get

$$\begin{array}{l} E_{Li} = \dfrac{{m_\alpha }}{{m_\alpha + m_{Li} }}Q = 0.84\,{\rm MeV} \\ E_\alpha = \dfrac{{m_{Li} }}{{m_\alpha + m_{Li} }}Q = 1.47\,{\rm MeV} \\ \end{array}$$

Two final state objects, the ⁷Li^* nucleus and the alpha particle, are almost exactly back-to-back. The cross section for this reaction as a function of energy is shown in Fig. 7.1. The natural abundance of ¹⁰B is 19.9%.

Fig. 7.1

Neutron capture cross sections versus neutron energy for ¹⁰B, ⁶Li and ³He. The data for this figure were obtained from [8] in Chap. 1

Lithium-6. The neutron absorption reaction is

$$\begin{array}{l@{\quad}l} {{}_3^6 {\rm{Li}} + {}_0^1 {\rm{n}} \to {}_1^3 {\rm{H}} + {}_2^4 \alpha } & {Q = 4.78\,{\rm MeV}} \\\end{array}$$

The cross section for this reaction is also given in Fig. 7.1. The natural abundance of ⁶Li is 7.4% and lithium is available in an isotopically enriched form.

Helium-3. The neutron absorption reaction is

$$\begin{array}{l@{\quad}l} {{}_2^3 {\rm{He}} + {}_0^1 {\rm{n}} \to {}_1^3 {\rm{H}} + {}_1^1 p} & {Q = 0.764\,{\rm MeV}} \\\end{array}$$

The natural abundance of ³He is extremely low; only 0.000137% of all naturally occurring helium is ³He! Commercial ³He is made in nuclear reactions. The neutron absorption cross section of ³He is shown in Fig. 7.1.

Gadolinium-157. The isotope ¹⁵⁷Gd has a very large capture cross section for thermal neutrons: 255,000 barns! The natural abundance of ¹⁵⁶Gd is 15.7%. There are several final states containing gamma rays and conversion electrons. A 72 keV conversion electron is present in 39% of the neutron capture events and neutron detection is usually based on the observation of this final state electron. The gadolinium reaction will not allow easy discrimination between neutrons and gamma rays, since an electron from a gamma interaction will not easily be distinguished from the conversion electron. Gadolinium can only be used when gamma rejection is less important.

Uranium and plutonium. The fission cross sections of ²³³U, ²³⁵U and ²³⁹Pu are large for slow neutrons (see http://Fig. 2.19). These reactions can therefore be used for slow neutron detection. The Q value in these reactions is always very large, typically 200 MeV, allowing easy discrimination between gamma rays and neutrons. However, these nuclei are all alpha emitters and this can give rise to pulses that may be confused with neutron capture events. One needs to rely on pulse height discrimination to distinguish the neutron events from alpha emissions.

Proportional tubes using one of the above neutron capture reactions are commonly used for slow neutron detection. Either a gas containing ¹⁰B or ³He can be used, or a tube lined with ¹⁰B or with one of the fissile isotopes ²³³U, ²³⁵U or ²³⁹Pu. These counters will also be sensitive to gamma rays, because the gamma rays will interact in the walls of the tube and produce electrons in the active gas volume. Such an electron will deposit about 2 keV/cm of gas and therefore a gamma ray will almost never deposit more than a few 10 keV in the counter. The neutron capture cross sections considered above give rise to very ionising alpha particles or nuclei and the range of these in the counter gas is of the order of centimetres. One or both of the fragments will usually deposit all their energy in the gas. If individual pulse heights are recorded, these detectors are therefore very efficient in discriminating between neutrons and gamma rays. This is illustrated in Fig. 7.2.

Fig. 7.2

Gamma interactions and neutron interactions in a proportional counter filled with ³He or BF₃. A neutron interaction gives rise to two very ionising tracks, while a gamma ray will usually interact in the walls of the detector and give rise to a minimum ionising track

Only BF₃ or ³He are used as active chamber gas in the proportional tubes. ³He with ≈5% of quenching gas is a good working gas in a proportional counter. The detector will also work well at a pressure of several bar. Increasing the pressure is often used to increase the neutron detection efficiency. The mean free path of thermal neutrons in ³He at one atmosphere is 7.3 cm (see Exercise 2). However, the lower Q value compared to boron makes distinguishing neutron interactions from gamma interactions more difficult with ³He. Moreover, ³He is expensive; commercial ³He is made in nuclear reactions and its price was approximately 200 €/litre of gas at standard temperature and pressure in 2008.

BF₃ is not a very good working gas for a proportional counter, probably because BF₃ is slightly electronegative. Often tubes filled with BF₃ are used at reduced pressure where the operating conditions are more stable. BF₃-filled proportional tubes are also prone to ageing. Furthermore, this gas is very toxic and is also corrosive. However, the high Q value of this reaction helps in distinguishing neutron interactions from gamma interactions.

If the diameter of the tube is very large compared to the typical range of the reaction products in the gas, nearly all the interactions give rise to the same pulse height. In this case, the pulse height spectrum in ³He shows one clear peak and BF₃ it shows two peaks corresponding to the two reaction channels. The range of the reaction products in the gas is of the order of centimetres and the proportional tubes are usually only a few centimetres in diameter. As a result, one of the reaction products will often hit the wall of the tube before it reaches the end of its range. The result is a pulse height spectrum showing a broad shoulder below the total absorption peak as illustrated in Fig. 7.3. This reduces the ability to discriminate between gamma rays and neutrons.

Fig. 7.3

Pulse height spectrum in a proportional tube filled with BF₃ exposed to a neutron flux. The step structure is due to one of the reaction products hitting the wall of the tube before it reaches the end of its range. The figure to the right shows a neutron interaction in a proportional tube where the reaction is fully contained in the active gas of the chamber. Such an event would be in the total absorption peak at the right of the pulse height spectrum

An alternative approach is to line the inner walls of the proportional tube with a suitable neutron-sensitive material. In this case, any proportional chamber gas, such as argon–isobutane can be used. For lining the inner wall of the detector, ¹⁰B is often used. Obviously, the layer of ¹⁰B should be very thin (about 1 mg/cm²), otherwise the reaction products will be absorbed in the ¹⁰B layer itself and not enter into the active gas of the counter. As a result, the detection efficiency for neutrons of this type of detector is only of the order of 1%, much lower than what can be achieved with a neutron-sensitive gas. The pulse height spectrum obtained with such a chamber will be more or less flat from zero to a maximum value corresponding to1.47 MeV. This is the maximum energy the alpha particle can deposit in the gas. Because of this flat pulse height spectrum, this type of detectors is less efficient in discriminating between neutrons and gamma rays.

One of the big limitations of proportional counters used as neutron detectors is the slow rise-time of the pulse and the concomitant poor time resolution. This rise-time is often several microseconds. A good time resolution is essential in some applications, for example for ‘time of flight measurements’.

When a good time resolution is important, neutron-sensitive scintillators are preferred. A commonly used neutron-sensitive scintillator is LiI doped with ≈1% of europium. The lithium provides the neutron sensitivity. This scintillator material is somewhat similar to NaI:Tl. It has a light yield of about 14,000 photons/MeV and a decay time of 300 ns. LiI is also very hygroscopic. Other scintillator materials that are often used are a scintillator made from fusing B₂O₃ and ZnS and a plastic scintillator based on boron-loaded plastic. Such boron-loaded plastic scintillators are commercially available with 5% of boron content and with a light yield that is 75% of a typical plastic scintillator.

7.2 Neutron Detectors for Nuclear Reactors

In nuclear reactors, most of the power is generated through fission induced by slow neutrons. It is therefore important for the reactor control to measure the slow neutron flux in the reactor. It is customary to distinguish between ‘in-core’ detectors and ‘out-of-core’ detectors. Particularly, in-core detectors must work at very high neutron fluxes, at very high temperature and need to be very small.

For reactor monitoring, gas-filled detectors are almost always used because of the low gamma sensitivity and the good radiation hardness of this type of detector.

In Sect. 7.1, we have considered proportional counters working in the pulse-readout mode. The big advantage of the pulse-readout mode is that it allows a very good rejection of the gamma rays based on pulse height. However, at event rates exceeding ≈10⁶ counts/s, it becomes very difficult to use the pulse-readout mode. In addition, at very large fluxes it is impossible to use detectors with gas amplification, because the space charge due to the positive ions in the tube becomes so large that it introduces strong non-linear effects. The only possibility is to use gas chambers working in the ionisation mode and measuring the ionisation current; therefore, the detector becomes much more sensitive to gamma radiation. Some gamma rejections can be obtained by measuring the fluctuations on the detector current. This is the ‘Campbell technique’ and is discussed in Sect. 8.6. Another way to correct for the gamma background is by using two identical ionisation chambers, one detector lined with a neutron-sensitive layer and a second identical detector but without a neutron-sensitive layer. The two chambers have the same sensitivity to gamma rays. The difference between the ionisation currents in both detectors gives the neutron-induced signal.

In pressurised water reactors (PWR), the routine monitoring of the neutron flux is usually done with ‘out-of-core’ detectors. In addition, there are usually in-core detectors for fuel management. The out-of-core detectors measure neutron fluxes in the range 0–10¹⁰ neutrons/cm²/s. In boiling water reactors, there are usually in-core detectors. These work in the range 10⁴–10¹⁴ neutrons/cm²/s. There are usually different detectors for the start-up of the reactors, for monitoring during full power operation and for the intermediate regime. The neutron flux ranges for these different detectors are illustrated in Fig. 7.4. In the start-up regime the neutron fluxes are low, but the gamma fluxes are relatively high and good gamma rejection is essential. Detectors working in pulse readout mode are normally used. At full power the neutron fluxes are always very large and only detectors working in the current readout mode can be used. The gamma flux in the core of a reactor working at full power is typically 10⁸ R/h (R stands for roentgen, see Sect. 3.2).

Fig. 7.4

Typical neutron flux ranges seen by in-core and out-of-core neutron detectors in nuclear reactors. The unit in this figure is number of neutrons per cm² and per second

A typical in-core neutron detector for a boiling water reactor is the fission chamber shown in Fig. 7.5. A small cylindrical gas volume is filled with argon at a pressure of several atmospheres. The walls of the chamber are lined with highly enriched ²³⁵U₃O₈. One difficulty with these devices is the burn-up of the neutron-sensitive material. One year of operation will typically correspond to an integrated neutron flux of 1.7 10²¹ and a reduction of the signal by as much as a factor of two has been reported when simple lining with ²³⁵U₃O₈ is used. One method for reducing the effects of burn-up in fission chambers is to combine fertile and fissile material in the neutron-sensitive lining of the detector. In this case, the fertile isotope will gradually be converted in fissile nuclei and compensate for the burn-up of the original fissile material. For this, mixtures of ²³⁸U and ²³⁹Pu or mixtures of ²³⁴U and ²³⁵U are used.

Fig. 7.5

A typical in-core fission chamber used in BWR neutron flux monitoring systems

Fission chambers that have been exposed for a long time (several days) to a high neutron flux show a memory effect due to the build-up of fission products within the chamber. Immediately after exposure, a residual current of ≈0.1% of the full current is observed. This goes to 10^–5 after 10 days.

Another detector that is widely used for reactor monitoring is the so-called ‘self-powered detector’. These devices are based on the use of a material with a relatively large cross section for neutron capture followed by a subsequent beta decay. The detector measures the current caused by the beta emissions over a very thin isolating gap. The insulating material in the gap usually consists of magnesium oxide or of aluminium oxide. No voltage is needed to collect charges and this explains the name ‘self-powered detector’. Figure 7.6 shows very schematically the geometry of this kind of detector. For the emitter, vanadium or rhodium are commonly used. Table 7.1 summarises some of the important properties of these materials when used as emitter in self-powered detectors. The somewhat lower cross section of vanadium turns out to be an advantage because it reduces the burn-up of the detector. Because of the decay time of the beta emissions, it takes several times this half-life before the detector signal fully reflects a change in neutron flux.

Fig. 7.6

Schematic representation of a self-powered neutron detector for in-core neutron flux monitoring

Table 7.1 Emitter materials commonly used in self-powered detectors

One of the primary disadvantages of self-powered detectors based on beta emission is this slow response time. To avoid this, sometimes, other types of self-powered detectors are used. These are based on prompt gamma emission that follows neutron capture in certain materials. Cobalt and cadmium emitters are often used for this purpose, but this type of detector tends to be less sensitive to neutrons and more sensitive to gamma rays.

7.3 Fast Neutron Detection

The detectors for slow neutrons discussed in Sects. 7.1 and 7.2 rely on the very large cross section for slow neutron capture by certain isotopes. Without the addition of a moderator, these detectors are not well suited for detecting fast neutrons. The elastic cross section for fast neutrons is large in several materials. Detecting the recoil nucleus in elastic scattering is therefore a good method for detecting fast neutrons and this forms the basis for a wide variety of neutron detectors. Most detectors for fast neutrons are based either on using neutron moderation or on using elastic scattering. These two classes of neutron detectors are discussed below.

7.3.1 Detectors for Fast Neutrons Based on Moderation

For several isotopes, the neutron capture cross sections for slow neutrons are several orders of magnitude larger than typical cross sections for fast neutrons. It is therefore possible to build efficient detectors for fast neutrons that are based on first slowing down the neutrons and then detecting them. Several useful detectors are based on this principle.

The spherical neutron dosimeter, sometimes called Bonner counter, is one of these. This instrument consists of a small detector for slow neutrons, surrounded by a sphere of moderator material, usually polyethylene or paraffin. The slow neutron detector is either a LiI scintillator or a small ³He counter. The moderator sphere is typically 10–12 inch in diameter, while the LiI scintillator is only a few millimetres in size.

If a low-energy neutron enters the detector, it will quickly slow down and subsequently it has a good chance of being absorbed somewhere in the moderator before it can reach the LiI scintillator. As the energy of the neutron increases, the detection efficiency increases, because the neutron has a greater chance to reach the LiI scintillator before it is absorbed in the moderator. As the energy is increased further, the detection efficiency decreases again since the neutron has less chance to be fully thermalised in the moderator. The result is a neutron detection efficiency that first increases with energy, reaches a maximum and then decreases again. The interest in this type of detector stems from the fact that the energy dependence of the detection efficiency mimics the energy dependence of the dose equivalent for biological damage delivered per neutron between 0 and ≈10 MeV. The similarity of the two energy dependences is purely accidental, but allows very useful neutron dosimeters to be made. For a detector consisting of a 12-inch sphere of polyethylene and a 4-mm LiI scintillator, the sensitivity is 3000 counts/mrem. The advantage of using a ³He counter instead of a LiI scintillator is the reduced sensitivity to gamma rays. With a more elaborate design of the absorber sphere, it is possible to extend the sensitivity to neutrons with energy larger than 10 MeV. Neutron dosimeters based on this principle are available from several companies. Figure 7.7 shows an example of such a commercial neutron dosimeter.

Fig. 7.7

Fuji Electric NSN10014 neutron dosimeter. The detector consists of a ³He proportional counter in a polyethylene sphere. It can be used for neutrons with energy between 0.025 eV and 8 MeV. Figure courtesy of Fuji Electric

Often a counter with a detection efficiency independent of the neutron energy is required. It turns out that this can be achieved by using a cylindrical geometry with a slow neutron detector in the axis and a cylinder of moderator material around it. This type of counter is often called a ‘long counter’ because of its shape. For the slow neutron detection, usually a ³He proportional tube is used. Some additional holes and neutron absorbers are often needed to obtain a satisfactory energy response. Figure 7.8 shows an example of a simple long counter.

Fig. 7.8

Typical long counter. If this type of detector is exposed to a flux of neutrons coming from the right-hand side, its sensitivity is independent of the energy of the neutron for neutron energies of up to a few 10 MeV

This detector has the desired response only if the neutrons are coming from a point situated on axis and to the right-hand side in the figure. The detection efficiency of a long counter as shown in Fig. 7.8 is only ≈0.25%, but a more elaborate design with several parallel ³He detectors allows this to be increased considerably while maintaining the flat energy response.

The long counter can also provide some indication of the neutron energy spectrum if the ³He counter records the longitudinal position of the neutron interaction. Figure 7.9 shows the longitudinal distribution of the neutron absorption point in a long counter exposed to neutrons of various energies. If this counter is exposed to neutron radiation of unknown energy spectrum, it is possible to derive the energy spectrum of these neutrons by fitting the shape of the observed interaction depth distribution to a superposition of response curves of neutrons with different energies.

Fig. 7.9

Calculated depth distribution of the neutron absorption point for the neutrons of different energy in a long counter. In this example, we assumed a cylindrical moderator of 30 cm diameter and having a first part with 40 cm of polycarbonate followed by 60 cm polyethylene. The distributions for different neutron energies are normalised such as to all have the same height. The normalisation factors are indicated in the figure. Figure from [1], with permission

7.3.2 Detectors Based on the Observation of the Recoil Nuclei

When detecting fast neutrons, one often wants to detect the energy of these neutrons. This is called neutron spectroscopy. The long counter discussed previously gives some limited spectroscopic information, but for this purpose usually detectors depending on the observation of the recoil nucleus in elastic scattering are used. The most important target nucleus is hydrogen, because in neutron elastic scattering on hydrogen, the recoil nucleus can receive up to the total energy of the incoming neutron. Moreover, the elastic scattering cross section of neutrons on hydrogen is large and well known. The cross sections for elastic collisions of neutrons on a few relevant light nuclei are given in Fig. 7.10.

Fig. 7.10

Total elastic cross section for neutrons on hydrogen, deuterium and carbon. The energy dependence of the cross section on carbon between 2 and 10 MeV is extremely complex and is only represented in a very approximate way in the figure. The data for this figure were obtained from [4] in Chap. 1

Let us assume that we have neutrons of a given energy interacting in a hydrogen-rich scintillator material. The pulse height spectrum of the scintillator will be equal to the energy spectrum of the recoil protons. The recoil protons have an energy spectrum that depends on the neutron energy. If we have neutrons with an unknown energy spectrum, it is possible to derive the neutron energy spectrum by fitting the shape of the observed pulse height spectrum of the scintillator to a superposition of response curves of the counter to neutrons of different energies.

If a neutron scatters on a target nucleus A, the direction and the energy of the scattered target nucleus are related by energy and momentum conservation. We are considering here neutrons with energy of at most a few 10 MeV. Since the rest mass of a neutron is 939.56 MeV, a non-relativistic approximation is sufficient. We leave it as an exercise for the student to show that we have the following relation (see Exercise 4)

$$E_{\rm recoil} = E_{\rm neutron} \frac{{4m_A m_n }}{{\left( {m_A + m_n } \right)^2 }}\cos ^2 \theta $$

((7.1))

In this equation the notations are as follows:

• E _recoil = energy of the recoil nucleus

• E _neutron = energy of the neutron

• m _A = mass of nucleus A

• m _n = mass of neutron

• θ = angle of the recoil nucleus relative to the direction of the incoming neutron in the laboratory frame. See Fig. 7.11 for a definition of the angles.

Fig. 7.11

Definition of the scattering angle in the centre-of-mass system and in the laboratory system. The symbol ϕ denotes the polar angle of the nucleus A around the direction of the incoming neutron

Furthermore, the scattering angle in the centre-of-mass frame Θ and the scattering angle in the laboratory frame $\d{}\uptheta$ are related by (see Exercise 5)

$$\cos \theta = \sqrt {\frac{{1 - \cos \Theta }}{2}} $$

((7.2))

Therefore, the relation between the recoil energy and the scattering angle Θ in the centre-of-mass frame is given by

$$E_{\rm recoil} = E_{\rm neutron} \frac{{2m_A m_n }}{{\left( {m_A + m_n } \right)^2 }}[1 - \cos \Theta ]$$

((7.3))

Consider the case of a head-on collision between a neutron and a target nucleus A. In the centre-of-mass frame, the nucleus A bounces back in the direction it came from without changing its energy. In the centre-of-mass frame the angle is Θ =180°. In the laboratory frame, the nucleus A continues in the direction of the neutron and the angle of the scattered nucleus A is θ = 0°. In this case, the energy of the recoil nucleus A is maximum and is given by

$$E_{\rm recoil - \max } = E_{\rm neutron} \frac{{4m_A m_n }}{{\left( {m_A + m_n } \right)^2 }}$$

If the collision in the centre-of-mass system is at small angle Θ, the angle in the laboratory frame is θ ≈ 90°. In this case, the energy of the recoil nucleus is small and in the limit Θ→ 0, this energy goes to zero.

The energy spectrum of the recoil nuclei depends on the angular distribution of the neutron scattering. Let us define $\sigma (\Omega)$ as the differential cross section for elastic scattering of the neutron into the solid angle dΩ, with dΩ = dcos Θd $\varphi$ and P(cosΘ) as the probability density function for elastic scattering under an angle Θ, both quantities being defined in the centre-of-mass frame. Let us furthermore use the symbol σ _t to denote the total elastic cross section. Because of the symmetry of the problem, the cross section $\sigma (\Omega)$ does not depend on the azimuthal angle ϕ, but only on the polar angle Θ. Therefore we can write:

$$P(\cos \Theta )\,\, d\cos \Theta = \left(\int {\frac{{\sigma (\Omega )}}{{\sigma _t }}\, d\varphi} \right)\,\, {d\cos \Theta \,=\, 2\pi } \frac{{\sigma (\Omega )}}{{\sigma _t }}\,\, d\cos \Theta $$

If we define P(E _r) as the probability distribution of the recoil energy E _r, we have

$$ P(E_r ) = P(\cos\Theta ) \left| {\frac{{d\cos \Theta }}{{dE_r }}} \right| $$

And therefore, using Eq. (7.3)

$$P(E_r )\, dE_r = \frac{{2\pi }}{{E_{\rm neutron} }}\frac{{\sigma (\Omega )}}{{\sigma _t }}\frac{{(m_A + m_n )^2 }}{{2 m_A m_n }} dE_r $$

There is no simple way to find the angular distribution for elastic scattering. For many nuclei, this distribution is peaked in the forward and backward direction.

In the case of hydrogen, and for the energies considered here, the elastic cross section is almost isotropic in the cm frame, i.e. $\sigma (\Omega)$ = σ _t/(4π). The recoil energy spectrum therefore is simply a constant between 0 and the maximum value! The maximum value is the neutron energy itself. See Fig. 7.12. Assume that we have a mono-energetic beam of neutrons with energy E _n and with a flux Φ(E _n). The total number of counts in the spectrum will be proportional to $\varPhi$(E _n) σ _t(E _n). The number of counts in the pulse height spectrum F(E), in the interval (E, E+ΔE) will be given by

$$\begin{array}{l@{\quad}l} {F(E)\Delta E = \dfrac{{\Delta E}}{{E_n }}\Phi (E_n )\, \sigma (E_n )} \hfill & {if\ E_n> E} \\ {F(E)\Delta E=0} \hfill & {if\ E_n< E_n } \hfill\\\end{array}$$

Fig. 7.12

Pulse height distribution of a scintillator exposed to a neutron beam with a mixture of neutron energies. The value of F(E ₀) is the sum of all recoil distributions for neutrons with an energy larger than E ₀

For a beam of neutrons with spectrum Φ(E _n), the pulse height will be proportional to

$$F(E) = \int\limits_{E_{} }^\infty {\Phi (E^\prime) \frac{{\sigma (E^\prime)}}{{E^\prime}} dE^\prime} $$

There is therefore a simple relation between the neutron flux and the derivative of the pulse height spectrum

$$\frac{{dF(E)}}{{d(E)}} = - \Phi (E) \frac{{\sigma (E)}}{E}$$

For measuring the recoil spectrum, plastic scintillators are normally used. Several plastic scintillators contain only hydrogen and carbon and are very well suited for this purpose. The neutron energy spectrum is directly related to the derivative of the pulse height spectrum! However, this simple relation can only be an approximation due to the following reasons:

• the plastic scintillator also contains other elements, at least also carbon, and elastic neutron scattering on carbon should be included in the analysis; moreover, other reactions besides elastic scattering are possible on carbon

• the recoil track sometimes is not fully contained in the scintillator; to minimise this effect one needs to use a large piece of scintillator material

• scattered neutrons can interact a second time in the scintillator; to minimise this effect one needs to use a very small piece of scintillator material

• the response of the scintillator is not linear for very ionising particles, such as the recoil protons

• the scintillator has a finite, i.e. less than perfect, energy resolution

• there usually is background due to gamma rays

• the need for an electronics threshold to cut the noise

All these factors make it non-trivial to obtain a reliable neutron energy spectrum from the pulse height spectrum observed with a scintillator. An exhaustive discussion of the solution to these problems is beyond the scope of the present text. Besides plastic scintillators, proportional tubes filled with some gas with low atomic charge Z are also used in the same way for neutron spectroscopy.

It is also possible to measure the neutron energy spectrum by directly measuring the scattering angle and the energy of the scattered nucleus and get the neutron energy on an event-by-event basis using Eq. (7.1). This avoids many of the difficulties discussed above, but can only be used if there is a well-collimated neutron beam. Such a proton recoil telescope is shown in Fig. 7.13(a). Neutrons are incident on a thin target foil, usually some organic polymer. The energy of the recoil proton is measured in two detectors, a thin detector measures the energy loss dE/dx and a second thick detector measures the total energy of the recoil proton. Selecting on the ratio of the pulse heights in these two detectors allows recoil particles other than protons to be eliminated and also eliminates some other background. Often these two detectors are at an angle relative to the neutron beam in order to avoid interactions of the neutrons directly in the detectors. Gas detectors, semiconductor detectors and scintillators can all be used for this purpose.

Fig. 7.13

(a) Schematic representation of a proton recoil telescope (b) Characteristic pulses in a capture-gated spectrometer (c) Schematic representation of a capture-gated neutron spectrometer

The setup is in a vacuum to prevent the recoil proton from losing too much energy in the gas. The biggest drawback of this type of detector is the low-detection probability for neutrons, typically ≈10⁻⁵.

Another neutron spectrometer is the ‘capture-gated neutron spectrometer’, described below. The principle of this type of detector is illustrated in Fig. 7.13(b). A large volume (>1 litre) of boron-loaded plastic scintillator or a boron-loaded liquid scintillator is exposed to the neutron beam. If a neutron enters the scintillator, it will slow down by elastic collisions with the hydrogen or other light atoms present in the scintillator. It will slow down in a number of steps and in each step it will lose some of its energy. All these elastic collisions happen in a short time, typically in 50 ns. The light pulses generated in each of these elastic collisions all add up to one single pulse. After having lost all its energy, the neutron will be very slow and will continue to wander around in the scintillator until a boron atom absorbs it. The time before such an absorption takes place can be quite long, several 10 μs. In the absorption by a ¹⁰B nucleus, the final ⁷Li nucleus and the alpha particle together have a kinetic energy of 2.31 MeV and the corresponding energy is always absorbed in the scintillator. Such a neutron capture event will, therefore, have a characteristic signature consisting of a first pulse of energy proportional to the kinetic energy of the neutron followed within ≈20 μs by a second pulse with a characteristic amplitude. If the total event rate in the detector is sufficiently low, the chance association of two unrelated pulses faking a good event will be low. The big advantage of a capture-gated neutron spectrometer compared to a proton recoil spectrometer is that its detection efficiency can be of the order of ≈10% and that it does not require the neutron to come from a well-defined direction.

7.4 Exercises

• 1. Consider the neutron absorption reaction below, assume thermal neutrons.

  $$\begin{array}{l@{\quad}l}{{}_2^3 {\rm{He}} + {}_0^1 {\rm{n}} \to {}_1^3 {\rm{H}} + {}_1^1 p} & {Q = 0.764\,{\rm MeV}} \\\end{array}$$

  Use energy and momentum conservation to derive the expression giving the kinetic energy for two final state particles and calculate value of these for the reaction above.

• 2. A commonly used detector for thermal neutrons is a proportional tube filled with ³He gas. Calculate the mean free path of the neutrons in the gas if this gas is at a pressure of 5 atmospheres. If the tube has an inner diameter of 4 cm, what is the probability that a thermal neutron going through its centre will be detected?

• 3. Calculate the fractional decrease in sensitivity of a self-powered detector with rhodium emitter after exposure during 6 months to a flux of 3 × 10¹³ neutrons/cm²/s.

• 4. Derive equation (7.1).

• 5. Derive equation (7.2).

• 6. Consider a proportional tube filled with ³He and used as a slow neutron detector. The gas gain of the tube is 1000 and the capacitance of the anode wire is 100 pF. What will be the amplitude of a neutron pulse [in mV] be if the integration time of the pulse is very long?