2.1 Efficiency definition

Neutron detection efficiency is usually subdivided into the absolute and intrinsic efficiency. The absolute efficiency (ε_a) is defined as

here, N is the number of neutron pulses recorded by detector, and N_s is the number of neutrons emitted by neutron source. Because the ε_a depends on both the detector properties and the geometric arrangement of source/detector, it is difficult to be tested.

The intrinsic efficiency (ε_i) is defined as

here, N is the same as above, N_d is the number of neutron incidents on detector. Supposed that the solid angle of the detector subtended to point neutron source is Ω, the ε_a equals to Ω×ε_a/4π. If the detector covers a point source in a solid angle of 4π, the same result can be obtained by Eqs.(2) and (3). Thus, it is convenient to scale the absolute efficiency by using intrinsic efficiency. The intrinsic efficiency can be described in the following section unless additional instruction.

Because it is difficult to determine the absolute and intrinsic efficiency, the relative efficiency (ε_r) is usually used and defined as

here N_ref is the counts recorded by the reference detectors, and ε_ref is its detection efficiency.

2.2 Efficiency-determined method

Neutron as neutral particle travels in straight line, and deviates from its path when actually colliding with another due to scattering into a new direction or absorption. Table 1 shows the total cross sections of thermal neutron interaction with some elements (referenced from ENDF/B-VII.0). The elements are major compositions for some inorganic scintillators, and the cross sections of thermal neutron with host elements in most of inorganic scintillator are small and even ignorable. Consequently, the energy loss in the thermal range is very small. In another aspect, their maximum energy loss at a collision, which is easily calculated, is no more than 2%. So, the energy loss caused by the host elements is ignorable. Hence the two destinations for incident neutrons in the scintillator are either escaped out or captured by the neutron sensitive elements like ⁶Li, ¹⁰B and ^155,157Gd.

For inorganic scintillator detector based on nuclear reaction of neutron sensitive elements, like ⁶Li, ¹⁰B and ^155,157Gd, the neutron can penetrate into the scintillator materials directly until the nuclear interaction occurs. Once a photomultiplier (PMT) coupled with the scintillator can detect the scintillating light caused by the nuclear reaction, it will record an effective pulse. Experimentally, the detection efficiency of electronic system for a scintillation detector can be realized nearly 100% by choosing the suitable PMT and its threshold setup.

Supposed that the element distribution in the thick scintillator (L) is uniform where L can be divided into equal thicknesses (L_n), we have the equal detection efficiency (L/n). Also, the thick scintillator can be considered to consist of these thin scintillators with perfect junctions, which cannot affect their uniformity and optical properties. Fig.1 depicts a thick scintillator. Dashed lines are n-th partition divisions of Scin_i (i=1,2 ,… n), and identical for each other.

Fig.1Full-screen View

Schematic diagram of a square thick scintillator with the thickness (L).

N₁ is defined as the neutron numbers detected by the Scin_1; and N_n, the total tiles of Scin_1 to Scin_n. The detection efficiency of the thick scintillator is defined as ε_t. Then, its detection efficiency for the Scin_1 is

And ε_t is

If the attenuation length of scintillation light is longer than L, ε_t is expressed by using ε as the following analysis. For an incident neutron, the detected probability is ε in the Scin_1, and its undetected probability is 1–ε. Since all the tiles for Scin_i (i=1,2,…n) are identical and the energy loss are ignorable, the undetected probability for the Scin 2 is 1–ε, the detected probability of both Scin_1 and Scin_2 for the incident neutron becomes 1–(1–ε)². After the neutron passed the Scin_n, the detected probability for union tiles of Scin_1 to Scin_n is

From Eqs.(5)–(7), Eq.(8) is obtained.

Eq.(8) shows that the scintillator detection efficiencies are obtained by their relative counts. Determining the efficiency of thick scintillator from the thinner scintillator efficiencies is actually the relative efficiency way under unknown any efficiency.

3.1 Glass properties and test setup

The lithium glass compositions are listed in Table 2. The abundance of ⁶Li is around 90%, and its mass density is 2.31 g/cm³. Here, the lithium glass of 1-mm and 3-mm thicknesses in 5-cm diameter are adopted The light yields were measured around 5671 photons per neutron and 3768 photons per MeV gamma rays deposition^[12]. The 3-mm thick lithium glass can be considered to be comprised of the three 1 mm with perfect junctions, thus the n in Eq.(8) is equal to 3.

The test setup is shown in Fig.2. A point neutron source (²⁵²Cf) with activity of 5×10⁶ Bq is shielded in a box. The emitted neutrons are thermalized into thermal range and guided out through a channel with a 10-cm diameter, where the thermal neutron emission frequency is around 1–2 Hz/cm². The glass scintillator, greased with silicon oil, is coupled with a PMT (XP2020) with the gain of 1.2×10⁷. Tyvek films are used for the packages in order to collect the scintillation light, and the efficiency of whole test system, including that the PMT quantum efficiency, is around 10%. Because the PMT is sensitive to single photon, scintillation lights caused by neutrons can be detected efficiently by the PMT. To shield gamma rays, a lead plate with the 5-cm thickness is fixed in the front of the PMT. In the background test, an additional cadmium plate with the 3-mm thickness is placed between the moderator and lead plate to absorb neutrons.

Fig. 2Full-screen View

Test setup of neutron count rates.

In test, the signal from the PMT is sent into a charge sensitive amplifier (CSA), its signal output is discriminated by a discriminator (Lecroy 623B) and sent into a counter (Caen Mod.N145) to record the counts. The CSA is used mainly for shaping and amplifying detector signals to avoid the multiple output pulse discriminations and the missed discrimination for a small pulse.

To ensure each signal can be discriminated and recorded by the counter, the threshold of discriminator is selected as low as possible. This is easily realized for the high light output of the glass and the high gain of PMT. Under this condition, the efficiency of this electronic system and the light collection can be considered as around 100%. Thus the efficiency of neutron detector is only determined by the lithium glass contribution.

Fig.3Full-screen View

(a) The original pulse output without amplification, (b) the original pulse and its amplified shape after CSA.

Figure 3(a) shows a neutron original pulse of the PMT output. Because a low threshold can cause multiple discrimination of the same pulse, the CSA is necessary. The channel 1 is the original pulse direct output from PMT; and Channel 2, after the CSA, indicating that the pulse becomes smoother and larger in Fig.3(b) than in Fig.3(a). Consequently, multiple discriminations can be avoided in most cases, and the probability of the missed discriminations decreases. The discriminator, set with a 90-mV threshold, is comparably low according to the pulse height. Though the pulse after CSA is lasting up to 8 μs, it enough responds to the neutron flux in this experiment.

3.2 Experimental efficiencies

The detection efficiencies are measured by two measurement steps of the background counts, and the total counts of backgrounds and signals. The former is recorded by a cadmium plate between the lead plate and moderator; and the latter, without cadmium plate.

Table 3 shows that the counts of lithium glass with the 1- mm and 3-mm thicknesses are tested by the setup (Fig.2). C_a and C_b are the counts without and with cadmium plate, respectively. C_a–C_b means the neutron events after background counts are subtracted.

From Eq.(8), the C_a– C_b for the 1-mm and 3-mm lithium glass corresponds to the N₁ and N_3. Supposed that the efficiency of 1-mm lithium glass is ε, an efficiency equation of one variable is

This equation can be solved as that the ε equal to 65.6%; and 1–(1–ε)³, 95.9%, as listed in Table 3.

3.3 Theoretical efficiencies

The nuclear reaction probability of neutron was simulated by ⁶Li glass using Geant4. Because the efficiency of electronic system and light collection can be considered as 100% for the efficiency detection, the PMT is ignorable. The lithium glass is placed on the x‒y plane, and its center is superposed with the glass origin. A point beam gun with the 25.3-MeV energy shoots thermal neutrons from the glass origin of (0 mm, 0 mm, 10 mm). The physics list uses the QGSP_ BERT_HP recommended by Geant4 at low energy range^[13]. The neutron reaction probabilities of ⁶Li (n,α)³H is recorded after 100 000 neutron shots at the two pieces of lithium glass. The captured efficiency approaches the neutron detection efficiencies, as listed in Table 4.

Compared with the simulations, the detection efficiencies are calculated by Eq.(1) That the σequals to 940 barns is the neutron cross section with the 25.3-MeV energy, as listed in Table 4.

The efficiency discrepancies between Tables (3) and (4) may be caused by the following uncertainties. Firstly, Table 3 just described the interaction probabilities of ⁶Li(n,α)³H. For a neutron incident, each interaction may not cause absolutely an effective pulse height recorded by the experiment, but the simulation and analytical calculation can reach these results. Secondly, the efficiencies in Table 4 assumed that all the neutrons are 25.3 MeV, but neutron energies actually distribute around 25.3 MeV after the moderator (Fig.2).

At a given threshold of 555 pC^[12], the detection efficiency for the 1-mm lithium glass is 65.2%; and 3 mm, 95.8%, this approaches our results in this paper. In addition, the suppression capability is 1.8×10^–3 at the 95.8% efficiency. It is said that the presented method is credible in detection efficiency determination of neutron scintillator.