1 INTRODUCTION

Results of a number of experiments have initiated discussion on the possible existence of a sterile neutrino that has a much smaller cross section of interaction with matter than, e.g., electron antineutrinos from a nuclear reactor. It is assumed that both the oscillation effect at short distances from the reactor and a shortage of the reactor antineutrino flux at long distances can be observed due to the transition of reactor antineutrinos to a sterile state. The process of oscillations into a sterile state can be represented at short distances by the following formula:

$$P({{\bar {\nu }}_{e}} \to {{\bar {\nu }}_{e}}) = 1 - {{\sin }^{2}}2{{\theta }_{{14}}}{{\sin }^{2}}\left( {1.27\frac{{\Delta m_{{14}}^{2}L}}{{{{E}_{{\bar {\nu }}}}}}} \right),$$
(1)

where L [m] is the length of the antineutrino path from the reactor, \({{E}_{{\bar {\nu }}}}\) [MeV] is the antineutrino energy, \(\Delta m_{{14}}^{2}\) [eV2] is the difference between the squared masses of an electron neutrino and a sterile neutrino, and sin22θ14 is the mixing angle of the electron and sterile neutrinos.

Anomalies were observed in several accelerator and reactor experiments: LSND [1], MiniBooNE [2], and reactor anomaly [3], as well as in the GALLEX/GNO, SAGE, and BEST experiments with radioactive sources [4–6]. Finally, the oscillation effect with parameters \(\Delta m_{{14}}^{2}\) = 7.3 eV2 and \({{\sin }^{2}}2\theta \) = 0.36 at a confidence level of 2.9σ was detected in the Neutrino-4 experiment [7].

The Neutrino-4 experiment has been carried out since late 2013 at the SM-3 reactor (Dimitrovgrad, Ul’yanovsk oblast, Russia) in the neutrino laboratory in room 162. The SM-3 research reactor is one of the best places to conduct such an experiment due to its high power of 100 MW, compact core (42 × 42 × 35 cm), highly enriched fuel, and some structural features of the building (the laboratory rooms are separated from each other by thick concrete walls). The idea behind the experiment is to use a mobile multisection detector to measure the antineutrino flux and spectra at different distances from the reactor (6−12 m). The detector consists of 5 × 10 vertical sections with a single photomultiplier tube (PMT) at the top.

The second neutrino laboratory is created for the experiment at the SM-3 reactor in room 170. It is possible to measure the antineutrino flux in this room at distances from a wider range (6−15 m) than in the existing laboratory. Measurements will be performed with a new advanced detector [8]. A number of auxiliary methods will also be used to suppress the correlated background and to reduce the background of random coincidences. These methods include the pulse-shape discrimination of signals, increase in the efficiency of the active shielding, increase in the gadolinium concentration, and optimization of the design of the passive shielding.

2 DETECTOR DESIGN

The detector consists of four identical modules located on a mobile platform together with the active and passive shielding (Fig. 1). Movement of the detector allows the entire range of distances to the reactor core to be covered. Each of the four modules consists of 5 × 5 horizontal sections with dimensions of 21.6 × 21.6 × 116.6 cm. The walls between sections are rigidly fixed and are used to prevent light from leaving each section. The detector will move during measurements to different positions over distances that are multiples of the section’s size. Therefore, each point will be measured by different sections, and a possible difference in the efficiency of the detector sections will be averaged. The sections are filled with a liquid scintillator, which is mineral oil (CH2) with loaded gadolinium. The light yield in the scintillator is 104 photons per 1 MeV. Two Hamamatsu R5912 PMTs are attached to the ends in each section.

Fig. 1.
figure 1

Diagram of the detector of reactor antineutrinos on a mobile platform: (1) antineutrino detector, (2) mobile platform, (3) copper, (4) borated polyethylene, (5) borated rubber, (6) vertical panels of the active shielding, and (7) upper panels of the active shielding.

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The design diagram of a single module is shown in Fig. 2. The liquid scintillator is separated from the PMT by a transparent Plexiglas wall with a thickness of 3 cm. A cylindrical light guide is located between the wall and the PMT. There is an air gap between the PMT surface and the transparent wall instead of the optical contact.

Fig. 2.
figure 2

Design diagram of a single module: (1) scintillator, (2) Plexiglas wall, (3) air gap, and (4) PMT.

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The scintillation detector is based on the use of an inverse β-decay reaction \({{\tilde {\nu }}_{e}} + p \to {{e}^{ + }} + n\). The resulting positron annihilates with the emission of two 511‑keV γ rays in opposite directions. The resulting neutron is absorbed by gadolinium with the emission of a γ-ray cascade with a total energy of ~8 MeV. The detector measures two consecutive signals from a positron and a neutron (the so-called correlated signals). The relationship between the positron and antineutrino energies is linear in the first approximation: \({{E}_{{\tilde {\nu }}}}\) = \({{E}_{{{{e}^{ + }}}}}\) + 1.8 MeV. Therefore, the antineutrino spectrum is reconstructed in the experiment from the measured positron spectrum.

3 SIMULATION OF LIGHT COLLECTION

A model in which the trajectory of each photon is calculated has been developed for simulation of the experiment using the Monte Carlo method. The antineutrino spectrum from 235U decay was used in the calculations. It was assumed that the antineutrino beam was directed along the detector axis. Such an assumption is possible when the detector is located at a distance of 6−15 m from the reactor core. The direction of positron emission was assumed to be isotropic, and the exponential path length of photons in the scintillator was 4 m. Photons suffered specular reflection from the walls with a reflection probability of 0.95. Figure 3 represents the distribution of PMT signals (the number of detected photons) from positrons with different energies, which was obtained by Monte Carlo simulation in view of the 511-keV energy deposited by each of the two γ rays. The width of the distribution is 500 keV, and it does not depend on the positron energy, which is basically determined by the incomplete absorption of γ rays within the section. This fact also explains the presence of two peaks in the distribution at low energies. Using the data in Fig. 3, it is possible to establish the relationship between the photon counts and the positron energy.

Fig. 3.
figure 3

Distribution of PMT counts from positron events with energies of 1−7 MeV.

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Figure 4 shows the PMT counts versus the location of a positron event with a positron energy of 4 MeV. Multiple rereflections between the walls worsened the efficiency of light transfer for right angles of incidence on the specular walls of the light guide. Therefore, less light reached the PMT from distant positions than from near ones. In this regard, the effect of total internal reflection from the scintillator−air interface at small angles of incidence was used in the setup to improve the uniformity of light collection from different distances.

Fig. 4.
figure 4

PMT counts of detector sections vs. the location of a positron event with a positron energy of 4 MeV.

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The distributions of signals from positron and neutron events are shown in Fig. 5. The detection threshold for a positron signal in the experiment is 1.5 MeV. The detection efficiency for positrons at this threshold is \({{\varepsilon }_{{{{e}^{ + }}}}}\) = 0.817(5).

Fig. 5.
figure 5

Distribution of signals from positron events (1) for the positron spectrum and the neutron event when using PMTs (2) only of the section in which the event occurred and (3) PMTs of all sections.

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A threshold of 3.2 MeV should be used when measuring the neutron signal in order to suppress the background of random coincidences associated with natural radioactivity. In this case, the detection efficiency for neutrons is εn = 0.722(5) if PMT counts of all sections of the detector module are taken into account. If the PMT counts of only one section in which the event occurred are taken into account, εn = 0.217(5). Based on the fact that approximately 20% of neutrons are captured by hydrogen with the release of ~2.2 MeV, the efficiency in view of the PMTs of all sections in the module is εn = 0.578(5). As a result, the detector efficiency obtained by simulation with account of the thresholds for the positron and neutron signals is ε = 0.472(5). Figure 6 shows the dependence of the detector efficiency on the thresholds when the PMT count of all sections of the module are taken into account.

Fig. 6.
figure 6

Detector efficiency vs. the thresholds of the positron and neutron signals.

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It should nevertheless be noted that, since the data-processing method used in the experiment is based on relative measurements, the detector efficiency is not included in the task, although it affects the measurement accuracy.

4 SIMULATION OF THE ANTINEUTRINO FLUX

The method used in the experiment is based on relative measurements in which the spectrum shape is ignored (i.e., on model-independent data analysis). The method is based on the following equation:

$$R_{{ik}}^{{\exp }} = ({{N}_{{ik}}} \pm \Delta {{N}_{{ik}}})L_{k}^{2}{\text{/}}{{K}^{{ - 1}}}\sum\limits_k^K {({{N}_{{ik}}} \pm \Delta {{N}_{{ik}}})L_{k}^{2}} ,$$
(2)

where the numerator is the count of antineutrino events with a specified energy with the correction for the geometric factor L2; the denominator is the count of antineutrino events with the same energy, averaged over all distances; \(i\) is the number of the energy range; and \(k\) is the number of the distance range.

Data sampling should be carried out by parameter \(L{\text{/}}E\) since the oscillation effect is governed by this parameter, as can be seen from Eq. (1). This is a method of the so-called coherent addition of measurement results, which makes it possible to directly observe antineutrino oscillations as a result of data sampling by variable \(L{\text{/}}E\).

The antineutrino flux was simulated based on the size of the reactor core and its spatial location relative to the antineutrino detector. Antineutrinos are uniformly generated inside the core with an isotropic escape direction. The simulation was carried out for points at a distance corresponding to the step of detector movement and for antineutrino-energy resolutions of 0.10, 0.25, 0.50, and 0.75 MeV. The simulation results demonstrating the oscillation effect are shown in Fig. 7.

Fig. 7.
figure 7

Simulation of the \({{N}_{{ik}}}L_{k}^{2}{\text{/}}{{K}^{{ - 1}}}\sum\limits_k^K {{{N}_{{ik}}}L_{k}^{2}} \) ratio at different energy resolutions of the detector (on the left) and the oscillation effect (on the right): simulation (1) with the antineutrino oscillations at \({{\sin }^{2}}2{{\theta }_{{14}}}\) = 0.36 and \(\Delta m_{{14}}^{2}\) = 7.3 eV2 and (2) without the oscillations.

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The statistical accuracy in simulating the \(\Delta {{N}_{{ik}}}{\text{/}}{{N}_{{ik}}}\) ratio in the calculations was 1%, which was much better relative to the experiment. The results of the Monte Carlo simulation make it obvious how the expected oscillation effect in the \((E,L)\) plane should look like. The next important conclusion is that the oscillation process is attenuated, and this attenuation depends on the energy resolution of the detector.

It is clear from the simulation that the detector resolution is very important for detecting the oscillation effect. In addition, the oscillation effect can be revealed by constructing the dependence of the measured ratio according to Eq. (2) on \(L{\text{/}}E\). It should be noted that separate summation of the matrix elements with respect to the energy or distance significantly reduces the possibilities for detecting the oscillation effect.

5 CONCLUSIONS

The computer model of the new detector of reactor antineutrinos with a horizontal arrangement of sections has been developed for the Neutrino-4 experiment. The calculations needed for designing the setup have been carried out. The simulated antineutrino spectrum has been obtained; it can be compared in the future to the experimental spectrum. The effect that should be measured for the specified parameters of oscillations and the energy resolution of the detector has been calculated as a result of the simulation.

A number of reactor-based experiments are currently performed in the world with the aim of searching for sterile neutrinos at short distances: DANSS [9], NEOS [10], PROSPECT [11], and STEREO [12]. The Neutrino-4 experiment has demonstrated the best sensitivity in the region of large \(\Delta m_{{14}}^{2}\) values owing to the compact reactor core, the multisection structure of the detector, and the layout of spectrum measurements at different distances in a fairly wide range of distances near the reactor. All these advantages will be preserved in the new laboratory. The creation of the second neutrino laboratory at the SM-3 reactor and the new detector offers a chance to obtain the final answer to the question of the existence of a sterile neutrino with the oscillation parameters observed in the Neutrino-4 experiment.