Current status of multilayer neutron interferometry with gaseous samples at J-PARC

This article is part of a collection of articles related to the International Conference on Neutron Scattering, ICNS2025.

Several few-body nuclear models, such as the Argonne v₁₈ potential including three-nucleon forces and chiral effective field theories, predict the coherent scattering length (b_c) for light nuclei. Reliable measurements of b_c therefore provide important tests of these models. We have developed a measurement system for determining b_c of gaseous samples using a multilayer-type neutron interferometer at J-PARC, and successfully observed the phase shifts of ³He and ⁴He gases. From the observed phase shifts, we obtained for ³He b_c = 3.99 ± 0.23 (stat.) ± 0.66 (sys.) fm and for ⁴He b_c = 2.95 ± 0.11 (stat.) ± 0.67 (sys.) fm (stat. and sys. denote statistical uncertainty and systematic uncertainty, respectively). To achieve higher precision, we are currently upgrading the experimental setup.

1. Introduction

The coherent scattering length (b_c) describes neutron s-wave scattering and is a key parameter for understanding few-body nuclear systems. Few-body nuclei such as ³He and ⁴He are described by several phenomenological models, including the Argonne v₁₈ (AV18) potential with three-nucleon interactions (3N), the R matrix approach (Hofmann & Hale, 2003) and chiral effective field theories (Bagnarol et al., 2023), which predict b_c.

Therefore, measurements of the b_c of ³He and ⁴He (denoted hereafter as and ) can serve as benchmarks for studies of few-body nuclear systems.

Experimentally, b_c values have been measured using several methods, including scattering cross-section measurements (Haddock et al., 2019), reflectometry (Kitchens et al., 1974), diffraction (Shull & Shaw, 1973) and, most prominently, neutron interferometry (Ioffe et al., 1998). For instance, the b_c values of H and D, obtained using neutron interferometers (NIs) with relative precisions of 3.0 × 10⁻⁴ (Koester & Nistler, 1975) and 4.5 × 10⁻⁴ (Schoen et al., 2003), respectively, are consistent with the predictions of AV18 and AV18 with 3N. However, relative discrepancies of approximately 2 × 10⁻² for and 7 × 10⁻³ for persist among the latest measurements using Si crystal NIs.

We aim to resolve these discrepancies with a relative precision of 10⁻³ using pulsed neutrons and a multilayer-type NI. While b_c for solid samples has already been measured using a multilayer-type NI, this paper reports its first application to gaseous samples with a newly fabricated gas cell. We present the results as a proof of principle for this method and discuss developments towards higher-precision experiments.

2. Experiment

A neutron interferometer splits a neutron wave into two paths and recombines them to produce interference. The potential difference between the two paths appears as a phase shift in the interference fringes. Since the first implementation in 1974 (Rauch et al., 1974), NIs have found applications across diverse domains of physics (Colella et al., 1975; Rauch et al., 1975; Hasegawa et al., 2003).

The phase shift Δϕ is described by

where m is the neutron mass, λ is the neutron wavelength, L is the interaction length with the potential, ΔE is the potential difference between the two paths and h is Planck's constant. The sensitivity of an NI is proportional to λ and L. Consequently, extending the path length of an NI and using a long wavelength enhances its sensitivity. A conventional NI made from an Si single crystal relies on Bragg scattering, which prevents its operation at λ longer than the Si lattice spacing. The interaction length L and the size of the NI are constrained by the dimensions over which high crystallinity can be maintained.

2.1. Multilayer neutron interferometer

We developed an NI using multilayer neutron mirrors. A multilayer neutron mirror consists of periodic layers of two materials (Ni/Ti) with different Fermi pseudo-potentials for neutrons. We can utilize cold neutrons which satisfy the reflection condition. Because the layer spacing is larger than the lattice spacing of an Si single crystal, neutrons with longer λ can be utilized than in a conventional NI. For the application of multilayer mirrors to a Jamin-type NI (shown in Fig. 1), we used a pair of beam-splitting etalons (BSEs) (Kitaguchi et al., 2003; Seki et al., 2010). Each BSE is composed of two multilayer mirrors on SiO₂ substrates, separated by an air gap of 211 µm.

Figure 1 Experimental setup of the Jamin-type NI employing beam-splitting etalons (BSEs).

The NI with BSEs not only allows the extension of L but also enables the insertion of large samples that would be difficult to accommodate in a conventional NI, expanding the flexibility of the experimental setup. In the present measurement, a gas cell with a total width of 40 mm was inserted between the two paths, providing L = 8 mm. The value of L is potentially scalable up to 1000 mm.

2.2. Experimental setup

We conducted experiments on the low-divergence branch of the J-PARC beamline MLF BL05 (NOP) (Mishima et al., 2009). The neutron wavelength used by a multilayer-type NI is determined by the time-of-flight (TOF) method, reducing time-varying disturbances in the analysis process. The multilayer-type NI and the sample insertion assembly were placed on a vibration isolation table inside a thermostatic chamber. To ensure the stability and alignment of the mirror substrates, the rotation of the entire NI and the relative angles between the two BSEs were precisely controlled and maintained using high-precision stepping motors. We observed an interferogram using pulsed neutrons (Fujiie et al., 2024). The bandwidth of λ is from 0.9 to 1.1 nm. The phase determination accuracy was comparable to that of a conventional NI. In our previous work, we had already measured b_c for several nuclei with solid samples and confirmed that these values were consistent with previous studies, except for V (Fujiie et al., 2024).

2.3. Gas cell

For measuring the b_c of gaseous samples, we designed a gas cell (shown in Fig. 2) which was machined from pure aluminium alloy (A1050) at RIKEN. In b_c measurements using an NI, one path passes through the sample while the other passes through a vacuum, thereby producing the phase shift. For a conventional NI, the centimetre-scale path separation allows the use of a two-chamber gas cell separated by a partition. However, in a multilayer-type NI, the beam separation is only 380 µm, so neutrons pass through the corner radius formed during fabrication, making it difficult to determine L through the gas region accurately.

Figure 2 Cross-section view of the gas cell. The red region contains the gaseous sample, while the green region is evacuated.

To address this problem, recess machining was performed to create surfaces perpendicular to the neutron path. By creating a 1 mm extension in the x-axis direction, neutrons are directed perpendicularly onto the gaseous sample. Neutrons pass through the red region, 2 mm in Path 1 and 10 mm in Path 2; therefore the effective L contributing to the phase shift is 8 mm.

2.4. Experiment procedure and analysis

Measurements were repeated with and without the sample to minimize disturbances, as illustrated in Fig. 1, with mea­sure­ments taken every 10 min. We used a position-sensitive detector with time resolution, consisting of a resistance-division photomultiplier tube (RPMT) and a ZnS/⁶LiF scintillator. The detector was 0.3 m away from the interferometer setup (shown in Fig. 1). The details are described by Hirota et al. (2005).

The sample gases were filled at 50256 ± 6 Pa at 299.497 ± 0.06 K for ³He and at 100017 ± 10 Pa at 299.196 ± 0.06 K for ⁴He, measured by a piezoresistive transducer and a platinum resistance thermometer. The gas cell was evacuated by a turbo molecular pump to 3.00 × 10⁻³ Pa before filling, and the residual vacuum pressures before filling the gases were 1.00 × 10⁻² Pa for ³He and 1.17 × 10⁻² Pa for ⁴He. Table 1 sum­marizes the assessment of sample contamination. The levels were below the experimental uncertainty and therefore negligible for these measurements.

Table 1
Impurity list for samples

Sample	Impurity level
^3He	<10^−3
^4He	<10^−6

Figs. 3 and 4 show the interference fringes obtained over 10 min under conditions with the gas cell filled with ³He, ⁴He and evacuated, respectively, and with the gas cell inserted and removed from the beam path. In Figs. 3 and 4, the vertical axis I(λ) is defined by

where I_H and I_O are the intensities of the O and H beams, respectively, and and are those with a Cd block inserted. We fitted the obtained interference fringes using the fitting function

where A denotes the contrast of the interferogram. The coefficients P_L and P_R represent the inverse proportional and proportional terms, respectively, and they are derived by geometric optics (Fujiie et al., 2024). Specifically, P_R accounts for the phase shift contributed by the SiO₂ substrate. The third term, P_S = Nb_ct, is the interaction with the sample, where N is the number density of atoms and t is the sample thickness. The TOF region used for the fit was set from 37 to 49 ms, which corresponds to the reflecting momentum transfer range of the multilayer mirror, 0.232 < Q < 0.292 nm⁻¹. Through relative measurements, P_S was isolated as the difference between the wavelength-proportional terms with and without the sample. Scattering lengths were calculated from the phase shifts of each sample (shown in Fig. 3) after subtracting the value obtained in the vacuum measurement (shown in Fig. 4).

Figure 3 Interference fringes for (left) ^3He and (right) ^4He. Red and blue lines correspond to data with the cell out and in, respectively. Black lines indicate fits using equation (3).

Figure 4 Interference fringes for the double-path vacuum measurement. Red and blue lines correspond to data with the cell out and in, respectively. Black lines indicate fits using equation (3).

The extracted phase shifts were  = 0.38 ± 0.022 (stat.) rad, = 0.57 ± 0.022 (stat.) rad and Δϕ^Vac = 0.19 ± 0.015 (stat.) rad (where stat. means statistical uncertainty). Consequently, the results were  = 3.99 ± 0.23 (stat.) fm and = 2.95 ± 0.11 (stat.) fm, with measurement times of 6 and 8 h, respectively. The relatively large statistical uncertainties were caused by a decrease in fringe contrast. The decrease in contrast caused by the insertion of the cell is attributed to small-angle scattering of neutrons by the 18 mm-thick (in total) aluminium wall (shown in Fig. 2).

2.5. Uncertainties

The systematic uncertainties are summarized in Table 2. The dominant systematic uncertainty is the phase distribution in the beam cross section, which is described below. In the condition with no cell, the phase of the interferogram in the TOF varied in the vertical position on the detector, indicating that the neutron phase was distributed along the y axis. We suspect that this effect was caused by a misalignment of the BSEs. We divided the data into three regions along the y axis and analysed each region to derive phase shifts, but the results were inconsistent. The systematic uncertainties arise from the weighted average taken for the three data points, expanding the error bar such that χ²/ndf = 1, where χ² is the chi-squared parameter and ndf the number of degrees of freedom.

Table 2
A summary of systematic uncertainties for b_c

	(fm)	(fm)
Temperature	±0.00079	±0.00059
Pressure	±0.00063	±0.00023
Phase distribution	±0.66	±0.67

3. Results

Figs. 5 and 6 compare our results with previous work (Kitchens et al., 1974; Kaiser et al., 1977; Kaiser et al., 1979; Alfimenkov et al., 1981; Huffman et al., 2004; Ketter et al., 2006; McReynolds, 1951; Genin et al., 1963; Rorer et al., 1969; Haddock et al., 2019; Haun et al., 2020). The methods used were cross section (CS), reflectivity (RE) and neutron interferometer (NI). Our results were  = 3.99 ± 0.23 (stat.) ± 0.66 (sys.) fm and  = 2.95 ± 0.11 (stat.) ± 0.67 (sys.) fm (where sys. means sys­tematic uncertainty). In this first gaseous sample measurement, a significant phase shift was successfully observed, and several issues in the experimental setup for future measurements were identified.

Figure 5 Comparison of measured with previous results.

Figure 6 Comparison of measured with previous results.

4. Discussion

The experimental results revealed a vertical phase distribution and temporal instability, leading to reduced visibility and an underestimation of the phase shift. We recently identified that this distribution stems primarily from the roll angle mis­alignment of the BSEs. Because these systematic effects have not yet been fully quantified, the actual uncertainty in these preliminary results is likely to be larger than that reported above. Furthermore, small-angle scattering from the aluminium degraded the contrast. To address these issues, we are upgrading the setup with high-rigidity stages and low-thermal-expansion materials.

5. Future prospects

To overcome the current limitations, we are preparing a new cell using SiO₂ crystals to eliminate contrast degradation from small-angle scattering. We will also correct the BSE roll angle misalignment by making adjustments, and improve the stability by introducing more rigid components. Furthermore, introducing supermirrors optimized for the J-PARC MLF BL05 spectrum is expected to increase the neutron flux by a factor of 20. With these upgrades, and can be measured with a relative precision of 10⁻³ in 6 and 20 h, respectively.

6. Summary

To study the few-body system in nuclei, we performed measurements of and using a multilayer-type NI at J-PARC. The precision of b_c was limited by statistical uncertainties due to the small-angle scattering from aluminium and setup-related systematic uncertainties. By integrating SiO₂ cells, a high-rigidity stage and supermirror upgrades, we aim to achieve higher-accuracy measurements.