Magnetic-lens-generated polarized neutron beam with enhanced intensity and Q resolution for small-angle neutron scattering

Hiroi, K.; Nakabe, R.; Oku, T.; Kumada, T.; Motokawa, R.

doi:10.1107/S1600576725010246

research papers

JOURNAL OF
APPLIED
CRYSTALLOGRAPHY

ISSN: 1600-5767

Volume 59| Part 1| February 2026| Pages 69-79

https://doi.org/10.1107/S1600576725010246

Open

access

Magnetic-lens-generated polarized neutron beam with enhanced intensity and Q resolution for small-angle neutron scattering

Kosuke Hiroi,^a,^b Rintaro Nakabe,^a Takayuki Oku,^b Takayuki Kumada ^a ^* and Ryuhei Motokawa ^a ^*

^aMaterials Sciences Research Center, Japan Atomic Energy Agency, 2-4 Shirakata, Tokai, Ibaraki 319-1195, Japan, and ^bJapan Proton Accelerator Research Complex (J-PARC) Center, Japan Atomic Energy Agency, 2-4 Shirakata, Tokai, Ibaraki 319-1195, Japan
^*Correspondence e-mail: [email protected], [email protected]

Edited by E. P. Gilbert, Australian Centre for Neutron Scattering, ANSTO, Australia (Received 22 June 2025; accepted 14 November 2025)

We installed a 30 mm-bore 3.2 m-long magnetic lens in the small-angle neutron scattering diffractometer (SANS-J) at the Japan Research Reactor 3 to focus the neutron beam near the sample position for measurements at Q > 0.1 nm⁻¹. The focused beam at the sample position was over three times more intense than the standard non-focused beam, while the Q resolution was improved. The positive spin component of the neutron beam was focused near the sample, whereas the negative spin component was defocused and blocked by the slit just in front of the sample, producing a polarized beam. The 8 mm-diameter focusing polarized beam achieved a polarization of 0.95–0.96 and an intensity up to 22 times greater than that of a non-focusing polarized beam with the same collimation length. Using this beam with a remanent supermirror-coated spin analyser, we demonstrate that polarization analysis measurements of hydrogen-containing samples can be completed within tens of minutes.

Keywords: neutron magnetic lenses; polarization analysis; polarized small-angle neutron scattering.

1. Introduction

A lens is a common optical component, but it is used much less frequently in neutron diffractometers, except for small-angle neutron scattering (SANS) with monochromatic cold neutron sources (Radulescu, 2025 ; Kumada et al., 2023a ; Barker et al., 2022 ; Cremer et al., 2020 ; Heller et al., 2018 ; Wood et al., 2018 ; Radulescu et al., 2016 ; Heller et al., 2014 ; Zhang et al., 2014 ; Han et al., 2013 ; Wignall et al., 2012 ; Iwase et al., 2011 ; Koizumi et al., 2007 ; Oku et al., 2007 ). Because the refractive indices of materials for thermal and cold neutron beams are close to 1, many biconcave lenses with small radii of curvature are required to focus the beams to long focal lengths, f (Choi et al., 2000 ). In addition, because f is inversely proportional to the square of the neutron wavelength, λ, these lenses are only effective for monochromatic cold neutrons.

Fig. 1 shows the neutron optics in the collimator of the 20 m-long small-angle neutron scattering diffractometer (SANS-J) at the Japan Research Reactor 3 (JRR-3) of the Japan Atomic Energy Agency (JAEA). Seventy biconcave MgF₂ lenses, each with a 25 mm radius of curvature, are installed just in front of the sample. The lenses have a combined focal length of f = 4820 mm at λ = 0.65 nm. The lenses transfer the image of the neutron beam from the narrow upstream slit to the detectors at the downstream end of the diffractometer, enabling measurements of scattering down to a momentum transfer, Q, of 0.002 nm⁻¹ (Kumada et al., 2023a). The neutron transmittance of the MgF₂ lenses is 0.61 for a 15 mm-diameter neutron beam and decreases significantly for larger-diameter beams because the thickness of the lens increases as it moves away from the central axis. In addition, the MgF₂ lenses produce diffuse scattering, which overlaps with the scattering signal from the sample (Kumada et al., 2024 ). Therefore, tighter focusing cannot be achieved by installing more MgF₂ lenses.

Figure 1
Photograph of the neutron optics in the SANS-J collimator. The components are (A) upstream four-jaw slit, (B) downstream slit, (C) MgF₂ lenses, (D) preexisting magnetic lens, (E) supermirror polarizer, (F) gradient-RF neutron spin flipper and (G) extended magnetic lens.

A 1.2 m-long-sextupole magnetic neutron lens is also installed in SANS-J to focus polarized neutron beams onto the detector at the downstream end [Fig. 2 (a)]. This lens focuses and defocuses positive and negative spin-polarized neutron beams relative to the magnetic field direction, with f = +4820 and −4820 mm, respectively, at λ = 0.65 nm (Oku et al., 2007). The magnetic lens can focus the positive spin-polarized neutrons entering the lens bore with a diameter, ϕ_lens, of 30 mm, without transmission loss or diffuse scattering. However, the negative spin-polarized neutrons, some of which pass through the supermirror polarizer, are defocused by the lens, pass through the downstream slit just behind the lens and overlap with the scattering positive spin-polarized neutrons from the sample on the detector, producing background for scattering measurements. For this reason, we have recently used MgF₂ lenses instead of the magnetic lens even for polarized neutron scattering measurements.

Figure 2
Conventional layouts for (a) the polarized focusing beam projected onto the detector at the downstream end (Oku et al., 2007

) and (b) the polarized non-focusing beam projected onto the detector at L₂ = 1835 mm; new layouts for (c) the loose-focusing beam and (d) the tight-focusing beam; and conceptual drawings of the focusing and polarization of (e) the loose-focusing beam and (f) the tight-focusing beam. In the conventional layout for the unpolarized non-focusing beam, the supermirror polarizer in (b) is removed. The dashed lines in (e) indicate the trajectory of negative spin-polarized neutrons. The yellow lines and ellipse in (f) show the virtual lens, illustrating the combined focusing action of the preexisting and extended lenses.

However, here we re-evaluate the advantages of the magnetic lens—namely, its lack of transmission loss and its relatively large bore diameter compared with the effective focusable diameter of the MgF₂ lens—and propose a new layout employing an extended 3.2 m-long array of magnetic lenses with a focal length of approximately 2400 mm for scattering measurements at Q > 0.1 nm⁻¹. The lenses focus positive spin-polarized neutrons from the upstream slit within the lens bore's solid angle onto or near the sample position, rather than the detector [Figs. 2(c) and 2(d)]. Meanwhile, most of the defocusing negative spin-polarized neutrons are blocked by the downstream slit located just in front of the sample. As a result, the extended magnetic lens increases the neutron beam intensity at the sample position while simultaneously polarizing the beam.

The focusing beam provided by the extended magnetic lens is also useful for unpolarized neutron scattering measurements. Typically, the intensity of an unpolarized neutron beam is increased by installing Ni guide tubes in the collimator to shorten the collimation length for high-Q SANS measurements, but at the cost of an enlarged beam size at the detector. Since the detection area of the ³He main detector of SANS-J is only 0.4 m², which is much smaller than that of other SANS diffractometers (Radulescu, 2025; Barker et al., 2022; Cremer et al., 2020; Heller et al., 2018; Wood et al., 2018; Radulescu et al., 2016; Heller et al., 2014; Zhang et al., 2014; Han et al., 2013; Wignall et al., 2012), the increased beam size confines Q-resolved SANS signals to a very narrow Q range. Thus, the collimation length of SANS-J is not shortened even for measurements at Q > 0.1 nm⁻¹ (Kumada et al., 2023a).

In contrast, beam focusing using the extended magnetic lens enhances the beam intensity while maintaining—or even decreasing—the beam size at the detector, making it suitable for diffractometers with small detectors like SANS-J. For unpolarized SANS measurements, a similar increase in beam intensity and decrease in beam size can be achieved simultaneously by moderately shortening the collimation length and decreasing the slit aperture. However, for polarized SANS measurements, the advantage of the extended magnetic lens becomes significant, as it produces a polarized neutron beam without the transmission loss associated with a supermirror polarizer. On the basis of simple geometrical-optics simulations of intensity enhancement and polarization, we report basic scattering data and demonstrate that polarization analysis measurements can be performed using a remanent supermirror-coated spin analyser.

2. Experimental

2.1. Optical layout

Figs. 2(a)–2(d) compare the conventional and new layouts for polarized neutron scattering at SANS-J. The incident neutron beam from the end of the 20 mm-wide 50 mm-high Ni guide tube is monochromated with a velocity selector (Kuroda Precision Industries Ltd, Japan). The monochromated beam, with λ = 0.65 nm and wavelength resolution Δλ/λ = 0.15, is collimated using a four-jaw slit (A_u = 20 mm square aperture) at L₁ = 10100 mm upstream of the sample, and a downstream slit (ϕ_s = 8 or 14 mm circular aperture) located 350 mm in front of the sample, to measure the scattering with the detector at L₂ downstream of the sample. Neutron spins are flipped using a gradient radio frequency (RF) neutron spin flipper (SF) downstream of the magnetic lenses.

In the conventional layout, the incident neutron beam is polarized using a 2500 mm-long Z-shaped Fe/Si supermirror polarizer (PN04-38, Swiss Neutronics). The polarized neutron beam is focused onto the ³He main detector at L₂ = 10245 mm with the 1200 mm-long preexisting lens [Fig. 2(a)], or collimated by the upstream and downstream slits without the lens at L₂ ≤ 3845 mm [Fig. 2(b)]. In the new layout, an extended magnetic lens, consisting of 500 and 1500 mm-long segments with ϕ_lens = 30 mm (Oku et al., 2010 ) and a focal length f_e = 3140 mm, is installed. The loose-focusing beam [Fig. 2(c)] is designed to be focused near the ³He main detector at L₂ = 1845 mm using the extended lens alone for high-intensity high-Q-resolution scattering measurements. The tight-focusing beam [Fig. 2(d)] is focused onto the sample position using both the extended magnetic lens and the preexisting lens, enabling high-intensity high-neutron-polarization (P_n) scattering measurements.

Figs. 2(e) and 2(f) are conceptual drawings showing how the positive and negative spin-polarized neutrons are focused and defocused by the magnetic lenses. In this model, the object position in the horizontal direction is taken at the end of the 20 mm-wide Ni guide tube, located 1200 mm upstream of the upstream slit. This choice reflects the fact that neutrons do not propagate inward horizontally from the outer edge at the A_u = 20 mm upstream slit. The extended lens and the preexisting lens are each approximated as a single 30 mm-diameter thin lens, located at object distances s_e1 and s_e1 + d downstream from the object position, respectively. In the loose-focusing beam configuration, the positive spin-polarized neutrons form a square image with side length A_f = (s_e2/s_e1)A_u at the image distance s_e2 = s_e1f_e/(s_e1 − f_e) downstream of the extended lens. The extended lens is positioned closer to the downstream slit than to the upstream slit to narrow the beam both at the focal point and at the downstream slit. Here, the slit width ϕ_s is 14 mm for general SANS measurements and 8 mm for measurements of small samples and for polarization analysis. In contrast, the negative spin-polarized neutrons are defocused downstream of the lens with a divergence of ϕ_lens/ $[s_{\rm e2}']$ , where $[s_{\rm e2}']$ = s_e1f_e/(s_e1 + f_e) is the absolute virtual image distance upstream of the lens. While the intensity of the non-focusing beam is proportional to the solid angle subtended by the aperture of the downstream slit as seen from the object, the intensity of the focusing positive spin-polarized beam is proportional to the solid angle subtended by the lens bore with ϕ_lens from the object, multiplied by the transmission ratio of the downstream slit.

In the tight-focusing beam configuration, the preexisting lens transfers the image at the focal point of the extended lens to produce a square image with a side length A_f = (s_p2/s_e1)A_u at the image distance s_p2 = s_p1f_p/(s_p1 + f_p) downstream of the preexisting lens, where s_p1 = s_e2 − d = s_e1f_e/(s_e1 − f_e) − d is the absolute virtual object distance downstream of the preexisting lens with the focal length f_p = 4820 mm. The combination of the extended lens and the preexisting lens can be represented as a single virtual lens that focuses the positive spin-polarized neutrons with the object distance s₁ = [s_e1/(s_e1 + s_p2)](s_e1 + d + s_p2), the image distance s₂ = [s_p2/(s_e1 + s_p2)](s_e1 + d + s_p2) and the focal length f = s₁s₂/(s₁ + s₂) and defocuses the negative spin-polarized neutrons with the virtual focal length of −s₁s₂/(s₁ + s₂).

Table 1 compares the calculated object length s₁, image lengths s₂ and for the positive and negative spin-polarized neutrons, respectively, and focal point distance X_f from the sample. This table also compares the intensity enhancement of the loose- and tight-focusing beams relative to the unpolarized non-focusing beam, ɛ, which is calculated by using the geometric model in Figs. 2(e) and 2(f). P_n was obtained from the transmission ratios of the downstream slit for the positive and negative spin-polarized neutrons. Both ɛ and P_n of the tight-focusing beam are higher than those of the loose-focusing beam because of the tighter focusing of the positive spin-polarized neutrons and wider defocusing of the negative spin-polarized neutrons at the downstream slit. ɛ of the loose-focusing beam with ϕ_s = 14 mm is equal to that with ϕ_s = 8 mm because the beam size at the downstream slit exceeds ϕ_s; thus, the intensity of both the non-focusing and loose-focusing beams is proportional to $[\phi_{\rm s}^2]$ . In contrast, ɛ of the tight-focusing beam with ϕ_s = 14 mm is smaller than that with ϕ_s = 8 mm because the beam size becomes smaller than ϕ_s = 14 mm; thus, the intensity of the tight-focusing beam is no longer proportional to $[\phi_{\rm s}^2]$ .

Table 1
Calculated f, s₁, s₂, , X_f, A_f, ɛ and P_n for the loose- and tight-focusing beams with A_u = 20 mm

For the loose-focusing beam, s₁ = s_1e, s₂ = s_2e and $[s_2' = s_{\rm 2e}']$ are used. A positive X_f indicates that the focal point lies downstream of the sample. Beam broadening due to Δλ and gravity (Hammouda & Mildner, 2007) was not included in A_f, as these contributions are much smaller than (s₂/s₁)A_u in the present configurations.

								ϕ_s = 8 mm		ϕ_s = 14 mm
		f (mm)	s₁ (mm)	s₂ (mm)	s₂′ (mm)	X_f (mm)	A_f (mm)	ɛ	P_n	ɛ	P_n
Loose-focusing	Horizontal	3140	7790	5260	2238	1700	13.5	3.0	0.88	3.0	0.88
Loose-focusing	Vertical	3140	6540	6040	2121	2480	18.5	3.0	0.88	3.0	0.88

Tight-focusing	Horizontal	2400	8365	3370	1865	384	8.1	9.3	0.96	5.2	0.92
Tight-focusing	Vertical	2390	7147	3591	1791	638	10.1	9.3	0.96	5.2	0.92

We measured the beam images at the sample position using the neutron CCD camera (100 mm × 100 mm, Neutron Optics Grenoble, France) and at the detector position using the highly position-sensitive photomultiplier tube (PS-PMT; R3239, Hamamatsu, Japan) that is generally used for ultra-small-angle neutron scattering measurements (Hirota et al., 2005 ; Koizumi et al., 2007).

2.2. Polarization analysis

The neutron polarization analysis measurements were performed using the tight-focusing beam with A_u = 20 mm and ϕ_s = 8 mm, and a spin analyser consisting of remanent FeCoV/TiN_x supermirrors: 2.5Q_c concave and 1.5Q_c convex, where Q_c is the critical Q for total reflection of the Ni mirror, with detection solid angle of 0.07 sr (PN03-25, SwissNeutronics) (Böni et al., 1999 ; Iwase et al., 2007 ; Noda et al., 2013 ). The scattering neutrons transmitted through the spin analyser were measured by a high-angle detector consisting of a horizontal array of 31 position-sensitive detectors, each 8 mm in diameter and filled with 0.5 MPa ³He gas (E6882-300, J5, Canon, Japan), at L₂ = 920 mm (Fig. 3). For the polarization measurement of the non-scattered direct beam, the 20 mm-diameter beam stopper in front of the spin analyser was removed. For the polarization analysis measurement, the beam stopper was placed at the left end of the spin analyser. The samples measured were 1 mm-thick H₂O, 1 mm-thick silver behenate powder (>95.0%, Tokyo Chemical Industry Co. Ltd, Japan) and 3 mm-thick V_0.96Ni_0.04 alloy (Taiyo Koko Co. Ltd, Japan), which has a coherent scattering cross section of 0.

Figure 3
Layout for the polarization analysis measurement. The ³He high-angle detector with the remanent supermirror-coated spin analyser was moved in front of the vacuum tube containing the ³He main detector and the PS-PMT (Iwase et al., 2007

Because the positions at which the scattered neutrons were detected were shifted horizontally according to the reflection at the curved supermirrors in the spin analyser, the ring-shaped Bragg peaks of silver behenate (see below) were used to calibrate Q of the scattered neutrons at each detector pixel. The sensitivity distribution of the detector was calibrated by the scattering intensity of a 1.2 mm-thick polyethylene sample. The scattering intensity of each sample was converted to absolute units based on the scattering intensity of the glassy carbon standard sample (Thermo Fisher Scientific Inc., USA).

3. Results and discussion

3.1. Comparison with unpolarized non-focusing beam

Fig. 4(a) shows CCD images of the loose- and tight-focusing beams at the sample position (L₂ = 0 mm) without a downstream slit. Fig. 4(b) compares the PS-PMT images of the non-focusing and focusing beams with ϕ_s = 14 mm at L₂ = 1845 and 3845 mm. At L₂ = 1845 mm, the loose-focusing beam had a clearer square image than the tight-focusing beam, indicating that the focal point of the loose-focusing beam was closer to the detector than that of the tight-focusing beam. Compared with the non-focusing beam, the statistical variance σ_r² was smaller for the loose-focusing beam and larger for the tight-focusing beam. At L₂ = 3845 mm, the square image in both the loose- and tight-focusing beams became less distinct due to the increased distance from the focal point to the detector. The σ_r² value of the loose-focusing beam was somewhat larger than that of the non-focusing beam, while that of the tight-focusing beam was considerably larger due to the larger beam divergence. Fig. 4(c) shows the radially averaged normalized intensity distribution obtained from the images in Fig. 4(b). Whereas the non-focusing, loose-focusing and tight-focusing beams are all similar at L₂ = 1845 mm, the loose- and tight-focusing beams became broader than the non-focusing beam at L₂ = 3845 mm. These results indicate that the technique of beam focusing close to the sample position can be used for high-Q SANS measurements only, where L₂ < s₂.

Figure 4
(a) CCD images of the focusing beams at the sample position without the downstream slit, (b) PS-PMT images of the unpolarized non-focusing beam and the focusing beams with ϕ_s = 14 mm at L₂ = 1845 and 3845 mm, and (c) radially averaged intensity distribution obtained from (b). A_u = 20 mm was used for all the measurements.

The $[ \sigma_{\rm r}^2]$ values of the non-focusing beam at L₂ = 1845 and 3845 mm were very close to those calculated using the analytical model presented later in this paper (44.66 and 64.5 mm², respectively). The tight-focusing beam produced a clear rectangular image whose widths in the horizontal and vertical directions were close to A_f in Table 1, indicating that the beam focused very close to the sample position as expected. However, the loose-focusing beam produced a blurred rectangular image whose widths were notably smaller than A_f in Table 1, and the image at L₂ = 0 mm is smaller than that at L₂ = 1845 mm. These results indicate that the extended magnetic lens produces a tighter focus than calculated, with the focal point located closer to the sample than to the detector. The single thin-lens model may have underestimated the focusing power of the extended lens.

The intensity enhancement ɛ of the focusing beams relative to the unpolarized non-focusing beam, obtained from the PS-PMT image measurements, is plotted in Fig. 5. The trend of ɛ values agrees with the calculated results in Table 1 except for the loose-focusing beam with ϕ_s = 8 mm, whose value was larger than the calculated value. This discrepancy probably arises because, as discussed above, the beam was more tightly focused than calculated.

Figure 5
Intensity enhancements ɛ of the focusing beams relative to the unpolarized non-focusing beam. The enhancement ɛ_p relative to the polarized focusing beam, as shown in Table 2

, is also plotted.

Fig. 6 compares the intensity distributions of the non-focusing and focusing beams at Q > 0.1 nm⁻¹ measured with the ³He main detector at L₂ = 1845 mm. The intensity distribution of the non-focusing beam in this Q range was attributed to the air scattering of the beam around the sample position (Kumada et al., 2024). The intensity of the focusing beams increased proportionally to that of the non-focusing beam by ɛ, indicating that parasitic scattering from the magnetic lenses was not generated or at least its intensity was much smaller than the intensity of the air scattering.

Figure 6
Intensity distribution of the non-focusing and focusing beams with A_u = 20 mm and ϕ_s = 14 mm at L₂ = 1845 mm, as measured by the ³He main detector.

Generally, the collimation length L₁ is shortened by installing Ni guide tubes in the upstream section of the collimator, so that it matches the sample-to-detector distance L₂. The neutron beam is transported through the Ni guide tubes without significant intensity loss. The beam intensity increases because the solid angle subtended by the downstream slit, as viewed from the slit at the end of the Ni guide tube, is larger than that seen from the slit at the upstream end of the collimator. However, the ΔQ/Q obtained with the L₁ = L₂ = 2 m layout [Fig. 7(a)] is so poor that the SANS curves obtained with the layout do not coincide with the curve with the L₁ = L₂ = 10 m layout in the overlapped Q range between 0.1 and 0.4 nm⁻¹, resulting in a decrease in structural analysis accuracy. This issue is particularly problematic for SANS diffractometers with small detectors, such as SANS-J, because the Q range covered in a single measurement at each L₂ is severely limited by the small detection area of the detector. ΔQ/Q must be sufficiently small to ensure overlap of SANS curves measured at different L₂ settings within the overlapping Q range.

Here, we quantitively compare the intensity enhancements and the smearing of SANS curves between the focusing beams and the collimator-shortened non-focusing beam. The Q resolution was calculated using the standard Q variance formula (Hammouda & Mildner, 2007 ):

$[\sigma _Q^2 = {\left({{{2\pi } \over \lambda }} \right)^2}{{\sigma _{\rm r}^2} \over {L_2^2}} + {{{Q^2}} \over 6}{\left({{{{{\Delta}}\lambda } \over \lambda }} \right)^2}. \eqno(1)]$

Here, for the non-focusing beam, $[ \sigma_{\rm r}^2]$ is given by

$[\sigma _{\rm r}^2 = {\left({{{{L_2}} \over {{L_1}}}} \right)^2}{{A_{\rm{u}}^2} \over 6} + {\left({{{{L_1} + {L_2}} \over {{L_1}}}} \right)^2}{{\phi _{\rm{s}}^2} \over 8} + {2 \over 3}{\left({{{{{{\Delta}}_{\rm d}}} \over 2}} \right)^2}. \eqno(2)]$

For the focusing beam, if ϕ_lens < ϕ_ss₂/X_f,

$[\sigma _{\rm r}^2 = {\left({{{{s_2}} \over {{s_1}}}} \right)^2}{{A_{\rm{u}}^2} \over 6} + {2 \over 3}{\left({{{{s_1} + {s_2}} \over {{s_1}}}} \right)^2}{\left({{{{{\Delta}}\lambda } \over \lambda }} \right)^2}{{\phi _{{\rm{lens}}}^2} \over 2} + {2 \over 3}{\left({{{{{{\Delta}}_{\rm d}}} \over 2}} \right)^2}, \eqno(3)]$

and, if ϕ_lens > ϕ_ss₂/X_f,

$[\sigma _{\rm r}^2 = {\left({{{{s_2}} \over {{s_1}}}} \right)^2}{{A_{\rm{u}}^2} \over 6} + {2 \over 3}{\left({{{{s_1} + {s_2}} \over {{s_1}}}} \right)^2}{\left({{{{{\Delta}}\lambda } \over \lambda }} \right)^2}{{\phi _{\rm{s}}^2} \over 2}{{s_2^2} \over {X_{\rm f}^2}} + {2 \over 3}{\left({{{{{{\Delta}}_{\rm d}}} \over 2}} \right)^2}, \eqno(4)]$

as long as the focal point is located at the detector. In these equations, Δ_d = 7 mm is the spatial resolution of the ³He main detector. Anisotropy of Δ_d and the gravity effect were neglected. The prefactor of the first term on the right side of equations (2), (3) and (4) differs from that given by Hammouda & Mildner (2007), as it has been modified for a rectangular first slit. ΔQ/Q is obtained from $[\sigma_Q^2]$ :

$[\Delta Q/Q= 2\sqrt{2\ln (2)\, \sigma_Q^2}.\eqno(5)]$

Since both the loose- and tight-focusing beams with ϕ_s = 14 mm, where ϕ_lens < ϕ_ss₂/X_f, have the focal point in front of the detector, $[\sigma_{\rm r}^2]$ and ΔQ/Q of these beams at L₂ = 1845 mm are larger than those calculated using equations (3) and (5).

In SANS-J, scattering curves are typically measured using the main detector positioned at L₂ = 1845 and 10245 mm. At L₂ = 1845 mm, while scattered neutrons with Q > 1.2 nm⁻¹ can be detected without being blocked by a 35 mm-diameter beam stopper, the practically accessible minimum Q is 0.2 nm⁻¹. At L₂ = 10245 mm, the accessible maximum Q is about 0.3 nm⁻¹, which is limited by the detector size. For accurate structure analysis, the Q resolution of the scattering curve measured at L₂ = 1845 mm must be sufficiently high to ensure good overlap with the curve obtained at L₂ = 10245 mm within the overlapping Q range of 0.2–0.3 nm⁻¹.

Fig. 7(a) compares ΔQ/Q as a function of Q for the focusing beams with that for the collimator-shortened non-focusing beam (A_u = 20 mm, ϕ_s = 14 mm and L₂ = 1845 mm). For the collimator-shortened non-focusing beam, decreasing L₁ increases the beam intensity proportionally to $[L_1 ^{- 2}]$ , but at the cost of Q resolution. As shown in Fig. 7(b), the degradation of Q resolution leads to smearing of the SANS curve, which is particularly problematic for analyses of structured curves. With L₁ = 2000 mm, the distinct modulation of the SANS curve of a microphase-separated lamellar cast film, obtained using the non-focusing beam with L₁ = 10100 mm and L₂ = 5000 mm (Noda et al., 2011 ), is smeared out. We consider that the beam with L₁ = 5000 mm provides a reasonable compromise between ɛ and ΔQ/Q within the adjustable layout of SANS-J (ɛ = 4 at a 17% increase in ΔQ/Q at Q = 0.2 nm⁻¹ compared with L₁ = 10100 mm). These values are close to those of the tight-focusing beam (ɛ = 3.9 with an 11% increase). The loose-focusing beam achieved ɛ = 3.1 with a 4% decrease in ΔQ/Q. Similar performance (ɛ = 2.8 with identical ΔQ/Q) can be obtained with the non-focusing beam with L₁ = 4000 mm and ϕ_s = 9.2 mm (not shown). Thus, the focusing beams achieve an intensity enhancement while maintaining, or even slightly decreasing, ΔQ/Q in a manner similar to that of the non-focusing beam when L₁ and ϕ_s are reduced.

Figure 7
(a) ΔQ/Q as a function of Q for the loose- and tight-focusing beams and the collimator-shortened non-focusing beam with A_u = 20 mm, ϕ_s = 14 mm and L₂ = 1845 mm. The grey dashed and solid lines correspond to the non-focusing beam with ϕ_s = 8 mm and the focusing beam with ϕ_s = 14 mm, respectively, at L₂ = 10245 mm. The curves were simulated using the experimentally obtained $[\sigma_{\rm r}^2]$ values in Fig. 4

(b) for the non-focusing beam with L₁ = 10100 mm, and for the loose- and tight-focusing beams. For the other beam configurations, the $[\sigma_{\rm r}^2]$ values calculated with equations (2) and (3) were used. (b) SANS profile of the microphase-separated lamellar poly(styrene-b-isoprene) cast film (yellow symbols) obtained using the non-focusing beam with A_u = 20 mm, ϕ_s = 8 mm, L₁ = 10100 mm and L₂ = 5000 mm (Noda et al., 2011

). The plot also shows simulated SANS curves using ΔQ/Q in (a) for the experimental beam (yellow narrow line); the non-focusing beam with A_u = 20 mm, ϕ_s = 14 mm, L₁ = 10100, 5000 and 2000 mm, and L₂ = 1845 mm (dotted, dash–dotted and dashed lines); and the loose- and tight-focusing beams with L₂ = 1845 mm (solid lines), down to where ΔQ/Q = 1. The double-ended purple arrow shows the Q range where signals are hidden by the beam stopper of SANS-J at L₂ = 1845 mm.

3.2. Comparison with polarized non-focusing beam

The focusing beams offer a distinct advantage for polarized neutrons, because the beams are polarized without the supermirror polarizer whose transmission is 0.3. Table 2 shows the intensity and intensity enhancement against the polarized non-focusing beam, ɛ_p, and P_nP_ana, as measured by the high-angle detector behind the spin analyser with polarization analysis efficiency P_ana. The maximum values of ɛ_p were 21.7 and 15.0 for the tight-focusing beam with ϕ_s = 8 and 14 mm, respectively. P_nP_ana was determined from the intensities of the direct beam when the SF was on, I_0,on, and off, I_0,off: P_nP_ana = |I_0,off − I_0,on|/(I_0,off + I_0,on). The P_nP_ana value of the polarized non-focusing beam was 0.86 at ϕ_s = 8 mm and 0.88 at ϕ_s = 14 mm, consistent with the previously reported value (Noda et al., 2013). Substituting the reported value of P_n = 0.99 for the supermirror polarizer (Oku et al., 2007; Noda et al., 2013) into P_nP_ana gave P_ana values of 0.87 and 0.89 at ϕ_s = 8 and 14 mm, respectively. The P_n values in parentheses were obtained by substituting the P_ana value into P_nP_ana. The P_n values for the tight-focusing beam were slightly smaller than P_n obtained by the supermirror polarizer, but high enough for polarized neutron scattering and polarization analysis measurements.

Table 2
Intensities (in counts per second, cps), ɛ_p and P_nP_ana of the polarized non-focusing, loose-focusing and tight-focusing beams, measured by the ³He high-angle detector placed downstream of the spin analyser

The value of P_n in parentheses was the reported value taken from Oku et al. (2007) for the non-focusing beam (italic) and obtained by substituting P_ana = 0.87 (ϕ_s = 8 mm) and P_ana = 0.89 (ϕ_s = 14 mm) into P_nP_ana for the focusing beams. All intensities include a uniform attenuation factor of 1/65.

		φ_s = 8 mm			φ_s = 14 mm
		Intensity (cps)	ɛ_p	P_nP_ana (P_n)	Intensity (cps)	ɛ_p	P_nP_ana (P_n)
Polarized non-focusing	SF off	5.1	–	–	11.2	–	–
	SF on	69. 7	–	–	172.0	–	–
	Total	74.8	1	0.86 (0.99)	183.1	1	0.88 (0.99)

Loose-focusing	SF off	898.2	–	–	1887.7	–	–
	SF on	162.2	–	–	265.6	–	–
	Total	1060.4	14.2	0.69 (0.81)	2153.3	11.8	0.75 (0.88)

Tight-focusing	SF off	1474.8	–	–	2505.0	–	–
	SF on	146.2	–	–	234.4	–	–
	Total	1621.0	21.7	0.82 (0.95)	2739.4	15.0	0.83 (0.96)

3.3. Polarization analysis measurements

Figs. 8(a) and 8(b) show two-dimensional scattering images of the silver behenate sample measured by the ³He high-angle detector behind the spin analyser, with SF off and on. Coherent diffraction peaks from the silver behenate sample were clearly observed with SF off but significantly weaker with SF on. The differential scattering cross sections, dΣ/dΩ, were obtained by circularly averaging these images. Assuming a spin-flipper efficiency of 1, the spin-flip differential scattering cross section, (dΣ/dΩ)_SF(Q), and non-spin-flip differential scattering cross section, (dΣ/dΩ)_NSF(Q), were determined from (dΣ/dΩ)_on(Q), (dΣ/dΩ)_off(Q) and P_nP_ana as

$[\eqalignno{{\left({{{{\rm{d }}\Sigma} \over {{\rm{d }}\Omega}}} \right)_{{\rm{NSF}}}}\left(Q \right) & = {1 \over {2{P_{\rm{n}}}{P_{{\rm{ana}}}}}}\Big[ \left({1 + {P_{\rm{n}}}{P_{{\rm{ana}}}}} \right){{\left({{{{\rm{d }}\Sigma} \over {{\rm{d }}\Omega}}} \right)}_{{\rm{off}}}}\left(Q \right) \cr & \quad - \left({1 - {P_{\rm{n}}}{P_{{\rm{ana}}}}} \right){{\left({{{{\rm{d }}\Sigma} \over {{\rm{d }}\Omega}}} \right)}_{{\rm{on}}}}\left(Q \right) \Big], &(6)}]$

$[\eqalignno{{\left({{{{\rm{d }}\Sigma} \over {{\rm{d}}\Omega }}} \right)_{{\rm{SF}}}}\left(Q \right) & = {1 \over {2{P_{\rm{n}}}{P_{{\rm{ana}}}}}}\Big[ - \left({1 - {P_{\rm{n}}}{P_{{\rm{ana}}}}} \right){{\left({{{{\rm{d }}\Sigma} \over {{\rm{d }}\Omega}}} \right)}_{{\rm{off}}}}\left(Q \right) \cr & \quad + \left({1 + {P_{\rm{n}}}{P_{{\rm{ana}}}}} \right){{\left({{{{\rm{d }}\Sigma} \over {{\rm{d }}\Omega}}} \right)}_{{\rm{on}}}}\left(Q \right) \Big].&(7)}]$

The spin-incoherent differential scattering cross section, (dΣ/dΩ)_s-inc(Q), and the sum of the coherent and isotope-incoherent differential scattering cross sections, (dΣ/dΩ)_others(Q), were given by

$[{\left({{{{\rm{d }}\Sigma} \over {{\rm{d }}\Omega}}} \right)_{{\rm{s}} \hbox{{-}} {\rm{in}}c}}\left(Q \right) = {1 \over p}{\left({{{{\rm{d }}\Sigma} \over {{\rm{d }}\Omega}}} \right)_{{\rm{SF}}}}\left(Q \right), \eqno(8)]$

$[{\left({{{{\rm{d }}\Sigma} \over {{\rm{d }}\Omega}}} \right)_{{\rm{others}}}}\left(Q \right) = {\left({{{{\rm{d }}\Sigma} \over {{\rm{d }}\Omega}}} \right)_{{\rm{NSF}}}}\left(Q \right) - {{1 - p} \over p}{\left({{{{\rm{d }}\Sigma} \over {{\rm{d }}\Omega}}} \right)_{{\rm{SF}}}}\left(Q \right). \eqno(9)]$

The spin-flipping probability for spin-incoherent scattering is p = 2/3 when a sample undergoes only a single scattering event, and it approaches 0.5 as the fraction of multiple-scattering events increases. We used p for each sample as obtained by substituting the spin-incoherent cross section of each element (Dianoux & Lander, 2003 ) into the general-purpose Monte Carlo simulation code PHITS (Sato et al., 2024 ; Iwamoto et al., 2022 ) to separate (dΣ/dΩ)_s-inc(Q) and (dΣ/dΩ)_others(Q). Fig. 8(c) shows (dΣ/dΩ)_s-inc(Q) and (dΣ/dΩ)_others(Q), which were obtained from Figs. 8(a) and 8(b) and equations (6)–(9). The diffraction peaks were clearly observed in (dΣ/dΩ)_others(Q), with no plateau signal, as expected from the calculated isotope-incoherent differential scattering cross section. Conversely, a plateau consistent with the calculated spin-incoherent differential scattering cross section was observed in (dΣ/dΩ)_s-inc(Q).

Figure 8
Two-dimensional polarized neutron scattering images of the silver behenate sample measured with the ³He high-angle detector behind the spin analyser for 1800 s each, with (a) SF off and (b) SF on. The dashed circle indicates the position of the beam stopper. (c) (dΣ/dΩ)_s-inc(Q) and (dΣ/dΩ)_others(Q) were obtained from (a) and (b) using p = 0.598. The dashed lines indicate the calculated spin- and isotope-incoherent differential scattering cross sections.

Contrary to our expectation, the diffraction peak was not eliminated from (dΣ/dΩ)_s-inc(Q). We attribute this to the fact that the P_ana value for the scattered neutrons was slightly lower than that for the non-scattered direct beam used in equations (6) and (7). Because of the collimation geometry, the spin analyser exhibits the highest spin-analysing performance for neutrons scattered from the sample centre, but reduced performance for those scattered from off-centre regions (Böni et al., 1999). In fact, (dΣ/dΩ)_s-inc(Q) and (dΣ/dΩ)_others(Q) determined using the beam with ϕ_s = 14 mm deviated more from the calculated values than those obtained with the beam with ϕ_s = 8 mm (data not shown). Thus, although the use of a narrower beam could in principle allow a more accurate determination of (dΣ/dΩ)_s-inc(Q) and (dΣ/dΩ)_others(Q), the significant loss of scattering intensity makes this approach impractical.

Fig. 9(a) shows (dΣ/dΩ)_s-inc(Q) and (dΣ/dΩ)_others(Q) of V_0.96Ni_0.04, which were obtained from (dΣ/dΩ)_SF(Q) and (dΣ/dΩ)_NSF(Q). Since this sample exhibited no coherent scattering, (dΣ/dΩ)_others(Q) corresponds solely to isotope-incoherent scattering. The values of (dΣ/dΩ)_s-inc(Q) and (dΣ/dΩ)_others(Q) agree with the calculated spin- and isotope-incoherent differential scattering cross sections. These results demonstrate that SANS-J can determine spin- and isotope-incoherent differential scattering cross sections down to 0.005 cm⁻¹ within its margin of error. Fig. 9(b) shows the data obtained with the non-focusing beam instead of the tight-focusing beam. The signal-to-noise ratio was too low to determine the differential cross sections. The remarkable improvement could not be expected even if the measurement time were set to be the same as that in Fig. 9(a). This result indicates that the detector behind the spin analyser can measure neutrons from only a limited region of the sample and that the acceptable solid angle of the spin analyser is very small (0.07 sr). The intensity enhancement using the tight-focusing beam enabled the polarization analysis of the sample.

Figure 9
(dΣ/dΩ)_s-inc(Q) and (dΣ/dΩ)_others(Q) of V_0.96Ni_0.04 obtained from (dΣ/dΩ)_on(Q) and (dΣ/dΩ)_off(Q) measured with (a) the tight-focusing layout for 7200 s each and (b) the non-focusing layout for 3600 s each using p = 0.65. The dashed lines indicate the calculated spin- and isotope-incoherent differential scattering cross sections.

Fig. 10 shows (dΣ/dΩ)_s-inc(Q) and (dΣ/dΩ)_others(Q) of the 1 mm-thick H₂O sample. Due to multiple scattering, the incoherent differential scattering cross section exceeded the sum of the incoherent differential cross sections of the atoms in the sample (Shibayama et al., 2009 ; Shibayama et al., 2005 ). However, the sum of (dΣ/dΩ)_s-inc(Q) and (dΣ/dΩ)_others(Q) was much smaller than the reported values of 0.89–1.01 cm⁻¹ (Shibayama et al., 2009; Shibayama et al., 2005) because of the poor sensitivity of the 8 mm-diameter high-angle detector filled with 0.5 MPa ³He gas for the inelastically scattered neutrons from the H₂O sample. Do et al. (2014 ) and Chen et al. (2023 ) reported that some of the scattered neutrons from H₂O gain energies consistent with their thermal energy at room temperature. The fraction of λ = 0.6–0.7 nm neutrons accelerated by the interaction with the 1 mm-thick H₂O sample was about 33% of the scattered neutrons. The ³He tube's detection efficiency was 88% for the elastically scattered neutrons with λ = 0.65 nm, but only 42% for the inelastically scattered neutrons with the room-temperature thermal energy (λ = 0.17 nm). Even with this non-negligible fraction of accelerated neutrons incident on the spin analyser, (dΣ/dΩ)_others(Q) remains close to zero, as expected.

Figure 10
(dΣ/dΩ)_s-inc(Q) and (dΣ/dΩ)_others(Q) of the H₂O sample obtained from (dΣ/dΩ)_on(Q) and (dΣ/dΩ)_off(Q) measured for 1800 s each, using p = 0.60. The dashed lines indicate the calculated spin- and isotope-incoherent differential scattering cross sections.

As shown in Figs. 8–10 , the combination of the tight-focusing beam with the remanent supermirror-coated spin analyser enabled polarization analysis measurements. However, the performance of the remanent supermirror-coated spin analyser is still inferior to that of ³He spin filters reported elsewhere (Babcock et al., 2013 ; Chen et al., 2017 ; Gentile et al., 2000 ; Chen et al., 2023; Okudaira et al., 2021 ; Okudaira et al., 2020 ; Takahashi et al., 2025 ). To overcome this limitation and fully exploit the intensity-enhanced tight-focusing polarized beam, we plan to install an in situ ³He spin filter developed at the Materials and Life Science Experimental Facility (MLF), Japan Proton Accelerator Research Complex (J-PARC), at SANS-J. This upgrade will enable high-quality polarization analysis measurements with the tight-focusing polarized beam.

Furthermore, we will apply the tight-focusing polarized beam to spin-contrast-variation SANS (SCV-SANS) measurements, which reveal the structure of composite materials through proton-polarization-dependent polarized neutron scattering (Knop et al., 1991 ). Although SCV-SANS measurements were previously performed at SANS-J using a polarized non-focusing beam with a dynamic nuclear polarization apparatus (Kumada et al., 2009 ; Kumada et al., 2010 ; Noda et al., 2016 ), they have more recently been conducted at BL15 (TAIKAN) in J-PARC MLF due to its higher flux of polarized beam (Kumada et al., 2023b ). By resuming SCV-SANS at SANS-J with the tight-focusing polarized beam, we will establish a complementary experimental environment to J-PARC, thereby highlighting the unique role of SANS-J in advancing polarized neutron scattering studies.

4. Conclusion

The use of extended magnetic lenses increased the intensity of the non-polarized beam by a factor of 3.1–6.2 and of the polarized beam by 11.8–21.7, while maintaining or even improving the Q resolution for scattering measurements at Q > 0.1 nm⁻¹. Furthermore, the tight-focusing beam, combined with a remanent supermirror-coated spin analyser, enabled separation of coherent and isotope-incoherent scattering from spin-incoherent scattering within 1–4 h, more than an order of magnitude faster than the several days needed with the non-focusing beam. We have already employed these focusing beams for both unpolarized and polarized neutron scattering measurements at Q ≥ 0.1 nm⁻¹. The loose-focusing beam offers high intensity with excellent Q resolution, while the tight-focusing beam provides high intensity together with high neutron polarization, making it particularly effective for scattering measurements of small samples and polarization analysis measurements.

Acknowledgements

We thank the JAEA machine shop for fabricating the instruments. We also thank Dr Hiroki Iwase of the Neutron Science and Technology Center at the Comprehensive Research Organization for Science and Society for his valuable input. The experiments at SANS-J were performed under the JRR-3 user programme (proposal Nos. 2023-I814, 2024-I007 and 2025-I203).

Conflict of interest

We have no conflict of interest.

Data availability

The data supporting the results can be accessed upon request.

Funding information

The following funding is acknowledged: Grant-in-Aid for Scientific Research from the Ministry of Education, Culture, Sports, Science and Technology, Japan (grant No. 21H03741).

References

Babcock, E., Salhi, Z., Appavou, M. S., Feoktystov, A., Pipich, V., Radulescu, A., Ossovyi, V., Staringer, S. & Ioffe, A. (2013). Phys. Proc. 42, 154–162. CrossRef CAS Google Scholar
Barker, J., Moyer, J., Kline, S., Jensen, G., Cook, J., Gagnon, C., Kelley, E., Chabot, J. P., Maliszewskyj, N., Parikh, C., Chen, W., Murphy, R. P. & Glinka, C. (2022). J. Appl. Cryst. 55, 271–283. Web of Science CrossRef CAS IUCr Journals Google Scholar
Böni, P., Clemens, D., Kumar, M. S. & Pappas, C. (1999). Physica B 267–268, 320–327. Google Scholar
Chen, W. C., Barker, J. G., Jones, R., Krycka, K. L., Watson, S. M., Gagnon, C., Perevozchivoka, T., Butler, P. & Gentile, T. R. (2017). J. Phys. Conf. Ser. 862, 012004. CrossRef Google Scholar
Chen, W. C., Krycka, K. L., Watson, S. M., Barker, J. G., Gaudet, J., Burrall, H. & Borchers, J. A. (2023). J. Phys. Conf. Ser. 2481, 012006. CrossRef Google Scholar
Choi, S.-M., Barker, J. G., Glinka, C. J., Cheng, Y. T. & Gammel, P. L. (2000). J. Appl. Cryst. 33, 793–796. Web of Science CrossRef CAS IUCr Journals Google Scholar
Cremer, J. T. Jr, Filter, H., Klepp, J., Geltenbort, P., Dewhurst, C., Oda, T. & Pantell, R. H. (2020). Rev. Sci. Instrum. 91, 013704. Google Scholar
Dianoux, A. & Lander, G. (2003). Neutron data booklet. OCP science. Google Scholar
Do, C., Heller, W. T., Stanley, C., Gallmeier, F. X., Doucet, M. & Smith, G. S. (2014). Nucl. Instrum. Methods Phys. Res. A 737, 42–46. Web of Science CrossRef CAS Google Scholar
Gentile, T. R., Jones, G. L., Thompson, A. K., Barker, J., Glinka, C. J., Hammouda, B. & Lynn, J. W. (2000). J. Appl. Cryst. 33, 771–774. Web of Science CrossRef CAS IUCr Journals Google Scholar
Hammouda, B. & Mildner, D. F. R. (2007). J. Appl. Cryst. 40, 250–259. Web of Science CrossRef CAS IUCr Journals Google Scholar
Han, Y.-S., Choi, S.-M., Kim, T.-H., Lee, C.-H., Cho, S.-J. & Seong, B.-S. (2013). Nucl. Instrum. Methods Phys. Res. A 721, 17–20. Web of Science CrossRef CAS Google Scholar
Heller, W. T., Cuneo, M., Debeer-Schmitt, L., Do, C., He, L., Heroux, L., Littrell, K., Pingali, S. V., Qian, S., Stanley, C., Urban, V. S., Wu, B. & Bras, W. (2018). J. Appl. Cryst. 51, 242–248. Web of Science CrossRef CAS IUCr Journals Google Scholar
Heller, W. T., Urban, V. S., Lynn, G. W., Weiss, K. L., O'Neill, H. M., Pingali, S. V., Qian, S., Littrell, K. C., Melnichenko, Y. B., Buchanan, M. V., Selby, D. L., Wignall, G. D., Butler, P. D. & Myles, D. A. (2014). J. Appl. Cryst. 47, 1238–1246. Web of Science CrossRef CAS IUCr Journals Google Scholar
Hirota, K., Shinohara, T., Ikeda, K., Mishima, K., Adachi, T., Morishima, T., Satoh, S., Oku, T., Yamada, S., Sasao, H., Suzuki, J. & Shimizu, H. M. (2005). Phys. Chem. Chem. Phys. 7, 1836–1838. Web of Science CrossRef PubMed CAS Google Scholar
Iwamoto, Y., Hashimoto, S., Sato, T., Matsuda, N., Kunieda, S., Çelik, Y., Furutachi, N. & Niita, K. (2022). J. Nucl. Sci. Technol. 59, 665–675. Web of Science CrossRef CAS Google Scholar
Iwase, H., Endo, H., Katagiri, M. & Shibayama, M. (2011). J. Appl. Cryst. 44, 558–568. Web of Science CrossRef CAS IUCr Journals Google Scholar
Iwase, H., Koizumi, S., Suzuki, J., Oku, T., Sasao, H., Tanaka, H., Shimizu, H. M. & Hashimoto, T. (2007). J. Appl. Cryst. 40, s414–s417. Web of Science CrossRef CAS IUCr Journals Google Scholar
Knop, W., Hirai, M., Olah, G., Meerwinck, W., Schink, H. J., Stuhrman, H. B., Wagner, R., Wenkow-EsSouni, M., Zhao, J., Schärpf, O., Crichton, R. R., Krumpolc, M., Nierhaus, K. H., Niinikoski, T. O. & Rijllart, A. (1991). Physica B 174, 275–290. CrossRef CAS Web of Science Google Scholar
Koizumi, S., Iwase, H., Suzuki, J., Oku, T., Motokawa, R., Sasao, H., Tanaka, H., Yamaguchi, D., Shimizu, H. M. & Hashimoto, T. (2007). J. Appl. Cryst. 40, s474–s479. Web of Science CrossRef CAS IUCr Journals Google Scholar
Kumada, T., Motokawa, R. & Iwase, H. (2024). J. Appl. Cryst. 57, 728–733. Web of Science CrossRef CAS IUCr Journals Google Scholar
Kumada, T., Motokawa, R., Oba, Y., Nakagawa, H., Sekine, Y., Micheau, C., Ueda, Y., Sugita, T., Birumachi, A., Sasaki, M., Hiroi, K. & Iwase, H. (2023a). J. Appl. Cryst. 56, 1776–1783. Web of Science CrossRef CAS IUCr Journals Google Scholar
Kumada, T., Nakagawa, H., Miura, D., Sekine, Y., Motokawa, R., Hiroi, K., Inamura, Y., Oku, T., Ohishi, K., Morikawa, T., Kawamura, Y. & Kawai, K. (2023b). J. Phys. Chem. Lett. 14, 7638–7643. Web of Science CrossRef CAS PubMed Google Scholar
Kumada, T., Noda, Y., Hashimoto, T. & Koizumi, S. (2009). Physica B 404, 2637–2639. Web of Science CrossRef CAS Google Scholar
Kumada, T., Noda, Y., Koizumi, S. & Hashimoto, T. (2010). J. Chem. Phys. 133, 054504. Web of Science CrossRef PubMed Google Scholar
Noda, Y., Koizumi, S., Masui, T., Mashita, R., Kishimoto, H., Yamaguchi, D., Kumada, T., Takata, S., Ohishi, K. & Suzuki, J. (2016). J. Appl. Cryst. 49, 2036–2045. Web of Science CrossRef CAS IUCr Journals Google Scholar
Noda, Y., Kumada, T., Hashimoto, T. & Koizumi, S. (2011). J. Appl. Cryst. 44, 503–513. Web of Science CrossRef CAS IUCr Journals Google Scholar
Noda, Y., Yamaguchi, D., Putra, A., Koizumi, S., Sakaguchi, Y., Oku, T. & Suzuki, J. (2013). Phys. Proc. 42, 46–51. CrossRef CAS Google Scholar
Oku, T., Iwase, H., Shinohara, T., Yamada, S., Hirota, K., Koizumi, S., Suzuki, J., Hashimoto, T. & Shimizu, H. M. (2007). J. Appl. Cryst. 40, s408–s413. Web of Science CrossRef CAS IUCr Journals Google Scholar
Oku, T., Kira, H., Shinohara, T., Takata, S., Arai, M., Suzuki, J. & Shimizu, H. M. (2010). J. Phys. Conf. Ser. 251, 012078. CrossRef Google Scholar
Okudaira, T., Oku, T., Ino, T., Hayashida, H., Kira, H., Sakai, K., Hiroi, K., Takahashi, S., Aizawa, K., Endo, H., Endo, S., Hino, M., Hirota, K., Honda, T., Ikeda, K., Kakurai, K., Kambara, W., Kitaguchi, M., Oda, T., Ohshita, H., Otomo, T., Shimizu, H. M., Shinohara, T., Suzuki, J. & Yamamoto, T. (2020). Nucl. Instrum. Methods Phys. Res. A 977, 164301. Web of Science CrossRef Google Scholar
Okudaira, T., Ueda, Y., Hiroi, K., Motokawa, R., Inamura, Y., Takata, S., Oku, T., Suzuki, J., Takahashi, S., Endo, H. & Iwase, H. (2021). J. Appl. Cryst. 54, 548–556. Web of Science CrossRef CAS IUCr Journals Google Scholar
Radulescu, A. (2025). QuBS 9, 6. Web of Science CrossRef Google Scholar
Radulescu, A., Szekely, N. K., Appavou, M.-S., Pipich, V., Kohnke, T., Ossovyi, V., Staringer, S., Schneider, G. J., Amann, M., Zhang-Haagen, B., Brandl, G., Drochner, M., Engels, R., Hanslik, R. & Kemmerling, G. (2016). J. Vis. Exp. 118, e54639. Google Scholar
Sato, T., Iwamoto, Y., Hashimoto, S., Ogawa, T., Furuta, T., Abe, S., Kai, T., Matsuya, Y., Matsuda, N., Hirata, Y., Sekikawa, T., Yao, L., Tsai, P., Ratliff, H. N., Iwase, H., Sakaki, Y., Sugihara, K., Shigyo, N., Sihver, L. & Niita, K. (2024). J. Nucl. Sci. Technol. 61, 127–135. Web of Science CrossRef CAS Google Scholar
Shibayama, M., Matsunaga, T. & Nagao, M. (2009). J. Appl. Cryst. 42, 621–628. Web of Science CrossRef CAS IUCr Journals Google Scholar
Shibayama, M., Nagao, M., Okabe, S. & Karino, T. (2005). J. Phys. Soc. Jpn 74, 2728–2736. Web of Science CrossRef CAS Google Scholar
Takahashi, S., Kiyanagi, R., Okudaira, T., Takada, S., Kobayashi, R., Okuizumi, M., Ino, T., Asai, K., Tsuchikawa, Y., Oikawa, K., Harada, M., Ohhara, T., Suzuki, J., Fujita, M., Ikeda, Y., Kakurai, K. & Oku, T. (2025). Nucl. Instrum. Methods Phys. Res. A 1075, 170410. Web of Science CrossRef Google Scholar
Wignall, G. D., Littrell, K. C., Heller, W. T., Melnichenko, Y. B., Bailey, K. M., Lynn, G. W., Myles, D. A., Urban, V. S., Buchanan, M. V., Selby, D. L. & Butler, P. D. (2012). J. Appl. Cryst. 45, 990–998. Web of Science CrossRef CAS IUCr Journals Google Scholar
Wood, K., Mata, J. P., Garvey, C. J., Wu, C.-M., Hamilton, W. A., Abbeywick, P., Bartlett, D., Bartsch, F., Baxter, P., Booth, N., Brown, W., Christoforidis, J., Clowes, D., d'Adam, T., Darmann, F., Deura, M., Harrison, S., Hauser, N., Horton, G., Federici, D., Franceschini, F., Hanson, P., Imamovic, E., Imperia, P., Jones, M., Kennedy, S., Kim, S., Lam, T., Lee, W. T., Lesha, M., Mannicke, D., Noakes, T., Olsen, S. R., Osborn, J. C., Penny, D., Perry, M., Pullen, S. A., Robinson, R. A., Schulz, J. C., Xiong, N. & Gilbert, E. P. (2018). J. Appl. Cryst. 51, 294–314. Web of Science CrossRef CAS IUCr Journals Google Scholar
Zhang, H., Cheng, H., Yuan, G., Han, C. C., Zhang, L., Li, T., Wang, H., Liu, Y. T. & Chen, D. (2014). Nucl. Instrum. Methods Phys. Res. A 735, 490–495. Web of Science CrossRef CAS Google Scholar

This is an open-access article distributed under the terms of the Creative Commons Attribution (CC-BY) Licence, which permits unrestricted use, distribution, and reproduction in any medium, provided the original authors and source are cited.

JOURNAL OF
APPLIED
CRYSTALLOGRAPHY

ISSN: 1600-5767

Volume 59| Part 1| February 2026| Pages 69-79

https://doi.org/10.1107/S1600576725010246

Open

access

Format		BIBTeX
		EndNote
		RefMan
		Refer
		Medline
		CIF
		SGML
		Plain Text
		Text

Format		BIBTeX
		EndNote
		RefMan
		Refer
		Medline
		CIF
		SGML
		Plain Text
		Text

Search IUCr Journals		doi		Advanced search
Author		volume	page

research papers\(\def\hfill{\hskip 5em}\def\hfil{\hskip 3em}\def\eqno#1{\hfil {#1}}\)

Magnetic-lens-generated polarized neutron beam with enhanced intensity and Q resolution for small-angle neutron scattering

1. Introduction

2. Experimental

2.1. Optical layout

2.2. Polarization analysis

3. Results and discussion

3.1. Comparison with unpolarized non-focusing beam

3.2. Comparison with polarized non-focusing beam

3.3. Polarization analysis measurements

4. Conclusion

Acknowledgements

Conflict of interest

Data availability

Funding information

References

research papers