Neutron depolarization theory in the larmor and the scattering approach

The neutron depolarization theory in the Larmor and the scattering approach is presented. An extension of the former is proposed, as a result of which both approaches result in basically the same formulas. The intrinsic anisotropy, which is the phenomenon that for magnetically isotropic media the depolarization is still dependent on the mutual orientation of the polarization vector and the propagation direction of the neutron beam, is discussed furthermore. It is shown that this phenomenon is caused by local stray fields around magnetic inhomogeneities as well as eventual correlations between the shape of these inhomogeneities and the orientation of the local magnetization.     

Experiments with neutron polarization analysis

Neutron polarization analysis experiments of the past 25 years are reviewed. In that time the technique has progressed from a curiosity to being a useful tool to be used when needed. In early experiments, the polarization of the scattered beam was analysed in the same direction as the polarization of the incident beam but, in some later experiments, full three-dimensional polarization analysis has been employed. This article starts by writing down the interactions which the neutron has with condensed matter and deriving the cross-sections for scattering and final polarizations of the scattered beam. This is done displaying the spin state functions of the neutron explicitly. A variety of experiments is then reviewed, commencing with the elastic and inelastic scattering experiments performed by Moon, Riste and Koehler in the late 1960s. Elastic scattering experiments where it is important to separate nuclear and magnetic cross-sections such as antiferromagnetic defect scattering are reviewed together with separation out of the nuclear spin scattering for various purposes. Of particular interest are the fully three-dimensional analysis experiments which reveal more about the structure and domain populations of certain antiferromagnets. Inelastic experiments for which polarization analysis is vital are those on paramagnets at high temperatures where it is necessary to discriminate against phonon scattering. Spin glasses are treated as frozen paramagnets. Polarization analysis also has another role to play in the separation of magnetic modes in both paramagnets and ordered magnets, and several of these experiments are reviewed. Finally it is possible to tag the polarization of a neutron beam in time and space and to measure the result at another time and place and this through various techniques yields information about the change in neutron energy on scattering. The techniques of pseudo-random flipping time of flight, neutron spectral modulation and neutron spin-echo spectroscopy are briefly reviewed but the techniques of polarized-neutron-beam management are left to another review.     

硼中子俘获治疗的蒙特卡罗方法模拟

用通用蒙特卡罗程序MCNP模拟了粒子在人脑中的输运过程. 吸收剂量率主要来自以下四个反应:¹⁰B(n,α)⁷Li,¹⁴N(n,p)¹⁴C,¹H(n,γ)²D,快中子弹性散射反应.对肿瘤区的贡献主要来自硼中子吸收反应.结果表明,超热中子比热中子适合于深肿瘤的治疗,而热中子对浅肿瘤的治疗有优越性,比如皮肤癌.同确定论方法的结果相比,蒙特卡罗方法不失为一种模拟中子俘获治疗的好工具.     

Study of matter at high pressure using small angle scattering and depolarization of neutrons

Abstract

The method of studying matter under high pressure using the measurement of the transmitted neutron beam is proposed. Method is based on the very small angle scattering and depolarization of neutrons combined with the anvil pressure technique. Test experiments have been carried out demonstrating feasibility of the method for studying phase transitions accompanied with the change of density or magnetization and equations of state. The obtainable pressure range of the method is discussed.     

Analysis of the magnetic domain structure of electrodeposited nickel studied by neutron depolarization

A polarized monochromatic neutron beam is transmitted through a nickel sheet which has been electrodeposited onto a copper backing. The polarization direction of the incoming beam may be adjusted in three orthogonal directions, while the polarization after transmission through the sample can be analyzed in three independent directions. In this way a (3×3) depolarization matrix can be determined, of which the diagonal elements give the depolarization factors in the successive directions. At zero applied magnetic field and perpendicular transmission no depolarization is observed when the polarization vector is perpendicular to the sheet. The depolarization factors in the other two directions nearly follow a cosine dependence on the neutron wavelength. A structure consisting of domains with magnetization directions perpendicular to the sheet could explain the results. By varying the angle of transmission of the neutron beam with respect to the plane of the sheet one can determine the mean domain size and to some extent the nature of the distribution function of the domain size in the plane of the sheet. In addition, the depolarization has been studied as a function of a magnetic field applied in a direction in the plane of the sheet. The results are compared with magnetization measurements performed in a magnetic field applied in the same direction.     

A neutron polarization analysis study of Ce2Fe17 in its paramagnetic phase

Spin-flip (paramagnetic) scattering and neutron depolarization studies were performed on Ce₂Fe₁₇ in its paramagnetic phase on the Dhruva neutron polarization analysis spectrometer. The absence of normalQ dependence of the scattered spin flip intensity shows that Ce₂Fe₁₇ is not a normal paramagnetic and there exist superparamagnetic clusters of sufficiently large dimensions (～100Å). The observed neutron depolarization gives an indication of the dynamics of these Ce₂Fe₁₇ superparamagnetic clusters.     

Neutron depolarisation imaging: Stress measurements by magnetostriction effects in Ni foils

In this article we present first proof-of-principle neutron depolarization imaging measurements on Ni foils under mechanical stress. The magnetostrictive effect in Ni leads to a reorientation of the magnetic domains in the material depending on the applied force. This in turn leads to a change of the depolarization a neutron beam suffers from transmission of the sample. We propose to use this method as a new technique for the spatially resolved measurement of mechanical stress.     

Retrieval of the complex reflection coefficient from nano scale thin films by using polarized neutrons and magnetic substrates

A method is proposed for overcoming the famous ‘phase problem’ in neutron specular reflectometry. It is shown that the complex reflection coefficient of any unknown non magnetic layer, with real scattering length density, can be determined by using a magnetic transmitted media and by measuring the polarization of the reflected beam relative to the incident beam. The method follows directly from a recent one which is limited to a one-dimensional neutron polarization. Here, the theory is generalized for a neutron polarization of arbitrary direction. We show that some combinations between the polarization of the incident and reflected beam must be used to determine the reflection coefficient. Also, it is shown that instead of full polarization or reflectivity analysis, some combinations between polarization and reflectivity can be used in the analysis process. The method is supplemented with a schematic example to test the method and its stability in the presence of experimental uncertainties and roughness of the interfaces. PACS 61.12.Ha; 28.20.-v     

Matrix analysis of neutron spin-echo

We describe the general action of a neutron spin-turn coil by a rotation matrix, and the nett action of a sequence of spin-turns is then evaluated as the product of the relevant matrices. In the ideal neutron spin-echo configuration, the spin-turn sequence used is shown to have a resultant action described by the unit matrix if there is only elastic scattering, so that an initially polarized beam is transmitted with unchanged polarization. This is spin-echo focussing. Measurement of changes in the final polarization then provides information on the sample dynamics.Spin-echo focussing permits high resolution to be coupled with a broad incident wavelength spread. We calculate in detail the effect of this polychromaticity on the spinturn coils involved, and present experimental confirmation. General spin-echo configurations are then considered. Finally, we take into account the effect of spin-flip scattering from spin-incoherent samples, and show that spin-flip effects may be decoupled from dynamic effects in the analysis of spin-echo intensity.The techniques evolved are relevant to both monochromatic and polychromatic spinecho spectrometry. Emphasis has been placed on practical aspects of establishing correct spin-turn conditions and analysing spectrometer response in terms of relative transmitted intensity.     

Parity non-conservation effects in neutron elastic scattering reactions

Energy dependence of parity non-conservation effects is derived for neutron elastic scattering on nuclei: emission asymmetry and the rotation of the polarization plane for the polarized neutron beam and longitudinal polarization for unpolarized neutrons. Both potential scattering and scattering through the compound-nucleus resonances (multi-level approximation) are taken into account. The expressions obtained are compared with experimental data on thermal neutron scattering.     

Measurement of neutron elastic scattering cross sections for carbon at 134 MeV

Angular differential neutron elastic scattering cross sections have been measured by using a ⁷Li(p,n) quasi-monoenergetic neutron beam. The neutron beam whose peak energy is 134 MeV was incident upon a natural carbon sample, and the scattering neutrons were measured by liquid organic scintillators with the time-of-flight (TOF) technique. The results were compared with the existing experimental data measured by a recoil-proton telescope, and the evaluated nuclear data of JENDL/HE-2007 and ENDF/B-VII.0.     

Polarization contrast enhancement of images of biological tissues under the conditions of multiple scattering

The concept of laser polarization probing of biological tissues under the conditions of scattering of high multiplicities is analyzed and approbated experimentally. The effect of the degree of depolarization of the scattered background on the signal-to-noise ratio in coherent images of an optically anisotropic architectonic of the morphological structure of a biological tissue and of the polarization correction of the probing beam on the contrast enhancement of these images are considered.     

Neutron spin echo: A new concept in polarized thermal neutron techniques

A simple method to change and keep track of neutron beam polarization non-parallel to the magnetic field is described. It makes possible the establishment of a new focusing effect we call neutron spin echo. The technique developed and tested experimentally can be applied in several novel ways, e. g. for neutron spin flipper of superior characteristics, for a very high resolution spectrometer for direct determination of the Fourier transform of the scattering function, for generalised polarization analysis and for the measurement of neutron particle properties with significantly improved precision.     

Determining the structural parameters of fractal and nonfractal objects in multiple small-angle neutron scattering experiments

An experimental procedure employing setups with standard resolution characteristics for multiple small-angle neutron scattering in fractal and nonfractal media is described. Specific features of the proposed method, which are related to a limited resolution of the spectrometer, are considered in the case of large-scale inhomogeneities with the characteristic size exceeding the inverse spatial resolution. A new approach to the extraction of information about the fractal dimension of the system studied is demonstrated, which takes into account the dependence of the attenuation and broadening of the transmitted neutron beam on the sample thickness.     

Using a grating analyser for SEMSANS investigations in the very small angle range

Spin-echo modulation small-angle neutron scattering (SEMSANS) is based on the detection of spatial beam modulation, which is induced by triangular spin echo precession regions and subsequent spin analyses. In order to detect such signal and exploit it for small angle scattering investigations neutron detection with sub-millimeter spatial resolution is required. Here an approach is reported where instead of a position sensitive detector an absorption grating is used to analyze the beam modulation stepwise. The spin-echo length scan in this case is performed by varying the sample-to-detector distance. The real space correlation functions of reference sample structures in the range 10² nm, i.e. giving rise to small-angle scattering in the very small-angle range, are recorded and analyzed successfully.     

Calculation of neutron depolarization in a uniaxial ferromagnet

We consider a ferromagnetic system which is divided into domains with magnetization directions perpendicular to the plane of the sheet. This system is traversed by a polarized thermal neutron beam with the direction of the polarization vector perpendicular to the magnetization directions of the domains. On the basis of a few assumptions, we calculate the depolarization as a function of the direction of the neutron beam with respect to the plane of the sheet and in terms of the distribution function of the domain sizes as seen in a direction in the plane of the sheet. The result of this calculation is compared to a computer simulation of the same problem and to an experimental result published earlier.     

Depolarization of a neutron beam in Laue diffraction by a noncentrosymmetric crystal

The depolarization of a neutron beam executing Laue diffraction in a thick (～3.5 cm) noncentrosymmetric α-quartz crystal is observed. This effect was predicted by us earlier and suggested for measuring the electric dipole moment (EDM) of a neutron. The effect is due to an interaction of the magnetic moment of a moving neutron with a strong crystal electric field, as a result of which the neutron spin rotates in opposite directions for waves of two types excited in the crystal. The effect is studied for neutron diffraction by a system of crystallographic (110) planes at Bragg angles close to π/2, up to 87°. It is shown that, for a crystal of thickness L=3.5 cm, a direct beam initially polarized along the reciprocal lattice vector becomes depolarized upon diffraction, irrespective of the value of Bragg angle, whereas the beam polarized perpendicular to the diffraction plane retains its polarization. The Eτ value determining the sensitivity of the method to EDM is experimentally estimated.     

Physical design of target station and neutron instruments for China Spallation Neutron Source

The China Spallation Neutron Source(CSNS)is the first accelerator-based multidiscipline user facility to produce pulsed neutrons by tungsten target under collision of a pulsed proton beam with a beam power of 100 kW at a repetition rate of 25 Hz.In this paper,we focus on the physical design of CSNS target station and neutron instruments.Under optimized design,the flat tungsten target and the compact target-moderator-reflector coupling enhance effective cold and thermal neutron output from moderators.Three wing-type moderators supply four different characteristics of neutrons to 19 beamlines primarily for neutron scattering applications.Layout of neutron instruments are conceptually planned for total 20 beamlines,the configuration and specification have been determined for three day-one neutron instruments.All designs are optimized for the Phase I of 100 kW with a upgradable capacity to 500 kW.     

Study of multiple small-angle neutron scattering by the warren method

A procedure for studying multiple small-angle neutron scattering using a double-crystal spectrometer is presented. It is based on measuring the linear coefficient of beam attenuation caused by smallangle scattering. The method has been substantiated theoretically, and the range of its applicability has been determined.     

Multiple scattering of muons in beryllium

The defocussing and the depolarization of a high energy muon beam in a beryllium filter, often used to eliminate accompanying pions, have been studied. The quantum mechanical transport equation of Waldmann, which can also be used to describe the multiple scattering of Dirac particles, is solved with a distorted wave Born approximation. Calculations are done for both the Thomas-Fermi and the Hartree-Fock potential of the beryllium atom. It is shown that the Hartree-Fock potential leads to a less divergent beam. The depolarization of a longitudinally polarized muon beam in passage through a thin beryllium foil is also studied.