Neutron reflectometry with registration of secondary radiation V.D. Zhaketov1, A.V. Petrenko1, Yu.M. Gledenov1, Yu.N. Kopatch1, N.A. Gundorin1, Yu.V. Nikitenko1,*, V.L. Aksenov1 1Joint Institute for Nuclear Research, Dubna, Russia *[email protected] Neutron reflectometry is a method for measuring the spatial profile of the neutron interaction potential with the medium. The interaction potential is the sum of neutron interaction potentials with separate isotopes of the medium. To determine the neutron interaction potential with the structure units, secondary radiation is simultaneously registered with neutrons. Channels for registering secondary radiation of charged particles, gamma rays and neutrons, having experienced spin flip, have been developed on the REMUR spectrometer of the IBR-2 reactor in Dubna (Russia). The necessity of registering secondary radiation in neutron reflectometry is justified, a method developed for measuring secondary radiation is described and the results of testing channels for registering secondary radiation on the REMUR spectrometer are presented in the paper. Keywords: neutron reflectometry, total reflection, secondary radiation Introduction. Currently, it is relevant to study the phenomena of development of the current neutron reflectometry method are proximity occurring at the interface between two media, namely, outlined. superconductor and ferromagnetic [1-3]. Due to mutual impact of ferromagnetic and superconductor, caused by the finite values of Basic relations. For the range of the neutron wave vector k /d, the coherent wave lengths of phenomena, there is significant where d is the distance between atoms of the medium, neutron modification of magnetic phenomena and superconducting propagation in the medium is described by the interaction potential properties. This becomes obvious, in particular, in the change of of the neutron with the medium [13]: the spatial distribution of magnetization. In this case, it is important to establish the correspondence of the magnetic spatial profile 푈(푧) = 푉 − 푖푊 = 훼Σ푔푁푔푏푔 + 흁푩 − 푖[훽(Σ푔푁푔Σ푝휎푔푝 + 푁푛휎푛 + (spatial dependence of magnetization) with the nuclear spatial 푁 휎 + 푁 휎 ) + 훾 휎 ] (1) profiles of elements(isotopes) of the contacting layers. For 푚 푚 푛푚 푛푚 푛푒 푛푒 determining the spatial magnetic profile, standard reflectometry of where Ng(z) is density of the g-type nuclei, bg is the amplitude of polarized neutrons is used, which measures the energy of the elastic coherent neutron scattering by the g-type nucleus, g,p is the nuclear-magnetic interaction (hereinafter, the interaction potential) interaction cross section with the g-type nucleus to form p-radiation of a neutron with the medium [4]. At the interface between two media, the interaction with the energy Ep, n, m, nm and Nn, Nm, Nnm are the neutron potential is the sum of interaction potentials of elements penetrating scattering cross section and the density of nuclear, magnetic and each other. In this regard, standard neutron reflectometry does not nuclear magnetic inhomogeneities of the medium, ne is the allow one to identify to what kind of elements the changes of the inelastic neutron scattering cross section by the medium, ne is the interaction potential and, in particular, of the magnetic profile, are dimension factor, B is the magnetic field induction vector, related. For defining the potential profile of the neutron interaction =2ħ2/m, =ħv/2, ħ is the Planck constant, is the neutron with separate elements, it is necessary to register secondary magnetic moment, m is the neutron mass, v is the neutron velocity. radiation from isotopes of elements [5]. The type of radiation and The neutron transport through a layered structure follows the the radiation energy are the signs identifying isotopes of elements. reflection coefficient R(Q), the transmission coefficient T(Q) and Charged particles, gamma rays and nuclear fission fragments are the neutron absorption coefficient M(Q). For coefficients, the flux considered as secondary radiation. In a broader interpretation, balance equation for the initial “i” and final “j” spin states of the secondary radiation should include neutrons, incoherently scattered neutron is at nuclei, neutrons inelastically scattered by atoms and the medium, 푖푗 푖푗 푖푗 as well as diffusely scattered neutrons at interfaces and Σ푗 (푅 (푄) + 푇 (푄) + 푀 (푄)) = 1 (2) inhomogeneities in the layers of the structure. The signs of such secondary radiation are the angular distribution and the transfer The partial absorption coefficient is the ratio of the absorbed energy of scattered neutrons. The particular secondary radiation 푗 neutron flux 퐽푔(퐸푝), corresponding to the secondary radiation with includes neutrons having experienced a coherent spin flip in a 푖 noncollinear magnetic structure. In this case, at neutron the energy Ep, to the initial neutron flux 퐽0 propagation, neutrons are “absorbed” in the initial spin state and, 푗 푗 푗 푗 푗 푗 ( ) 푗 correspondingly, neutrons occur in final spin state. For determining 푖푗 퐽푔(푘푧,퐸푝) [퐽 (푧,푘푧)=푛 휈푧]푁푔 푧 휎푔,푝(푘푧)푑푧 푀푔,푝 = 푖 = ∫ 푖 (3) the spatial distribution of elements and increasing the sensitivity of 퐽0(푘0푧) 퐽0 measurements, neutron standing wave regime are used [6,7]. 푗 푗 푗 푗 푗 In [8,9], the registration of secondary gamma radiation where 퐽 (푧, 푘푧 ) = 푛 (푧, 푘푧 )휈푧 is neutron flux in medium, from the structures containing a 5 nm-thick gadolinium layer was 푗 푗 푛 (푧, 푘푧 ) is neutron probability density (hereinafter, just neutron reported. In [10], secondary radiation was registered in the form of 푗 6 density), 휈푧 is z – component of neutron velocity, 푘푧 = charged particles emitted by the Li isotope after neutron capture by 2 2 2 them. In [11, 12], the REMUR neutron reflectometer (Dubna, √푘0푧 − (푘푣 − 푖푘푤) − 흁푩 and k0z= k0sin are z - components of the Russia) was described, in which charged particles and gamma rays neutron wave vector in the medium and vacuum, correspodently, 2푚푉 2푚푊 were registered together with neutrons. In this paper, justification 푘 = √ and 푘 = √ are critical wave vectors, connected 푣 ℏ 푤 ℏ of the necessity for registration of secondary radiation has been with real V and imaginary W parts of potential, correspondently, performed. Model calculations of the neutron absorption coefficient is neutron magnetic moment, is initial glancing angle. have been carried out for the case of bilayers and periodic 푖푗 Further, it will be useful to represent 푀푔,푝 in terms of other structures. Developed on the REMUR spectrometer, the channels 푖푗 for registering secondary radiation, namely, charged particles, physical quantities. Thus, 푀푔,푝 can be expressed in terms of gamma rays and spin-flipped neutrons are described. The results of imaginary part of the partial interaction potential: channels testing are presented. Prospects for the further 푗 푖푗 2푚 푊푔,푝푛 푊푔,푝 = ℏ휈푧푁푔휎푔,푝/2; 푀푔,푝 = 2 ∫ 푖 푖 푑푧 (4) 2 2 ℏ 푛0푘0푧 2 푗(푧, 푘푧) = 휈푧 ∙ 푛푠푤 ⋅ {휂푒푠푤 = [|푡푎| |푡푣푝| /|1 − 푟푎 ∙ 푟푝+푟| ] / 2 A different view using wave functions: [(1 − |푟푝푟 × 푟푝푎| × exp⁡(−2푘푧,퐼퐿)) + 4|푟푝푎 × 푟푝푟| × 2 휑푓푎 휑푓푟 2 exp⁡(−2푘푧,퐼퐿)푠푖푛 (푘푅퐿 + + )]} (8) 푖푗 푖푗 2 푘푔,푝 2 2 푀푔,푝 = ∫|푦 | 푖 푑푧 (5) 푘0푧 where nsw is the density of standing waves and esw is the density 푗 푖푗 휓 2 2푚 푗 transformation factor resulting from wave interference, ta is where 푦 (푧, 푘푧) = 푖 , 푘푔,푝 = 2 푊푔,푝 = 푁푔휎푔,푝푘푧 . 휓0 ℏ amplitude of the transmitted wave of the amplifying layer [6], tvp is 푖푗 As it follows from (5), 푀푔,푝 is determined by the amplitude of the transmitted wave of the “vacuum - phase-shifting 2 coefficient of transformation of the neutron density |푦푖푗| . In the layer” interface, rp+r is reflection amplitude of structure ”phase- 2 shifting layer + reflector”, ra is amplitude of the reflected wave from contrast standing wave regime 푖푗 is in the range from zero to |푦 | the amplifying layer, rpa, pa are, correspondingly, amplitude and 2 four and in the enhanced standing wave regime |푦푖푗| can reach phase of the amplitude of the reflected wave from the structure of 4·104 for real structures, while due to increased neutron density the “phase-shifting layer interface + amplifying layer ”, rpr, pr - with spin flip to the third power in respect to increased neutron are, correspondingly, amplitude and phase of the amplitude of the 2 2 density without spin flip, |푦푖푗| = (|푦푖푖| )3, where ij [14-16]. reflected wave from the structure of the “phase-shifting layer interface + reflector”, L is thickness of the phase-shifting layer. The neutron absorption coefficient corresponding to unregistered secondary radiations is determined from the relation In case of the resonance Lkz + pa/2+pr/2= m, the density transformation factor has the form 푀푖 = 1 − 푅푖 + 푇푖 − Σ 푀푖 − Σ 푀푖 (6) 푟푒푠 푝 1푝 푠 2푠 푛 2 2 2 휂푒푠푤 = = [|푡푎| |푡푣푝| /|1 − 푟푎푟푝+푟| ] /[1 − |푟푝푎 × 푟푝푟| × 푛0 where M1 and M2 are absorption coefficients of two contacting 2 exp⁡(−2푘푧,퐼퐿)] (9) layers. In the case of two isotopes at the interface, in order to At rfa 1, rfr 1 and kz,I 1/L, esw 1 is performed. Estimates solve (6) it is sufficient to identify the neutron absorption coefficient in one of the isotopes. show, that in the case of slightly absorbing nuclear layers, esw can reach about 4·104. In the case of a magnetic structure, the gain value We now turn to the issue of the neutron wave field. of the neutron reflection coefficient with spin flip under certain Standard reflectometry, measuring the reflection and transmission conditions increases quadratically and can reach 1.6·109 [14]. coefficients, “operates” in the traveling neutron wave regime. The neutron density in this case decays deep into the structure at an Model calculations. exponential rate. Due to the phase change of the neutron wave at passing a separate layer of the structure on , the layer thickness is 1 1 defined from the relation 푑 = 휋 ( − ), where kz1 and kz2 are the 푘푧2 푘푧1 values of the wave vector at which the neutron reflection intensity has local maxima.