Study of the heavy-fermion compound CeRu<Subscript>2</Subscript>Si<Subscript>2</Subscript> by the small-angle neutron scattering method

In order to directly observe neutron scattering by heavy fermion quasiparticles at low temperatures, a CeRu₂Si₂ single crystal has been studied by the small-angle neutron scattering method. In the experiment, neutron scattering is observed at T = 0.85 K for momentum transfers q ≤ 0.04 Å^?1, which is treated as the orbital component of magnetic scattering by heavy fermion quasiparticles. It has been found that the application of a magnetic field H = 1 T leads to both an increase in the observed scattering and its anisotropy with respect to the field direction. Moreover, measurements in the magnetic field reveal additional scattering for q > 0.04 Å^?1, which is well described by a Lorentzian and is interpreted as neutron magnetic scattering by spin-density fluctuations with a correlation radius R_c ≈ 30 Å.     

Neutron optics of strongly absorbing media and interaction of long-wave neutrons with gadolinium films

The modern state of neutron optics of absorbing media is briefly surveyed. In all probability, there are no physics arguments that would constrain, in the case of strong absorption, the applicability of the commonly accepted Fermi-Foldy dispersion law for neutron waves. In accord with previously known results, it is found that the coefficient of reflection of neutrons from the boundary of a strongly absorbing medium tends to unity with decreasing velocity of neutrons incident on this medium. At low neutron energies peculiar to the case of ultracold neutrons, the complex scattering length for neutron-nucleus interaction proves to be constant, whence it follows that the cross section for neutron capture by a free nucleus obeys the 1/v law. The cross section for the analogous process on nuclei within a medium is described by the 1/v′ law, where v′=?k′/m, with k′ being the real part of the neutron wave number in the medium. As the incident-neutron velocity v decreases, the velocity v′ in a medium tends to some limiting value. From the coefficient of reflection of cold neutrons that is measured as a function of the wavelength and the angle of incidence, a refined value is found for the real part of the scattering length for neutron interaction with gadolinium nuclei. An experiment was performed where ultracold neutrons were transmitted through thin samples containing natural gadolinium. In analyzing the results of this experiment, use was made of the value found here for the real part of the neutron-nucleus scattering length. The experiment indicates that the imaginary part of the scattering length is a constant or, what is the same, that, for neutron velocities ranging from 4 to about 120 m/s, the 1/v law for the cross section for neutron capture by a free nucleus is valid to within 6%.     

Moments of inertia of neutron stars in relativistic mean field theory: The role of the isovector scalar channel

With the inclusion of the isovector scalar channel in the meson-nucleon couplings, taking DD-MEδ as an effective interaction, the moments of inertia of neutron stars possessing various stellar masses are studied within the density dependent relativistic mean field(RMF) theory. The isovector scalar channel contributes to the softening of the neutron-star matter equation of state(EOS)and therefore the reduction of the maximum mass and radius of neutron stars. Smaller values of the total moment of inertia I and the crustal moment of inertia ?I are then obtained in DD-MEδ via numerical procedure in comparison with those in other selected RMF functionals. In addition, the involvement of the isovector scalar channel lowers the thickness of the neutron star crust and its mass fraction as well. The sensitivity to both the crustal mass and stellar radius causes the crustal moment of inertia to be more obviously reduced than the total one, eventually leading to a suppression on the fraction of crustal moment of inertia?I/I in DD-MEδ. The results indicate the crustal moment of inertia as a more sensitive probe of the neutron-star matter EOS than the total one, and demonstrate that the isovector scalar meson-nucleon couplings in the RMF theory could exert influence over the physics of pulsar glitches.     

Description of small-angle neutron scattering data for nickel–chromium–aluminum alloy within quantum mechanics and classic polydisperse sphere model

The modified Yukawa potential is used to fit the nucleus model parameters to the data on small-angle neutron scattering on nickel—chromium—aluminum alloy for the product of the transferred momentum Q and the effective nucleus radius R, satisfying the condition QR ≤ ?. The analytical polydisperse sphere model is used to calculate the neutron scattering intensity and to determine the most probable macroscopic sphere radius R ₀ at QR ₀ ≥ 3?.     

Calculation of the Cross Sections for Neutron Scattering at Spin Waves in Helimagnets

An analytical dependence of the cross section for the small-angle scattering of polarized neutrons at spin waves in helimagnets formed because of Dzyaloshinskii—Moriya interaction in cubic crystals without an inversion center (the space group is P2₁3) is obtained. It is assumed that the dispersion of spin waves in helimagnets with the wave vector k _s polarized by a magnetic field is larger than the critical field H_C2 of the transition to the ferromagnetic phase and has the form E _q = A(q ? k _s ) + gμ_B(H ? H_С2). It is shown that the cross section for neutron scattering at the two-dimensional map of angles (θ _x , θ _y ) is two circles of the radii θ_C with the centers ±θ _S , corresponding to the Bragg angle of diffraction by a helix oriented along the applied magnetic field H. The radii of these two circles θ_C are directly related to the stiffness of spin waves A of the magnetic system and depends on the applied magnetic field: \(\theta _C^2 = \theta _0^2 - \frac{{g{\mu _B}H}}{{{E_n}}}{\theta _0}\), where \({\theta _0} = \frac{{{h^2}}}{{2A{m_n}}}\) and E _n and m _n are the neutron energy and mass. It is shown that the scattering cross section depends on the neutron polarization, which is evidence of the chiral character of spin waves in the Dzyaloshinskii—Moriya helimagnets even in the completely polarized phase. The cases of neutron scattering at magnons where θ₀ ≤ θ _S and θ _S ≥ θ₀ are considered. The case of neutron scattering at spin waves in helimagnets is compared with analogous scattering at ferromagnets where θ _S → 0.     

Small-angle neutron scattering at fractal objects

The calculation of the correlation function of an isotropic fractal particle with the finite size ξ and the dimension D is presented. It is shown that the correlation function γ(r) of volume and surface fractals is described by a generalized expression and is proportional to the Macdonald function (D–3)/2 of the second order multiplied by the power function r ^(D–3)/2. For volume and surface fractals, the asymptotics of the correlation function at the limit r/ξ < 1 coincides with the corresponding correlation functions of unlimited fractals. The one-dimensional correlation function G(z), which, for an isotropic fractal particle, is described by an analogous expression with a shift of the index of the Macdonald function and the exponent of the power function by 1/2, is measured using spin-echo small-angle neutron scattering. The boundary case of the transition from a volume to a surface fractal corresponding to the cubic dependence of the neutron scattering cross section Q ^?3 leads to an exact analytical expression for the one-dimensional correlation function G(z) = exp(?z/ξ), and the asymptotics of the correlation function in the range of fractal behavior for r/ξ < 1 is proportional to ln(ξ/r). This corresponds to a special type of self-similarity with the additive law of scaling rather than the multiplicative one, as in the case of a volume fractal.     

Low-Energy Parameters of Neutron–Neutron Interaction: Analysis of Data Obtained in <Emphasis Type="Italic">nd</Emphasis> and <Emphasis Type="Italic">dd</Emphasis> Breakup Reactions

Data obtained in recent years for the neutron–neutron scattering length in nd and dd breakup reactions are analyzed. Serious discrepancies between experimental data from different studies may be explained by the effect of three-nucleon forces depending on the velocity of separation of a neutron–neutron pair and a charged fragment. It is shown that the data under analysis can be approximated by a smooth curve representing the dependence of the scattering length on the parameter R, which determines the fragment-separation distance after a fixed time. This dependence makes it possible to obtain the scatteringlength value for R→∞—that is, in the absence of the effect of three-nucleon forces.     

Determination of <Emphasis Type="Italic">T</Emphasis>-noninvariant amplitude for polarized-neutron interaction with polarized nuclei by the oscillating-field method

A solution for the T-noninvariant amplitude for polarized-neutron interaction with polarized nuclei in the region of the p-wave resonance is analyzed, this amplitude being extracted from two-dimensional neutron spectra obtained within Ramsey’s method. Here, the dimensionalities are the neutron energy and the radio-frequency phase at the instance of neutron entrance in an oscillating field. The spindensity-matrix formalism is used to derive an expression that describes the shape of the neutron spectrum and the corresponding expressions for the neutron-counting asymmetries both with respect to the direction of the P-odd field and with respect to the direction of the T-noninvariant field. It is shown that, for an appropriate choice of parameter values, there are exact solutions for the imaginary parts of the P-odd and T-noninvariant amplitudes and for their interference with the amplitude of strong spin-spin interaction.     

Parameterization of the spectra of configurations 3<Emphasis Type="Italic">p</Emphasis>4<Emphasis Type="Italic">f</Emphasis> and 3<Emphasis Type="Italic">p</Emphasis>5<Emphasis Type="Italic">f</Emphasis> of a phosphorus ion P II. Gyromagnetic ratios

In the one-configuration approximation, in the formalism of irreducible tensor operators, and in the intermediate (real) coupling scheme, numerical values of the fine-structure parameters are determined for the 3p4f and 3p5f highly excited configurations of the P II phosphorus ion with the energy-operator matrix in the LK-coupling approximation. With these values of the fine-structure parameters, the energy-operator matrix is numerically diagonalized in the LS-coupling approximation. The gyromagnetic ratios calculated in both basis sets in the absence of a field are compared with one another, as well as with their vector counterparts and the experimental g-factors available for the 3p4f configuration. The experimental and theoretical g-factors calculated with the LS basis set are in good agreement with the sole exception of the ³ F ₂ level. Note that the calculation of g-factors from the Zeeman splitting in the linear region totally confirmed their agreement with the values calculated in the LS basis set (g _LS ) in the absence of a field. The gyromagnetic ratios are the main objectives of this and previous papers, especially for configurations for which experimental data are absent. Apart from the g-factors, the specific features of Zeeman splitting (the crossings and anticrossings of magnetic components) in the 3p5f configurations were determined. These data are to be compared with results of future experiments. Comparison of gyromagnetic ratios calculated in the intermediate coupling scheme with their vector counterparts showed that most levels of the configurations studied are closer than in the LK-coupling scheme.     

Spin observables in <Emphasis Type="Italic">np</Emphasis> elastic scattering in the energy range 200–600 MeV. Complete experiment

A survey of available experimental data on the measurement of spin observables in neutron-proton (np) elastic scattering in the neutron energy range 200–600 MeV is presented. Sixteen spin observables (the polarization of recoil particles P _0n00, the analyzing power A _00n0, the spin correlation parameters A _00nn , A _00ss , A _00sk , and A _00kk , the spin transfer parameters K _0nn0, K _0ss0, and K _0sk0, the depolarization parameters D _0n0n , D _0s0s , and D _0s0k , and the three-spin parameters N _0nkk , N _0skn , N _0ssn , and N _0sns for energies of 200–590 MeV and scattering angles in the center of mass system of 60°–164°) were studied in experiments using polarized neutron beams and polarized proton targets at the Paul Scherrer Institute. The results of these investigations present a complete set of precision data on np elastic scattering which, along with the complete set of data for proton-proton (pp) elastic scattering obtained earlier, provides a basis for unambiguous determination of the amplitudes of the scattering matrix for nucleon-nucleon (NN) elastic scattering for the channel with the isotopic spin I = 0 and makes it possible to describe NN interaction in a model-independent way.     

Study of the atom-phonon coupling model for (SC) partition function: first order phase transition for an infinite linear chain

In spin-conversion (SC) compounds containing molecules organized around an iron (II) ion the fundamental level of the ion is low spin (LS), S = 0, and its first excited one is high spin (HS), S = 2. This energy diagram is due to the ligands field interaction on 3d electrons and to the spin pairing energy. Heating the compound increases the magnetic susceptibility which corresponds to a change of populations of both levels and consequently a change of spin value of the molecules. This mechanism, called spin conversion (SC), can be accompagnied by thermal hysteresis observed by studying magnetic susceptibility or high spin fraction. In that case one considers that the (SC) takes place through a first-order phase transition due to intermolecular interactions. In the atom-phonon coupling model the molecules are considered as two-level systems, or two-level atoms, and it is assumed that the elastic force constant value of the spring which links two atoms first neighbours is depending on the electronic states of both atoms. In this study we calculate the partition function of a linear chain of N atoms (N ≤ 16) and we describe the role of phonons and that of the parameter Δ which corresponds to the distance in energy between both levels. The chain free-energy function is F _atph . We introduce for the chain a free-energy function defined by the set (F _HS , F _LS , F _barr ) and we show that F _atph tends towards the previous set when N → ∞. The previous set allows to describe a first order phase transition between a (LS) phase and a (HS) one. At the crossing point between the function F _LS and F _HS , and around this point, there is an intermediate free-energy barrier which prevents the chain to change phase which can lead to thermal hysteresis. The energy gap between the free-energy function F _atph and that defined by the set (F _HS , F _LS , F _barr ) is small. So we can expect that a nanoparticule takes for free-energy function that defined by the set and then displays a thermal hysteresis.     

Spectroscopy of surface-enhanced raman scattering of a complex with charge transfer between a bis-crown-containing stilbene and a bis-ammonium-alkyl derivative of dipyridylethylene

The structure of a charge transfer complex (CTC) formed by a bis-crown-containing stilbene (1) and a dipyridylethylene derivative (2) is studied by surface-enhanced Raman scattering spectroscopy. It is found that an excess of 2 leads to the formation of a 1: 1 CTC structure ([1·2]), whereas an excess of 1 leads to the stabilization of a sandwichlike 2: 1 CTC structure ([1·2·1]). It is also revealed that 1 and diperchlorate of 1-ammoniumpropyl-4-methylpyridinium (5) form a 1: 1 CTC structure, which is much less stable. Analysis of the surface-enhanced Raman scattering data suggests that, in complete agreement with the Mulliken theory, the CTCs under study are ordinary molecular complexes in the ground state and the interaction of a molecular complex with a photon excites the former. The excitation is accompanied by a significant transfer of the electron density from the donor 1 to the acceptor 2 (5). The structural fragments of the molecules responsible for the intermolecular interaction and charge transfer are ascertained using model compounds. The charge transfer in donor-acceptor pairs occurs between the electronic systems of trisubstituted benzene and pyridine. A CTC of the [1·2] or [1·2·1] type contains two equivalent donor-acceptor pairs; however, only one of them is involved in the charge transfer.     

Notes on number density fluctuations and the scattering cross section for electromagnetic waves scattered from a thermal nonequilibrium plasma

The scattering cross section and the Doppler spectrum for electromagnetic waves scattered by the electron density fluctuations of a plasma, where the mean kinetic temperature of the electronsT _e may differ from that of the ionsT _i , has been obtained among others byFejer, Buneman, Renau, Camnitz andFlood, andSalpeter. These authors use different methods of approach to calculate the autocovariance of the electron number-density fluctuations (from the mean) and then obtain the scattering cross section. Because of the differing results, the methods, concepts, and derivations of the scattering cross section are carefully examined in this paper. It is shown that the short-time dynamical considerations incorporated in the formulation of the statistical theory of the electron number-density fluctuations of the plasma as used by several authors (for instanceFejer, Buneman, Salpeter,) leads to results of limited validity. In addition, a fundamental error in calculating the electron density fluctuations leads these latter authors to an incorrect scattering cross section. The theory of scattering of electromagnetic waves from a plasma, where the electrons arenot in thermal equilibrium with the ions but statistical equilibrium exists, is developed in a general way. The covariance of the number-density fluctuations from the mean of the charged species of the plasma and the scattering cross sectionσ(q) are obtained. In particular it is shown that for a wavelength λ much greater than the effective Debye lengthd, the backscattering cross section increases and approaches complete incoherent scattering asT _e /T _i increases. This result is explained by noting that in the case of thermal equilibrium, the predicted value of the back-scattering cross section is smaller than that of the backscattering cross section from completely uncorrelated electron density fluctuations because the electrostatic interaction between the charged particles of the plasma, which is a function ofT _e andT _i , introduces a certain amount of organization in otherwise completely uncorrelated electron density fluctuations. When the mean temperature of the electrons increases relative to that of the ions, the organization introduced in the fluctuations diminishes because of the increasing thermal agitation of the electrons relative to that of the ions, and the backscattering process approaches that of incoherent backscattering (Thomson-type scattering). The spectrum function of incoherent scattering of electromagnetic waves from a nonequilibrium plasma is obtained and some cases of current interest are plotted.     

Current status of research on <Emphasis Type="Italic">T</Emphasis> invariance in neutron-nuclear reactions

In this work, the current state of research on T invariance in neutron-nuclear reactions is considered. The promising character of investigations in this field related to possible enhancement of T-invariance violation in compound states of medium and heavy nuclei is underlined. Progress in preparation of experimental tests of T invariance using three-and five-vector correlations in cross sections of interaction of polarized neutrons with aligned nuclei is described in detail. T-invariance tests in reactions of radiative neutron capture and in coherent scattering of polarized neutrons on crystals are also considered.     

Schiff moment of the mercury nucleus and the proton dipole moment

The Schiff moment of the ¹⁹⁹Hg nucleus is calculated using finite range P-and T-violating weak nucleon-nucleon interaction. Both the contributions of the P-and T-odd interaction and of internal nucleon electric dipole moments to the Schiff moment of ¹⁹⁹Hg are calculated. The contribution of the proton electric dipole moment is obtained via core-polarization effects treated in the framework of RPA with effective residual interactions. We derive a new upper bound |d _p |<5.4×10^?24e cm for the proton electric dipole moment.     

Abnormal features of neutron-nucleus low-energy interaction and the mechanism of inhibition of neutron-induced reactions

The features of the distant interaction of thermal and slow neutrons with nuclei are examined. From the Dirac equation analysis it was shown that this interaction is determined by the potential barrier located outside the nucleus. The height of the barrier is proportional to Z ²/A ^4/3 and reaches 110eV for even-even nuclei like U²³⁸ and 25-65eV for even-odd U²³⁵ , U²³³ , Pu²⁴¹ nuclei. This barrier is connected with the non-linear ponderomotive interaction of the neutron abnormal magnetic moment with the strong electric field of a nucleus. The barrier penetrability for thermal neutrons equals 0.9-0.98. For cold neutrons the penetrability decreases greatly and for ultracold ones it becomes very small. At unlimited decrease of the neutron energy, E \( \rightarrow\) 0 , the cross-section of any neutron-nucleus reaction \( \sigma_{{f(tot)}}^{}\) \( \rightarrow\) 0 . So such reactions become impossible. In this work the existence of separated neutron potential wells symmetrically located at r ₀ \( \approx\) (1.3-4.5)×10^-12 cm \( \approx\) (1.7-5)×R from even-odd U²³⁵ , U²³³ , Pu²⁴¹ nuclei is predicted. These wells with depths 0.1-5eV are the result of combined ponderomotive and pure magnetic interactions of the neutron abnormal magnetic moment with nucleus electric and magnetic fields. The presence of distant wells leads to the possibility of the existence of virtual or quasi-stationary neutron-nucleus molecules. Such wells can be virtual traps for thermal and cold neutrons. It was predicted that the neutron halo phenomenon may be connected with such traps.     

High-pressure effect on the crystal and magnetic structures of the frustrated antiferromagnet YMnO<Subscript>3</Subscript>

The high-pressure (to 5 GPa) effect on the crystal and magnetic structures of the hexagonal manganite YMnO₃ is studied by neutron diffraction in the temperature range 10–295 K. A spin-liquid state due to magnetic frustration on the triangular lattice formed by Mn ions is observed in this compound at normal pressure and T > T_N = 70 K, and an ordered triangular antiferromagnetic state with the symmetry of the irreducible representation Γ₁ arises at T < T_N. The high-pressure effect leads to a spin reorientation of Mn magnetic moments and a change in the symmetry of the antiferromagnetic structure, which can be described by a combination of the irreducible representations Γ₁ and Γ₂. In addition, it is observed that the ordered magnetic moment of Mn ions decreases from 3.27 μ_B (5 GPa) to 1.52 μ_B (5 GPa) at T = 10 K and diffuse scattering is enhanced at temperatures close to T_N. These effects can be explained within the model of the coexistence of the ordered antiferromagnetic phase and the spin-liquid state, whose volume fraction increases with pressure due to the enhancement of frustration effects.     

Single-particle properties of <Emphasis Type="Italic">N</Emphasis> = 12 to <Emphasis Type="Italic">N</Emphasis> = 20 silicon isotopes within the dispersive optical model

Experimental neutron and proton single-particle energies in N = 12 to N = 20 silicon isotopes and data on neutron and proton scattering by nuclei of the isotope ²⁸Si are analyzed on the basis of the dispersive optical model. Good agreement with available experimental data was attained. The occupation probabilities calculated for the single-particle states in question suggest a parallel-type filling of the 1d and 2s _1/2 neutron states in the isotopes ^{26,28,30,32,34}Si. The single-particle spectra being considered are indicative of the closure of the Z = 14 proton subshell in the isotopes ^30,32,34Si and the N = 20 neutron shell.     

Spin fluctuations in the stacked-triangular antiferromagnet YMnO<Subscript>3</Subscript>

The spectrum of spin fluctuations in the stacked-triangular antiferromagnet YMnO₃ was studied above the Néel temperature using both unpolarized and polarized inelastic neutron scattering. We find an in-plane and an out-of-plane excitation. The in-plane mode has two components just above T _N : a resolution-limited central peak and a Debye-like contribution. The quasi-elastic fluctuations have a line width that increases with q as Dq ^z and the dynamical exponent z = 2.3. The out-of-plane fluctuations have a gap at the magnetic zone center and do not show any appreciable q dependence at small wave vectors.     

Dimension of an optimum impurity cluster and multiple-occupancy corrections in the theory of scattering of vibrational excitations in a solid solution

A relationship is derived for the correlation length L determining the size of the region in a solid solution in which excitations are scattered coherently. The correlation length depends on the fraction of impurity atoms x in the solid solution and the lattice dimension d. In the physical analysis of single-particle scattering processes in the solid solution and calculations, it is sufficient to take into account clusters with the number of cells n corresponding to the correlation volume L ^d . A theoretical analysis is illustrated by calculations of the spectral functions of the solid solution at different values of x and n. The multiple-occupancy corrections (polynomials in powers of x) to scattering diagrams are calculated using the method of sequential breaking apart of the interaction lines in the diagrams for the self-energy part. The method used was previously applied to the case of scattering by a single impurity. In this paper, the efficiency of the method is checked for scattering by multi-impurity clusters. It is demonstrated that the method can be useful in analyzing and estimating the contributions of scattering diagrams.