Neutron Inelastic Scattering Cross Sections Research Articles

The heavy fermion compound YbAgCu4

We re-examine the experimental data for the specific heat, the magnetic susceptibility, magnetization, and inelastic neutron scattering for the moderately heavy-electron compound YbAgCu4 within the framework of the single-ion Anderson model. Such an analysis has previously given excellent agreement between theory and experiment for numerous light heavy-fermion compounds. We extend here previous interpretations for the specific heat and magnetization within the Coqblin–Schrieffer model to a common set of model parameters by incorporating a weak valence admixture. The crystalline field splitting in this compound appears to be small compared to the Kondo temperature. Existing exact solutions of the Anderson model within the framework of Bethe’s ansatz are used for the thermodynamic properties. A simple resonant-level model is introduced to parametrize the Kondo resonance and to qualitatively interpret the inelastic neutron scattering cross section.

Neutron and proton dynamics of 48Ca levels and gamma -ray decays from neutron inelastic scattering.

Differential cross sections were measured for the $^{48}\mathrm{Ca}$(n,n'\ensuremath{\gamma}) reactions at incident energies between 4.8 and 8.0 MeV. Excitation energies, spins, level lifetimes, \ensuremath{\gamma}-ray branching ratios, and \ensuremath{\gamma}-ray production cross sections were determined. Members of the doublet at 4.50 MeV are clearly identified and assigned spins of ${4}^{+}$ and ${3}^{\mathrm{\ensuremath{-}}}$. Inelastic neutron scattering cross sections were inferred from the \ensuremath{\gamma}-ray branching ratios and production cross sections. The inferred cross sections are in excellent agreement with those measured in a separate neutron detection experiment, and with a recent vibrational model coupled-channels analysis of the $^{48}\mathrm{Ca}$(n,n') data. Comparison of level excitations produced by neutrons and other hadrons with electomagnetic strengths shows very different mixtures of neutron and proton particle-hole amplitudes for different levels.

Dynamics of commensurate ( N×2; N=3,4) and incommensurate phases of an argon monolayer adsorbed on MgO(100)

Calculations of the dynamics of three different geometries of an Ar monolayer adsorbed on the MgO(100) substrate are developed within the harmonic approximation in order to determine the dispersion relations, the vibrational spectrum and the inelastic neutron scattering cross section. Several energy loss peaks are obtained for the (3×2), (4×2) commensurate and hexagonal incommensurate geometries. Their shapes and energies strongly depend on the geometry of the adsorbed phase and they can be interpreted as the result of unequivalent adsorption sites for the monolayer atoms. The comparison with the first available inelastic scattering spectra for the (3×2) structure shows that it is possible, at high resolution, to exhibit the various peaks and to interpret them with the present calculations.

Fast-neutron total and scattering cross sections of 58Ni and nuclear models

Neutron total cross sections of 58Ni are measured from approximately=1 to >10 MeV using white-source techniques. Differential neutron elastic scattering cross sections are measured from approximately=4.5 to 10 MeV at approximately=0.5 MeV intervals with >or=75 differential values per distribution. Differential neutron inelastic scattering cross sections are measured, corresponding to fourteen levels with excitations up to approximately=4.8 MeV. The measured results, combined with relevant data available in the literature, are interpreted and the physical implications discussed in the contexts of optical-statistical, dispersive-optical and coupled-channels models.

Microscopic Fermi liquid theory of NMR relaxation and neutron scattering in the metallic copper oxides

We calculate the NMR relaxation rates for the Cu and O sites, the temperature dependent magnetic susceptibility and the inelastic neutron scattering cross section using the dynamical RPA susceptibility derived previously. This approach is a Fermi liquid based scheme in which the Cu d electrons are (on the basis of considerable experimental evidence) assumed to be quasi-localized. These narrow band effects lead to low energy scales, T coh below which the Cu d electrons are fully coherent and a “one component” picture is applicable. Above this characteristic temperature the d electrons begin to lose their coherence, although they are still strongly coupled to the p orbitals. This coherence energy scale, along with the exchange interactions J H completely determine the characteristic temperatures and frequencies which appear in NMR and neutron data. Our calculations of 1/ T 1 on the Cu sites suggest that the cuprates are not as close to a magnetic instability as has been assumed elsewhere. This is because the coherence energy scale (which appears in the “bare” Lindhard function for the renormalized band structure) already provides an intrinsic “soft” frequency. Consequently, we find that antiferromagnetic interactions are playing a less dominant (but not insignificant) role in magnetic measurements. Analysis of the oxygen relaxation suggests that the sharp antiferromagnetic peaks invoked elsewhere to yield form factor cancellation effects may not be sufficiently robust to explain the data. Indeed, careful numerical calculations yield some degree of non-Korringa behavior on the oxygen sites due to imperfect cancellations of the transfer-hyperfine-coupling induced relaxation. Finally, our calculations of the neutron cross section show incommensurate peaks in the diagonal ( q, q) and off-diagonal ( q, π) directions, which are found to reflect the detailed Fermi surface geometry of the LaSrCuO system. These peaks become increasingly more incommensurate as the hole concentration increases. These predictions and their comparison with future experiments may help to determine the applicability of Fermi liquid based approaches to the cuprates.

Determination of the inelastic neutron scattering cross section by the spectral moments method: application to incommensurate crystals and quasi-crystals

If the author works directly with the dynamic matrix, the spectral moments method allows the direct determination of the response of harmonic materials without any calculation of eigenvalues or eigenvectors. The method selects directly in the frequency spectrum the active modes with the right magnitude. The author presents a new development of this method and applies it to the determination of the inelastic neutron scattering cross section of systems. He illustrates these results via applications to several models: a perfectly dimerised chain, chains with incommensurate distortions and quasi-crystals.

Ferromagnetic multilayers: Statics and dynamics.

A theory of periodic multilayers consisting of two alternating ferromagnetic materials with different transition temperatures is presented. The theory is based on an inhomogeneous Ginzburg-Landau (GL) functional, where the GL coefficients are chosen to model the alternating layers and interface interactions. The transition temperature of the composite material is derived by use of the linear stability analysis of the inhomogeneous GL functional. The static magnetization profiles for different temperatures are calculated analytically. It is shown that the magnetization penetrating into the low-temperature ferromagnet falls off inversely with distance close to ${T}_{1}$ and exponentially far above ${T}_{1}$, where ${T}_{1}$ is the lower transition temperature. We also consider the average magnetization of this multilayer system and its characteristic temperature dependence. The spin dynamics are studied by use of a generalized Bloch equation. Different limiting cases as well as the general situation with both dipolar and exchange interactions are considered. The magnon dispersion relation is computed and by symmetry considerations, it is shown that the gaps vanish at certain values of the wave vector k. The inelastic neutron scattering cross section is calculated. With appropriate modifications the theory can be applied to other systems undergoing phase transitions, such as ferroelectrics.

On the calculation of the dynamic structure factor from band structure models: application to iron

The accuracy of numerical calculations of dynamic response functions based on band structure models is examined. The particular cases studied are the spin and orbital parts of the inelastic neutron scattering cross sections. Application is made to paramagnetic iron. A surprising dominance of the orbital part over the spin part is reported.

Fast neutron elastic and inelastic scattering cross sections of54Fe

As a continuation of the work on determining the neutron scattering cross sections of /sup 54/Fe at 1.5, 2.0, 2.5, and 3.0 MeV, the neutron scattering cross sections at 5.0 +- 0.14, 6.0 +- 0.12, and 7.0 +- 0.10 MeV were measured. For this the differential neutron scattering cross sections of /sup 54/Fe were measured on the EG-5 electrostatic accelerator with the help of a fast-neutron time-of-flight spectrometer: elastic, inelastic with excitation of the first 2+ level (E/sub level/ = 1.408 MeV), and the total inelastic with excitation of the second 4+ level (E/sub level/ = 2.538 MeV) and the third 0+ level (E/sub level/ = 2.561 MeV). Neutrons produced in the reaction D(d, n)/sup 3/He were scattered by a cylindrical /sup 54/Fe sample, placed at a distance of 10 cm from the target. The spectra of the scattered neutrons were measured with a scintillation detector over a base line of 2.7 m at 13 angles in the range 20-150/sup 0/, and the differential elastic and inelastic neutron scattering cross sections were determined from them

Theoretical study of magnetic excitations in Ni3Al

Inelastic neutron scattering studies of the transition metal alloy Ni3Al have revealed highly unusual spin-wave behavior, that spin waves have been observed only in a small region around the Brillouin zone center (q≂0). Results from calculations of the inelastic neutron scattering cross section based on itinerant electron theory for Ni3Al have led to a relatively simple explanation of this phenomenon. To our knowledge, this is the first calculation of this type for an alloy system. The calculations yield the well-defined Goldstone mode (spin wave) at q=0 but no spin-wave peaks were found for the smallest calculable nonzero momentum transfer, which was just outside the range of q where spin waves were observed experimentally. The reason is simply that the spin wave runs immediately into a region of high density of Stoner excitations (single-particle spin-flip excitations) as q is increased from zero. This system, therefore, represents the extreme limiting case of the itinerant electron theory prediction of spin waves disappearing into the Stoner continuum.

Dynamics of a disordered monatomic solid with continuous distribution of force constants.

The average local-information transfer approximation (ALITA) Green's function 〈G${\ensuremath{\rightarrow}}_{\mathrm{Q}}$(\ensuremath{\omega})〉 (where Q and \ensuremath{\omega} are the wave vector and the frequency, respectively) and related longitudinal (L) and transverse (T) dispersion curves, frequency spectrum and neutron inelastic scattering (NIS) cross section have been calculated for a monatomic solid, disordered with respect to interatomic coupling and atomic configuration. Rectangular, elliptic, and Lorentz distributions of the self-force constants in the nearest-neighbor central-force model have been assumed. It has been found that the frequency spectrum of such a system is dominated by a huge peak at the average Einstein frequency due to the T curve, and a bump at lower frequency representing the first minimum in the L curve. Force disorder manifests itself in extending the range of frequencies and in rounding off the details of the spectrum corresponding to configuration disorder. Besides, the plane-wave deformations with wave vectors in certain ``Q gaps'' cannot contribute to normal modes of vibration in disordered solids. The NIS cross section at large momentum transfer \ensuremath{\Elzxh}Q leads directly to the spectrum of Einstein frequencies. If this spectrum has a sharp edge at 0, then essential deviations from the Debye type of frequency spectrum and from the ${T}^{3}$ law for vibrational specific heat at low temperatures do appear.

Theoretical investigation of neutron scattering cross sections in Si and Ge.

The development of high-flux high-energy pulsed neutron sources makes it possible to study electronic transitions in solids which are in the electron-volt range. A theoretical study has been carried out to determine the feasibility of using such sources to obtain information about the band structure of semiconductors. Calculations of the inelastic neutron scattering cross sections for germanium and silicon based on an empirical pseudopotential description of the energy bands have been com- pleted. This study is an extension of previous work to more realistic (larger) momentum transfers. The calculated cross sections were found to be quite small for realistic experimental conditions. Measurement of these relatively small cross sections could, however, provide important information about the band structure of semiconductors which cannot be obtained from most other experimental techniques.

A comparison of measured and calculated neutron inelastic scattering cross sections for vibrational states from 680 to 1060 keV in 238U

Abstract Neutron inelastic scattering cross sections measured via the TOF technique at Lowell are compared to theoretical calculations carried out at LANL for states in 238U from 680 to 1060 keV for incident neutrons up to 2.2 MeV.

Fast Neutron Inelastic Scattering Cross Sections of238U for States between 680 and 1530 keV

Neutron inelastic scattering cross sections for /sup 238/U levels between 680- and 1530-keV excitation energy have been measured in the incident neutron energy range from 0.9 to 2.2 MeV. The (n,n') time-of-flight (TOF) technique was used to obtain direct differential inelastic cross sections. Neutrons were generated using the /sup 7/Li(p,n)/sup 7/Be reaction. Experimental parameters were optimized to achieve an energy resolution of <15 keV. Level cross sections were deduced from the measured 125-deg differential scattering cross sections. The validity of this procedure was confirmed by measuring the angular distributions for nine levels at En=1.5 and 2.0 MeV. Background due to fission induced by fast neutrons was subtracted. The TOF spectra were unfolded using the method of the response function. The data were corrected for multiple scattering and neutron attenuation in disk scattering geometry using an analytic method. Theoretical calculations of the cross sections were carried out using reaction models appropriate to the description of compound nucleus and direct interaction processes. The data are compared to (n,n'..gamma..) results and the ENDF/B-V evaluation.

Inelastic scattering cross section of 172,174 Yb using tof technique

Neutron inelastic scattering cross sections have been measured for ten low lying states in 172,174 Yb isotopes using time-of-flight technique. Neutrons were detected by 8 large NE213 detectors, 1m ...

Neutron Inelastic Scattering Cross Sections for States Above 700 keV in232Th

Fast neutron inelastic scattering cross sections for levels between 700- and 1400-keV excitation energy in /sup 232/Th have been measured using the (n,n') time-of-flight (TOF) technique. Measurements of 125-deg differential cross sections were made using neutrons with a typical energy spread of 8 to 10 keV, generated by the /sup 7/Li(p,n)/sup 7/ Be reaction. The incident neutron energies covere three regions: (a) 950 to 1550 keV in 50-keV intervals with the TOF spectrometer optimized to detect 200 to 600-keV scattered neutrons, (b) 1200 to 2000 keV in 100-keV intervals with the spectrometer optimized to detect 400- to 800-keV scattered neutrons, and (c) 1700 to 2100 keV in 100-keV steps with the spectrometer optimized for 800- to 1300-keV scattered neutrons. Throughout the experiment, an overall energy resolution of <15 keV was maintained. Level cross sections were deduced from the 125-deg differential scattering cross sections and are compared with (n,n'..gamma..) measurements and the ENDF/B-V evaluation. Angular distributions for states in the 700- to 900-keV region have been measured at 1.2, 1.5, and 2.0 MeV.

A low-energy optical-model analysis of 208Pb and 209Bi

New measurements of differential elastic and inelastic neutron scattering cross sections for 208Pb and 209Bi at energies 4–7 MeV are presented. Elastic scattering data have sufficient accuracy to reveal clearly differences between cross sections in these neighboring nuclei. Phenomenological and microscopic, spherical, optical-model analyses are performed with compound elastic scattering accounted for using the statistical model. The methods of Moldauer, Tepel et al. and Hofmann et al. for calculating the latter are compared. The improvement to the low-energy phenomenological description resulting from inclusion of a surface-peaked real component to the potential is examined. A possible connection between the observed energy dependence of the real potential and the anomalous behavior of the nucleon reduced mass near the Fermi energy is discussed. Microscopic calculations of the optical potential are made using the methods of Brieva and Rook and Jeukenne et al. Inelastic scattering cross sections for the 7 2 − and 13 2 + single-particle states of 209Bi and the first two excited states of 208Pb, the 3 − and 5 − collective states, are presented. Direct inelastic scattering from these states is calculated using the DWBA or coupled-channel formalism. Compound inelastic scattering is calculated using the statistical model.

Direct neutron scattering from 182W and 184W

Differential elastic and inelastic neutron scattering cross sections for 182W and 184W have been measured at incident energies 4.87 and 6.00 MeV. Cross sections for the first (0 +, 2 +, 4 +, 6 +), second (0 +, 2 +), and some higher excitations are presented. Angular distributions exhibit direct reaction characteristics, suggesting that compound cross sections for these states are small. This is supported by statistical-model calculations. Coupled-channel calculations of cross sections are made using a phenomenological deformed optical potential. Quadrupole and hexadecapole deformations have been searched to optimize fits. The necessity of introducing a β 6 deformation is investigated. Electric multipole transition matrix elements, used in the coupled-channel analysis, are obtained from the rotation-vibration model and the dynamic-deformation theory.

Direct neutron scattering from W and W

Differential elastic and inelastic neutron scattering cross sections for 182W and 184W have been measured at incident energies 4.87 and 6.00 MeV. Cross sections for the first (0+, 2+, 4+, 6+), second (0+, 2+), and some higher excitations are presented. Angular distributions exhibit direct reaction characteristics, suggesting that compound cross sections for these states are small. This is supported by statistical-model calculations. Coupled-channel calculations of cross sections are made using a phenomenological deformed optical potential. Quadrupole and hexadecapole deformations have been searched to optimize fits. The necessity of introducing a β6 deformation is investigated. Electric multipole transition matrix elements, used in the coupled-channel analysis, are obtained from the rotation-vibration model and the dynamic-deformation theory.

Fast-neutron scattering from indium

Broad-resolution neutron total cross sections of elemental indium were measured over 0.8-4.5 MeV at intervals of <or approximately=50 keV. Differential neutron elastic-scattering cross sections were measured over 1.5-3.8 MeV at intervals of <or approximately=50 up to 100 keV, at 10-20 scattering angles distributed between 20 and 160 degrees. (n,n' gamma ) measurements were made for neutron energies of 0.86-2.4 MeV at intervals of approximately=100 keV and at a gamma-ray emission angle of 55 degrees . The gamma-ray results were associated with the excitation of 36 levels in indium and were used to deduce the neutron inelastic-scattering cross sections for levels by excitation energies of approximately=1.9 MeV. The experimental results are discussed in terms of the optical-statistical model and the characteristics of the excited levels of indium.