Discording power of Hamiltonian interactions

In this paper, we report the coherent scattering cross sections of some lanthanides at low momentum transfer in four angular ranges of (0°?4°), (0°?6°), (0°?8°) and for ²⁴¹Am (59.54 keV) and ¹³⁷Cs (661.6 keV) gamma rays. The coherent scattering cross sections were derived by subtracting the small contribution of the corresponding angle integrated incoherent scattering cross sections from the experimentally measured total (coherent + incoherent) scattering cross sections for the elements and energies of interest. The coherent scattering cross sections were found to agree with the corresponding theoretical cross sections within the range of experimental errors. The theoretical coherent scattering cross sections were computed by numerically integrating the S-matrix data of the elements in the angular ranges of interest. The incoherent scattering cross sections were based on the compilations which make use of the non-relativistic Hartree-Fock (NRHF) model for the atomic charge distribution.     

Delbrück scattering of 9 MeV photons from tantalum

The differential elastic scattering cross section of 9.0 MeV photons by ¹⁸¹Ta has been measured at angles between 25° and 140° and a good agreement was obtained between the measured and predicted values at θ = 35–90°. In calculating the theoretical cross sections the coherent scattering contributions of nuclear Thomson (NT), nuclear resonance (NR) and Delbrück (D) amplitudes were included while that of Rayleigh (R) scattering was excluded. The D-amplitudes were taken from a recent calculation by Mork and Papatzacos. Evidence for the contribution of the real D-amplitude is obtained.     

Neutron interactions with germanium isotopes and amorphous and crystalline GeO2

Coherent neutron scattering lengths and total cross sections have been measured on elemental and oxide samples of ordinary Ge and of isotopically enriched substances. From the experimental results the following values were obtained:

the coherent scattering lengths (in fm) of the bound atoms Ge(8.185±0.020);⁷⁰Ge(10.0±0.1);⁷²Ge(8.51±0.10);⁷³Ge(5.02±0.04);⁷⁴Ge(7.58±0.10) and⁷⁶Ge(8.2 ±1.5);

the absorption cross sections at 0.0253 eV (in barn) for Ge(2.20±0.04);⁷⁰Ge(2.9±0.2);⁷²Ge(0.8±0.2);⁷³Ge(14.4±0.4) and⁷⁴Ge(0.4±0.2);

the free cross sections for epithermal neutrons and the zero energy scattering cross sections.

On the basis of this data, the isotopic- and spin-incoherent cross sections and thes-wave resonance contributions to the coherent scattering lengths have been determined and discussed. Transmission measurements at 0.57 meV on amorphous and crystalline GeO₂ yielded for the amorphous sample an inelastic cross section eight times larger than for the crystalline samples. This effect corresponds to a clearly higher density of low energy states in the amorphous than in the crystalline substances.     

Neutron scattering lengths of the isotopes of thulium,ytterbium and lutetium

Coherent neutron scattering lengths and total cross sections have been measured on samples of ordinary Tm, Yb and Lu and on isotopically enriched compounds. From the experimental data for 0.57 meV neutron energy the following data were obtained: the coherent scattering lengths (in fm) of the bound atoms¹⁶⁹Tm (7.07+0.03);¹⁷⁰Yb (6.8±0.1);¹⁷¹Yb (9.7±0.1);¹⁷²Yb (9.5±0.1);¹⁷³Yb (9.56±0.10);¹⁷⁴Yb (19.2±0.1);¹⁷⁶Yb (8.7± 0.1); Yb (12.41±0.03);¹⁷⁵Lu (7.28±0.09);¹⁷⁶Lu (6.3±0.2) and Lu (7.21±0.03); the thermal absorption cross sections (in barn) for¹⁶⁹Tm (100±2); Yb (34.8±0.8) and Lu (74±2). In combination with the resonance parameters the measured coherent scattering lengths allowed the determination of potential scattering radii R′ which are of particular interest for the permanently deformed and deformable nuclei in the rare-earth region.     

A neutron diffraction study of liquid chloroform

Neutron diffraction studies of the isotopes of chloroform CD³⁵Cl₃ and CD³⁷Cl₃ in liquid phase were carried out at 20°C and a wavelength of 0·7 Å. The data were corrected for background, absorption, multiple scattering and inelastic effects. The coherent distinct differential cross section was separated into intramolecular and intermolecular contributions. The latter, together with intermolecular contributions from neutron scattering data on chloroform of natural isotopic chlorine composition and from X-ray data, was employed to determine four expansion coefficients of the molecular pair correlation function.     

One-centre matrix elements of the spin-other orbit operator in linear molecules: diagonal terms

The quasi-elastic scattering of cold neutrons from liquid and solid C₆H₆ and C₆D₆ has been measured at temperatures between 260 K and 325 K for incident wavelengths between 4·07 Å and 7·05 Å and for angles of scatter between 20° and 90° by means of a chopper time-of-flight apparatus. From the results, the total quasi-elastic intensity and the width of the corresponding broadening, presumed Lorentzian, were extracted. The broadening of the incoherent component in the scattering is discussed in terms of various models designed to combine the effects of centre of mass and jump rotational diffusion. All the models could be fitted to the results, using a root-mean-square jump length approximately equal to the nearest H-H distance. Using the ‘effective mass approximation’ the model can be extended to cover the coherent contributions to the scattering. When this is done, it is found that the fit is rather better if the rotational jumps are assumed not to contribute to the coherent broadening. The mean interval between jumps at 293 K was found to be 2·2 ± 0·5 × 10^-12 s with an activation energy of 2·1 ± 0·6 kcal/mole, in good agreement with 1·4 × 10^-12 s and 1·8 kcal/mole obtained by N.M.R. techniques.     

Interactions of slow neutrons with nuclides of antimony,tellurium and iodine

Coherent neutron scattering lengths and total cross sections have been measured on samples of ordinary Sb, Te, I and on isotopically enriched compounds. From the experimental data for neutron energies of 0.57 meV, 1.26 eV and 5.2 eV the following data were obtained: the coherent scattering lengths (in fm) of the bound atoms Sb (5.57±0.03);¹²¹Sb(5.71±0.06),¹²³Sb(5.38±0.07); Te(5.80±0.03) and for its isotopes of the mass number 122(3.8±0.2); 123(?0.05±0.25?i·0.100); 124(7.95±0.10); 125(5.01±0.08); 126(5.55±0.07); 128 (5.88±0.07); 130(6.01±0.07). the thermal absorption cross sections (in barn) for Sb(4.91±0.05);¹²¹Sb(5.77±0.12);¹²³Sb(3.8±0.2); Te(4.05±0.05) and I(6.15±0.06). The combination of the measured values of scattering lengths and -cross sections resulted in data for coherent and incoherent cross sections. Taking account of resonance data a complete set of spin state- and reconance scattering lengths has been obtained and discussed.     

Epithermal neutron diffraction from a gadolinium alloy (Gd0.9Y0.1)

The coherent nuclear scattering amplitude of natural Gd was determined by epithermal neutron diffraction with neutron energy of 1.4 eV to be 1.4 ± 0.1 × 10^?12 cm.     

Anomaly in α-scattering from 6Li between 35 and 45 MeV

The elastic scattering of α-particles on ⁶Li nuclei has been measured from 20° to 170° (c.m.) and the inelastic scattering to the first excited state of ⁶Li has been measured for forward and backward angles. The elastic scattering angular distributions are calculated (i) in terms of pure potential scattering, (ii) in terms of potential scattering with an l-cut-off on the imaginary part of the potential and (iii) in terms of the coherent addition of the potential scattering amplitude and of the exchange amplitude. The third method gives the best fit to the data. The inelastic angular distributions are compatible with the macroscopic calculations, except in the very backward region where exchange phenomena are also shown to dominate.     

A neutron-diffraction study of liquid acetonitrile

Neutron-diffraction studies on liquid acetonitrile CD₃C¹⁵N at 20°C were carried out at neutron wavelengths of 0·5 Å and 0·7 Å. The data were corrected for background, absorption, multiple scattering and inelastic effects (Placzek correction) and then were normalized to absolute differential cross section by comparison with vanadium standard. The absolute coherent distinct differential cross section was separated into intermolecular and intramolecular contributions. From the latter the molecular structure in the liquid was determined.     

Scattered ultrasound for incoherent insonification in transmission imaging

Spatially incoherent ultrasound is produced by the scattering of coherent ultrasonic waves at statistically moved particles. Incoherent insonification is much more uniform at near-field distances than coherent ultrasound. The lateral resolution is improved and the coherent ‘ringing’ in a sharply imaged object disappears.     

Interactions of slow neutrons with the chromium isotopes

Neutron transmission experiments and determinations of coherent scattering lengths were performed on natural chromium and enriched samples of⁵⁰Cr,⁵²Cr,⁵³Cr and⁵⁴Cr. By means of the Christiansen-filter-technique we obtained new values for the scattering lengths of the bound atoms:b(^natCr)=3.635±0.007 fm,b(⁵⁰Cr)=?4.50±0.05 fm,b(⁵²Cr)=4.914±0.015 fm,b(53Cr)=?4.20±0.03 fm, andb(⁵⁴Cr)=4.55±0.10 fm. The transmission experiments with neutrons of 510 ΜeV, 1.26 eV and 5.19 eV energy resulted in data for the absorption cross sectionσ _a (^natCr) =3.05±0.08 b and for the scattering cross section at “zero energy”:σ ₀ (^natCr)=3.381±0.010 b. Data for incoherent and spin-state scattering and for the potential-scattering radius of the nuclei could be deduced from these results.     

Interaction of slow neutrons with natural terbium,holmium and erbium and its isotopes

Coherent neutron scattering lengths and total cross sections have been measured on samples of ordinary Tb, Ho and Er and on isotopically enriched Er-compounds. From the experiment the following data were obtained:

• - the coherent scattering lengths (in fm) of the bound atoms ¹⁵⁹Tb(7.34 ± 0.02), ¹⁶⁵Ho(8.44 ± 0.03), ^ordEr(7.79 ± 0.02), ¹⁶²Er(9.01 ± 0.11), ¹⁶⁴Er(7.95 ± 0.14), ¹⁶⁶Er(10.51 ± 0.19), ¹⁶⁷Er(3.06 ± 0.05), ¹⁶⁸Er(7.43 ± 0.08), and ¹⁷⁰Er(9.61 ± 0.06)
• - the thermal absorption cross sections (in b) ¹⁴¹Pr(12.7 ± 0.6), ^ordNd(58 ± 1), ¹⁵⁹Tb(30 ± 2), ¹⁶⁵Ho (65 ± 2), ^ordEr (145 ± 2), ¹⁶⁶Er (18 ± 2), ¹⁶⁷Er(568 ± 9), ¹⁶⁸Er(2.3 ± 0.3), and ¹⁷⁰Er(15 ± 1). In combination with the resonance parameters, the measured coherent scattering lengths allowed the determination of potential scattering radii R′ which are of particular interest for the optical model theory.

     

Interaction of slow neutrons with nuclides of scandium,titanium, vanadium and manganese

Total cross section measurements at various neutron energies were performed on metallic and oxide samples of natural Sc, Ti, V, and Mn. By means of the Christiansen filter technique the coherent scattering lengths were determined on natural and isotopically enriched samples of Ti-, V-, and Mn-compounds. From the measured values we deduced the following data:

? the absorption cross sections (at 0.0253 eV in barn) of^natTi (6.43±0.06) and of^natV (5.06±0.04);

? the bound coherent scattering lengths (in fm) of^natTi (?3.370±0.013),⁴⁶Ti (4.72±0.05),⁴⁷Ti (3.53±0.07),⁴⁸Ti (?5.86±0.02),⁴⁹Ti (0.98±0.05),⁵⁰Ti (5.88±0.10),^natV (?0.443±0.014), and Mn (?3.750±0.018);

? the free potential radii (in fm) of Sc (3.60 ±0.10),⁴⁶Ti (3.50±0.10),⁴⁷Ti (3.60±0.10),⁴⁸Ti (3.90±0.10),⁴⁹Ti (4.10 ±0.15),⁵⁰Ti (4.50±0.15),⁵¹V (5.20±0.20), and Mn (6.50±20).

On the basis of the well known resonance parameters in combination with new fits of bound levels the spin state scattering lengths, the spin incoherence, and the obtained potential radii are discussed. Total cross section calculations were performed by multi-level formalism and are compared with the measurements.     

Phenomenology of nuclear shadowing in deep-inelastic scattering

We investigate shadowing effects in deep-inelastic scattering from nuclei at small valuesx < 0.1 of the Bjorken variable. Unifying aspects of generalized vector meson dominance and color transparency we first develop a model for deep-inelastic scattering from free nucleons at smallx. In application to nuclear targets we find that the coherent interaction of quark-antiquark fluctuations with nucleons in a nucleus leads to the observed shadowing atx < 0.1. We compare our results with most of the recent data for a large variety of nuclei and examine in particular the Q² dependence of the shadowing effect. While the coherent interaction of low mass vector mesons causes a major part of the shadowing observed in the Q² range of current experiments, the coherent scattering of continuum quark-antiquark pairs is also important and guarantees a very weak overall Q² dependence of the effect. We also discuss shadowing in deuterium and its implications for the quark flavor structure of nucleons. Finally we comment on shadowing effects in high-energy photon-nucleus reactions with real photons.     

Intense interactions of molecules with a short-wavelength electromagnetic radiation field: II. Resonance scattering of radiation and fluorescence

Within the framework of the nonadiabatic approach developed in the preceding paper, the resonance scattering, resonance Raman scattering, and resonance fluorescence are studied in detail for diatomic and triatomic molecules, and polyatomic symmetric and antisymmetric top molecules, which interact with the field of short-wavelength radiation with a wavelength λ ≥ Å and an intensity up to 10¹⁴ W/cm². The coherent excitations of high-lying Rydberg and autoionizing states are taken into account. Analytical expressions for calculating the tensors and cross sections of the above processes are derived.     

High intensity effect on two-photon resonant,coherent Raman scattering via excitonic molecules in CuCl and CuBr

Two-phonon resonant, coherent Raman scattering (four-photon degenerate coherent scattering) via excitonic molecules has been studied as a function of intensity of incident light in CuCl and CuBr. Observed line-shaped of coherent scattering spectra broadens as excitation intensity is raised. This broadening is found to be closely correlated with that of the two-photon absorption. These results are qualitatively explained by taking account of the excitation intensity-dependence of χ⁽³⁾, but cannot be explained by the autoinization model.     

Measurement of the coherent neutron scattering length of 3He by neutron interferometry

A precise determination of the coherent scattering length of ³He with a neutron interferometer yields a value a_c = 4.29 ± 0.04 fm. A comparison with varoous theoretical perdictions is made and its relation to the few-body problem is discussed. A combination with other experimental results yield as most probable values for the free singlet- and triplet scattering length a_s = 8.0 ± fm and a_t = 3.05 ± 0.07 fm, respectively.