Connection between the Absorptive Part of the Scattering Amplitude and That of the Feynman Integral Associated with the Tetrahedron Graph

We compute the spin asymmetry and polarization of the final-state baryon in its rest frame in two-body meson–baryon low-energy scattering with an unpolarized initial state to lowest non-trivial order in BChPT. The required absorptive amplitudes are obtained analytically at the one-loop level. We discuss the polarization results numerically for several meson–baryon processes. Even at low energies above threshold, where BChPT can reasonably be expected to be applicable, sizable values of polarization are found for some processes.

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STUDIES OF Λ(1405) WITH K-MESIC ATOMS

International Journal of Modern Physics A ◽

10.1142/s0217751x11051731 ◽

2011 ◽

Vol 26 (03n04) ◽

pp. 402-407

Author(s):

SŁAWOMIR WYCECH

Keyword(s):

Binding Energy ◽

Atomic Hydrogen ◽

Scattering Amplitude ◽

Absorptive Part ◽

Experimental Tests ◽

P Wave ◽

Subthreshold Region ◽

Radiative Transitions ◽

Mesic Atom

Experimental tests of the Λ(1405) properties are suggested. These could reflect the position and shape of this state in the [Formula: see text] channel. The first test consists in precise determinations of the level widths in the highest accessible K -mesic atom states. One needs to study the dependence of these widths on the binding energy of the valence protons in the involved nuclei. The second test consists in the measurement of radiative transitions from the P-wave atomic hydrogen levels to the Λ(1405) state. In both cases one can study the absorptive part of [Formula: see text] scattering amplitude in the subthreshold region.

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Study of charge transfer in FeTi

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100075270 ◽

1983 ◽

Vol 41 ◽

pp. 296-297

Author(s):

J. Taft∅

Keyword(s):

Charge Transfer ◽

Charge Distribution ◽

Electron Scattering ◽

Periodic System ◽

Electron Distribution ◽

Scattering Amplitude ◽

Transition Elements ◽

Hartree Fock ◽

Cscl Structure ◽

The Right

It is well known that for reflections corresponding to large interplanar spacings (i.e., sin θ/λ small), the electron scattering amplitude, f, is sensitive to the ionicity and to the charge distribution around the atoms. We have used this in order to obtain information about the charge distribution in FeTi, which is a candidate for storage of hydrogen. Our goal is to study the changes in electron distribution in the presence of hydrogen, and also the ionicity of hydrogen in metals, but so far our study has been limited to pure FeTi. FeTi has the CsCl structure and thus Fe and Ti scatter with a phase difference of π into the 100-ref lections. Because Fe (Z = 26) is higher in the periodic system than Ti (Z = 22), an immediate “guess” would be that Fe has a larger scattering amplitude than Ti. However, relativistic Hartree-Fock calculations show that the opposite is the case for the 100-reflection. An explanation for this may be sought in the stronger localization of the d-electrons of the first row transition elements when moving to the right in the periodic table. The tabulated difference between fTi (100) and ffe (100) is small, however, and based on the values of the scattering amplitude for isolated atoms, the kinematical intensity of the 100-reflection is only 5.10-4 of the intensity of the 200-reflection.

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Single Atom Image Contrast in Fixed Beam Dark Field Electron Microscopy

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100051840 ◽

1974 ◽

Vol 32 ◽

pp. 366-367

Author(s):

Wah Chi

Keyword(s):

Scattering Amplitude ◽

Present Report ◽

Dark Field ◽

Image Contrast ◽

Single Atom ◽

Optical Theorem ◽

Hartree Fock ◽

Heavy Atoms ◽

Beam Stop ◽

Fixed Beam

Resolution and contrast are the important factors to determine the feasibility of imaging single heavy atoms on a thin substrate in an electron microscope. The present report compares the atom image characteristics in different modes of fixed beam dark field microscopy including the ideal beam stop (IBS), a wire beam stop (WBS), tilted illumination (Tl) and a displaced aperture (DA). Image contrast between one Hg and a column of linearly aligned carbon atoms (representing the substrate), are also discussed. The assumptions in the present calculations are perfectly coherent illumination, atom object is represented by spherically symmetric potential derived from Relativistic Hartree Fock Slater wave functions, phase grating approximation is used to evaluate the complex scattering amplitude, inelastic scattering is ignored, phase distortion is solely due to defocus and spherical abberation, and total elastic scattering cross section is evaluated by the Optical Theorem. The atom image intensities are presented in a Z-modulation display, and the details of calculation are described elsewhere.

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LACBED with Quantitative Anomalous Absorption Corrections

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100136246 ◽

1990 ◽

Vol 48 (2) ◽

pp. 528-529

Author(s):

C.J. Rossouw ◽

L.J. Allen ◽

P.R. Miller

Keyword(s):

Momentum Transfer ◽

Scattering Amplitude ◽

Incident Beam ◽

Waller Factor ◽

Beam Momentum ◽

Anomalous Absorption ◽

Quantitative Calculation ◽

Ewald Sphere ◽

Image Position ◽

Incident Beam Energy

An Einstein model for thermal diffuse scattering (TDS) has enabled quantitative calculation of the absorptive potential V'(r). This allows anomalous absorption to be accounted for in LACBED contrast. Fourier coefficients Vg-h of the absorptive component from each atom α are calculated from integrals of the formwhere fα is the scattering amplitude and M(Q) the Debye-Waller factor. Integration over the Ewald sphere (dΩ) requires the momentum transfer q to have values up to 2ko (the incident beam momentum). Dynamical ‘dechannelling’ is accounted for by the terms g ≠ h. The crystal absorptive potential is obtained by coherently summing over these atomic absorptive potentials within the unit cell. Unlike the elastic potential, the absorptive potential is a strong function of incident beam energy Eo, since the range of momentum transfer q and associated solid angles dΩ change with the Ewald sphere radius.Fig. 1 shows a LACBED pattern of the zeroth order beam from Si aligned along a <001> zone axis.

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Direct imaging of charge transfer

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100165860 ◽

1996 ◽

Vol 54 ◽

pp. 680-681

Author(s):

Yimei Zhu ◽

J. Tafto

Keyword(s):

Charge Transfer ◽

Electron Diffraction ◽

Scattering Amplitude ◽

High Temperature Superconductors ◽

Charge Carriers ◽

Image Charge ◽

Net Charge ◽

Long Time ◽

Electron Holes ◽

First Time

The electron holes confined to the CuO2-plane are the charge carriers in high-temperature superconductors, and thus, the distribution of charge plays a key role in determining their superconducting properties. While it has been known for a long time that in principle, electron diffraction at low angles is very sensitive to charge transfer, we, for the first time, show that under a proper TEM imaging condition, it is possible to directly image charge in crystals with a large unit cell. We apply this new way of studying charge distribution to the technologically important Bi2Sr2Ca1Cu2O8+δ superconductors.Charged particles interact with the electrostatic potential, and thus, for small scattering angles, the incident particle sees a nuclei that is screened by the electron cloud. Hence, the scattering amplitude mainly is determined by the net charge of the ion. Comparing with the high Z neutral Bi atom, we note that the scattering amplitude of the hole or an electron is larger at small scattering angles. This is in stark contrast to the displacements which contribute negligibly to the electron diffraction pattern at small angles because of the short g-vectors.

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