scholarly journals New parameterization of the trinucleon wave function and its application to the π 3He scattering length

2003 ◽  
Vol 16 (3) ◽  
pp. 437-446 ◽  
Author(s):  
V. Baru ◽  
J. Haidenbauer ◽  
C. Hanhart ◽  
J.A. Niskanen
1973 ◽  
Vol 51 (17) ◽  
pp. 1850-1860
Author(s):  
M. Razavy

The problem of multiple scattering by two rigid spheres is studied in the context of an effective range theory. At low energies, by expanding the total wave function in powers of the momentum of the incident particle, it is observed that the coefficients of different terms of the expansion are solutions of either Laplace or Poisson equations. These equations are separable in bispherical coordinates. Using the method of separation of variables, one can determine the scattering amplitude and its first and second derivatives with respect to momentum, at zero energy. In particular, a simple expression is obtained for the scattering length of two hard spheres. With the help of the Green's function in bispherical coordinates, it is shown that for any wavenumber, the scattered wave satisfies an inhomogeneous integral equation in two variables. Hence, the exact wave function and the scattering amplitude can be found numerically for all energies.


2005 ◽  
Vol 140 ◽  
pp. 305-307 ◽  
Author(s):  
S. Aoki ◽  
M. Fukugita ◽  
K-I. Ishikawa ◽  
N. Ishizuka ◽  
Y. Iwasaki ◽  
...  

2013 ◽  
Vol 91 (2) ◽  
pp. 188-190 ◽  
Author(s):  
Joseph DiRienzi ◽  
Richard J. Drachman

While carrying out investigations on Ps–He scattering it was discovered that it would be possible to improve the results of a previous work on zero-energy scattering of ortho-positronium by helium atoms. The previous work used a model to account for exchange and also attempted to include the effect of short-range Coulomb interactions in the close-coupling approximation. The three terms that were then included did not produce a well-converged result but served to give some justification to the model. Now we improve the calculation by using a simple variational wave function, and derive a much better value of the scattering length. The new result is compared with other computed values, and when an approximate correction due to the van der Waals potential is included the total is consistent with an earlier conjecture.


1979 ◽  
Vol 19 (4) ◽  
pp. 1568-1575 ◽  
Author(s):  
Irving Aronson ◽  
Robert Blau ◽  
Chemia J. Kleinman ◽  
Leonard Rosenberg ◽  
Larry Spruch

Author(s):  
Peter Rez

In high resolution microscopy the image amplitude is given by the convolution of the specimen exit surface wave function and the microscope objective lens transfer function. This is usually done by multiplying the wave function and the transfer function in reciprocal space and integrating over the effective aperture. For very thin specimens the scattering can be represented by a weak phase object and the amplitude observed in the image plane is1where fe (Θ) is the electron scattering factor, r is a postition variable, Θ a scattering angle and x(Θ) the lens transfer function. x(Θ) is given by2where Cs is the objective lens spherical aberration coefficient, the wavelength, and f the defocus.We shall consider one dimensional scattering that might arise from a cross sectional specimen containing disordered planes of a heavy element stacked in a regular sequence among planes of lighter elements. In a direction parallel to the disordered planes there will be a continuous distribution of scattering angle.


Author(s):  
D.E. Jesson ◽  
S. J. Pennycook

It is well known that conventional atomic resolution electron microscopy is a coherent imaging process best interpreted in reciprocal space using contrast transfer function theory. This is because the equivalent real space interpretation involving a convolution between the exit face wave function and the instrumental response is difficult to visualize. Furthermore, the crystal wave function is not simply related to the projected crystal potential, except under a very restrictive set of experimental conditions, making image simulation an essential part of image interpretation. In this paper we present a different conceptual approach to the atomic imaging of crystals based on incoherent imaging theory. Using a real-space analysis of electron scattering to a high-angle annular detector, it is shown how the STEM imaging process can be partitioned into components parallel and perpendicular to the relevant low index zone-axis.It has become customary to describe STEM imaging using the analytical treatment developed by Cowley. However, the convenient assumption of a phase object (which neglects the curvature of the Ewald sphere) fails rapidly for large scattering angles, even in very thin crystals. Thus, to avoid unpredictive numerical solutions, it would seem more appropriate to apply pseudo-kinematic theory to the treatment of the weak high angle signal. Diffraction to medium order zero-layer reflections is most important compared with thermal diffuse scattering in very thin crystals (<5nm). The electron wave function ψ(R,z) at a depth z and transverse coordinate R due to a phase aberrated surface probe function P(R-RO) located at RO is then well described by the channeling approximation;


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