scholarly journals Phase Shifts of p-3He Scattering at Low Energies

2000 ◽  
Vol 103 (1) ◽  
pp. 107-125 ◽  
Author(s):  
Y. Yoshino ◽  
V. Limkaisang ◽  
J. Nagata ◽  
H. Yoshino ◽  
M. Matsuda
Keyword(s):  
Phase Shifts ◽  
Low Energies

Vacuum polarization and D-wave α−α scattering

1969 ◽  
Vol 47 (1) ◽  
pp. 113-115 ◽  
Author(s):  
Mark W. Kermode
Keyword(s):  
Cross Sections ◽  
Differential Cross ◽  
Vacuum Polarization ◽  
Center Of Mass ◽  
Phase Shifts ◽  
Differential Cross Sections ◽  
Wave Phase ◽  
Low Energies ◽  
D Wave

The D-wave phase shifts for α−α scattering at low energies are obtained from (i) new analyses of the differential cross sections and (ii) the effects of vacuum polarization. The results are −0.4° (−0.4°), −0.2° (−0.4°), +0.2° (−0.4°), −0.2° (−0.2°), and 0.3° (0.2°) for the center-of-mass energies 0.3, 0.425, 0.5, 0.75, and 1.0 MeV, respectively. It is felt that these results are significant.

scholarly journals The WKB Method for a Complex Potential

1957 ◽  
Vol 10 (1) ◽  
pp. 110 ◽  
Author(s):  
CBO Mohr
Keyword(s):  
Complex Potential ◽  
Optical Model ◽  
Phase Shifts ◽  
Potential Well ◽  
Wkb Method ◽  
Complex Phase ◽  
Factors Affecting ◽  
Low Energies ◽  
Exact Calculations

The extension of the WKB method to a complex potential, as used in the optical "model of the nucleus, is discussed. The formula for the complex phase shifts is formally deduced, and its accuracy tested against exact calculations for a square potential well and a well with sloping sides. At low energies there occur large discrepancies; the WKB phases vary regularly with energy, whereas the exact values oscillate violently about the WKB values in a characteristic way and marked resonances occur. The factors affecting the accuracy of the method are discussed.

Proton-ProtonP-Wave Phase Shifts at Low Energies

1969 ◽  
Vol 182 (4) ◽  
pp. 1031-1034 ◽  
Author(s):  
Leon Heller ◽  
Michael S. Sher
Keyword(s):  
Phase Shifts ◽  
Wave Phase ◽  
Low Energies

The method of polarized orbitals for the elastic scattering of slow electrons by ionized helium and atomic hydrogen

1964 ◽  
Vol 281 (1385) ◽  
pp. 151-163 ◽  
Keyword(s):  
Differential Equations ◽  
Cross Sections ◽  
Wave Scattering ◽  
Iterative Solution ◽  
Phase Shifts ◽  
First Derivative ◽  
Modified Method ◽  
Good Accord ◽  
Low Energies ◽  
Orbital Phase

The method of polarized orbitals is analyzed for scattering by hydrogen or ionized helium, and is shown to require modification for p -wave scattering; with this change the polarizedorbital phase shifts for all angular momenta are associated with a variational principle. As the additional terms in the p -wave equation involve the first derivative, a novel numerical method (similar to Numerov’s method) was devised for the convenient and rapid solution of linear second-order differential equations containing the first derivative, and extended to the integro-differential equations arising in the non-iterative solution of the present problem . Polarized-orbital phase shifts are presented for the singlet and triplet scattering by ionized helium of 8- , p- and d -wave electrons, at energies up to the ionization threshold. At low energies these agree closely with the predictions of the quantum-defect method, provided that the modified equation is used for p -wave scattering. Electron-hydrogen p -wave phase shifts were also obtained with this equation; the new phase shifts increase slightly (≤ 5%) the total cross-sections calculated by Temkin & Lamkin (1961). The simpler exchange polarization approximation yields phase shifts in quite good accord with those of the (modified) method of polarized orbitals.

Proton collisions with hydrogen atoms at low energies: quantum theory and integrated cross-sections

1977 ◽  
Vol 353 (1675) ◽  
pp. 575-588 ◽  
Keyword(s):  
Quantum Theory ◽  
Cross Sections ◽  
Phase Shifts ◽  
State Theory ◽  
Partial Wave Analysis ◽  
Quantum Mechanical ◽  
Wave Analysis ◽  
Hydrogen Atoms ◽  
Proton Collisions ◽  
Low Energies

Cross-sections for collisions of protons with hydrogen atoms have been computed by partial wave analysis within the perturbed stationary state theory. Phase shifts with 6 decimal accuracy were obtained by the use of adiabatically corrected 1Sσ g and 2Pσ u H + 2 potentials together with accurate numerical methods. The phase shifts and the integrated cross-sections derived from them are reported for 57 values of the energy ranging from 0.0001 eV (1.2 K) to 10 eV. These accurate quantum mechanical results differ from semi-classical results especially at energies below 0.1 eV.

scholarly journals Renormalization of Chiral Nuclear Forces with Multiple Subtractions in Peripheral Channels

2017 ◽  
Vol 2017 ◽  
pp. 1-15 ◽  
Author(s):  
E. F. Batista ◽  
S. Szpigel ◽  
V. S. Timóteo
Keyword(s):  
Phase Shifts ◽  
Renormalization Scale ◽  
Nuclear Forces ◽  
Nucleon Interaction ◽  
Subtraction Point ◽  
Low Energies

We analyse the renormalization of the of two-nucleon interaction with multiple subtractions in peripheral waves considering two chiral forces at N3LO. Phase shifts at low energies are then computed with several subtraction points below μ=10 fm−1. We show that for most peripheral waves the phase shifts have nearly no dependence on the renormalization scale. In two cases the phase shifts converge slowly as the renormalization scale approaches μ=1 fm−1 and in one case the phase shifts presented oscillations with respect to the subtraction point μ.

Fresnel interference in point-projection imaging of purple membrane

1995 ◽  
Vol 53 ◽  
pp. 846-847
Author(s):  
X. Zhang ◽  
J. Spence ◽  
W. Qian ◽  
D. Taylor ◽  
K. Taylor
Keyword(s):  
Detection Efficiency ◽  
Mean Free Path ◽  
Purple Membrane ◽  
Unit Cell Dimension ◽  
Experimental Point ◽  
Membrane Thickness ◽  
Low Energies ◽  
Channel Plate ◽  
Point Projection ◽  
Inelastic Mean Free Path

Experimental point-projection shadow microscope (PPM) images of uncoated, unstained purple membrane (PM, bacteriorhodopsin, a membrane protein from Halobacterium holobium) were obtained recently using 100 volt electrons. The membrane thickness is about 5 nm and the hexagonal unit cell dimension 6 nm. The images show contrast around the edges of small holes, as shown in figure 1. The interior of the film is opaque. Since the inelastic mean free path for 100V electrons in carbon (about 6 Å) is much less than the sample thickness, the question arises that how much, if any, transmission of elastically scattered electrons occurs. A large inelastic contribution is also expected, attenuated by the reduced detection efficiency of the channel plate at low energies. Quantitative experiments using an energy-loss spectrometer are planned. Recently Shedd has shown that at about 100V contrast in PPM images of thin gold films can be explained as Fresnel interference effects between different pinholes in the film, separated by less than the coherence width.

Sign in / Sign up

Export Citation Format

Share Document