Impact Parameter Representation of the Scattering Amplitude

1971 ◽  
Vol 49 (14) ◽  
pp. 1885-1898 ◽  
Author(s):  
M. Razavy
Keyword(s):  
Elastic Scattering ◽  
Phase Shift ◽  
Differential Cross Section ◽  
Cross Section ◽  
Impact Parameter ◽  
Differential Cross ◽  
Scattering Amplitude ◽  
Potential Methods ◽  
Energy Dependent ◽  
The Impact

From the Lippmann–Schwinger equation, the exact and different approximate relations for the impact parameter form of the total scattering amplitude on- and off-the-energy shell are derived. The relation between the impact parameter phase shift and the range of potential is studied, and several methods of determining the potential from the impact parameter phase shift for local, nonlocal, and energy dependent interactions are obtained in Blankenbecler and Goldberger's approximation. By considering solvable examples it is shown that the Glauber's approximation, in certain cases, may be valid for all scattering angles. Finally for completely elastic scattering or for a purely absorptive potential, methods of finding the impact parameter phase shift from the differential cross section for scattering are given.

scholarly journals Secondary dips and the asymptotics

2018 ◽  
Vol 33 (06) ◽  
pp. 1850040 ◽  
Author(s):  
S. M. Troshin ◽  
N. E. Tyurin
Keyword(s):  
Elastic Scattering ◽  
Differential Cross Section ◽  
Cross Section ◽  
Impact Parameter ◽  
Differential Cross ◽  
Energy Region ◽  
Proton Proton ◽  
Asymptotic Energy ◽  
The Impact

We point out how to detect experimentally the energy region where asymptotics start to manifest themselves by relating the appearance of the secondary dips in the differential cross-section of elastic scattering [Formula: see text] with the beginning of the asymptotic energy region. The consideration relies on differential characteristics. The impact parameter picture of proton–proton interactions is used.

scholarly journals The scattering of alpha particles by helium

1959 ◽  
Vol 251 (1265) ◽  
pp. 143-155 ◽  
Keyword(s):  
Elastic Scattering ◽  
Phase Shift ◽  
Differential Cross Section ◽  
Excitation Energy ◽  
Cross Section ◽  
Differential Cross ◽  
Incident Energy ◽  
Phase Shifts ◽  
Alpha Particles

In order to obtain information about the levels of even spin and parity of 8 Be at energies above 11 MeV, the differential cross-section for the α-particle-helium elastic scattering has been measured at a series of beam energies from 23·1 to 38·4 MeV, for many c.m.s. angles between 30 and 90°. Phase shifts up to L = 8 have been calculated for each energy. Combining these results with previous figures for lower energies, the phase shifts δ 0 , δ 2 and δ 4 are thus known as functions of incident energy from 0·15 MeV to 38·4 MeV. The behaviour of the phase shift δ 4 confirms the existence of a previously suggested level with I = 4 at an excitation energy of about 11·4 MeV in 8 Be. The phase shifts δ 6 and δ 8 are small, as expected if the rotational series of levels in 8 Be term inates with I = 4.

Differential cross-section measurements in positron–argon collisions

1996 ◽  
Vol 74 (7-8) ◽  
pp. 505-508 ◽  
Author(s):  
R. M. Finch ◽  
Á. Kövér ◽  
M. Charlton ◽  
G. Laricchia
Keyword(s):  
Elastic Scattering ◽  
Differential Cross Section ◽  
Inelastic Scattering ◽  
Energy Range ◽  
Cross Section ◽  
Cross Sections ◽  
Differential Cross ◽  
Coupling Effect ◽  
Channel Coupling ◽  
Scattering Cross

Differential cross sections for elastic scattering and ionization in positron–argon collisions as a function of energy (40–150 eV) are reported at 60°. Of particular interest is the energy range 55–60 eV, where earlier measurements by the Detroit group found a drop in the elastic-scattering cross section of a factor of 2. This structure has been tentatively attributed to a cross channel-coupling effect with an open inelastic-scattering channel, most likely ionization. Our results indicate that ionization remains an important channel over the same energy range and only begins to decrease at an energy above 60 eV.

Differential Cross Section Measurements for the Elastic Scattering of Protons byN14

1957 ◽  
Vol 105 (1) ◽  
pp. 210-212 ◽  
Author(s):  
C. R. Bolmgren ◽  
G. D. Freier ◽  
J. G. Likely ◽  
K. F. Famularo
Keyword(s):  
Elastic Scattering ◽  
Differential Cross Section ◽  
Cross Section ◽  
Differential Cross

PROTON–4He ELASTIC SCATTERING AT ~ 1 GeV

2005 ◽  
Vol 14 (05) ◽  
pp. 787-798 ◽  
Author(s):  
Z. A. KHAN ◽  
MINITA SINGH
Keyword(s):  
Elastic Scattering ◽  
Differential Cross Section ◽  
Cross Section ◽  
Differential Cross ◽  
Phase Variation ◽  
Glauber Model ◽  
Slight Improvement ◽  
Polarization Data ◽  
Eikonal Expansion ◽  
Rotation Function

Based on the (spin-independent) Sugar–Blanckenbecler eikonal expansion for the T-matrix, we parametrize the (spin-dependent) NN amplitude (SNN) which successfully describes the pp and pn elastic scattering observables at ~ 1 GeV up to the available momentum transfers. Using SNN, we calculate the differential cross-section, polarization, and spin-rotation function of ~ 1 GeV protons on 4 He within the framework of the Glauber model. The analysis also includes the phase variation in the NN amplitude. It is found that the use of SNN, in comparision with the usually parametrized one-term amplitude, improves the agreement with the experimental data. The introduction of a global phase variation provides only a slight improvement over the results with a constant phase. However, if we allow different phases in the central- and spin-dependent parts of the NN amplitude, the agreement with the polarization data improves further without affecting the differential cross-section results.

Enskog-Boltzmann-Equation for a Fluid of Nonspherical Particles

1982 ◽  
Vol 37 (7) ◽  
pp. 660-664
Author(s):  
H. Thurn ◽  
S. Hess
Keyword(s):  
Boltzmann Equation ◽  
Differential Cross Section ◽  
Cross Section ◽  
Differential Cross ◽  
Position Vector ◽  
Nonspherical Particles ◽  
Fixed Orientation ◽  
General Relations ◽  
The Impact ◽  
Special Case

Abstract The Enskog-Boltzmann-equation is generalized to fluids of nonsperical particles with fixed orientation, i.e. for overdamped rotational motion. General relations between the interparticle position vector at the instant of contact, the impact parameter and the differential cross section are derived. The dependence of these quantities of the orientations of the colliding particles is studied for the special case of hard ellipsoids.

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