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Title: Optical potential in proton-nucleus scattering

Abstract

The optical potential for 40 MeV protons is calculated for the spin zero nuclei 12C, 40Ca, 58Ni, 120Sn, and 208Pb.

Authors:
 [1]
  1. Michigan State Univ., East Lansing, MI (United States)
Publication Date:
Research Org.:
Michigan State Univ., East Lansing, MI (United States)
Sponsoring Org.:
US Atomic Energy Commission (AEC)
OSTI Identifier:
4766012
Report Number(s):
COO-1051-33
NSA Number:
NSA-23-037286
DOE Contract Number:
AT(11-1)-1051
Resource Type:
Thesis/Dissertation
Resource Relation:
Other Information: Thesis. UNCL. Orig. Receipt Date: 31-DEC-69
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; CALCIUM 40; CARBON 12; ELASTIC SCATTERING; LEAD 208; MEV RANGE; NICKEL 58; NUCLEAR MODELS; NUCLEAR POTENTIAL; OPTICAL MODEL; PROTON BEAMS; PROTONS; TIN 120; PROTONS/scattering by nickel-58, tin-120, and lead-208 at 40 MeV, optical potential for, (T); TIN ISOTOPES Sn-120/proton elastic scattering at 40 MeV, optical potential for, (T); LEAD ISOTOPES Pb-208/proton elastic scattering at 40 MeV, optical potential for, (T); NUCLEAR MODELS/optical, potential for proton-nucleus scattering; CALCIUM ISOTOPES Ca-40/proton elastic scattering at 20 and 40 MeV, cross sections and optical potential for, (T); NICKEL ISOTOPES Ni-58/proton elastic scattering at 40 MeV, optical potential for, (T); CARBON ISOTOPES C-12/protons elastic scattering at 20 and 40 MeV, cross sections and optical potential for, (T); PROTONS/scattering by carbon-12 and calcium-40 at 20 and 40 MeV, cross sections and optical potentials for, (T)

Citation Formats

Slanina, Donald A. Optical potential in proton-nucleus scattering. United States: N. p., 1969. Web. doi:10.2172/4766012.
Slanina, Donald A. Optical potential in proton-nucleus scattering. United States. doi:10.2172/4766012.
Slanina, Donald A. Wed . "Optical potential in proton-nucleus scattering". United States. doi:10.2172/4766012. https://www.osti.gov/servlets/purl/4766012.
@article{osti_4766012,
title = {Optical potential in proton-nucleus scattering},
author = {Slanina, Donald A.},
abstractNote = {The optical potential for 40 MeV protons is calculated for the spin zero nuclei 12C, 40Ca, 58Ni, 120Sn, and 208Pb.},
doi = {10.2172/4766012},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Wed Jan 01 00:00:00 EST 1969},
month = {Wed Jan 01 00:00:00 EST 1969}
}

Thesis/Dissertation:
Other availability
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  • Current applications of multiple scattering theory to describe the elastic scattering of medium energy protons from nuclei have been shown to be quite successful in reproducing the experimental cross sections. These calculations use the impulse approximation, wherein the scattering from individual nucleons in the nucleus is described by the scattering amplitude for a free nucleon. Such an approximation restricts the inelastic channels to those initiated by nucleon-nucleon scattering. As a first step in determining the nature of p + nucleus scattering at 800 MeV, both total reaction cross sections and (p,p') inclusive cross sections were measured and compared to themore » free p + p cross sections. We conclude that as much as 85% of all reactions in a nucleus proceed from interactions with a single nucleon in the nucleus, and that the impulse approximation is a good starting point for a microscopic description of p + nucleus interactions at 800 MeV.« less
  • Results of two studies of small angle elastic scattering are presented. The first experiment measured hadron-nucleus elastic scattering at 70, 125, 175 GeV/c incident momentum. The second experiment is a high statistics study of hadron-proton elastic scattering at 200 GeV/c incident momentum. Hadron-nucleus elastic scattering was measured formore » $$\mu^{\pm}$$, $$K^{\pm}$$, $p$, and $$\bar{p}$$ scatterinq from Be, C, Al, Cu, Sn, and Pb targets at .incident beam momenta of 70 and 175 GeV/c and for $$\mu^+$$, $K^+$, and $p$ scattering from Be, Al, and Pb targets at an incident beam momentum of 125 GeV/c. In all cases the minimum -t is 0.001 $(GeV/c)^2$ ; the maximum -t is 0.07, 0.16. 0.30 ($GeV/c)^2$ for incident beam momenta of 70, 125, 175 GeV/c respectively. Parameterizations of the differential cross section, $$d\sigma/dt$$, in the forward direction are presented....« less
  • Microscopic first-order optical potential calculations of intermediate energy proton-nucleus elastic scattering are made using the Kerman, McManus, and Thaler multiple-scattering theory. Comparisons are made between various on-shell (local) prescriptions for the factorization of the folding integral, with both local and nonlocal off-shell prescriptions. All calculations are purely microscopic, parameter free, and performed entirely with the momentum-space representation. In particular, the Lippmann-Schwinger integral equation is solved using relativistic kinematics. A computer code, WIZARD 1, is developed to handle all aspects of the calculations. The first-order optical potential calculations employ the realistic free nuclon-nucleon t-matrix models of Love-Franey and Picklesimer-Walker, along withmore » reasonable representations for the nuclear densities based on either three-parameter Fermi shapes or shell-model constructions. This work represents the first systematic study of the influence of non-local and off-shell effects in the first-order theory of the optical potential for protons over a range of energies and targets. Results indicate that the usual on-shell (local) factorization of the t-matrix is not an adequate treatment of the folding integral at momentum transfers beyond that which corresponds to the maximum physical nucleon-nucleon value. This result implies the need for a model of the reaction mechanism which prescribes how the off-shell momenta and energy of the t-matrix are to be folded with the nuclear density matrix. It is concluded that the full folding calculation of the Fermi averaging integral is necessary, particularly at lower energies, to fully calibrate the use of first-order theory for the optical potential.« less
  • The optical potential model is a convenient means of characterizing the interaction of the pion with the nucleus. Its simplicity makes it practical for the calculation of elastic scattering and pion distorted waves for more complicated processes. Its success in reproducing the early pion data and the existence of new, higher quality data motivate the present investigation. An optical potential for pion-nucleus interactions in the energy range 0 to 250 MeV pion kinetic energies is constructed with the Watson multiple scattering series and the ..pi..N transition amplitude as starting point. The pion-nucleon to pion-nucleus center of mass transformation is calculatedmore » to first order in the ratio of total pion energy to nucleon mass. Multiple scatttering corrections in low energy approximation are included to second order in the s-wave and to all orders in the p-wave (the Lorentz-Lorenz or Ericson-Ericson effect). True pion absorption terms, proportional to the square of the nuclear density, are included in both s and p-wave parts of the potential. Pauli blocking is approximated, and an energy shift due to the Coulomb interaction is incorporated. The potential parameters are taken from the experimental ..pi..N phase shifts and theoretical calculations. The potential, of Kisslinger type, is incorporated in coordinate space computer codes which calculate pionic atom level shifts and widths, elastic scattering differential cross sections, and total and partial cross sections. These calculations are compared to the current experimental data. It is found that at low energies (0 to 50 MeV) the potential produces elastic cross sections which fit the data provided the s-wave repulsion is increased. The pionic atom level data require more absorptive strength than that given by current calculations, as well as increased repulsion consistent with the scattering results. The general features of the resonance region elastic scattering and total cross sections are well reproduced.« less