NUCLEAR STRUCTURE AND SIMPLE NUCLEAR REACTIONS

Journal Article · Fri Jul 01 00:00:00 EDT 1960 · Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D

DOI:https://doi.org/10.1103/PhysRev.119.324· OSTI ID:4182277

Benioff, P A

Recently it has become increasingly evident that some assumptions in the nuclear model used for the Monte Carlo calculations yield cross section values which are not in accord with experiment. In particular, calculations of (p,pn)- reaction cross sections in the Rev energy range give values which are low by factors of two to nine when compared to experimental values. The calculated cross sections show a smooth variation with the tanget atomic weight whereas the experimental values show quite an erratic variation. Reasons which were advanced to account for this lack of agreement are the lack of a nuclear surface and failure to account for shell effects in the nuclear model used. A theory is developed to take account of surface and shell effects and thereby describe the observed magnitude and variation of the cross sections for simple nuclear reactions as exemplified by the (p,pn) reaction. At multi-Bev energies to which this treatment is restrictad, the main contribution to the (p,pn)-reaction cross section comes from inelastic collisions between the incident protons and target neutrons, with all the p-n collision products escaping without further interaction. Approximations and assumptions used include the impulse approximation, 0 tained lab scattering angle for the inelastic p-n collision products, classical trajectories for the incident and scattered particles, and a quantum-mechanical treatment for the tanget nucleons. The multi- Rev, n-p, cloud-chamber data was used to determine the average total exit cross section for the inelastically scattered particles. The only neutron shells in the target nucleus contributing to the (p,pn) reaction are those for which the instantaneous knocking out of a neutron creates a productneutron hole state stable to particle emission. The combination of these assumptions gives integral expressions which, when evaluated on the IBM-701 computer for the independent particle harmonic-osciilator sheil model, give the (p,pn) reaction cross sections as a function of the nuclear density distribution and the number of available shells. For the low Z nuclei where the available shells can be unambiguously determined, the results give a halfcentral-density radius parameter, r/sub 0/, (r/sub 0./ = R/sub 1/2//A/sup 1/2/), of about 1.2 fermis compared to 1.03 fermis for the charge half radius from the electron-scattering work. Use of reasonable limits on the value of r/sup 0/ allows one to set the minimum number of shells available for some targets. For example, the Zn/sup 64/ , Cu/sup 65/, and Cu/sup 65/ (p,pn) cross sections require that a large part or all the 1f/sub 7/2/ neutro be available, or, equivalently, that a lf/sub 7/2/ neutro state (across a major shell) in the prcduct nucleus have less than 8- to 9- Mev excitation energy. The results show that the energy associated with nuclear rearrangement to particie-stable product states must be less than 8 to 9 Mev. In several cases, the upper limit can be lowered considerably (to 1.5 Mev and 0 Mev in the cases of O/sup 16/ and N/sup 14/, respectively). (auth)

• Research Organization: Univ. of California, Berkeley, CA (United States)
• NSA Number: NSA-14-020997
• OSTI ID: 4182277
• Journal Information: Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D, Vol. Vol: 119; Other Information: Orig. Receipt Date: 31-DEC-60
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

PHYSICS
ATOMS
CLOUD CHAMBERS
COMPUTERS
COPPER 63
COPPER 65
CROSS SECTIONS
DENSITY
DISTRIBUTION
ELECTRIC CHARGES
ENERGY
ENERGY LEVELS
ENERGY RANGE
IMPULSE APPROXIMATION
INELASTIC SCATTERING
INTERACTIONS
MASS
MONTE CARLO METHOD
NEUTRONS
NITROGEN 14
NUCLEAR MODELS
NUCLEAR REACTIONS
NUMERICALS
OXYGEN 16
PROTON BEAMS
PROTONS
QUANTUM MECHANICS
SCATTERING
SURFACES
ZINC 64