PION PRODUCTION IN PION-NUCLEON COLLISIONS

Thesis/Dissertation · Sun Jan 01 04:00:00 EST 1961

OSTI ID:4776777

Carruthers, P A

The reaction pi + N -- 2 pi + N is studied in the vicinity of the higher resonances in the pion-nucleon cross section. The Low equation for the production amplitude is transformed into an integral equation by isolating the true onemeson intermediate states and discarding higher order contributions. The only part kept in the inhomogeneous term corresponds to the collision of a pion in the nucleon cloud with the incident pion in the resonant T = J = 1 state, which is simulated by an unstable vector boson. Crossed terms are neglected and the 2 pi -N state is described by the static model. The terms kept in the surn over states describe the rescattering (off the nucleon) of one of the outgoing pions. The required off-the-energy-shell elastic scattering amplitude is approxirnated by the 3-3 resonance formula. With these simplifications the Low equation for the production amplitude reduces to an easily soluble linear integral equation. The rescattering amplitude, which dominates the inhomogeneous term in the resonance region, is proportional to the 3-3 scattering amplitude of one of the outgoing pions. Although the result provides some support for the isobar model, it is important to note that the largeness of the rescattering term arises from scattering far off the energy shell, rather than by real'' excitation as in the phenomenological isobar model. Quantitative calculations for the D3/2 channel leading to a p-wave (J = 3/2) and an s-wave pion produce a maximum in the cross section near 600 Mev incident pion lab energy. For a pi - pi resonance energy squared (s) = 10, agreement with experiment is obtained with a width about one third that suggested by nucleon electromagnetic structure. In the examined approximation, the 600-Mev D/sub 3/2/ isospin-1/2 resonance occurs at the same energy as the 800-Mev D/sub 3/2/ isospin-3/2 resonance. It is assumed, but not proved, that the neglected terms are responsible for the splitting of the resonance energies. When this splitting is taken into account, the predicted charge state ratios near the second resonance agree with data. The third'' resonance occurs for the state having two p-wave pions, according to the derived theory, although no numerical calculations are made for this case. This point of view suggests that the F/sub 5/2, P/sub 3/2,/ and P/sub 1/2/ incident channels contribute to the third resonance. (Dissertation Abstr., 22: No. 7, 1962.)

• Research Organization: Originating Research Org. not identified
• NSA Number: NSA-17-000781
• OSTI ID: 4776777
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

LOW EQUATION
PHYSICS