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• W1977314908 abstract "Long-range interactions of negative pions with protons resulting in single and double pion production are examined in terms of a meson field theory model in which it is assumed that there is a pion-pion interaction and that the single virtual pion exchange graphs are dominant in large-impact-parameter collisions. This pion exchange leads, in single pion production, to an excited state, ${ensuremath{pi}}^{*}$, which decays into two pions, and, in double pion production, also to an excited state, ${N}^{*}$, which decays into a pion and a nucleon. For sufficiently high relative energy of the incident ${ensuremath{pi}}^{ensuremath{-}}$ and proton, each of these processes can occur for small values of the invariant square of the virtual pion four-momentum, ${ensuremath{Delta}}^{2}$, in which case the virtual pion carries very little transverse three-momentum. For small ${ensuremath{Delta}}^{2}$ it is shown that it is reasonable to neglect final state interactions between the decay products of the ${ensuremath{pi}}^{*}$ and those of the ${N}^{*}$. It is found that in the limit ${ensuremath{Delta}}^{2}ensuremath{rightarrow}ensuremath{-}{ensuremath{mu}}^{2}$, where $ensuremath{mu}$ is the pion rest mass, the virtual pion behaves kinematically, in the ${ensuremath{pi}}^{*}$ barycentric system, as an incoming pion which scatters elastically with the incident ${ensuremath{pi}}^{ensuremath{-}}$, and also behaves, in the ${N}^{*}$ barycentric system, as an incoming pion which scatters elastically with the incident proton. Thus, for small ${ensuremath{Delta}}^{2}$ in the physical region the ${ensuremath{pi}}^{*}$ and ${N}^{*}$ vertices are defined as the corresponding off-the-mass-shell scattering amplitudes. A ratio of appropriately defined double-to-single pion production cross sections is obtained which is independent of the details of the assumed pion-pion interaction, and depends only on the relative strengths of ${N}^{*}$ and $N$ formation. This ratio is estimated by means of the $p$-wave static nucleon model, applied in appropriate coordinate systems. For incident 5-Bev/c pions this model leads to double pion production which is important compared to single pion production, both because of the $frac{3}{2}ensuremath{-}frac{3}{2}$ pion-nucleon resonance and because of important phase-space factors. Kinematical considerations similar to those described above suggest that this model may also be the theoretical genesis of the two fireballs model proposed for ultrarelativistic nucleon-nucleon collisions." @default.
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• W1977314908 date "1960-10-15" @default.
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• W1977314908 title "Pion Production from<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline><mml:mrow><mml:msup><mml:mrow><mml:mi>π</mml:mi></mml:mrow><mml:mrow><mml:mo>−</mml:mo></mml:mrow></mml:msup></mml:mrow><mml:mo>−</mml:mo><mml:mi>p</mml:mi></mml:math>Collisions in the Long-Range Interaction Model" @default.
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• W1977314908 doi "https://doi.org/10.1103/physrev.120.599" @default.
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