Single-pion production in ${\ensuremath{\pi}}^{\ensuremath{-}}\ensuremath{-}p$ interactions has been studied at 905, 960, and 1100 MeV. Comparison with the isobar and one-pion-exchange (OPE) mechanisms of pion production shows that, below 1 BeV, pion production occurs primarily through the formation of an intermediate excited state of the nucleon (isobar), while at higher energies the influence of the $\ensuremath{\rho}$ resonance in the $\ensuremath{\pi}\ensuremath{\pi}$ system becomes increasingly important. There is some evidence for an $I=2$ state in the events at the lower energies.

Internal symmetries such as isotopic spin are not necessarily arbitrary constraints to be imposed at the beginning of a calculation. The bootstrap requirement that all particles be determined as composite states of one another leads naturally to symmetric solutions for masses and coupling constants. (auth)

and I. M. Shmushkevich for useful discussions.We use this term, scattering amplitude, for the sake of brevity.The whole following consideration is true for any invariant amplitude for the transition of two particles into two particles.

Analyses have been made for 871 four-prong events and 463 two-prong events corresponding to multiple pion production, resulting from $p\ensuremath{-}p$ interactions at 2 Bev in the BNL 20-in. hydrogen bubble chamber. Cross sections have been obtained for all the observable double and triple pion production processes; the branching ratios predicted by the extended isobar model are shown to be in fair agreement with the data, but there are significant differences. The c.m. momentum distributions are also in fair agreement with the predictions of the model, although there are ambiguities in the interpretation. The pion-nucleon $Q$ values give clear evidence for the importance of the ($\frac{3}{2}, \frac{3}{2}$) resonant state in multiple pion production, but consideration of this state alone does not provide an explanation of the features of double pion production. Some contribution from another state, possibly the $I=\frac{1}{2}$ nucleon isobar, is necessary. In double production, the c.m. angular distributions of the nucleons show backward-forward peaking suggestive of a one-pion exchange process. The angular distributions of the nucleons from triple production are almost isotropic.

3600 two-pronged events, obtained in $p\ensuremath{-}p$ interactions at 2 Bev in the BNL 20-in. hydrogen bubble chamber, have been analyzed. Cross sections have been measured for elastic scattering, for the two modes of single-pion production, $p+p\ensuremath{\rightarrow}p+n+{\ensuremath{\pi}}^{+}$, $p+p\ensuremath{\rightarrow}p+p+{\ensuremath{\pi}}^{0}$, and for strange-particle production. The branching ratio for the two one-pion production reactions is $\frac{\ensuremath{\sigma}(pn{\ensuremath{\pi}}^{+})}{\ensuremath{\sigma}(pp{\ensuremath{\pi}}^{0})}=4.17\ifmmode\pm\else\textpm\fi{}0.25$. Momentum distributions and $Q$ values indicate that single-pion production proceeds almost entirely through the ($\frac{3}{2}, \frac{3}{2}$) resonant state. The data have been considered in terms of the extended isobar model and also a one-pion exchange model for production. The branching ratio and momentum distributions can be explained by including a small effect from the $I=\frac{1}{2}$ resonant state in addition to the dominant $I=\frac{3}{2}$ resonance. The c.m. angular distribution of the nucleons in single-pion production shows very marked backward-forward peaking indicating a one-pion exchange mechanism. Absolute differential cross sections as a function of laboratory kinetic energy have been calculated from Selleri's equation for the $\mathrm{pn}{\ensuremath{\pi}}^{+}$ reaction. There is good agreement with the data for low four-momentum transfers [${q}^{2}<0.15$${(\mathrm{B}\mathrm{e}\mathrm{v}/\mathit{c})}^{2}$], but for higher momentum transfers the theoretical cross sections are larger than the experimental cross sections.

The branching ratio, r = n/sub 1//n/sub 2/, for the reactions pi /sup -/ + p yields pi /sup -/ + pi /sup +/ + n and pi /sup -/ + p yields pi /sup -/ + pi /sup 0/ + p was measure d in a hydrogen bubble chamber for an incident pion energy of 905 plus or minus 2 Mev. It was found to be 1.70 plus or minus 0.17. Values of r from hydrogen bubble chamber data at energies near 900 Mev, determined by various authors, are tabulated and found to give an approximately constant r in the 800- to 1100-Mev ensrgy range. The low results of investigations by Walker et al., obtained in emulsions are discussed. (D.L.C.)

Using the bubble chamber technique, 4000 pi /sup -/-p events at 1.25 Bev incident pion energy were measured. 968 events of the type pi /sup -/ + p yields pi /sup -/ + pi /sup +/ + n, and 566 of the type GUTS kinematic fitting program and ionization density measurements. Strong evidence was obtained for a pi - pi resonance in an I = 1 state. (L.N.N.)

Proton interactions at 2 Bev were observed at the cosmotron in the 20- in. hydrogen bubble chamber. From the measurement of about 4000 two-prong events, 1300 events of the type p + p yields p + n + pi /sup +/ were identified, using digitalized equipment and the GUTS kinematic fitting program, together with ionization density measurements. In comparing the results with the theory of Selleri (NSA:l59719), general agreement prevails but with significant deviations. (L.N.N.)

Branching rstios for incident pion kinetic energies from 810 to 1100 Mev are tabulsted. Pion-pion interactions and pion production branching ratios at the third resonance are discussed. (L.T.W.)

ABS>Photographs of interactions in a hydrogen bubble chamber irradiated by 0.96-Bev pi /sup -/ were analyzed. Measurements revealed 415 events of the reaction pi /sup -/ + p yields n + pi /sup +/ + pi /sup -/ and 267 events of the reaction pi /sup -/+ p yields p + pi /sup o/ + pi /sup -/. It is shown that the angular distributions are quite different and the observed ratio of proton to neutron events with fast pi /sup -/ is 0.9 plus or minus 0.2. Q values for the different nucleon-pion combinations were computed from the observed momenta. The distributions of Q values are plotted for pion-pion combinations in each reaction, with backward-nucleon events and forward-nucleon events plotted separately. No evidence is seen of pcaking for ( pi /sup -/ pi / sup +/), either for forward or backward neutrons or for ( pi /sup -/ pi /sup o/) forward protons. The Q distribution of ( pi /sup -/ pi /sup o/) for backward protons shows a distinct peak at about 325-Mev, which is suggestive of a 600Mev resonant di-pion'' state (T = 1 or 2). This event is being analyzed. (B.O.G.)

The masses of particles with an ionization less than about twice the minimum value emitted in cosmic-ray stars in a photographic emulsion have been determined by observations on the grain density and scattering of suitably long tracks. About 100 tracks with an average length of 16.5 mm were analyzed using a single emulsion exposed to cosmic rays in a high-altitude balloon flight of nine hours duration. The results show groups of pions, protons, deuterons, heavy mesons with mass $\ensuremath{\sim}925{m}_{e}$ and the possibility of a group with mass closer to that of the proton. This latter is uncertain, however, with the present resolution and could be a statistical fluctuation on the edge of the proton distribution.