The Absorption of Pions by Deuterons

Abstract

T HE study of the absorption of positive pions by deuterons, which, together with its inverse, has been used to determine the spin of the meson, 1 -2 has been extended. We present here results on the energy dependence of the angular distribution and of the total cross section, in the hope that they will prove useful in the attempt to understand the pion-nucleon interaction.The reaction is -K + -\-d-*p-\-p. The reaction rate is determined by the rate of recoil proton pairs in coincidence with incoming mesons, incident successively on water and heavy water targets. The experimental technique has already been described. 1 The water cells are 1" thick along the beam direction. The energy dispersion due to target thickness and meson beam inhomogeneity is approximately ±7 Mev. The angular dispersion is approximately ±14°. Despite this poor resolution the coincidence rate of recoil protons is only ^1/minute in the Nevis meson beam of ~500/sec. The uncertainties in the result are almost entirely statistical; the geometrical factors have been calculated with greater accuracy, and the combined uncertainties in counting efficiency and beam composition are less than 10 percent.The results are given in Table I. All parameters as well as differential cross sections are in the center of mass system. The recoil angles listed are averaged over the angular dispersion. This affects only the angles near 90°, since, because of the symmetry, 90° is the extreme angle, and larger angles are recorded as smaller angles. When the proton counter axes are set at 90° relative to the meson beam, the average detection angle is 83°.It is possible to represent the angular dependence as a+/3 cos 2 0, since meson angular momenta with respect to the deuteron of more than two Planck units should not contribute appreciably at these energies. The best fits to such a distribution are given in Table II, together with absolute cross sections.In Table II we have also included the results of Cartwright, Richman, Wilcox, and Whitehead. 3 The angular distribution found at Berkeley and our results are only in fair agreement.There is no large change in the angular distribution in the energy range 25-53 Mev for the incident meson in the center of mass system. The total cross section increases by a factor 2.25±0.32.To see the implication of this result on the meson nucleon interaction, it is necessary to separate the effects of the nuclear binding in initial and final states as well as the kinematical factors. The effects of the binding on the angular distribution are complicated, and are discussed in the following note. 4 The kinematical factors are TABLE I. Differential cross sections for the absorption of pions by deuterons in the center of mass system. Rms statistical errors are given. £«=25 Mev Em =40 Mev Em =53 Mev 6cm dtr/dQ cmVsterad 6cm d<r/dQ Ocm da/dQ Ecm Angular distribution Total cross section 21.5 Mev* 10.7 (cos20+0.07) X10-23sterad/cm2 2.8±0.8 X10-27 cm2 25 Mev 9 (cos20+O.22) X10~28 sterad/cm2 3.1 ±0.3 X10-27 cm 2 40 Mev 18 (cos20+O.2) X10"28 stera...

Pion Production in Pion-Nucleon Collisions

“…9 Figure 7 shows the angular correlation between the two pions for the inelastic scattering cases at 0.93 Bev. 4 The theoretical curve obtained from the isobar model is in reasonable agreement with the data. The calculated curve is given by…”

“…(1). The momentum spectra of Walker et al 4 and of Eisberg et al h give the momentum distributions of the pions integrated over all angles. In this case, independently of the angular distribution of the isobar with respect to the incident direction, G T is given by the following expression, provided one assumes that the isobar decays isotropically in its own rest system 7 :…”

“…1 and 2, we show the momentum spectra for the reaction 7r~+^-->7r~+7r" f +w at incident pion energies 7V=0.93 and 1.37 Bev. 4,5 In these figures, the w + and iT mesons have been lumped together, so that the corresponding prediction of the isobar model is da/dp ir =J Ttl +J T (9) The dot-dashed curves in Figs. 1 and 2 show the separate momentum spectra J T> i and J Tt 2.…”

“…2(a) of I were obtained using an incident pion energy T*-1.0 Bev. Actually the two parts of the experiment of Walker et al 4 (see their Table I) were carried out at energies of 0.90 and 0.96 Bev, so that it is more realistic to perform the calculations for an average T T =0.93 Bev. The results shown in the present paper were calculated for this energy.…”

“…2 ment with the experimental data at these energies. 4,5 This method of comparison is independent of the ratio of the r=i and 7 , = f inelastic cross sections, and also the relative phase between the matrix elements, upon which the separate spectra of the 7r + and -K~ mesons would depend.…”