Pion Reactions Research Articles

Alpha emission in fast pion reactions

Alpha emission in fast pion reactions

Interactions of4.09−GeVcpositive pions with protons:π+p→ four charged particles plus neutrals

The reactions of positive pions with protons yielding four charged particles and one or more neutrals have been studied, especially the reaction ${\ensuremath{\pi}}^{+}p\ensuremath{\rightarrow}{\ensuremath{\Delta}}^{++}{\ensuremath{\omega}}^{0}\ensuremath{\rightarrow}p{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{0}$. The results presented in this paper were obtained from a 100 000-picture exposure of the Argonne-MURA 30-in. liquid hydrogen bubble chamber, with a beam of incident pions of $4.09\frac{\ensuremath{-}\mathrm{G}\mathrm{e}\mathrm{V}}{c}$ momentum. Comparisons have been made with corresponding results of other experiments at various incident beam momenta, and with the predictions of some theoretical models of the ${\ensuremath{\pi}}^{+}p$ interaction.

Pion reaction cross sections and nuclear sizes

Measurements have been made of the reaction cross sections of π − and π + mesons for the nuclei C, Ca, Ni, Sn and Pb at beam momenta of 0.71, 0.84, 1.00, 1.36, 1.58 and 2.00 GeV /c. Additionally measurements have been made for Al, 120Sn, Ho and 208Pb at momenta of 0.84, 1.00, 1.36 and 1.58 GeV /c. The ratio of π − to π + reaction cross sections has been analysed in terms of neutron density distributions using the Watson multiple-scattering theory. The effects of second-order contributions and of the various choices of wave equation have been considered. It is found that the distributions of neutrons and protons in heavy nuclei must have very similar radial parameters. Good agreement is obtained between the measured and calculated values for the reaction cross sections, without any adjustment of parameters.

Positive pion reactions with 12C : W. B. Jones and J. M. Eisenberg, Nuclear Physics A154 (1970) 49

Positive pion reactions with 12C : W. B. Jones and J. M. Eisenberg, Nuclear Physics A154 (1970) 49

Positive pion reactions with 12C

Positive pion scattering and absorption by spherical nuclei are considered. The opticalmodel treatment of the former process includes a non-linear dependence upon the density of scattering centers originally suggested by Kroll. Explicit results are given for the 12C nucleus and compared with those obtained with the Kisslinger model. Pion optical-model wave functions, both with and without the Kroll modification, are used in a distorted wave calculation of differential cross sections for proton emission following pion absorption, and the results are compared with each other and with experiment for the case of 12C.

Elementary particle approach to some nuclear pion reactions

Elementary particle approach to some nuclear pion reactions

Charge-exchange reactions of pions on nuclei

The cross sections for the reactions ( π ±, π 0) on nuclei are calculated in the energy around the (3, 3) resonance using the impulse approximation. It is shown that the cross sections in particular contain information about the proton-neutron correlations in nuclei; information not usually contained in the cross sections for the usual electron scattering on nuclei. Numerical estimates are given in the case of charge exchange scattering on 16O and 13C. The results were not found to be in agreement with the available data as long as the initial and final state interactions were neglected.

Elementary-particle approach to some nuclear pion reactions

An elementary-particle approach is applied to the nuclear pionic pion capture and charge-exchange pion-nucleus scattering under the soft-pion hypothesis. A relation between the muon capture, radiative pion capture and pionic pion capture is discussed.

Multi-step contributions to particle production in nuclei

Coherent and incoherent production of particles in atomic nuclei is investigated for high energies using coupled equations of optical model form for the wave functions of the particles. We include multi-step (cascade) processes for coherent production and one incoherent step preceded or followed by coherent scattering or production for incoherent production. Calculations are performed for a coupled π. A 1. A 3 system. Given the cross sections for the corresponding reactions of pions on nucleons, we find that for coherent A 1 production the one-step process is likely dominant whereas for A 3 production two-step processes can be of considerable importance. The incoherent production cross section is changed appreciably if two-step processes are included. The unknown coupling of the A 3 to the A 1 as well as the possibility of an appreciable contribution of other intermediate boson states makes the detailed calculation of A 3 production in nuclei difficult.

Pion reactions with light nuclei at the 3-3 resonance

The reactions of positive and negative pions with light nuclei have been studied over the energy range 80 to 280 MeV by detecting the residual radio-activity. Charge exchange, (π +, π 0), is shown to be closely related to the corresponding nucleon reaction, (p, n), but it is difficult to account for the ratio of the cross sections of 13C(π +, π 0) 13N and of 14N(π +, π 0) 14O in detail. Most of the reaction cross section of pions is made up by processes such as 12 C → π 11 C , i.e. single nucleon knockout. Previously this was accounted for quantitatively in terms of quasi-free scattering, which predicts a ratio of 3 : 1 for the 11C production by π − and π + (influence of the 3-3 resonance of the π-nucleon interaction). The ratio observed is 1.0±0.1 for 12 C → 11 C , 14 N → 13 N and 16 O → 15 O . The simplest explanation is that the activity is the result of roughly equal amounts of quasi-free scattering and inelastic scattering exciting the giant dipole resonance of the target nucleus. Alternatively, a more complicated interaction of pions with nucleon pairs could account for almost any ratio. Cross sections for 22 π-reactions at 180 MeV are presented together with excitation functions for 5 of these reactions.

Simple but new calculations on single and double charge-exchange of pions by light nuclei

The cross-section for single and double charge-exchange nuclear reactions with pions for 1p-shell nuclei is calculated using the Glauber method. The results are obtained for the reactions of pions of (80÷200) MeV by boron (π+ +11B → π0 +11C) and lithium (π+ +7Li → π− +7B).

Reactions of nuclei with pions at the 3 - 3 resonance

Activation cross-sections of reactions of pions with light nuclei have been measured over the energy range 80 to 280 MeV. Most of the reactions appear to be of single-particle character, but quasi-free scattering does not show the expected ratio of 3 for π − π + .

Current commutation relations and pionic reactions

The consequences imposed by the particular form of the equal-time commutators of current densities, which follows from the algebra of current operators, can be studied in two ways. It is possible to obtain first the consequences of the support conditions imposed on the equal-time commutator of two field theory operators, and then, to obtain the further relations imposed by the particular structure which appears in the algebraic relations. This is the approach followed here. In so doing, particular attention is paid to nearby singularities and the only assumption made is that, once the contribution of these terms has been obtained, the remainder is a slowly varying function. The other, and currently used, approach consists in obtaining directly relations, which already include the strong constraints imposed by the algebraic relations, notwithstanding the more general and weaker constraints imposed on the Fourier transform of an equal-time commutator of two field operators. These more general and weaker constraints alone yield, in particular, the consistency relations imposed by the PDDAC (pion dominance of the divergence of the axial current) hypothesis. Several relations for pionic reactions are presented.

Jets with strange particles produced by 25 GeV/c protons on protons

132 jets with K-meson or hyperon produced by 25 GeV/ c protons have been analysed. The fraction of the baryon total energy going into production of mesons is 0.45 ± 0.03 in the proton-proton c.m. system. There is a strong correlation between total energy in the c.m. system and the number of charged prongs for hyperons but no correlation for mesons. The pion laboratory energy distribution is proportional to E lab −1.53±0.27 (between 1 and 5 GeV) and the hyperon distribution is proportional to E lab −0.94 ±0.15 (between 2 and 15 GeV). The K-meson energy distribution cannot be described by a simple power law. High-energy pions (above 8 GeV) are almost absent, indicating that there is no abundant production of nucleon excited states in the forward direction . The average number of pions in reactions with YK is 4.3 ± 0.6 and with K K is 3.7 ± 0.4. The results are discussed in terms of different theoretical models.

On $\bar{K}$-NInteraction and a Possible Maximum of Cross Sections for Pion Reactions

On $\bar{K}$-<i>N</i>Interaction and a Possible Maximum of Cross Sections for Pion Reactions

S-Wave Interaction in π-NSystem and Dispersion Relation

Dispersion relations applied to pion reactions have explained the value of alpha /sub 1/-- alpha /sub 3/ ( alpha /sub 1/, alpha /sub 3/ = s-wave pha se shifts for isotopic spin states I = 1/2, 3/2), but the separate value of alpha / sub 1/ or alpha /sub 3/ has not yet been explained. This is done by setting G/ sub r/(O, mu , M, f/sup 2/) = G/sub r/(O,O, M, f/sup 2/), where G/sub r/(k, m, M, f/sup 2/) is the physical equivalent of G(k, mu , M, f/sup 2/) in the dispersion relation for pi -p forward scattering amplitudes, 1/2STAD/sub -/( omega ) + D/sub +/( omega )!. The results, used in combination with the value of 0.27 for alpha /sub 1/-- alpha /sub 3/, give alpha /sub 1/ = 0.16 and alpha / sub 3/ = --0.11, in good agreement with experimental data analysis for low-energy pion scattering. (D.L.C.)

Pion Reactions in One Nucleon System and Nucleon Isobars

In this paper, we try to jnterpret the pion·nucleon interaction on the basis of the nucleon isobar modeL. As a complementary wily t<l the strong coupling and phenomenological theories, we start from the field theoretical viewpoint which will be useful to connect the present phenomenological theory of pions to the future theory of fields. We treat the nucleon isobars.as elementary particles and describe them by the Rarita-Schwinger equation of particles with spin 3/2. Hence the'familiar Feynman-Dyson method is immediately applicable to the calculation of matrix elements of such processes involving nucleon isobars as' the pion-proton scattering and the pion-production by r-rays on proton. The qualitative features are governed mainly by the mass, width, spin and isotopic spin of the isobar, so that our results roughly agree with those of the strong coupling and phenomenological theories. In some detailed respects, however, our results show differences from other theories; the agreement with experiments is improved for the angular distributions of 7r /' scattering and photo-production of charged pions, but becomes a little worse for that of neutral pions. Our method' is applied only to pion reactions in one nucleon system, for we know too little about two or more nucleon systems to extract the pure pion-nucleon interaction. Lastly, we discuss the validity of the nucleon isobars.

Pion Reactions in One Nucleon System and Nucleon Isobars

In this paper, we try to interpret the pion-nucleon interaction on the basis of the nucleon isobar model. As a complementary way to the strong coupling and phenomenological theories, we start from the field theoretical viewpoint which will be useful to connect the present phenomenological theory of pions to the future theory of fields. We treat the nucleon isobars as elementary particles and describe them by the Rarita-Schwinger equation of particles with spin 3/2. Hence the familiar Feynman-Dyson method is immediately applicable to the calculation of matrix elements of such processes involving nucleon isobars as the pion-proton scattering and the pion-production by γ-rays on proton. The qualitative features are governed mainly by the mass, width, spin and isotopic spin of the isobar, so that our results roughly agree with those of the strong coupling and phenomenological theories. In some detailed respects, however, our results show differences from other theories; the agreement with experiments is improved for the angular distributions of γ-p scattering and photo-production of charged pions, but becomes a little worse for that of neutral pions. Our method is applied only to pion reactions in one nucleon system, for we know too little about two or more nucleon systems to extract the pure pion-nucleon interaction. Lastly, we discuss the validity of the nucleon isobars.

The S Matrix Method in Pion Reactions

A new method which is convenient for the phenomenological analysis to explore the mutual correlations among various pion reactions is presented based on the S matrix formalism. We first study the general properties of the S matrix as it is necessary for practical purposes. Next, utilizing the results we discuss the intimate correlations between the photo-meson production and pion-nucleon scattering. Finally, we apply this method to the qualitative investigation of another process, i.e. the elastic nucleon-nucleon scattering at extremely high energies, from which we can conclude that the scattered nucleons will be concentrated in the forward and backward directions in the centre of mass system.

The S Matrix Method in Pion Reactions

The <i>S</i> Matrix Method in Pion Reactions