Multiple Meson Production Research Articles

Angular Distributions of Secondary Particles Produced in High-Energy Nuclear Collisions and the Two-Center Model of Multiple Meson Production

The angular distributions of shower particles from 54 nuclear interactions of protons and neutrons with energies g ${10}^{12}$ ev in a stack of nuclear emulsions are analyzed. The method consists essentially in normalizing the angular distributions of all events in the $x=logtan\ensuremath{\theta}$ scale to the same dispersion $\ensuremath{\sigma}$. One finds a very significant deviation from the normal distribution predicted by hydrodynamical models. The deviation goes in the direction indicated by the two-center model (two maxima in the plot over the $x$ coordinate). The correlation between the separation of the two emitting centers and $\ensuremath{\sigma}$ is also in qualitative agreement with the model. The angular distribution in the rest system of the emitting centers is found to be roughly isotropic. The two-center model also offers an explanation for certain characteristic features observed for the angular distribution of events with a small number of shower particles (${n}_{s}\ensuremath{\leqq}5$). On the basis of this model a coefficient of inelasticity of \ensuremath{\approx}0.2 is obtained for these events.Interactions characterized by small evaporation (${N}_{h}\ensuremath{\leqq}5$) and small numbers of shower particles (${n}_{s}\ensuremath{\leqq}20$) show the characteristic two-maximum shape. The same shape is found for presumably central collisions with heavy nuclei in the emulsion (${N}_{h}g8, {n}_{s}g40$). However, the group of collisions with ${N}_{h}\ensuremath{\leqq}5$, ${n}_{s}g20$ does not show the two maxima. The last two observations cannot be explained by the present simple form of the two-center model.The results of this paper are in good agreement with a similar analysis carried out by Gierula, Mi\ifmmode \mbox{\k{e}}\else \k{e}\fi{}sowicz, and Zielinski.

A Semi-phenomenological Approach to Multiple Meson Production

A Semi-phenomenological Approach to Multiple Meson Production

On the Structure of Extensive Air Showers. II

Assuming a simple model of extremely high energy collisions we investigate the relation between the one-dimensional development of extensive air showers (EAS) and the mechanism of multiple mes.on production. The gross structure of EAS based on the model is given graphically or numerical!y, in a form useful, as a first step, for further investigations. In particular, varying the value of in­ elasticity of high energy collisions we discuss its effect on various quantities. As a preliminary con­ clusion it is shown that it seems difficult to explain the experimental result of the constancy of the attenuation length of the electron component over a ·wide range of primary energies, 10l4~10l7eV, without introducing any energy dependence of the inelasticity or a stronger energy dependence of multiplicity with increasing energy, though. it is desirable that further experiments furnish us with more abundant and reliable data. Attention will also be paid to the problem of what quantities must be measured to determine more directly and less ambiguously the angular and energy distribu­ tions of secondary particles produced by high energy collisions. § I. Introduction The purpose of this paper is to analyse the structure of extensive air showers (EAS). with a vtew of investigating the mechanism of multiple meson production in extremely high· energy collisions. The skeleton of EAS is the nucleonic cascade process in the atomosphere developed due to high energy collisions, through which particles of other components, namely electrons, photons; muons, etc., are produced secondarily. There are not very many analyses of EAS which treat this process directly, because the mathematical treatments are very difficult and the process of high energy collisions involves many un. known factors. The works which have been published may be roughly classified into two types : (a) Existing theories of multiple meson production are applied to. analyse EAS and they are examined accordin5 to whether or not they can explain experimental results well. (b) A phenomenological model is assumed and parameters introduced in it are fitted by comparison with experimental data. The works of Amaldi et aVl and Oda2l belong to the former and those of the Soviet group,3 ·4 ·5J Messel et al.6 •7l and Budini

Multiple production of mesons in pion-nucleon collisions

The model of Czyz, Ericson and Glashow for multiple meson production in energetic nucleon-nucleon collisions is applied to the analogous pion-nucleon process. The angular distributions of the shower particles of such events are predicted to display a single-cone structure, and to be forward peaked in the centre-of-mass system at primary energies greater than 400 GeV. The model should be applicable for pion energies beyond 50 GeV.

Multiple Meson Production by Photons in Hydrogen

The analysis of 235 events of double meson production by photons with energy up to 1.1 Bev (reaction $\ensuremath{\gamma}+p\ensuremath{\rightarrow}p+{\ensuremath{\pi}}^{+}+{\ensuremath{\pi}}^{\ensuremath{-}}$) observed in a ${\mathrm{H}}_{2}$ diffusion cloud chamber has produced the following results. The cross section rises rapidly at about 500 Mev to a value of approximately 70 \ensuremath{\mu}b. The angular, momentum, and $Q$ distributions of the reaction products cannot be satisfactorily accounted for either by a pure statistical model, or by a pure isobaric state model, or by a model assuming interaction of the incoming photon with the meson cloud of the proton, leading to $\ensuremath{\pi}\ensuremath{-}\ensuremath{\pi}$ interaction. The observation of 14 cases of the reactions $\ensuremath{\gamma}+p\ensuremath{\rightarrow}p+{\ensuremath{\pi}}^{+}+{\ensuremath{\pi}}^{\ensuremath{-}}+{\ensuremath{\pi}}^{0}$ and $\ensuremath{\gamma}+p\ensuremath{\rightarrow}n+{\ensuremath{\pi}}^{+}+{\ensuremath{\pi}}^{+}+{\ensuremath{\pi}}^{\ensuremath{-}}$ suggests that the combined cross section for these reactions is about 10 \ensuremath{\mu}b between 700 and 1000 Mev.

On the two fluid model in multiple production of mesons

The mechanism of multiple particle production in high energy nucleon-nucleon collisions is investigated using the two fluid model. The theoretical inelasticity is numerically calculated.

A Field Theoretical Investigation of Multiple Meson Production. I

Multiple meson production in pion-nucleon collisions is investigated by field theory. By introducing the interaction time and assuming that the free hamiltonian can be approximately put as a C-number during the calculation of the effect due to the interaction hamiltonian for the interaction time-interval, it is shown that multiple meson prcduction is caused by the pseudoscalar type interaction. Numerical results are obtained for the relative cross sections of n pion prcduction, the angular distribution, the momentum distribution of final nucleons, etc. These results are compared with the experimental dath in Bev and cosmic ray energy regions. The covariant phase space integration is carried out with the saddle point method and its final expression is comparatively simple. The probability distribution of charge states in the statistical theory is derived by an approximate formula instead of the tedious combination of Clebsh- Gordan coefficients. (auth)

Double maximum angular distributions in high energy nuclear collisions

A detailed statistical analysis of the shape of the angular distribution of secondary particles generated in 65 nuclear collisions for primary energies higher than 1012 eV has been presented. The double maximum shape of the distribution (in coordinate log tgθ) is a general feature of the events with high degree of anisotropy of secondaries in CM system. It has been found that the shape of the angular distribution is in agreement with the predictions of the two-centre model of multiple meson production both for nucleon-nucleon and nucleon-heavy nucleus collision. A new parameterD, which is a measure of the deviation from the normal shape of the distribution towards the two centre distribution and also a coordinate convenient for visualizing this deviation, have been introduced.

A new model for multiple meson production at high energies

A new approach to the multiple meson production processs is proposed, which is based upon the peripheral nature and energy-independent behaviour of high-energy nucleon-nucleon collisions. A specific model suggested by the analogy with Čerenkov radiation is described.

A method of analysis of events involving multiple meson production

A method is proposed for evaluating the primary energy in events which lead to multiple meson production. It is shown that, in principle, K-mesons could be distinguished from π-mesons if sufficient statistics were available. Several published events have been analyzed by this method and the results are compared with several theories.

Multiple meson production by 9GeV protons on emulsion nuclei

300 meson showers withns⩾4 produced by 9 GeV protons in an emulsion stack have been analysed as to their multiplicity and angular distributions. It is shown that light and heavy target nuclei can be safely distinguished by the criterionNh⩽4,Nh⩾7. The kinematical features of the collisions are consistent with emission of the shower particles from a single mass-center. The c.m.s. angular distribution of the shower particles is proved to be isotropic for all types of collisions. Individual c.m.s. Lorentz factors —γc have been estimated for every event. The distribution ofγc-values agrees well with the predictions of the tunnel model of nucleon-nucleus collisions. The average tunnel lenghts for heavy and light nuclei have been found proportional to the nuclear radii. An excess of very high —γc and very low —γc events has been tentatively interpreted as due to peripheric collisions with pions in the meson cloud surrounding the colliding nucleons. The fractional energy transfer to pions is found independent of the target nucleus and equal to ∼33%. One outgoing particle (at least in some cases a pion) is often observed to carry away a large fraction of the available energy.

Energy Determination from Multiple Meson Production by 6.3-Bev Protons in Nuclear Emulsion

864 stars produced by the 6.3-Bev proton beam of the Berkeley Bevatron were observed in nuclear emulsion. The average number of shower particles was 2.7 prongs per star. The energy of the primary particle was determined by three different methods: (a) the median angle method; (b) Castagnoli's method; (c) Cocconi's graphical method. It is found that the results of these three methods are in good agreement with each other and are high in each case by a factor of 2.

Preliminary remarks on a consequence of the two-centers model of multiple meson production

ABS>It is shown possible to determine the values THETA -bar and gamma - bar from equations in the two-center model of multiple meson production by using for the evaluation of gamma /sub 0/, gamma /sub 1/, and gamma /sub 2/ th e relations given in the theory. (C.J.G.)

Multiple Meson Production by Photons in Hydrogen

Pictures of a ${\mathrm{H}}_{2}$ diffusion cloud chamber with magnetic field taken at the 1.1-Bev Cornell synchrotron have been analyzed to study multiple meson production by photons on protons. They have yielded 108 cases of double charged meson production ($\ensuremath{\gamma}+p\ensuremath{\rightarrow}p+{\ensuremath{\pi}}^{+}+{\ensuremath{\pi}}^{\ensuremath{-}}$) and 4 cases of triple meson production.For each event of double meson production, the energy of the incoming photon and the angles and momenta of the emitted particles could be determined. The most significant results are the following.The cross section for double charged meson production rises rapidly around 500 Mev to approximately 70 microbarns, a value of the same order as the total cross section for single meson production.In the reaction leading to a charged meson pair, ${\ensuremath{\pi}}^{+}$ and ${\ensuremath{\pi}}^{\ensuremath{-}}$ play dissimilar roles, as evidenced by the marked dissimilarities in their center-of-mass angular and momentum distributions. The $Q$-distributions suggest the interpretation that the predominant mode of pair production in the energy range from 500 to 700 Mev is ${N}^{*}+{\ensuremath{\pi}}^{\ensuremath{-}}$, ${N}^{*}\ensuremath{\rightarrow}p+{\ensuremath{\pi}}^{+}$, where ${N}^{*}$ likely is the resonant $\frac{3}{2}$, $\frac{3}{2}$ excited state of the proton. The fact that the angular distributions for the protons and the ${\ensuremath{\pi}}^{\ensuremath{-}}$ mesons are asymmetric about 90\ifmmode^\circ\else\textdegree\fi{} indicates that the reaction does not derive from a single state, but from a mixture of at least two interfering states of different parity.

Field Theoretical Interpretation of Multiple Meson Production

The formula for the cross section of multiple production of mesons is derived under the following assumptions: the interaction between a nucleon and a meson( ith Cr deposite ) is present only for a finite time interval 0 to t with the free Hamiltonian H/sub o/ regarded as a C-number; the concept of renormalization is assumed to get only the relative cross section of n meson( ith Cr deposite ) production. (C.J.G.)

Photoproduction of ChargedπMesons from Nuclei

The -ray beam from the Cornell synchrotron was used to investigate the photoproduction of low-energy charged The effects of mesons from several nuclei at 35 to the beam direction. Maximum photon energies used were 800 Mev and 1 Bev. The yields of 40 and 80 Mev The effects of /sup +/ and 40 Mev The effects of mesons were observed with a detection system whose aperture was known absolutely. It was found that in some cases the meson yields were proportional to the atomic number, A, of the target rather than the more usual A/ sup 2/3. The data are compared with the predictions of an optical model of the nucleus. The deviations observed can be partially explained in terms of the inelastic scattering of high-energy mesons and of multiple meson production. An excitation function was measured for 80 Mev The effects of /sup +/ mesons from carbon by varying the machine energy; this indicated the presence of an appreciable number of multiply produced mesons. (auth)

Preliminary remarks on a consequence of the isobar model of multiple meson production

Preliminary remarks on a consequence of the isobar model of multiple meson production

A model for multiple meson production in nucleon-nucleon collisions

The double lump structure of the produced mesons and the persistency of the original nucleons in high energy nuclear interaction are found. An empirical model of multiple meson production in a nucleonnucleon collision is constructed on these experimental bases. Assuming the symmetry about the two colliding nucleons in C.M.S. the collision is divided into two parts belonging to each nucleon. And, a physical quantity named «momentum of interaction» is introduced, which is the momentum difference between the initial and final state in each part. This quantity is considered to be a parameter representing the magnitude of the effect of the interaction in the collision. The average value of this quantity in high energy jets are found to be of the order of unity in nucleon mass units independently from the incident energy. Taking as a working hypothesis an empirical relation between the «momentum of interaction» and the recoil momentum of the target nucleon in L.S. which is suggested in the analysis of one high energy jet, the details of the collision are determined in our model by the magnitude of the incident energy and that of the «momentum of interaction». This model can explain the variety of the experimental data of high energy jets which have been accumulated up to now. The physical significance of the basic assumptions of this model should be searched for in future.

Possible consequences of the isobar and fire ball models

Two possible consequences, characteristic of the isobar model and the fire ball model of the multiple meson production, are discussed. One is the azimuthal asymmetry of secondary particles, and the other is the apparent anomaly of the inelasticity in meson-nucleon collision.

On the angular distribution of shower particles generated in high-energy nuclear interactions

The differential and integral angular distributions of shower particles produced in high-energy nuclear interactions are calculated according to the multiple meson production theories of Fermi, Landau and Heisenberg8–11) for nucleon-nucleon interaction. Angular distributions calculated according to the theory of Landau are given for nucleon-nucleus interaction too. It is shown by summarizing the experimental data of jets of energies higher than 1013 eV that the angular distribution alone does not show unambiguously which of the multiple meson production theories, if any, is the correct one.