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18Physics of Complex Systems, 2021, vol. 2, no. 3 _www.physcomsys.ru
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UDC 539.1.07+539.1.05 https://www.doi.org/10.33910/2687-153X-2021-2-3-132-138
Comparison of some properties of charged pions in p12C and n12C
collisions at 4.2 GeV/c
R. N. Bekmirzaev™, X. Bekmirzaeva1, Q. O. Khusniddin2, M. Mustafaeva1
1 Jizzax State Pedagogical Institute of Uzbekistan, 4 Sharof Rashidov Str., Jizzax 130100, Uzbekistan 2 Physical-Technical Institute of the Academy of Sciences of the Republic of Uzbekistan, 2B Chingiz Aitmatov Str., Tashkent 100084, Uzbekistan
Authors
Rakhmatulla N. Bekmirzaev, ORCID: 0000-0003-4895-5765, e-mail: bekmirzaev@mail.ru Xursanoy Bekmirzaeva, ORCID: 0000-0001-7740-8889, e-mail: bekmirzaeva@mail.ru Khusniddin Q. Olimov, e-mail: olimov@uzsci.net Marjona Mustafaeva, e-mail: marjona@mail.ru
For citation: Bekmirzaev, R. N., Bekmirzaeva, X., Khusniddin, Q. O., Mustafaeva, M. (2021) Comparison of some
properties of charged pions inp12C and n12C collisions at 4.2 GeV/c. Physics of Complex Systems, 2 (3), 132-138.
https://www.doi.org/10.33910/2687-153X-2021-2-3-132-138
Received 28 April 2021; reviewed 8 June 2021; accepted 8 June 2021.
Funding: The study did not receive any external funding.
Copyright: © The Authors (2021). Published by Herzen State Pedagogical University of Russia. Open access under CC BY-NC License 4.0.
Abstract. The new experimental data on various properties of the secondary charged pions produced in n12C collisions at 4.2 GeV/c are presented. A comparative analysis of the average multiplicities and various kinematic properties of the charged pions produced in n12C and p12C collisions at 4.2 GeV/cis is made. The experimental data are compared systematically with the predictions of the modified FRITIOF model. It is found that the modified FRITIOF model overestimates the average multiplicities of the charged pions in n12C (p12C) collisions at 4.2 GeV/c compared to the experiment. It is shown that this is due to the fact that the model overestimates the contribution of the intranuclear cascade processes in production of pions in the target fragmentation region compared to the experiment. It is also found that the model underestimates the multiplicity of the charged pions in the projectile fragmentation region. It is shown that this is due to the fact that the model underestimates the contribution of A resonances decays to the generation of the fast charged pions in the analyzed collisions.
Keywords: neutron-carbon collisions, proton-carbon collisions, intermediate energies, pion production, average multiplicities, total and transverse momentum distributions, rapidity distributions, emission angle distributions.
Introduction
This paper builds upon a series of previous papers (Olimov et al. 2007a; 2007b) and is devoted to the comparative analysis of various properties of the charged pions produced in p12C and n12C collisions at 4.2 GeV/c. The experimental data are compared with the results of Monte Carlo calculations in the framework of the modified version of the FRITIOF model (Bekmirzaev et al. 1984; Galoyan et al. 2002).
The experiment was performed using a 2-meter propane (C3H8) bubble chamber at the Laboratory of High Energies of Joint Institute for Nuclear Research (JINR, Dubna, Russia). The bubble chamber was irradiated by the beams of protons, deuteron and helium-4 nuclei accelerated to the momentum of 4.2 GeV/c per nucleon at the Dubna Synchrophasotron. The experimental data consist of 6736 p12C,
Physics of the Atomic Nucleus and Elementary Particles. Elementary Particle Physics
7071 d12C, 11974 4He12C, and 2798 n12C inelastic collision events. n12C collisions were selected from d12C and 4He12C interactions according to the procedures described in detail in (Olimov et al. 2007b).
The procedures used to determine particle momenta with a track projection length in the working volume of the chamber l < 4 cm, as well as separation of protons and mesons in the momentum region p > 750 MeV/c are described in (Olimov et al. 2007a).
Experimental results and their discussion
Table 1 shows the experimental data on the average multiplicities of charged pions (the mean number of the charged pions per one inelastic collision event) produced in p12C and n12C collisions at 4.2 GeV/c.
From Table 1 one can see that the average multiplicity of negative (positive) pions coincides with the average multiplicity of positive (negative) pions in p12C and n12C collisions, respectively. This result is obvious from the isotopic invariance of the strong interactions under consideration. However, as seen from Table 1, the model overestimates the average multiplicities in comparison with the experimental data by approximately 10%, both for negative and positive pions.
Table 1. Average multiplicities of n- and n+ mesons, as well as their absolute differences DR in the experiment and in the modified FRITIOF model in p12C and n12C collisions at 4.2 GeV/c
Quantity Type of collision
p1^ «12C
Experiment Model Experiment Model
<n(n-)> 0.36 ± 0.02 0.40 ± 0.01 0.64 ± 0.02 0.70 ± 0.01
<n(n+)> 0.63 ± 0.02 0.71 ± 0.01 0.37 ± 0.02 0.39 ± 0.01
AR 0.27 ± 0.03 0.31 ± 0.01 0.27 ± 0.03 0.31 ± 0.01
In order to determine the contribution of inelastic charge exchange reactions of the initial neutron (proton) to the formation of negative (positive) pions, let us consider the difference in the average multiplicities of the negative (positive) and positive (negative) pions in n12C (p12C) collisions (see the last line of Table 1). The numbers of protons and neutrons in the 12C- nucleus are the same, so the contribution of inelastic charge exchange reactions of the target nucleons to the formation of both the negative and positive pions of the final state should be the same due to the isotopic invariance of the strong interactions. Then the value of DR can be used as an estimate of the contribution of inelastic charge exchange reactions of the initial neutron (proton) to the formation of the final state negative (positive) pions in n12C (p12C) collisions. One can see from the data in Table 1 that, both in the experiment and in the modified FRITIOF model (Azimov et al. 1976; Galoyan et al. 2002) these contributions are equal for both types of collisions, respectively. If we consider that in the experiment the value of the inelastic charge exchange coefficient of the nucleon in nucleon-nucleus collisions (i.e. the average multiplicity of the initial nucleon lost during the collision process) is equal to 0.36 ± 0.01 (Galoyan et al. 2002), then, as can be seen from Table 1, three-fourths (%) of the inelastic charge exchange coefficient of the initial nucleon can be attributed to the formation of a single charged pion, and the remaining one-fourths (%)of this coefficient can be attributed to charge exchange reactions with nucleons of the target of the np^pn or pn^np type. Hence, it can be concluded that more than 42% of the negative (positive) pions are produced due to inelastic charge exchange of the initial neutron (proton) in n12C (p12C) collisions at 4.2 GeV/c.
We have observed that our version of the modified FRITIOF model (Bekmirzaev et al. 1984; Botvina et al. 1993) overestimates the average multiplicities of the charged pions in the interactions considered. It is interesting to understand to what extent this discrepancy is reflected in the kinematic characteristics of the charged pions.
In Table 2, we present the experimental data on the mean values of the total, longitudinal and transverse momenta, emission angles, and the longitudinal rapidity in the laboratory frame, and the partial inelasticity coefficient for n- and n+ mesons produced in p12C and n12C collisions at 4.2 GeV/c in comparison with the results of model calculations.
It follows from Table 2 that the average values of the transverse momenta of the charged pions in the experiment coincide, within statistical errors, for p12C and n12C collisions. It can also be noted that the average values of the longitudinal momentum, as well as of the longitudinal rapidity for the negative (positive) pions are greater than those for positive (negative) pions in n12C (p12C) collisions, respectively. This difference can be explained, as noted above, if we take into account both the contributions of inelastic charge exchange reaction (conversion) of incident neutron (proton) into the proton (neutron) and the negative (positive) pions, and of the A0 (A+) resonance decays into the nucleon and pion. The average values of the longitudinal rapidity of the charged pions, calculated according to the modified FRITIOF model, coincide with the results of the experiment within statistical errors.
Table 2 also presents the experimental and theoretical values of the partial inelasticity coefficients for n- and n+ mesons produced in p12C and n12C collisions, respectively. It should be noted that since the value of the incident momentum and the mass of the projectile-nucleon in the experiment are comparable, we have calculated the partial inelasticity coefficients of the charged pions as the ratio of the total energy of the secondary charged pions in a given individual collision event to the kinetic energy of the projectile nucleon. Table 2 shows that the average values of the partial inelasticity coefficients for the charged pions coincide, within statistical errors, in the experiment and the model. This indicates that distribution of the primary (incident) energy among the produced pions, or the ratios of the main mechanisms for pion production, is indeed taken into account correctly in the model.
Table 2. Average values of the total, longitudinal and transverse momenta (in MeV/c), the emission angle (in degrees), the longitudinal rapidity and the partial inelasticity coefficient (K) for n- and n+ mesons inp12C and n12C collisions at 4.2 GeV/c in the experiment and in the modified FRITIOF model
Quantity Type of collision
p^ n12C
Experiment Model Experiment Model
<P(n-)> 501 ± 8 495 ± 3 575 ± 10 526 ± 2
<P(n+)> 571 ± 7 527 ± 2 511 ± 7 492 ± 3
<Pl(n-)> 395 ± 9 381 ± 3 464 ± 11 414 ± 3
<Pl(n+)> 454 ± 7 414 ± 2 386 ± 12 376 ± 3
<Pt(n-)> 243 ± 3 233 ± 1 245 ± 3 243 ± 1
<Pt(n+)> 263 ± 3 242 ± 1 262 ± 5 234 ± 1
<Pt(n-)> 48.0 ± 0.7 45.8 ± 0.2 43.6 ± 0.7 43.9 ± 0.2
<Pt(n+)> 46.2 ± 0.5 44.0 ± 0.2 47.7 ± 0.9 46.3 ± 0.2
<Y(n-)> 0.89 ± 0.02 0.92 ± 0.01 1.00 ± 0.02 0.97 ± 0.01
<Y(n+)> 0.95 ± 0.02 0.97 ± 0.01 0.88 ± 0.02 0.91 ± 0.01
<K(n-)> 0.06 ± 0.01 0.06 ± 0.001 0.12 ± 0.01 0.12 ± 0.01
<K(n+)> 0.11 ± 0.01 0.12 ± 0.01 0.06 ± 0.01 0.06 ± 0.01
It is important to understand which region of the momentum distributions is responsible for the discrepancy observed between the multiplicities of the charged pions in the experiment and the model. For this purpose, we consider, first of all, the total momentum distributions for the negative and positive pions in n12C and p12C collisions.
Figs. 1 and 2 show the total momentum distributions of n- (a) and n+ (b) mesons in n12C (Fig. 1) and p12C (Fig. 2) collisions at 4.2 GeV/c, normalized by the total number of inelastic events (Nevents) and the width of the momentum interval (AP). The corresponding distributions calculated using the modified FRITIOF model are shown as histograms for comparison.
........................... .........................
0.5 1.0 1.5 2.0 2.5 3.0 0.5 1.0 1.5 2.0 2.5
P, GeV/c p, GeV/c
Fig. 1. The normalized total momentum distributions of the negative (a) and positive (b) pions in n12C collisions at 4.2 GeV/c. Histograms-the calculations within the framework of the modified FRITIOF model
(Bekmirzaev et al. 1984)
Fig. 2. The normalized total momentum distributions of the negative (a) and positive (b) pions in p12C collisions. Histograms—the calculations within the framework of the modified FRITIOF model
We can see from Fig. 1 that the experimental momentum distribution of n+ (b) mesons in n12C collisions is a single-modal one, it demonstrates a smooth decrease with the pion momentum, and does not have any irregularities up to the largest values of the total momentum. Regarding the experimental spectrum of n-(a) mesons in n12C collisions, although in general it is similar to the spectrum of n+ mesons, there is some deviation from the exponential dependence in the region of large momentump > 1 GeV/c, where the spectrum decreases more slowly with the increase of the total momentum. This observed "shoulder" is probably related to the production of fast n- mesons in n12C collisions due to inelastic charge exchange reactions (conversions) of the incident neutron into the n- meson and proton, and excitation of the incident neutron into intermediate A0 resonance, which decays swiftly into the same channel: n-meson and proton. It is important to note that, based on the kinematical considerations, the contribution of the leading delta resonance to the pion spectrum will be particularly noticeable in the region of the total momenta p3 1 GeV/c.
The corresponding reverse pattern is observed for the momentum distributions of n- (a) and n+ (b) mesons in p12C collisions in Fig. 2. Here, the irregularity in the momentum distribution of n+ mesons can be caused both by the inelastic charge exchange reaction (conversion) of the incident proton into n+ meson and neutron, and by the decay of the intermediate A+ resonance formed due to excitation of the incident proton.
Figs. 1 and 2 also show that the calculated momentum spectra of the charged pions for both n- (a) and n+ (b) mesons are single-modal ones and there are no deviations from the general smooth behaviour of the spectra with the increase in momentum. The theoretical data exceed the experimental ones for both n- (a) and (b) mesons for both types of collisions in the momentum range of p < 1 GeV/c. The model is apt to describe the shape of the experimental momentum distributions of the negative (positive) pions in n12C (p12C) collisions in the range 1 < p < 2 GeV/c. Regarding the high momentum tail of the momentum distributions (p3 1 GeV/c), the model systematically underestimates the negative (positive) pions in n12C (p12C) collisions when compared to the experimental data.
Hence, from comparison of the experimental data with model calculations we see that the modified FRITIOF model overestimates the average multiplicity of the charged pions in p12C and n12C collisions at 4.2 GeV/c by about 10%. It is important to mention that the model overestimates the number of pions in the target fragmentation region (p < 1 GeV/c) and underestimates their number (n- mesons for n12C collisions and n+ mesons for p12C collisions) in the projectile fragmentation region (p3 1 GeV/c).
Thus, the 10% excess of the calculated values of the average multiplicity of the charged pions in the model in comparison with the experiment is due to the fact that the model overestimates the contribution of intranuclear cascade processes to the production of pions in the target fragmentation region. This ultimately leads to lower average values of the momentum of the charged pions in the modified FRITIOF model (Bekmirzaev et al. 1984) compared to the experiment. The average multiplicity of the protons with momenta p > 140 MeV/c (the lower detection threshold for the reliable registration of the protons in the experiment) in p12C and n12C collisions in the experiment and the model are as follows: <n (n12C)> = 1.65 ± 0.02, <n (n12C)> , = 1.96 ± 0.01 and <n (p12C)> = 1.92 ± 0.02, <n (p12C)> , =
pv ' exp pv ' mod p ' exp p ' mod
2.32 ± 0.01. It can be seen that for both types of collisions the average multiplicity of protons is approximately 1.2 times greater in the model than in the experiment.
On the other hand, the fact that the model underestimates the number of pions in the region of projectile fragmentation, as well as the absence of a "shoulder" in the considered pion spectra (n- mesons for n12C collisions and mesons for p12C collisions) indicates that the model underestimates the contribution of D resonances to pion production in the projectile fragmentation region (p3 1 GeV/c).
Figures 3 and 4 show the normalized experimental data on the transverse momentum distributions of n- (a) and n+ (b) mesons in the analysed collisions compared with the calculated theoretical distributions (shown as histograms).
Figures 3 and 4 show that both the experimental and theoretical transverse momentum distributions of the charged pions are smooth and flat for both types of collisions with their tails extending up to pt = 1 GeV/c values. The model overestimates the experimental spectra in the region pt < 0.5 GeV/c and underestimates them at pt > 0.5 GeV/c. In fact, the behaviour of the theoretical transverse momentum distributions reflects the behaviour of the total momentum distributions previously discussed by us, because the emission angle distributions of the charged pions in both the model and the experiment are very close to each other. On the whole, the model qualitatively describes the data on the transverse momentum distributions of the charged pions.
Fig. 3. The normalized transverse momentum distributions of the negative (a) and positive (b) pions in n12C collisions. Histograms—the calculations within the framework of the modified FRITIOF model (Galoyan et al. 2002)
Fig. 4. The normalized transverse momentum distributions of the negative (a) and positive (b) pions in p12C collisions. Histograms—the calculations within the framework of the modified FRITIOF model
Conclusions
We have presented the new experimental data on various properties of the secondary charged pions produced in n12C collisions at 4.2 GeV/c. We have also performed a comparative analysis of the average multiplicities and various kinematic properties of the charged pions produced in n12C and p12C collisions at 4.2 GeV/ c. Experimental data were compared systematically with the calculations using the modified FRITIOF model.
It is shown that in n12C (p12C) collisions at 4.2 GeV/c around half of the negative (positive) pions are produced due to inelastic charge exchange reaction (conversion) of the initial neutron (proton) into proton (neutron) and the negative (positive) pion.
The momentum distributions of the negative (positive) pions proved to be more rigid than those of the positive (negative) pions produced in n12C (p12C) collisions. This fact can be related with production of the fast negative (positive) pions due to the inelastic charge exchange reaction (conversion) when the incident neutron transforms into n meson and proton, and the decay of the intermediate A0 resonance formed due to excitation of the incident neutron (or when the incident proton transforms into n+ meson and neutron, and the decay of the intermediate A+ resonance formed due to excitation of the incident proton) in n12C (p12C) collisions, respectively.
It is found that the modified FRITIOF model overestimates the average multiplicities of the charged pions in n12C (p12C) collisions at 4.2 GeV/c compared to the experiment. It is shown that this is due to the fact that the model overestimates the contribution of the intranuclear cascade processes in production of pions in the target fragmentation region compared to the experiment.
It is also found that the model underestimates the multiplicity of the charged pions in the projectile fragmentation region. It is shown that this is due to the fact that the model underestimates the contribution of decays of A resonances to the generation of the fast charged pions in the analysed collisions.
Conflict of interest The authors claim that there is no potential or actual conflict of interest.
References
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