Isotopic cross sections of 12C fragmentation on hydrogen measured at 1.87 and 2.69 GeV/nucleon
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2002 J. Phys. G: Nucl. Part. Phys. 28 1199 (http://iopscience.iop.org/0954-3899/28/6/304)
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INSTITUTE OFPHYSICSPUBLISHING JOURNAL OFPHYSICSG: NUCLEAR ANDPARTICLEPHYSICS
J. Phys. G: Nucl. Part. Phys. 28 (2002) 1199–1208 PII: S0954-3899(02)34280-4
Isotopic cross sections of
12C fragmentation on hydrogen measured at 1.87 and 2.69 GeV /nucleon
A Korejwo1, M Giller2, T Dzikowski2, V V Perelygin3and A V Zarubin3
1Division of Nuclear Physics and Radiation Safety, University of Lodz, ul Pomorska 149/153, 90-236 Lodz, Poland
2Division of Experimental Physics, University of Lodz, ul Pomorska 149/153, 90-236 Lodz, Poland
3Laboratory of Particle Physics, Joint Institute for Nuclear Research, 141980 Dubna, Moscow region, Russia
E-mail: akorejwo@kfj.fic.uni.lodz.pl, mgiller@kfd2.fic.uni.lodz.pl, td@kfd2.fic.uni.lodz.pl, perel@sunse.jinr.ru and azarubin@sunse.jinr.ru
Received 26 January 2002 Published 18 April 2002
Online atstacks.iop.org/JPhysG/28/1199 Abstract
We present new results of measurements of the isotopic cross sections of12C fragmentation in the energy region of a few GeV/n. The experiment has been performed at the Dubna synchrophasotron using the magnetic spectrometer ANOMALON, equipped with Cherenkov counters. In this experiment12C is the projectile and liquid hydrogen is a target. The isotopic cross sections obtained in the measurement are compared with the values predicted by the models: semi-empirical (Silberberg and Tsao) and parametric (Webber, Kish and Schrier). This work is a continuation of the previous one where similar results, but at 3.66 GeV/n, are presented.
1. Introduction
Knowledge of fragmentation cross sections of nuclei when hydrogen is the target is interesting not only from the point of view of nuclear physics. Indeed, the motivation of the present experiment stems from studies of the galactic propagation of low energy (∼GeV/nucleon) cosmic rays. It is well known that, due to confinement by galactic magnetic fields, these particles (nuclei stripped of electrons) spend enough time in the interstellar gas to collide with its atoms (mainly hydrogen) producing fragment nuclei. This phenomenon is responsible for the abundance of some elements such as Li, Be and B in the cosmic ray flux at the Earth’s atmosphere. From the measured ratios of the flux of the fragment nuclei to that of their ‘parents’ (mainly carbon and oxygen) one can obtain valuable information about the
‘grammage’ (path length in g cm−2) traversed by nuclei in the interstellar space. This is, however, only possible if all the relevant fragmentation cross sections are known. Moreover,
0954-3899/02/061199+10$30.00 © 2002 IOP Publishing Ltd Printed in the UK 1199
Figure 1. Layout of the spectrometer. MWPC 1–10: multiwire proportional chambers, S1−S3: scintillation counters, ˇCI, ˇCII, ˇC1− ˇC32: Cherenkov counters, T: liquid hydrogen target, SP-40:
analysing magnet.
cosmic ray grammage apparently decreases with energy and more quantitative conclusions about this can be drawn only if the energy dependence of the cross sections is known.
A series of measurements has been undertaken at the Joint Institute for Nuclear Research in Dubna (Russia) by the Polish-Russian collaboration. Fragmentation of12C and16O nuclei at three energies 1.87, 2.65 and 3.66 GeV/n occurred on the hydrogen target. Our results of12C fragmentation at 3.66 GeV/n have been published already [1]. Here, we present our further work with the12C beam for two lower energies: 1.87 and 2.69 GeV/n.
2. Experiment
The measurements have been performed at the Joint Institute for Nuclear Research (Dubna, Russia), using the ANOMALON set-up (figure1) at the synchrophasotron’s slow extraction beam VP-1. 12C nuclei from the beam fragment on the liquid hydrogen target (T), then pass the region with high magnetic field deflecting their trajectories, and finally hit the Cherenkov counters. The coordinates of the trajectories are determined by the set of the multiwire proportional chambers (MWPCs) to calculateA/Z of a fragment. The hit Cherenkov counter measures the fragment charge Ze.
The trigger system is the same as that for 3.66 GeV/n. It is based on the scintillation counters S1, S2, S3and Cherenkov counters ˇCI, ˇCII. The first part of the trigger (beam) consists of a coincidence of pulses from the detectors S1, S2, S3and ˇCI. The discrimination level for the ˇCIdetector has been set to eliminate the nuclei with Z< 6, i.e. to exclude events with the beam fragmentation occurring before the target is reached. As a second part of the trigger (interactions) the Cherenkov counter ˇCII, with two discriminators, has been used. One of the discriminators (set at low voltage for noise elimination) is connected in the coincidence with the beam signal. The second discriminator, connected in the anti-coincidence with the beam signal, is set to cut off the part of events without fragmentation (Z> 5.4). Thus, the scheme of the trigger can be presented as S1S2S3CˇICˇII¯ˇCII. The trigger pulse starts the data reading for a 100 ns time window. Counts of both parts of the trigger (beam and interactions) have been registered.
A detailed description of the magnetic spectrometer ANOMALON has been presented in our work containing the results of our measurement of isotopic cross sections at 3.66 GeV/n [1] (the parameters of spectrometer and description of liquid hydrogen target and data taking system—see [2, 3] and references therein). Therefore, we indicate here only the differences between the present and the reported [1] configurations of the apparatus.
12C fragmentation on hydrogen at 1.87 and 2.69 GeV/nucleon 1201
Figure 2. Charge spectra of fragments with reconstructed tracks. Squares and circles represent experimental data, thick curves the summarized fitted spectra and thin curves the Gaussian fits for each charge (shown only for 2.69 GeV/n).
Compared with the previous configuration, only the following elements of the set-up have been changed:
• position of proportional chambers between the target and the magnet (MWPCs 4–7) in the coordinate detector—to improve the precision of track reconstruction,
• position of Cherenkov detectors ˇC25− ˇC32 (formerly between MWPCs 9 and 10, now behind the MWPC 10); this modification reduces the probability of registration of two or more fragments, crossing the same Cherenkov detector simultaneously, interpreted as a single particle.
As in our previous measurement, the operation voltage for MWPCs 4–10 has been chosen to correspond to the efficiency plateau for the nuclei from Li to C, so the efficiency of track reconstruction for fragments with Z< 3 has been decreased. The voltage for MWPCs 1–3 was optimized for the projectile nuclei (Z= 6). The magnetic field in the SP-40 magnet (0.63 T and 0.83 T for 1.87 and 2.69 GeV/n, respectively) was set to assure that the deflection angle of primary beam particles be the same as that between the main and the second axis of the spectrometer (80 mrad).
The total number of registered events in the measurements at 1.87 GeV/n is about 1.1 × 106with the hydrogen target and 4× 105with the empty target (for background calculation).
At 2.69 GeV/n the total number of events registered with the target is about 6 × 105.
3. Data analysis and results
The method of data processing is generally the same as that described in [1], except for the angular distributions. The charge spectra, obtained from the Cherenkov counters crossed by all identified trajectories, have been composed and are shown in figure2. The fragment charges have been histogrammed under the condition that both tracks of the projectile and fragment
are reconstructed. For the tracks crossing Cherenkov detectors ˇC25− ˇC32, the mean charge of the fragment has been calculated using data from both detectors crossed (i.e. from the counter from ˇC25− ˇC32group and the counter from ˇC1− ˇC24group).
The events without fragmentation and events in which carbon isotopes (11C, 10C and 9C) have been produced, are partially discriminated by the trigger. The tracks of the fragments with Z < 3 were reconstructed with small efficiency with regard to the settings of MWPCs 4–10. The peak at the charge ∼2.7 e can be interpreted as caused by two helium nuclei produced at the same time, crossing the same Cherenkov detector simultaneously. In contrast to our measurements at 3.66 GeV/n, no other similar cases (e.g.
with helium and lithium nuclei) are measurable. The charge resolution of the Cherenkov hodoscope is about 0.28 e for fragments with 2 Z 5 and ∼0.25 e for carbon nuclei.
Additionally, the charge spectrum without track analysis has been constructed—for calculating the efficiency of track reconstruction. Applying the procedure of Gaussian fitting to the two spectra, we have determined the numbers of fragment nuclei for each Z (at Z= 6, besides carbon fragments, beam12C nuclei are also partially included).
The next step of the data analysis is different from that used in the data processing at 3.66 GeV/n, described in [1]. Instead of the angular distributions, we have now determined distributions of the inverse of the deflection angle of the nuclei and rescaled them to the A/Z distributions (figure3). As the fragment momenta per nucleon are approximately equal, then the deflection angle is, for small angles, inversely proportional toA/Z.
Figure3presents theA/Z distributions for charges close to the integer values (for instance Z= 4.8–5.2, 3.8–4.2, etc) determined for each track individually. An exception is made for carbon nuclei: in this case the upper limit of the charge interval Z= 5.8–7 is relatively higher.
The one-side broadening of this interval can be used because the charge spectra do not contain nuclei with Z> 6.
To calculate the numbers of nuclei of the individual isotopes in theA/Z spectra we must subtract the contributions of isotopes of the adjacent elements, e.g., the number of6Li nuclei in the Li spectrum is actually smaller than the area of the6Li peak, because this peak contains a contamination by4He. The correction was made by counting the events in the peak at A/Z = 1.5 (caused by3He contamination of the Li distribution) and multiplying it by the ratio of the4He to3He nuclei, determined in He spectrum (6Li and4He have the sameA/Z).
The total number of nuclei of a particular isotope has been calculated using the number of isotope nuclei in theA/Z spectrum, with the normalization by the ratio of the total number of nuclei of the specified element in the charge spectrum to the number of all nuclei of this element in theA/Z spectrum.
An analogous method of data processing (analysis of charge distribution andA/Z spectra) has been applied for background calculation (i.e. with no hydrogen in the target vessel) in the 1.87 GeV/n measurements.
4. Isotopic cross sections
We have calculated the isotopic cross sections of the fragmentation with the method described in [1]. In the calculations we took into account the number of nuclei of individual isotopes, the liquid hydrogen target thickness and the counts of the trigger detectors.
If the background interactions were negligible and the total efficiency of the detection (including the efficiencies of track reconstruction and data storage on hard disk) were 100%, the formula for the calculation of isotopic cross section could be written as follows:
12C fragmentation on hydrogen at 1.87 and 2.69 GeV/nucleon 1203
Figure 3. A/Z spectra of fragments with reconstructed tracks at 2.69 GeV/n. Squares show experimental data and full curves the summarized fitted spectra.
σ12C→AX= NAX
kN0(1 − e−nHσin)σin, (1)
where
NAX number of detectedAX nuclei,
σin inelastic cross section of12C+p interaction,
N0 number of beam nuclei (number of coincidences in counters S1, S2, S3and ˇCI), nH number of hydrogen nuclei in the target per unit area, in the plane perpendicular to the
beam direction,
k for He, Li and Be nuclei k= 1; for fragments with Z = 6, k is the fraction of the number of carbon nuclei passing through the counter ˇCII, accepted by the trigger.
With the same assumption concerning the efficiency, we have the following formula for the determination of k for carbon isotopes [4]:
k = NC
NC+N0− Nt. (2)
NCis the number of carbon nuclei (all isotopes) behind the target and Ntis the number of triggers.
The k value for boron is defined analogously as for carbon, i.e. as the fraction of the number of boron nuclei passing through the counter ˇCII, accepted by the trigger. The k factor for boron is determined based on the charge cut-off level obtained with the k for carbon and by the analysis of the amplitude spectra of ˇCII. In this measurement, the upper level of discrimination in ˇCIIdetector, set for partial cut-off of carbon nuclei, seals off about 23 per cent of events with boron production as well.
Actually, the background interactions, occurring in the mylar walls of the target, in the air in the target neighbourhood or in proportional chambers, give a significant contribution to the counts of the nuclei. Thus, we first calculated the productnbg· σin(bg), where nbg is the effective number (per unit area) of nuclei on which the background interactions occur and σin(bg)is the effective inelastic cross section for these interactions:
nbg· σin(bg)= lnkbgN0(bg)
N12C(bg) . (3)
The symbols in the formula (3) are the same as in formula (1) and the subscript ‘bg’ corresponds to the background data. Then we computed the productsnbg· σ(bg)12C→AX, using a formula similar to (1). Applying a similar method to the data obtained with hydrogen target, we have computed the ‘effective nσ’ for target and background interactions together, i.e. the sum of products of the number of nuclei per unit area and the cross section (including both target and background interactions). Hence, by subtraction of the background component we obtained the values ofnH· σ12C→AX, and finally, the isotopic cross sections of carbon nuclei fragmentation on hydrogen.
For determining the number of various nuclei produced in the experiment we have taken into account the efficiencies of track reconstruction and data recording. The efficiency of track reconstruction varies from about 50% for helium to over 80% for boron and carbon nuclei and is approximately the same at both energies. For hydrogen its value is considerably lower (about 4%)—as a result of a low voltage of the proportional chambers. The efficiency of data recording is the ratio of the number of events recorded and that of triggered. It varies from 7% to 30% for separate runs, dependent on beam intensity and on the stability of this intensity during beam extraction.
Because of the absence of the background measurement at 2.69 GeV/n, we used for this energy the average background data from 1.87 and 3.66 GeV/n measurements.
Our cross-section results have been corrected by a constant factor connected with the obtained value of the inelastic cross section. In this experiment we have determined the inelastic cross section for12C interaction with hydrogen as 238 mb at 1.87 GeV/n and 244 mb at 2.69 GeV/n, with relative error estimated for a few per cent. However, we have corrected our partial cross sections to getσin= (250 ± 2) mb. This value is extrapolated from the results obtained by Bobchenko et al [5] with a relative error of only 0.8% (the inelastic cross section was found constant in a wide energy range—see [5] and references therein).
The isotopic cross sections determined in our experiment are shown in table 1. For the results at 1.87 GeV/n we have computed the statistical and systematic errors (σstat
andσsyst) separately. The separation of errors is performed with regard to the fact that the ratio of cross sections for production of isotopes of the same element, e.g.10Be/9Be,
12C fragmentation on hydrogen at 1.87 and 2.69 GeV/nucleon 1205
Table 1. Isotopic cross sections of12C fragmentation on hydrogen.
1.87 GeV/n 2.69 GeV/n
Reaction12C→ σ (mb) σstat(mb) σsyst(mb) σ (mb)
11C 26.8± 2.2 2.1 0.7 25± 3
10C 1.4± 0.3 0.3 0.1 1.3± 0.4
9C 0.18± 0.08
12B 0.12± 0.08 0.08 0.01 0.12± 0.10
11B 25.8± 3.1 2.7 1.5 26± 4
10B 11± 4 3.9 0.7 13± 6
8B 0.39± 0.12 0.11 0.02 0.47± 0.14
10Be 4.1± 0.7 0.12 0.7 3.8± 0.9
9Be 6.6± 1.2 0.14 1.1 6.5± 1.4
7Be 7.8± 1.4 0.15 1.4 9.1± 1.9
9Li 0.36± 0.08 0.04 0.06 0.36± 0.10
8Li 1.27± 0.22 0.07 0.20 1.4± 0.3
7Li 11.8± 2.0 0.2 2.0 13± 3
6Li 17.7± 3.3 0.5 3.2 19± 4
6He 1.01± 0.12 0.06 0.10 1.4± 0.2
4He 156± 15 1 15 180± 30
3He 22.0± 2.2 0.24 2.2 30± 4
is charged by statistical errors only, but the systematic error is practically determined by one factor: the uncertainty in the track reconstruction efficiency which is the same for all isotopes of the element. The uncertainty of the contribution of the isotopes of other elements with the same A/Z (in the A/Z distribution) is included in statistical error. In particular, this contribution is large for 10B (the10B peak is significantly contaminated by 12C). At 2.69 GeV/n a simplified method of error calculation has been applied because of the absence of background measurements; in this case we have estimated the total errors only—the systematic and statistical errors together.
The boron data shown in table1differ from our preliminary results presented at the 27th International Cosmic Ray Conference [10]. It is caused by a recalculation of the k factor for boron. Additionally, we would like to correct the experimental errors for boron isotopes in our measurement at 3.66 GeV/n [1]: these errors should be approximately the same as those shown in table1for 1.87 GeV/n.
All the cross sections determined are the direct ones (not ‘decayed’) as the time of flight to the detector is very short when compared to the lifetime of any unstable nucleus involved. The decayed (cumulative) cross sections, relevant for fragmentation occurring in the interstellar space, can be easily calculated from these data and the decay scheme of nuclides.
5. Comparison of the results with other experimental data and predictions
From among the measurements of isotopic cross sections of12C fragmentation on hydrogen, the cross sections of11C and7Be production were measured more frequently than others. It is caused by properties of these nuclei. Both mentioned nuclides are radioactive and their lifetimes (T1/2= 20.4 min for11C and 53.3 days for7Be) are convenient for determination of the number of produced nuclei by a measurement of sample activity. Therefore, a majority
of the experimental results for these nuclei have been obtained with proton beam and target fragmentation.
Other products of fragmentation (except 3H and10Be) are stable or, on the contrary, have lifetimes too short for activity measurement. To detect these nuclei effectively, another method was applied—carbon projectile fragmentation on a target containing hydrogen. Such experiments with12C beam have been performed at LBL Bevalac (closed a few years ago) and SATURNE. Isotopic cross sections for production of beryllium, boron and carbon isotopes at projectile energy less than 1 GeV/n were measured using the method of CH2−C subtraction [6, 7] and with a liquid hydrogen target [8]. In the energy region above 1 GeV/n the isotopic cross sections of 12C fragmentation on hydrogen have been determined in the experiment performed with liquid hydrogen by Lindstrom et al and Olson et al [9] (later denoted by L&O)—at 1.05 and 2.1 GeV/n for the full charge range of product nuclei (Z from 1 to 7).
Figure4shows the isotopic cross sections obtained in various experiments, including ours.
References for11C results are specified in the figure. For other isotopes, the data marked as full data points (squares, circles and triangles) are taken from the references: at 0.365 GeV/n [8], at 0.403 GeV/n [6], at 0.6 GeV/n [7] and at 1.05 and 2.1 GeV/n [9]. Additionally, the
7Be data marked as open squares are taken from [11], the7Be data marked with R from Radin paper [12] and the9Be and10Be data marked with F from the paper of Fontes [13]. The curves show the cross sections calculated with the semi-empirical method of Silberberg and Tsao (see e.g. [14]), and with the parametric method of Webber, Kish and Schrier [7]. Both calculations were performed using the programmes available at Space Physics Data System [15].
6. Discussion
The experiment reported here completes our previous measurement carried out at 3.66 GeV/n with the identical beam and target combination. Using the same experimental set-up and practically the same method of data processing, we have obtained the isotopic cross sections at three energies (including previous experiment) for many final nuclei. Our isotopic results concern the energy region above 1 GeV/n, where experimental cross-sections data are scarce.
It should be added that isotopic composition of light elements in cosmic rays, not long ago known only for energy below 1 GeV/n, is also being measured at present at energies exceeding this value.
In principle, our results are close to the results of other experiments and indicate a weak energy dependence of cross sections in the analysed energy region. But, as seen in figure4, in some cases they are significantly different from other experimental data at similar energies and predictions of the models.
The determination of production cross section ratios10Be/9Be and10Be/7Be is a matter of particular interest for the cosmic ray escape time from the Galaxy.10Be is a radioactive nuclide with lifetime comparable with the confinement time of cosmic rays in the Galaxy—T1/2= 1.6 × 106years;9Be is stable and7Be decays only by electron capture, so in the cosmic rays at a few GeV/n it is stable as well, because at these energies cosmic rays are devoid of electrons.
Our10Be/9Be ratios are practically the same as that determined by L&O at an intermediate energy 2.1 GeV/n. However, our10Be/7Be ratio at 1.87 GeV/n is larger than that obtained by L&O by∼1.4 and larger by ∼2 than those predicted by the phenomenological formulae. At 2.69 GeV/n our result agrees with that of L&O within 17%, but diverges from the formulae by
∼1.6. Applying our larger values for10Be production in the Galaxy would indicate a longer cosmic ray propagation time.
12C fragmentation on hydrogen at 1.87 and 2.69 GeV/nucleon 1207
Figure 4. Isotopic cross sections of12C fragmentation on hydrogen: experimental data and model calculations. Full curves show the cross sections calculated for the semi-empirical model of Silberberg and Tsao and broken curves show the cross sections calculated for the parametric model of Webber, Kish and Schrier. Our data, at 1.87 and 2.69 GeV/n, and previous data, at 3.66 GeV/n, are marked by larger data points. See also text for supplementary information.
For3He production cross section, the discrepancy is evidently visible. Although the cross sections of other helium isotopes production are practically equal in L&O and our
measurements,3He cross section at all the three energies measured by us is several times smaller than that determined by L&O. Unfortunately, at present we cannot explain it.
As mentioned already, we were not able to determine the cross sections for production of hydrogen isotopes, because the systematic errors of cross sections are comparable with the values of these cross sections (in this case the efficiency of track reconstruction is a main source of error). We estimated only the ratios of cross sections for production3H,2H and1H:
σ3H/σ1H= 1.37 ± 0.11 and σ2H/σ1H= 1.2 ± 0.7 at 1.87 GeV/n. These ratios are roughly the same as those at 3.66 GeV/n. They can be compared with the L&O results at 2.1 GeV/n.
Hereσ3H/σ1H= 2.2 ± 0.6, but the authors inform that not all protons have been detected. The σ2H/σ1Hratio in our experiment is determined with the big error, what results from a large contamination of2H peak by4He. The L&O value ofσ2H/σ1Hequals 2.0± 0.5. Taking into consideration the experimental errors, our result is not in obvious contradiction with it.
Acknowledgment
M Giller thanks the Polish State Committee for Scientific Research for supporting this work under grant No 2 P03C 006 18.
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