The measurement of isotopic cross sections of 12C beam fragmentation on liquid hydrogen at 3.66 GeV/nucleon
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2000 J. Phys. G: Nucl. Part. Phys. 26 1171 (http://iopscience.iop.org/0954-3899/26/8/306)
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The measurement of isotopic cross sections of
12C beam fragmentation on liquid hydrogen at 3.66 GeV/nucleon
A Korejwo†, T Dzikowski‡, M Giller‡, J Wdowczyk‡, V V Perelygin§ and A V Zarubin§
† Division of Nuclear Physics and Radiation Safety, University of Lodz, ul. Pomorska 149/153, 90236 Lodz, Poland
‡ Division of Experimental Physics, University of Lodz, ul. Pomorska 149/153, 90236 Lodz, Poland
§ Laboratory of Particle Physics, Joint Institute for Nuclear Research, Joliot-Curie 6, 141980 Dubna, Moscow Region, Russia
E-mail:akorejwo@fic.uni.lodz.pl, td@kfd2.fic.uni.lodz.pl,
mgiller@kfd2.fic.uni.lodz.pl, perel@sunse.jinr.ru and azarubin@sunse.jinr.ru Received 26 April 2000
Abstract. An experiment with12C beam fragmentation on a liquid hydrogen target has been performed using the magnetic spectrometer, Anomalon, equipped with a Cherenkov charge detector, and the Dubna synchrophasotron at a projectile energy of 3.66 GeV/nucleon. A charge resolution of 0.26e (except for the hydrogen nuclei) and a mass resolution of 0.11–0.18 amu have been achieved.
Isotopic and elemental fragmentation cross sections have been obtained for fragments fromZ = 1 to 6. Decayed cross sections have also been calculated. We compare the measured cross sections with the results of other experiments and with calculations based on semi-empirical and parametric approaches.
1. Introduction
A knowledge of the cross sections for nuclei fragmentation on hydrogen in the GeV/nucleon energy region is important from both the nuclear-interaction point of view and that of high- energy astrophysics. This particular experiment was performed in order to supply more information about cosmic-ray propagation in the Galaxy.
It is well established that cosmic-ray particles, propagating in the Galaxy from their sources to the Solar System, undergo collisions with interstellar gas, which is mainly hydrogen. The most interesting result of this is that among the various cosmic-ray nuclei arriving in the Earth’s atmosphere, there are some which are practically absent in the ‘thermal energy’ matter of the Solar System, e.g. lithium, beryllium and boron. These nuclei are produced by fragmentation of heavier elements in their collisions with interstellar matter. Carbon and oxygen are the main producers of the Li, Be and B nuclei observed in the cosmic-ray flux. Knowledge of the cross sections for these processes is necessary in order to draw conclusions about the particle path lengths (in g cm−2) in interstellar matter. However, the number of cross sections that are needed far exceed the measured ones. So, in order to deduce the cosmic-ray path-length distribution some attempts have been made to predict values of the non-measured cross sections [1, 2]. In recent years, a wealth of fragmentation cross sections have been measured by the Transport Collaboration in the energy region of about 350–750 MeV/nucleon [3]. However, a comparison
0954-3899/00/081171+16$30.00 © 2000 IOP Publishing Ltd 1171
with the predicted values shows quite frequent discrepancies of a factor of approximately two, or by several experimental standard deviations. This shows that the existing phenomenological formulae are not sufficiently accurate for astrophysical purposes.
Of particular interest is the dependence of cosmic-ray propagation on energy. Above 1 GeV/nucleon, however, there have been far fewer cross sections measured. Nevertheless, the existing data and the semi-empirical formulae (not always good) have allowed the deduction that in the energy region of a few GeV/nucleon the mean path length decreases with energy (in the leaky-box model of particle propagation). To determine accurately how strong this dependence on energy is and whether the leaky-box model (i.e. the exponential path-length distribution) is valid, cross sections in this energy region have to be known.
This paper presents a measurement of isotopic fragmentation cross sections of one of the most important nuclei,12C, on hydrogen at 3.66 GeV/nucleon. Amongst other things, this provides data on the production of the radioactive isotope10Be, so that we can infer not only the grammage traversed by cosmic nuclei but also the time of propagation in interstellar space.
2. The experimental set-up
In this experiment the fragmentation of 12C projectiles on a hydrogen target has been investigated. In this case all the nuclei produced by beam fragmentation are emitted in a narrow cone along the beam direction and their momenta per nucleon are close to the projectile value.
Therefore, it is possible to detect all the nuclei that are produced, including those with very small energy in the projectile reference frame.
The experiment was performed using the Anomalon set-up [4, 5] and the synchrophasotron’s slow extraction beam VP-1 at the Joint Institute for Nuclear Research (JINR) in Dubna, Russia. The Anomalon magnetic spectrometer (figure 1) is based on a system of multiwire proportional chambers (MWPC) and an analysing magnet SP-40. It also includes a Cherenkov hodoscope for determining fragment charges, a trigger system consisting of scintillation and Cherenkov detectors, and a beam monitor. For the beam-fragmentation cross section measurements the Anomalon set-up was equipped with a liquid hydrogen target.
The multiwire proportional chambers were constructed at JINR [6]. They constitute a coordinate detector for determining the positions of the charged-particle tracks; the cathodes of the MWPCs are made of mylar foil with an aluminium layer; the total number of anode
Figure 1. A view from above of the Anomalon experimental set-up. MWPC 1–10, multiwire proportional chambers; S1–S3, scintillation counters; ˇCI, ˇCII, ˇC1– ˇC32, Cherenkov detectors; T, liquid hydrogen target; SP-40, analysing magnet.
wires (and readout channels) is 4736; and the gas mixture filling the chambers consists of 69%
argon, 28% isobutane, 2.8% propanol-2 and 0.2% freon 13B1. While the measurements were taking place a continuous flow of gas was applied through the chambers.
The first (in the beam direction) MWPCs (1–3) determine the parameters of the beam- particle (12C nucleus) track. The next group (MWPCs 4–7) measure the fragment tracks in front of the magnet, whereas MWPCs 8–10 measure the tracks behind the magnet. The sensitive area of proportional chambers 1–4 is 64× 64 mm2, while the other chamber dimensions increase along the beam direction, e.g. MWPC 10 is 1280 mm wide and 896 mm high. The wire spacing is 1 mm for chambers 1–4 and 2 mm for the others. Each of the MWPCs 1–7 consists of three sets of anode wires oriented with a 120◦ step (xuv geometry), MWPC 8 is constructed as axyv system, and chambers 9 and 10 are composed of two wire sets oriented horizontally and vertically (xy). The pulses from all the anode wires are collected using LeCroy 7700 readout electronics. All of the detectors were gated by a trigger system in time intervals of 100 ns with a time delay for each chamber chosen separately. The voltage of the proportional chambers was chosen so as to favour the detection of nuclei withZ = 3–6. The proportional chamber data were processed using the reading control system BUSP [7] and transmitted to the computer in a compressed form.
The axis of MWPCs 8–10 and the Cherenkov hodoscope is deflected from the primary beam direction by 80 mrad. The Cherenkov hodoscope consists of 32 detectors; the radiators are made of plexiglass; 24 detectors (each 60 mm wide and 350 mm high) are placed at a distance of 5.7 m from the centre of the magnet and the remaining eight of them (25 mm wide and 370 mm high) are situated near the second (deviated) axis of the spectrometer, in front of MWPC 10. All the detector photomultiplier tubes were connected with multichannel ADC converters. The data referring to the amplitudes of the pulses (for each detector separately) were collected by the computer.
The SP-40 analysing magnet has pole pieces that are 150 cm long and 100 cm wide, placed at a distance of 40 cm. The magnetic field (1.2 T) is set to ensure that the deflection angle for the primary beam particles is the same as the angle of deflection between the main and second axis of the spectrometer. The nuclei are deflected in the horizontal planezx.
The liquid hydrogen target was constructed at the Laboratory of High Energies at JINR [8].
The target (modified for this experiment) is 59 mm in diameter and 136 mm long (equivalent to 0.94 g cm−2). The total thickness of the two mylar windows is 67 mg cm−2.
3. Experimental data and the method of their processing
Triggering and beam-flux measurements were performed using the scintillation counters S1, S2, S3, and the Cherenkov detectors ˇCI, ˇCII. A trigger was accomplished using the following criteria:
(a) Detection of a beam particle in scintillation counters S1, S2, S3(Z = 6);
(b) Z = 6 in the Cherenkov detector ˇCI(to eliminate the beam particles which fragmented before the target),
(c) A cut-off of pulses with an amplitude corresponding toZ > 5.8 on the Cherenkov detector ˇCII(partial forZ = 6, total for Z > 6).
The amplitude of the signal from ˇCIIis an interaction indicator: because the intensity of the Cherenkov radiation is proportional toZ2, the amplitude of the pulse on the Cherenkov detector in the case when a fragmentation took place is smaller than in the case when no fragmentation occurred. However, the discrimination level partially allows us to register nuclei withZ = 6 (with a known cut-off ratio) in order to enable the detection of such interactions in which the
nucleus charge remains at 6, but the mass number decreases (e.g.12C→11C). A partial cut-off of signals corresponding toZ = 6 is set in order to reduce the recording of non-interesting data (without interaction). A full cut-off could cause a loss of information concerning the interactions12C→11C,12C→10C and12C→9C.
Therefore, all the interactions (except for those occurring in dead time) in which Z decreased and a fraction of the events in which the carbon nucleus reached the detector have been recorded. In this way the registration of carbon fragments withA < 12 was performed, but some events were collected with non-fragmented12C beam nuclei as well. Discrimination of these events was performed off-line.
The trigger conditions having been fulfilled, the detector responses were read out and written on a hard disk. The collection, including MWPCs, Cherenkov and scintillation- counters data corresponding to a passage of one beam nucleus through the target, was recorded as one event. The total number of registered events exceeds 106with the hydrogen target and 2.8 × 105with an empty target (for the background calculation).
From the MWPC data the track parameters were calculated in three sections (i.e. groups of MWPCs: 1–3, 4–7, 8–10) separately—for the beam nuclei, for fragments between the target and the magnet and for fragments behind the magnet. The method of trajectory reconstruction includes:
(a) The calculation of the x, y coordinates of points at which charged particles pass proportional chambers, based on a criterion that the strips (determined by anode wires which detect the signal) in all the sets of anode wires are overlapping; the dimensions of this overlapping give the uncertainty of the point coordinates.
(b) An estimation of the parameters of the straight tracks determined by points found in each of the sections separately (initially, all possible combinations were studied) with the least-squares method, with weights being determined by the uncertainty of the point coordinates. In this step, track equations of the form
x = Axz + Bx y = Ayz + By
for the first and second group of MWPCs and x= Axz+Bx y = Ayz+By
for the third group were obtained (z and z are the coordinates along the axes of the apparatus, main and deflected,x and xare horizontal coordinates normal to z and z respectively;y is the vertical coordinate).
(c) Finding the best-fitting track associated with each point in the last MWPC of the respective section (fulfilling the condition of a minimal sum of the squares of the distances between the experimental points and the estimated straight track). In this way exactly one single track corresponding to each point in the last chamber of the section was chosen for further selection.
(d) The selection of tracks in neighbouring sections in order to find tracks corresponding to the same trajectory and in this way allow for a full reconstruction of a trajectory in the detector. This selection is based on the criterion of a minimal distance between the tracks in the target and the centre of the magnet. Additionally, consistency between the inclination angles of both tracks in the planeszy (for the track part between the target and the magnet) andzy (for the track part behind the magnet) was taken into account. In this way practically all false tracks, reconstructed with the wrong points (these points were found especially in the blocks with a two-coordinate system, i.e. in MWPCs 9 and 10), were eliminated.
Finally, the trajectory equations, combined with the apparatus geometry, gave the deflection angle of the trajectory in the magnet and enabled us to calculate the coordinates of the Cherenkov detector hit by the nucleus. As the fragment momentum per nucleon is approximately equal to the projectile momentum per nucleon, theA/Z ratio of the fragment was calculated from the deflection angle given by the track parameters in front of and behind the magnet. The fragment charge was measured directly by the Cherenkov detectors, allowing the fragment mass to be calculated.
In the charge determination, the nonlinearity of the amplitude versusZ2was taken into account as well as the dependence of the amplitude on the coordinates of the crossing point of the fragment in the Cherenkov detector.
4. Results
For all trajectories the charge spectrum was constructed. It was obtained by processing the data from the Cherenkov counters crossed by the tracks.
Then, angular distributions (which can be interpreted as mass spectra) were determined for the tracks selected with a charge near integer values, for instanceZ = 5.9–6.1, 4.8– 5.2, etc. This selection was made in order to obtain spectra which were as ‘pure’ as possible, with a small contribution from elements with neighbouring charges (trajectories with differentZ and similarA/Z ratio are indistinguishable in angular distributions).
In some cases, however, as we shall see, the contribution of nuclei with a charge other than expected and the sameA/Z ratio is great (for instance, the contribution of12C nuclei in the10B peak in the angular distribution forZ ≈ 5).
An analogous method of data processing was applied to the background data (i.e. no hydrogen in the target tube).
4.1. The charge spectrum
The charge spectrum of fragments obtained from the Cherenkov detectors (with the amplitude spectrum recalculated to obtain a linearZ scale) in the measurements performed with the
Figure 2. The charge spectrum of fragments produced in the reaction12C + p.
Figure 3. The angular distribution of carbon isotopes.
Figure 4. The angular distributions for isotopes of elements withZ ≈ 5, 4, 3 and 2.
Figure 4. Continued.
liquid hydrogen target is shown in figure 2. The results of the measurements are shown as squares, and the full curve represents a spectrum which is a sum of Gaussian functions, fitted separately to each peak. It transpires that peaks corresponding to integerZ are not sufficient to reproduce the data. An additional peak atZ = 2.7, caused by two helium nuclei crossing the same Cherenkov detector simultaneously, has had to be taken into account. A similar effect (but significantly smaller) was allowed for atZ = 3.6, corresponding to simultaneous crossing of He and Li nuclei through the same detector.
The charge resolution of the Cherenkov hodoscope (defined as the standard deviation of the Gaussian distribution) is about 0.26e for fragments with Z = 2–6.
4.2. The mass spectra
Figure 3 presents the angular distributions for carbon isotopes (collected forZ = 5.9–6.1).
The results of the measurements are shown as squares, the broken curve represents the fitted shapes of individual peaks and the full curve represents the total fitted spectrum. The peak marked as11B is interpreted as a contribution of boron-11, caused by a tail of boron in this part of the charge spectrum. The assignment of the boron isotope to the examined peak is
determined mainly by the value of its deflection angle, appropriate for that calculated for boron-11. Of course, the10B peak is not visible because its position is the same as that of the huge12C peak.
The angular distributions for fragments of lower charges are presented in figure 4. In order to simplify the images, the distributions presented in figure 4 (for boron, beryllium, lithium and helium isotopes) are shown without the curves fitting the individual peaks. These spectra, similarly to the spectrum of carbon isotopes, are contaminated by other elements. This contamination was calculated for the isotopic cross section determination, using the ratios of the numbers of particular isotope nuclei analysed at diverse charge intervals. In particular, in the angular distribution obtained forZ ≈ 4, at the point at which8Be could be expected (were it not for the fact that it is unstable), only a contamination consisting of elements other than beryllium, but withA/Z = 2, is visible. Likewise, in the case of the boron isotope spectrum, the peak marked as10B contains a significant contribution of12C (A/Z is the same in both cases).
The mass resolution (one standard deviation) for the fragments detected in this experiment extends from 0.11 amu for hydrogen to 0.18 amu for the carbon isotopes.
5. The determination of cross sections
Isotopic cross sections (see table 1) were calculated by taking into account the numbers of registered nuclei, the target parameters and the counts of the trigger detectors. The total number of nuclei of particular isotopes was determined from partial isotopic data (including onlyZ values near the integer numbers) with use of the functions fitting the angular distribution.
The cross sections have been calculated using the following formula:
σ12C→AX= NAX
βXBAXkN0(1 − e−nσin)σin
whereNAXdenotes the number of detectedAX nuclei,σinis the inelastic cross section of the
12C + p interaction,βXis the coefficient including the efficiency of data reception and track reconstruction,BAXis the coefficient comprising background interactions (occurring outside the target),N0is the number of beam nuclei (the number of coincidences in counters S1, S2, S3
and ˇCI),n is the number of hydrogen nuclei in the target per unit area, in the plane perpendicular to the beam direction, and for the cross section of carbon fragment production,k is the fraction of the number of carbon nuclei passing through the counter ˇCII accepted by the trigger; for non-carbon nucleik = 1.
The coefficientβXcan be presented in the formβX= αXNe/Nt, whereαXis the efficiency of the track reconstruction,Neis the number of events (the number of recorded triggers) and Nt is the number of produced triggers;Nt ≈ 5Ne. TheαXvalues have been determined by comparison of the charge spectra: the first one obtained with track reconstruction (see figure 2), and the second one without track analysis, from the Cherenkov hodoscope only. Values ofαX
extend in the range from 0.018 for hydrogen to 0.70 for boron and carbon.
The background correction factorBAX has been calculated separately for each isotope using the results of measurements with an empty target and with hydrogen. Values ofBAXare determined as approximately 1.15 for He, Li, Be and B isotopes, about 1.3 for hydrogen and nearly 2 for carbon isotopes.
The value of the inelastic cross section of the12C + p reaction was taken as 250± 2 mb, based on values obtained with high precision by Bobchenko et al [9] at 11 energies in the range 4–8 GeV/nucleon.
Table 1. Isotopic cross section for the12C fragmentation on a hydrogen target at an energy of 3.66 GeV/nucleon.
Reaction σ σstat σsyst
12C→ (mb) (mb) (mb)
11C 29.2 ± 2.5 2.5 0.3
10C 3.6 ± 0.5 0.5 0.04
9C 0.24 ± 0.05 0.05 0.003
12B 0.12 ± 0.05 0.05 0.003
11B 27.7 ± 0.7 0.3 0.6
10B 12.3 ± 3.0 3.0 0.3
8B 0.44 ± 0.04 0.04 0.01
10Be 4.2 ± 0.6 0.16 0.5
9Be 6.7 ± 0.9 0.37 0.8
7Be 10.1 ± 1.3 0.23 1.3
9Li 0.25 ± 0.06 0.05 0.03
8Li 1.47 ± 0.23 0.11 0.20
7Li 12.5 ± 1.8 0.25 1.7
6Li 19.8 ± 2.7 0.5 2.6
6He 0.87 ± 0.31 0.29 0.11
4He 159± 21 1.2 21
3He 24.8 ± 3.2 0.40 3.2
3H 88(±31) 8 ∼30
2H 138(±41) 10 ∼40
1H 143(±42) 14 ∼40
Experimental errors were computed separately as statistical (including errors concerning the discrimination of contributions of isotopes with similar A/Z) and systematic. The systematic errors are due mainly to uncertainty regarding the efficiency of track reconstruction (varying withZ), other factors being negligible. In particular, for Z = 1 this efficiency is the smallest, and its relative error is the largest.
In this experiment there is no simple correlation between the number of registered nuclei and the statistical error. It is mainly caused by errors resulting from the subtraction of contributions of nuclei with charge other than the expected one but with the sameA/Z ratio.
For example, the statistical error of the10B production cross section is 10 times greater than the value calculated for11B, although the count number in the peak containing10B (figure 4) is only about 25% greater than the count number in the peak containing11B. In this case the peak marked as10B contains a significant12C contribution (subtracted in the cross section calculation), while the11B peak contains no contamination by other nuclides.
Systematic errors are particularly large for the cross sections of hydrogen fragments, because of the difficulty of accurately determining the efficiency of the track detectors (as mentioned above, a high voltage in proportional chambers was set to favour the detection of nuclei withZ = 3–6).
In table 1 the statistical (σstat) and systematic (σsyst) errors of fragmentation cross sections are reported. The errors of ratios of cross sections for the production of isotopes of the same element contain only statistical errors, because other factors (due primarily to the efficiency of detection) are nearly independent of the isotope masses (they are, however, dependent onZ) and cancel out. Thus, we have measured the ratios of beryllium isotopes quite accurately:σ10Be/σ7Be= 0.416 ± 0.018 and σ10Be/σ9Be= 0.627 ± 0.042. These ratios
Table 2.12C fragmentation elemental cross section at 3.66 GeV/nucleon.
Reaction σ σstat σsyst
12C→ (mb) (mb) (mb)
C 33.0 ± 2.7 2.6 0.35
B 40.6 ± 3.1 3.0 0.9
Be 21.0 ± 2.7 0.46 2.6
Li 34.0 ± 4.6 0.6 4.5
He 185± 25 1.3 25
H 360(±120) 19 ∼110
are crucial for the determination of the cosmic-ray lifetime in the Galaxy, as we will discuss in our concluding remarks.
The cross sections for the production of elements from hydrogen to carbon reported in table 2 are obtained by adding up the isotopic cross sections presented in table 1.
Systematic errors are summed up arithmetically. To determine the total error of the cross sections we adopt the square root of the sum of the squares of the systematic and statistical errors. The determination of the systematic errors for the hydrogen isotopes is considerably less precise than in other cases; therefore, the total uncertainties of the cross sections of production for these isotopes (due mainly to the systematic errors) are only a rough estimate.
6. The decayed cross sections
Many products of12C fragmentation are radioactive nuclei with a mean lifetime which is negligible in comparison with the time of cosmic-ray propagation in the Galaxy. As an example, carbon isotopes decay according to the schemes:
11C β
+,
20.4 min−→
11B 10C β
−→+
19.5 s
10B 9C β
−→+
0.127 sB→ 2α + p.
These lifetimes are, however, long in comparison with the times of flight in the detector.
Thus, in order to obtain cross sections relevant to the cosmic-ray propagation problem one needs to determine the so-called decayed cross sections, that is the cross sections for production of a given nuclide after the decay of the produced fragments. The decayed cross sections can be calculated if all the fragmentation cross sections and decay schemes are known.
Stable nuclides formed in12C fragmentation are: 11B,10B,9Be,7Li,6Li,4He,3He,2H and1H. Additionally, in the analysis of cosmic-ray propagation the nuclide7Be should be treated as stable (although its half-life period is 53.3 days) because the only way for it to decay is through electron capture, which practically cannot be realized in interstellar space. Another beryllium isotope,10Be, can also be treated as stable due to its long lifetime. To be precise, the list of stable products of interactions should also be supplemented by12C itself. This is due to the fact that in its interaction with a proton, a12N nucleus can be produced as well (the cross section of this process is 0.03 ± 0.01 mb at 2.1 GeV/nucleon [10]);12N decays to12C (β+decay) or to 3α + p.
Decayed cross sections and their errors can be simply calculated with the data collected in tables 1 and 2. From the above-mentioned stable nuclides the decayed cross section is considerably greater than the direct one only in the cases of11B (56.9 and 27.7 mb, respectively) and10B (15.9 and 12.3 mb). The decayed cross section for boron production is, of course, the sum of the values for11B and10B, i.e. 72.8 mb.
In the case of other elements, decayed isotopic cross sections for stable nuclides are close to the direct fragmentation cross sections—the differences are negligible in comparison with the experimental errors.
In this experiment the production of neutrons remains an unstudied channel. Because of neutron decay, this channel may add a non-computable contribution to the decayed cross sections for proton production.
7. Comparison with other experiments and predictions
The cross sections obtained in the present experiment are generally consistent with a smooth extrapolation from values at lower energies [2, 10–25].
Figure 5. The11C production cross section versus projectile energy per nucleon. The numbers next to the symbols correspond to reference numbers. Full curve, the Silberberg and Tsao calculations;
broken curve, Webber et al ’s calculations (see text).
Figure 6.10C (full squares) and9C× 5 (open squares) production cross sections versus projectile energy. The curves represent Silberberg and Tsao’s and Webber’s calculations (for9C only Silberberg and Tsao).
Figure 7. Isotopic cross sections for boron isotopes. Values at 0.403 GeV/nucleon [11]; at 0.6 GeV/nucleon [2]; at 1.05 and 2.1 GeV/nucleon [10]; at 3.66 GeV/nucleon (this work).
From among the12C fragmentation cross sections on hydrogen, the12C → 11C cross section is the best to explore (figure 5). This is due to the fact that11C is a radioactive nucleus with a lifetime suitable for determining the number of nuclei by the activation method (T1/2= 20.4 min). The majority of the existing data were obtained using this method, with a proton projectile and a carbon target.
In figure 5 we have also presented predictions of the11C cross sections using the two approaches mentioned in section 1. Both programs used for the calculations (as well as for other isotopic cross sections) are taken from the Space Physics Data System database [26].
Silberberg and Tsao’s [1] approach, usually called the semi-empirical approach, is given by the full curve; the second, by Webber et al [2], the so-called parametric approach, is represented by the broken curve (the same in figures 6–11). It can be seen that in this case the former gives a better agreement with the data at a few GeV/nucleon.
Figure 8. Isotopic cross sections for beryllium isotopes. Full squares: at 0.403 GeV/nucleon [11]; at 0.6 GeV/nucleon [2]; at 1.05 and 2.1 GeV/nucleon [10]; at 3.66 GeV/nucleon (this work).
Open squares: for7Be [22]; for9Be and10Be [23]. The broken curve in the energy region 2–4 GeV/nucleon is drawn by reference to Webber [27].
Cross section data for10C and9C are considerably scarcer. Figure 6 presents the 10C cross sections determined by Webber at 0.403 and 0.6 GeV/nucleon [11], Lindstrom et al and Olson et al at 1.05 and 2.1 GeV/nucleon [10], and obtained in this work at 3.66 GeV/nucleon.
There is a rather serious discrepancy (by a factor of two to three) between the value obtained in this experiment and both predictions, which appear to underestimate this cross section above 1 GeV/nucleon. Our result suggests an increase of the 10C cross section with energy. In the case of9C over 0.3 GeV/nucleon the accessible data are, besides our own, only these of Lindstrom et al and Olson et al [10].
Fragmentation cross sections for the production of nuclides withZ < 6 are shown in figures 7–11. Cross sections for boron nuclides behave rather smoothly, not showing any considerable changes at our energy (apart from a possible increase of12B production). The same can be seen for beryllium, although a slight increase of all its isotope cross sections may be a real effect. This is predicted, however, by Silberberg and Tsao’s formulae [1] which predict the same behaviour for lithium isotopes (figure 9)—confirmed by our measurements (apart from9Li where we obtained a smaller value than that at 2 GeV/nucleon). The absolute values for6Li and8Li seem to have been underestimated by these authors.
The 3He production measured here (figure 10), is smaller by a factor of two than at 2 GeV/nucleon, the other isotopes remaining almost constant (note the logarithmic scale on the vertical axis).
It should be noted that the cross sections for the production of hydrogen isotopes were also measured. The1H production cross section at 3.66 GeV/nucleon is considerably greater than that at 1.05 and 2.1 GeV/nucleon (figure 11). It indicates that the probability of proton emission increases with increasing energy.
Some previous results concerning3H production were obtained in other experiments in which cross sections were calculated on the basis of tritiumβ-activity measurements [24, 25].
The values of cross sections determined in those experiments, not marked in figure 11 (17–
20 mb with errors of about 20%, at energies of 2.1–6.2 GeV/nucleon), are a few times lower
Figure 9. Isotopic cross sections for lithium isotopes. Values at 1.05 and 2.1 GeV/nucleon [10];
at 3.66 GeV/nucleon (this work).
than those obtained in [10] and in this work. This may be caused by loss of tritium during the chemical treatment of the target.
8. Conclusions
We have measured isotopic cross sections for12C fragmentation on a liquid hydrogen target, in the energy region in which it is believed that they should not depend on energy. When compared with cross sections at 1–2 GeV/nucleon they do not show dramatic changes, although several of them are significantly different (see section 7). As we explained in section 1, a knowledge of
12C fragmentation cross sections on hydrogen, particularly in the GeV/nucleon energy region, is necessary for addressing the problem of cosmic-ray propagation in the Galaxy. A correct
Figure 10. Isotopic cross sections for helium isotopes. Values at 1.05 and 2.1 GeV/nucleon [10];
at 3.66 GeV/nucleon (this work).
Figure 11. Isotopic cross sections for hydrogen isotopes. Values at 1.05 and 2.1 GeV/nucleon [10]; at 3.66 GeV/nucleon (this work).
conclusion on the energy dependence of the mean escape path length of cosmic-rays from the Galaxy is only possible if the dependence on energy of the corresponding cross sections is well known. We have shown that it would be, in general, too crude to assume that12C fragmentation cross sections above∼ 2 GeV/nucleon do not depend on energy.
We have also determined with a good level of accuracy ratios of cross sections for unstable
10Be to the stable9Be and to7Be which only decays by electron capture. When compared with that at 2 GeV/nucleon, our values for 10Be/9Be and10Be/7Be increase by 12% and 20%, respectively. This has an implication for a determination of the surviving fraction of the radioactive10Be in the cosmic-ray flux at the Earth at 3.66 GeV/nucleon. If we consider, for example, the10Be/9Be cosmic-ray ratio, the bigger it is at production in interstellar space (that
is, the ratio of corresponding cross sections), the smaller is the deduced surviving fraction of
10Be and the bigger the resulting cosmic-ray lifetime in the Galaxy. To draw final conclusions, however, it would be necessary to take into account the contributions from spallation of other cosmic-ray nuclei to the10Be flux and to perform a more accurate measurement at the Earth’s atmosphere.
Our data are accessible in the SPDS database [26].
Acknowledgments
We thank Professor W R Webber for useful correspondence. This work was partially supported by the Polish State Committee for Scientific Research under grant no 2 P03C 006 18.
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