1. INTRODUCTION 2. THE EXPERIMENT AND MEASUREMENT TECHNIQUES

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1 THE ASTROPHYSICAL JOURNAL, 508:940È948, 1998 December 1 ( The American Astronomical Society. All rights reserved. Printed in U.S.A. PRODUCTION CROSS SECTIONS OF FRAGMENTS FROM BEAMS OF 400È650 MeV PER NUCLEON 9Be, 11B, 1C, 14N, 15N, 16O, 0Ne, Ne, 56Fe, AND 58Ni NUCLEI INTERACTING IN A LIQUID HYDROGEN TARGET. I. CHARGE CHANGING AND TOTAL CROSS SECTIONS W. R. WEBBER,1 J. C. KISH, J. M. ROCKSTROH, Y. CASSAGNOU,3 R. LEGRAIN,3 A. SOUTOUL,3 O. TESTARD,3 AND C. TULL4 Received 1998 May 14; accepted 1998 June 9 ABSTRACT We have measured the charge changing cross sections from 10 individual beams of isotopes from 8 di erent nuclei between Be and Ni which were accelerated to energies from 400È650 MeV nucleon~1 at the SATURNE Accelerator in France in 1993 and These nuclei interacted in a 1.5 g cm~ thick liquid hydrogen target and the fragments were observed. This is the Ðrst use of a pure hydrogen target to measure cross sections that has a thickness approximating the amount of hydrogen traversed by cosmic rays in our Galaxy. Several of the beam charges such as 9Be, 11B, 15N, and Ne have not had their fragmentation cross sections measured previously. The cross sections from the 1C, 14N, 16O, 0Ne, 56Fe, and 58Ni beams are compared with earlier measurements by our group using a CH [ C target subtraction technique to determine the hydrogen cross sections. The overall agreement between the new measurements and the earlier measurements using CH [ C subtraction is excellent with a systematic consistency between measurements of 3%È5%. Using these new cross sections the predictions of both the B/C and Z \ (1È3)/Fe ratios at D1 GeV nucleon~1 now agree with HEAO measurements to D1%È%, thus obviating the need for truncation of the exponential path length distribution path length distribution that is expected from uniform propagation models. Also, these new charge changing cross sections along with the isotopic cross sections reported in paper two of this series, deðne the production of cosmic-ray beryllium and boron nuclei in the galaxy and also the secondary isotopes 10Be, 13C, 14N, 15N, 18O, and all of the Fe secondary isotopes to a level of precision of 3%È5% or better. These cross sections are important for determining the abundance of these rare isotopes and others in the cosmic-ray sources as well as tracing the detailed propagation history of cosmic rays in the Galaxy. These measurements also provide high precision cross sections for the study of the nuclear physics of the interaction process. Subject headings: atomic process È cosmic rays È methods: laboratory 1. INTRODUCTION In this paper we report measurements of the total inelastic charge changing and also the individual elemental charge changing cross sections from beams of 9Be, 11B, 1C, 14N, 15N, 16O, 0Ne, Ne, 56Fe, and 58Ni nuclei of energies between 400È650 MeV nucleon~1 interacting in a 1.5 gcm~ thick hydrogen target. This work is a continuation of our earlier systematic study of cross sections in CH, C, and He targets (Webber, Kish, & Schrier 1990a, 1990b; Ferrando et al. 1988). The principal objective of these studies is to determine cross sections appropriate for the interstellar production of secondary nuclei during the propagation of cosmic rays in the Galaxy, with the ultimate objective of understanding to a precision of a few percent, the source elemental and isotopic composition of cosmic rays and the related nucleosynthesis. New high-precision measurements of cosmic rays from spacecraft such as Voyager, Ulysses, and now ACE in the low-z charge range, particularly for the isotopes 10Be, 13C, 14N, 15N, and 18O as well as the Fe secondary isotopes of the charges Ca, Ti, V, Cr, and Mn, require that the appropriate cross sections be known to an accuracy of a few percent in order to fully 1 Astronomy Department, New Mexico State University, P.O. Box 30001, Las Cruces, NM Spectra Research Incorporated, Portsmouth, NH Service dïastrophysique, Cen. Saclay, CEDEX, France. 4 Lawrence Berkeley Laboratory, University of California, Berkeley, CA interpret the propagation history of cosmic rays and to derive the source composition of the rare isotopes such as 13C, 15N, 18O, 5Cr, 55Mn, and 54Fe. The systematics of the nuclear physics involved in the secondary fragmentation may also be examined using this data with the goal of obtaining a predictive capability that allows calculation of the measured and unmeasured cross sections as part of the several hundred cross sections needed to accurately solve the cosmic-ray propagation problem. In this new study the cross sections are measured directly in a liquid hydrogen target, instead of using a CH [ C target subtraction to obtain the hydrogen cross sections as was done previously. Thus the cross sections measured using these two methods may be compared.. THE EXPERIMENT AND MEASUREMENT TECHNIQUES The conðguration of detectors adopted for the cross section measurements at the SATURNE accelerator in France is shown in Figure 1. The telescope is very similar to the one used in our previous measurements (Webber et al. 1990a) but with several signiðcant improvements. It basically consists of three separate modules: a charge identiðcation module, an isotope identiðcation module, and a fragment module. For the study of charge changing cross sections here only the charge identiðcation module was used. It consists of a 7.5 cm diameter ] mm thick CaF scintillator (S/) placed directly in front of the target to identify the charge of the incoming particle, and two 3 mm thick CaF scintillators, one 7.5 cm in diameter (S1A) and 940

2 NUCLEI INTERACTING IN A LIQUID H TARGET. I. 941 FIG. 1.ÈOutline drawing of telescope conðguration used for SATURNE measurements of cross sections in 1993 and 1994 the other 1.7 cm in diameter (S1), both directly behind the target to measure the charge of the outgoing particle. These materials are chosen for their good linearity of light output versus energy loss and low interaction cross sections which resulted in 5% of the beam particles interacting in the three charge deðning counters. The resolution, p, of each of the S1A and S1 counters was less than 0.10 charge units for the low-z beam particles increasing to 0.15 charge units for Fe secondaries. S/ had a charge resolution of 0.15È0.5 charge units. A liquid H chamber containing 1.5 ^ 0.01 g cm~ of H was placed between S/ and S1A. This chamber, which approximates the average amount of Hydrogen traversed by cosmic rays in the Galaxy, was 0 cm long and 7.5 cm in diameter. This thickness resulted in 0.17 of the 1C beam particles interacting in the target increasing to 0.30 for Ne beam particles and 0.45 for 56Fe beam particles. Each beam was focused onto a spot cm diameter at the front of the target. For one run (the 9Be and 11B run) a 1C beam was fragmented by a 0.5 cm thick piece of CH in the beam line. The beam magnets were then tuned to focus all fragments from these interactions with A/Z \.0 ^ 0.10 at the front of the target (thus providing the individual 9Be and 11Be beams). For each beam the liquid H target was alternated with an identical empty H chamber. The no target runs typically showed 1%È3% interactions along the beam line (as compared to D17%È45% with the target in place). These interactions occurred in the 1 m of air in front of the target, in the empty chamber, and in the S/ counter. The large acceptance angle of the telescope (14 for the charge module, 7 for the entire telescope) ensures that essentially all fragments made in the target are detected in the telescope (e.g., Webber et al. 1990a). Each counter in the telescope was coupled to a 4096 channel analyzer (1 bits) and a data word of approximately 300 bits was created for each event. This data was stored event on separate backup hard disks and the analysis was carried out using an IBM-PC computer. 3. DATA ANALYSIS AND THE DETERMINATION OF THE CHARGE CHANGING CROSS SECTIONS The data analysis procedures used to derive the total cross sections and the partial charge changing cross sections follow very closely those of our earlier analysis (Webber et al. 1990a, 1990b). In the present experiment the analysis is simpler since no CH [ C target subtraction is required, only a subtraction for the target out data, which itself is a smaller fraction in the most recent runs with the liquid H target. Also the fraction of interactions in the telescope elements S1A and S1 is smaller in the newest runs leading to an altogether cleaner and more straight forward analysis. A cross plot of the signals from S1A and S1 for the Ne beam with the target in is shown in Figure. From this cross plot, histograms of the combined signals from the S1A and S1 scintillators, subject to a very simple consistency criterion between these two counters, are constructed for both the target in and the target out data. Sample histograms are shown for the 400 MeV nucleon~1 15N beam, the 430 MeV nucleon~1 Ne beam, and the 573 MeV nucleon~1 56Fe beams in Figures 3, 4, and 5. Here the overall charge resolution p is found to be 0.10È0.15 charge units and the peak to valley ratio between the fragment charges is at least 10:1 so that charge overlap is insigniðcant. Also the target out events for each charge are only a small fraction of the target in data (5% or less). To obtain the total charge changing cross sections from the data in these Ðgures we have used the expression FIG..ÈCross plot of events in S1A and S1 for the 430 MeV nucleon~1 Ne beam interacting in the hydrogen target. EOF on Ðle C: WE.T after events. Number of events passing criteria \ Number of SYNC errors \ 0.

3 94 WEBBER ET AL. Vol. 508 FIG. 4.ÈSame as above for a 430 MeV nucleon~1 Ne beam. Dotted curve shows target out data. FIG. 3.ÈDistribution of fragments in the charge detection module for a 398 MeV nucleon~1 14N beam interacting in the hydrogen target (Webber et al. 1990a) j \ X /ln (NT ÉNNT/NT ÉNNT), (1) ZT T B Z Z B where X is the target thickness in g cm~ \ 1.5 ^ 0.01, T N is the total number of incident beam nuclei, and N is B Z the total number of beam nuclei that survive passage through the target without changing charge (are in the beam peak) in both the target in, NT, and target out, NNT, cases. This simple expression is accurate to 1% when NNT is a small fraction of NT (Chen et al. 1994). Here p \ A /6.0 ZT t ] 10~4j, where A is the average mass number of the ZT t target and p is the total cross section expressed in milli- ZT barns. The observed numbers NT and NT (normalized to B Z NT) and the total charge changing cross sections we have B measured are given in Table 1. To derive the individual charge changing cross sections into the lower Z elements from these data we Ðrst normalized the number of events in the beam charge peak to be FIG. 5.ÈSame as above for a 573 MeV nucleon~1 56Fe beam TABLE 1 TOTAL CHARGE CHANGING CROSS SECTIONSa Energyb Total Counts Fragments Onlyc p(mbarn)(e) Beam Charge (MeV nucleon~1) (]105) (]105) Fragment Fraction p(mbarn)(e) CH [ C 7Li (C) 9Be (C) 11B (A) 1C (A) (173)(B) 14N (A) (7)(B) 15N (A) 16O (A) (3)(B) 0Ne (A) (98)(B) Ne (A) 56Fe (A) (650)(B) 58Ni (A) (737)(B) a Errors; A \^1.5%È.5%, B \^.5%È5%, C \^5%È10%. b At mid-point of target. c Not corrected for target out.

4 No., 1998 NUCLEI INTERACTING IN A LIQUID H TARGET. I. 943 equal for the target in and target out data and then subtracted the normalized no target events from the events with the target in for each of the fragment charges. The resulting relative abundances of the fragment charges were then corrected for interactions in the S1A and S1 counters (3% correction for Ne) and this corrected total number of events for each fragment charge is expressed as a fraction of the number of surviving beam nuclei N. The sum of all of these secondary fragment fractions, & Z N (Z)/N, must be equal to the same fraction used in equation Zf Zf (1) to B derive the total cross sections thus assuring that the sum of all the partial charge changing cross sections is equal to the total charge changing cross section. These partial fractions form the basis for determining the individual elemental cross sections. This calculation is discussed in Webber et al. (1990b). Basically, because the target is relatively thick (and thus secondary fragments may further interact before leaving the target), we have used a one dimensional di usion equation of the form dn Zf (x)/dx \[p Zf N Z (x)/m tar ] & Z;Zf [p ZZf N Z (x)/m tar ], () to correct for these additional interactions (m \ mass of tar target nuclei). Here term one on the right-hand side represents the loss of the fragment charge and term two represents the production of the fragment charge from both the beam charge through the term involving p (the pro- ZB,Zf duction cross sections we wish to measure), plus the additional secondary ÏÏ production from fragments with Z between the beam charge and the fragment charge with production cross sections p. Here N (x) is the Z:ZB,Zf Zf (observed) relative abundance of a fragment with charge Zf at a depth x and with a total cross section p, p is the Zf ZB,Zf direct cross section from the beam charge Z to charge Zf and N (x) is the abundance of the primary beam charge or Z secondary charge Z [ Zf. In this equation it is assumed that the cross sections are not changing rapidly with energy and the derived cross sections are appropriate to the midpoint energy in the target. This program requires estimates of all of the relevant cross sections leading to the production of a particular secondary fragment. These are in addition to the direct primary cross section p itself. For the initial estimate of these secondary cross ZB,Zf sections, each cross section is set equal to the initial value determined for each of the Z [ Z di erences. These secondary cross sections are then f changed interactively to approach the cross sections for the particular charge change in question as calculated using the parametric formulation based on our earlier data (Webber et al. 1990c) and the resulting changes in the desired primary direct cross sections are studied. For example, for Carbon from a 0Ne beam the total contribution of all secondary interactions is D15% of the direct primary contribution, 0Ne ] C. Half of this secondary contribution (7%) comes from the unmeasured cross sections which need to be calculated using the parametric formula. The remaining fraction (8%) comes from cross sections already measured with the beams intermediate between C and Ne such as 14N and 16O. An overall error of ^10% on each of these secondary cross sections introduces a maximum error of ^1.5% in the desired primary cross section. The derived charge changing cross sections for the 4 new beams (9Be, 11B, 15N, and Ne) at energies of 400 MeV nucleon~1 are shown in Table. In Table 3 we show the data for the 6 beams (1C, 14N, 16O, 0Ne, 56Fe, and 58Ni) for which we have earlier data using the CH [ C target subtraction technique (Webber et al. 1990b). The earlier cross sections are also shown along with the quoted error. The errors on our new results are both charge dependent and systematic (a ecting all charges approximately equally). A detailed estimate of these errors for our earlier study is given in Webber et al. (1990b). All of the types of uncertainties discussed in this earlier paper also a ect the present results, but are generally smaller in the recent study for the reasons discussed earlier. Since, for each of the secondary fragments at least 4 ] 104 events were observed, the statistical errors are much smaller than the systematic ones. An estimate of the overall experimental uncertainties in this type of measurement comes in part from a comparison of the new results with our earlier ones using the CH [ C target subtraction technique shown in Table 3. For the errors in the new data with the H target we conservatively take the same errors quoted for our earlier CH [ C measurements. 4. COMPARISON WITH PREVIOUS MEASUREMENTS One objective of this study is to compare our new results with our earlier results (Webber et al. 1990a, 1990b). The systematics of the cross sections and the further reðnements of the previously derived parametric Ðts to describe the cross sections of both measured and unmeasured cross sections as a function of energy, (e.g., Webber et al. 1990d) will be left to a later paper where the data from the Transport collaboration which has measured nearly 0 beam-energy combinations, will also be utilized (e.g., Knott et al. 1996). In Table 3 we have shown a comparison of our earlier results using a CH [ C target subtraction technique and the results using the hydrogen target as a function of the charge change *Z for 1C, 14N, 16O, 0Ne, 56Fe, and 58Ni nuclei. In each case the energies of the earlier runs and the more recent runs are slightly di erent so that energy dependent cross section e ects could account for some of the di erences. It is apparent that the agreement between the two sets of measurements is quite good. To make this comparison more quantitative we have taken the ratio of the new hydrogen target charge changing cross sections to the earlier CH [ C cross sections for the 38 secondary charge cross sections for the above 6 beam nuclei. The distribution of this ratio has a p \ 4.9%. The claimed error for these reactions varies from ^3% for the most accurately measured secondary charges to 10%È15% for those secondaries with the largest *Z. So overall we believe that these cross sections can be measured (repeatability) to the few percent necessary to interpret the higher precision cosmic ray data now becoming available from spacecraft. 5. USE OF THESE CROSS SECTIONS IN GALACTIC PROPAGATION MODELS: CHANGES IN THE PREDICTIONS OF THE B/C AND Z \ (1È3)/Fe RATIOS Here we propose to examine the e ect these new cross sections (particularly those from the 11B, 15N, and Ne beams) have on the predictions of the production of secondary nuclei as cosmic rays traverse matter in our Galaxy enroute from their sources to us. We concentrate on the B/C and Z \ (1È3)/Fe charge ratios in this paper. These ratios are commonly used as a reference to determine the

5 944 WEBBER ET AL. Vol. 508 TABLE INDIVIDUAL CHARGE CHANGING CROSS SECTIONS: NEW BEAMSa Energy Events NT Events (MeV nucleon~1) Beam Fragment (]104) (]104) Fraction p(mbarn)(e) Be Li (D) B Be (B) Li (D) N C (B) B (B) Be (C) Ne F (B) O (B) N (B) C (B) B (C) a Errors: B \^3%È5%, C \^5%È10%, D \^10%È0%. amount of material traversed by cosmic rays as a function of energy. This is possible because both B and the (Z \ 1È3) nuclei are believed to be almost completely absent in the cosmic ray sources and therefore are purely the result of interstellar fragmentation of heavier nuclei, mainly 1C and 16O in the case of B and 56Fe in the case of Z \ 1È3 nuclei. Once the material path length is determined from these two ratios it may be used to propagate other nuclei or isotopes using the same propagation model in order to compare predictions with observations and to derive, for example, the source abundance of these nuclei or isotopes. The B/C and Z \ (1È3)/Fe ratios are particularly useful because they have now been measured to a precision ^3% at energies of 1 GeV nucleon~1 and below thanks to HEAO measurements above 600 MeV (Engelmann et al. 1990) and the ISEE-3 measurements at 100È300 MeV nucleon~1 TABLE 3 INDIVIDUAL CHARGE CHANGING CROSS SECTIONS: PREVIOUSLY MEASURED USING CH [ C SUBTRACTION Energy Events NT Events p(mbarn)(e) (MeV nucleon~1) Beam Fragment (]104) (]104) Fraction p(mbarn)(e) CH [ C C B (B) 44.(B) Be (C) 14.(C) Li (D) N C (B) 75.0(B) B (B) 7.(C) Be (D) 13.5(D) O N (B) 73.7(B) C (B) 65.5(B) B (C) 4.3(C) Be (D) 9.8(E) Ne F (B) 46.6(C) O (B) 78.1(B) N (B) 60.6(B) C (B) 57.8(B) B (E) 13.6(E) Fe Mn (B) 136.8(B) Cr (B) 10.1(B) V (B) 85.5(B) Ti (B) 85.1(B) Sc (B) 59.5(C) Ca (B) 53.9(C) K (C) 7.8(C) Ar (C) 4.9(C) Cl (C) 16.1(D) S (C) 16.5(D) P (D) 7.1(E) Si (D) 9.3(E) Ni Co (B) 119.5(B) Fe (B) 101.4(B) Mn (B) 9.0(B) Cr (B) 96.3(B) V (B) 6.5(B) Ti (B) 58.5(B) Sc (C) 30.4(C) Ca (C) 3.7(C) K (C) 18.9(C) Ar (C) 19.8(C) Cl (D) 11.6(D) S (D) 1.5(D) a Errors: B \^3%È5%, C \^5%È10%, D \^10%È0%, E \^0%È30%.

6 No., 1998 NUCLEI INTERACTING IN A LIQUID H TARGET. I. 945 (Krombel & Wiedenbeck 1988; Leske 1993), the V oyager measurements at 100È300 MeV nucleon~1 (Lukasiak et al. 1994, 1997), and Ulysses measurements at these same energies (DuVernois, Simpson, & Thayer 1996). The propagation model we use here as a reference is the SACLAY version of the Leaky Box ÏÏ model with an exponential distribution of path lengths. For the cosmic-ray path length we take j \ 15.1 b gcm~ at rigidities less than 3.6 GV. The general esc expression for the path length is j \ j b(r/r )~a gcm~1, where R is the rigidity above which esc rigidity 0 0 dependent escape commences 0 and a is the rigidity dependent index of the escape length here taken to be \0.60. j is a constant which reñects an escape time independent 0 of rigidity below R. This expression closely corresponds to j \ 35.1 br~ above 3.3 GV, which was found to provide esc a good Ðt to both the B/C and Z \ (1È3)/Fe ratios above and below 1 GeV nucleon~1 as described in Webber (1993). The input spectra for all species are taken to be power laws in rigidity with an exponent equal [.36. The interstellar medium is assumed to be 90% hydrogen and 10% helium and the additional energy loss due to ionized hydrogen near the Galactic plane is included in the calculations (Soutoul, Ferrando, & Webber 1990). We Ðrst used a coherent set of cross sections which include a combination of measured cross sections and parametric calculations of Webber et al. (1990c, 1990d) for hydrogen and those of Ferrando et al. (1988) for helium, the so called original ÏÏ cross sections. We used a force Ðeld ÏÏ approximation for the solar modulation where the modulation is deðned as / \ 1 / rb (CV /i) Édr, where C is the ComptonÈGetting coefficient, 3 r0 V is the solar wind velocity, i is the di usion coefficient, and r is the modulation bound- B ary (Gleeson & Axford 1968). The value of / \ 700 MV at the time of the HEAO measurements. Next we changed only the cross sections using the newly measured values and leaving all other propagation and modulation parameters the same. With the addition of the new cross sections we Ðnd that directly measured cross sections now account for greater than 95% of all the fragmentation to B and Z \ (1È3) nuclei from heavier nuclei. In Table 4 we illustrate the production of B by various heavier elements using a full propagation calculation. It is seen that roughly 50% of all B is produced by 1C and 5% by 16O. As noted earlier over 95% of the production into B has been measured either in this paper or in earlier measurements. The new cross sections decrease the total B production by %È3% below the original ÏÏ cross sections at energies of 1 GeV nucleon~1 and below. The predictions using the new cross sections are shown for solar modulation values of / \ 300, 500, and 700 MV as solid lines in Figure 6. For the six HEAO data points near 1 GeV nucleon~1 the agreement between the predictions and measurements is D1%È%. For the lower energy data points, which are a strong function of the modulation parameter /, the predictions lie % above the V oyager points for an assumed modulation level of 460 MV and 9% above the ISEE point taking a modulation level of 700 MV. For the Ulysses point, if we take the quoted modulation level of 840 MV (DuVernois et al. 1996), the prediction is 5% above the measurement. However, using the same prescription for determining the solar modulation level for the Ulysses data as was used for the other data points and as described by Ferrando et al. (1991, who presumably used a di erent IS He spectrum than the one used by the Ulysses experimenters), we Ðnd a value of / \ 480 MV for the Ulysses data, which in this case is only D5% below the predictions. This sensitivity to the modulation level is discussed later in this paper. Meanwhile, the situation for the Z \ (1È3)/Fe ratio is shown in Figure 7. The new cross sections increase the total production of the Fe secondaries by D3% at D600 MeV nucleon~1. Here the same path length that provides a good Ðt to the B/C ratio data is seen to also provide a reasonable Ðt to the Z \ (1È3)/Fe ratio measurements at both higher and lower energies. For the Ðve HEAO data points near 1 GeV nucleon~1 the Ðt between prediction and experiment is again within 1%È%. For the lower energy Voyager data points the prediction is 5% below the measurement. For the ISEE data point the prediction is D% higher than the measurement and for the Ulysses data point the prediction is D1% above the data point for a modulation level of 840 MV as quoted by the authors, but only 1% above the measurement if our estimated modulation level of 480 MV for the Ulysses data is used. So overall using the new cross sections we are able to Ðt HEAO observations and predictions of both the B/C and Z \ (1È3)/Fe ratios near 1 GeV nucleon~1 to an accuracy of 1%È% using this version of the Leaky Box propagation model. Previously it has not always been possible to TABLE 4 PRODUCTION OF B AT 600 MeV NUCLEON~1 p(mbarn) *p Fractional Contribution Transition (decayed) (percent) (percent) B11 ] C1 ] C13 ] N14 ] N15 ] O16 ] Ne0 ] Ne ] Mg4 ] Si8 ] FIG. 6.ÈMeasured and predicted cosmic-ray B/C ratio as a function of energy. Only cosmic-ray measurements of this ratio with a precision of 3% or less are used. Filled circles: Engelmann et al. (1990); open circles: I: Krombel & Wiedenbeck (1988); U: DuVernois, Simpson, & Thayer (1996); V1 and V: Lukasiak et al. (1994). The solid curves are predictions for j \ 15.1 ] b below 3.6 GV and values of / \ 300, 500, and 700 MV, using esc the new cross sections.

7 946 WEBBER ET AL. Vol. 508 FIG. 7.ÈMeasured and predicted Z \ (1È3)/Fe ratio as a function of energy. Symbols and lines are the same as Fig. 6, except I refers to Leske (1993) and V1 and V to Lukasiak et al. (1997). simultaneously predict both ratios. This has led to the introduction of the concept of a truncation of the PLD of cosmic rays wherein the nominal equilibrium exponential path length distribution is assumed to be deðcient in short path lengths as could be physically caused by an absence of nearby sources, for example (see Lezniak & Webber 1979; Garcia-Munoz et al. 1987). Recently Webber (1993) found the need for this truncation much reduced, based on the new cross sections published in 1990, and now the additional new cross sections presented here have further reduced the deviations of the possible cosmic-ray path length distribution from a pure exponential, thus placing more stringent limitations on the uniformity of the distribution of cosmic-ray sources and the propagation parameters. Di erences between predictions and measurements at low energies still exist at the 5%È10% level, but these di erences are strongly inñuenced by solar modulation conditions as described below. The interplay between solar modulation and propagation e ects at low energies is shown in Figures 8 and 9. These Ðgures show the B/C and Z \ (1È3)/Fe ratios, respec- FIG. 8.ÈB/C ratio measurements and predictions at 1 GeV nucleon~1 and lower energies plotted as a function of the assumed solar modulation level. The symbols for the measurements are the same as in Figs. 6 and 7. The numbers beside the symbols and lines refer to the energies in MeV nucleon~1. The dashed line shows the correction of the estimated modulation level for the Ulysses data using the procedure described in this paper. FIG. 9.ÈZ \ (1È3)/Fe ratio measurements and predictions at 1 GeV nucleon~1 and below plotted as a function of the assumed solar modulation level. The symbols are the same as Fig. 8. tively, with the ratios now being plotted as a function of the value chosen for the solar modulation parameter, /. The predictions for a Galactic propagation model with a path length \ 15.1 b at low energies are shown as solid lines for various energies at the Earth. The low-energy behavior of these predictions is e ectively anchored by the requirement that the HEAO data at D1 GeV nucleon~1 be predicted correctly, and by the fact that these HEAO values for both the B/C and Z \ (1È3)/Fe ratios are essentially independent of the modulation level. Therefore, given the HEAO values for these ratios at 1 GeV nucleon~1, the only way the ratios at low energies can be changed is by changing either the path length from its nominal value of 15.1 b or by changing the modulation parameter. A change in the value of path length by ^10% results in a change D4% in the B/C ratio at D100 MeV nucleon~1 and a change in the Z \ (1È3)/Fe ratio by D3% at D00 MeV nucleon~1.so these ratios are rather insensitive to path length changes and much larger changes in the ratios (at a Ðxed energy) can be achieved by changing the modulation parameter. The choice of the modulation parameter to assign to a measurement is generally left to the person making the measurement and di ers widely. A commonly accepted procedure would greatly reduce the wide disparity of path lengths and modulation parameters reported in the literature. For this we recommend using an estimated IS He spectrum and the measured 180È450 MeV nucleon~1 He intensity which is widely available from IMP and V oyager measurements (e.g., McDonald et al. 199). This is the method used by Ferrando et al. (1991), who used an IS helium spectrum equal to 1.0 particle m~ sr~1 s~1 at D300 MeV nucleon~1 (the midpoint of the above energy interval) and a simple force Ðeld modulation calculation to determine the 180È450 MeV nucleon~1 He intensity and therefore to determine /. The intensity of 180È450 MeV nucleon~1 He is a single valued function of / for both positive and negative solar magnetic polarity cycles and for di erent heliocentric radii as well as is illustrated by Figure 10 which shows this intensity as a function of / measured at the Earth by IMP and at various interplanetary radii as measured by Voyager and Pioneer 10 from 1978È1996 (McDonald et al. 199).

8 No., 1998 NUCLEI INTERACTING IN A LIQUID H TARGET. I. 947 FIG. 10.ÈMeasured intensity of 180È450 MeV nucleon~1 He nuclei at IMP (open circles), at Voyager (solid circles), and at Pioneer 10 (crosses)is shown as a function of the calculated modulation parameter, /. The calculations are shown for IS intensities of 1.5, 1.0, and 0.67 particles MeV~1 nucleon~1 ] Sr ] S ] M at 300 MeV nucleon~1. Data favors an IS intensity D0.90. The importance of standardizing the entire propagation and modulation procedure is illustrated by Figure 11 which shows the propagation path length used in this paper and several other recent papers appearing in the literature. The path length used by Stephens & Streitmatter (1998) is very similar to that used in this paper with the small di erences accounted for by the new cross sections used here and the more accurate propagational model used by Stephens & Streitmatter (1998). The di erences between these two IS path lengths and those of Heinbach & Simon (1995) and DuVernois et al. (1996) appear at both higher and lower energies and are difficult to understand. For example, at D1.5 GeV nucleon~1, where solar modulation e ects play a minimal role, the IS path length obtained by Heinbach & Simon (1995) is 10.0 g cm~, and DuVernois et al. (1996) Ðnd a value of 9. g cm~, while in this paper we Ðnd 1.6 g FIG. 11.ÈValue of j obtained from a Ðt to the B/C ratio from (1) this study. Also shown are the esc values of j from the work of () Stephens & Streitmatter (1997), and from two earlier esc studies, (3) DuVernois et al. (1996) and (4) Heinbach and Simon (1995). cm~, a di erence of D30% for what appears to be the same IS medium. A small part of this di erence could possibly be due to di erent cross sections, although all authors seem to use similar cross sections. A much larger e ect could be related to the presence of IS helium. In their original calculation using new measurements of cross sections in He targets, Ferrando et al. (1988) noted that the e ective IS path length in g cm~ in a medium containing 10% helium and 90% hydrogen by number had to be increased by at least 0% over that for pure hydrogen. This is because the He cross sections for B and Z \ (1È3) nuclei production are much less than would be predicted from a simple Z scaling of the hydrogen cross sections to helium with the result that the IS medium is e ectively diluted for the production of these secondaries as a result of the presence of He. In the Heinbach & Simon (1995) calculations, a separate formula for the He cross sections is used (which does not seem to predict the measured He cross sections correctly) and this alone could possibly account for the difference in IS path lengths at 1.5 GeV nucleon~1. Inthe propagation calculation by DuVernois et al. (1996), it is not speciðcally indicated how the He cross sections are scaled from the hydrogen ones, however, we note that the IS path length used by these authors is identical to the one used earlier by Garcia-Munoz et al. (1987). This original path length could not have incorporated the new He cross sections by Ferrando et al. (1988) since they were made at a later time. So again the He cross sections could play a major role in the di erent path lengths used by these authors. At energies below D1 GeV nucleon~1, other e ects must play a role in the di erences in path lengths obtained by the various workers because the di erences now become a factor of or greater as noted by Stephens & Streitmatter (1998). Here the solar modulation parameter chosen to Ðt the data becomes important and indeed even the choice of data used in the Ðt of the B/C and Z \ (1È3)/Fe ratios becomes important. For example, Heinbach & Simon (1995) Ðt a composite B/C ratio composed of many measurements along with an average solar modulation parameter equal to 490 MV and an interstellar path length DR which decreases faster at low energies than the Db dependence used in this paper. The use of these particular parameters is possible because the data used in the Ðt by Heinbach & Simon (1995) does not contain the higher precision lowenergy data now available and used in this paper. In the case of the smaller IS path length at low energies obtained by DuVernois et al. (1996), it appears that the choice of a larger modulation parameter for a given data set (presumably as a result of a higher estimated IS helium intensity) requires that to simultaneously Ðt the HEAO data points and the low-energy Ulysses data points in Figures 8 and 9, a much steeper fall o in the IS path length at low energies is needed. In spite of these large di erences in interstellar path lengths and solar modulation parameters between experimenters, the precision of the new Ðt to the data and the accuracy of the B/C and Z \ (1È3)/Fe data points themselves used in the Ðtting for the analysis in this paper means that Ðts to other observed abundance ratios in the same charge and energy ranges like the 13C/1C and 18O/16O ratios which are being made from new spacecraft experiments, can be made to the same level of accuracy (e.g., ^3%) as the Ðt to the B/C and Z \ (1È3)/Fe ratios using the tracer isotope technique of Stone & Wiedenbeck (1979),

9 948 WEBBER ET AL. provided one is careful to use a self-consistent set of propagation and modulation parameters that Ðt these ratios. 6. SUMMARY AND CONCLUSIONS We have measured the total and the individual charge changing cross sections from individual beams of 10 isotopes of 8 di erent charges ranging from 9Be to 58Ni at the SATURNE accelerator in France. These cross sections were measured at beam energies from 400 to 600 MeV nucleon~1 ina1.5gcm~ thick liquid hydrogen target which approximates the amount of interstellar hydrogen traversed by cosmic rays. Several of these isotopes such as the 9Be, 11B, 15N and Ne beams have had their cross sections measured for the Ðrst time. The other new cross sections measured in a pure hydrogen target are found to agree well with those measured earlier using a CH [ C subtraction technique, the standard deviation of the two sets of measurements is 4.9% for 38 di erent secondary cross section products from the 1C, 14N, 16O, 0Ne, 56Fe, and 58Ni beams. These new cross section measurements lead to predictions of both of the B/C and Z \ (1È3)/Fe ratios that agree with the precise HEAO measurements at D1 GeV nucleon~1 to within 1%È% using the same IS path length. This means that a truncation of the equilibrium exponential cosmic-ray path length distribution for small path lengths is unnecessary above 1 GeV nucleon~1. These new cross section measurements along with spacecraft measurements of the reference ÏÏ B/C and Z \ (1È3)/Fe ratios deðne the production of secondary cosmic rays D1 GeV nucleon~1 and below in the Galaxy to an accuracy of 3%È5%. This value for the secondary production can be used along with an interstellar path length and appropriate modulation parameters to interpret the observed abundances of radioactive isotopes such as 10Be and to determine more precise source abundances of rare isotopes such as 13C, 15N, and 18O as well as Fe secondary isotopes (see our companion paper on isotopic cross sections by Webber et al. 1998), to the same level of accuracy as the reference ratios using the tracer technique suggested by Stone & Wiedenbeck (1979). The authors appreciate the efficient and friendly support of the sta of the SATURNE accelerator during these runs. The US portion of these runs was supported under NASA grant NAGW-016. REFERENCES Chen, C. X., et al. 1994, Phys. Rev. C, 49, 300 Lukasiak, A., McDonald, F. B., & Webber, W. R. 1997, ApJ, 488, 454 DuVernois, M. A., Simpson, J. A., & Thayer, M. R. 1996, A&A, 316, 555 McDonald, F. B., Moraal, H., Reinecke, J. P. L., Lal, N., & McGuire, R. E. Engelmann, J. J., et al. 1990, A&A, 33, , J. Geophys. Res., 97, 1557 Ferrando, P., et al. 1988, Phys. Rev. C, 37, 1490 Soutoul, A., Ferrando, P., & Webber, W. R. 1990, 1st Int. Cosmic Ray Ferrando, P., Lal, N., McDonald, F. B., & Webber, W. R. 1991, A&A, 47, Conf. (Adelaide), 3, Stephens, S. A., & Streitmatter, R. E. 1998, ApJ, 505, 66 Garcia-Munoz, M., et al. 1987, ApJS, 64, 69 Stone, E. C., & Wiedenbeck, M. E. 1979, ApJ, 31, 606 Gleeson, L. J., & Axford, W. I. 1968, ApJ, 154, 1011 Webber, W. R. 1993, ApJ, 40, 188 Heinbach, U., & Simon, M. 1995, ApJ, 441, 09 Webber, W. R., Kish, J. C., & Schrier, D. A. 1990a, Phys. Rev. C, 41, 50 Knott, C. N., et al. 1996, Phys. Rev. C, 53, 347 ÈÈÈ. 1990b, Phys. Rev. C, 41, 533 Krombel, K. E., & Wiedenbeck, M. E. 1988, ApJ, 38, 940 ÈÈÈ. 1990c, Phys. Rev. C, 41, 547 Leske, R. A. 1993, ApJ, 405, 567 ÈÈÈ. 1990d, Phys. Rev. C, 41, 566 Lezniak, J. A., & Webber, W. R. 1979, Ap&SS, 63, 35 Webber, W. R., et al. 1998, ApJ, in press Lukasiak, A., Ferrando, P., McDonald, F. B., & Webber, W. R. 1994, ApJ, 405, 567