Production of residual nuclei by α-induced reactions on C, N, O, Mg, Al and Si up to 170 MeV

~

Pergamon

0969-8043(94)00124-3

Appl. Radiat. lsot. Vol.46, No. 2. pp. 93-112, 1995 Copyright ~D 1995ElsevierScienceLtd Printed in Great Britain.All rights reserved 0969-8043/95 $9.50+0.00

Production of Residual Nuclei by a-Induced Reactions on C, N, O, Mg, A1 and Si up to 170 MeV H.-J. L A N G E 1, T. H A H N 1, R. M I C H E L I*, T. S C H I E K E L 2, R. ROSEL'-, U. H E R P E R S : , H.-J. H O F M A N N 3, B. D I T T R I C H - H A N N E N 3, M. S U T E R 3, W. W O L F L I 3 a n d P. W. K U B I K 4 ~ZentrumFfir Strahlenschutz und Radio6kologie, Universitfit Hannover, Am Kleinen Felde 30, D-30167 Hannover, Germany, 2AbteilungNuklearchemie, Universit~itzu Krln, Otto-Fischer-Str. 12-14, D-50674 K61n, Germany, 3Institut fiir Teilchenphysik, ETH Hfnggerberg, CH-8093 Ziirich, Switzerland and 4paul Scherrer Institut, c/o ETH H6nggerberg, HPK CH-8093 Z/irich, Switzerland (Received 31 August 1994)

In order to provide thin-target cross sections as a basis for model calculations of the interactions of solar and galactic a-particles, irradiation experiments with a-particles were performed at the injector cyclotron at PSI/Villigen (Emax=ll9.7MeV) and at the isochronous cyclotron JULIC at KFA Jiilich (Emax---170.5 MeV). The stacked foil technique was used to investigate residual nuclide production from C, N, O, Mg, AI and Si. The product nuclides 7Be, ~-'Na,'-4Naand 28Mgwere measured by ~-spectromety, ~°Be and 26A1by accelerator mass spectrometry. The new data are compared with earlier measurements and analyzed using hybrid model of preequilibrium reactionsl

Introduction Cosmogenic nuclides are produced in interactions of solar and galactic cosmic ray particles with matter. They can be employed as stable or radioactive natural tracers to investigate a wide variety of geo- and cosmochemical processes. In particular, they can be used to describe the cosmic ray exposure history of lunar samples, meteorites and cosmic dust (Geiss et al., 1962; Lal, 1972; Reedy et al., 1983; Vogt et al., 1990). They provide the only tools with which the ancient solar activity as well as the spectral distributions and intensities of solar and galactic cosmic rays can be monitored on time scales of up to billions of years. Alpha-particles make up about 10-12% of the galactic and 2-10% of the solar cosmic ray particles (e.g. Simpson, 1983), and thus contribute significantly to the production of cosmogenic nuclides in extraterrestrial materials as well as in the earth's stratosphere. In any modelling of cosmic ray interactions with matter they have to be adequately taken into account. But, as of today, there was just one report dealing explicitly with solar-cosmic-a-particleinduced production of cosmogenic nuclides in lunar surface materials (Lanzerotti et al., 1973). In all existing models describing the production of cos*Author for correspondence.

mogenic nuclides in terms of particle fields inside an irradiated object, solar and galactic c~-particles are either not taken into account at all (Reedy and Arnold, 1972; Yokoyama et al., 1972; Michel and Brinkmann, 1980a; Michel et al., 1982) or they are accounted for with only rough estimates of relative energy input (Michel et al., 1991), only. The reason for this neglect is exclusively due to the lack of thin target cross sections for the relevant nuclear reactions, which are a necessary prerequisite for any adequate modelling of the interactions of cosmic a-particles with matter. Until recently, reliable data were available for just a few reactions. For some reactions the required excitation functions were poorly known, but for most no data exist at all. Therefore, we extended our earlier studies of ~-induced reactions on A1, Ti, V, Mn, Fe, Co and Ni for ~-energies up to 170.5MeV (Michel and Brinkmann, 1980b; Michel et al., 1980, 1983a, b) to investigate the production of radionuclides from the geo- and cosmochemically important target elements C, N, O, Mg, A1 and Si. This study covers the most important energies of solar ~-particles. The nuclides ~Be, 22Na, 24Na and -'8Mg were measured by y-spectrometry, and the long-lived radionuclides ~°Be, h/2=1.51 Ma (Hofmann et al., 1987), and 26A1, t~/2=716 ka (Samworth et al., 1972), by accelerator mass spectrometry (AMS). 93,

H.-J. Lange et al.

94

The new excitation functions provide the data to judge the quality of a priori calculations of cross sections of a-induced reactions. With this comparison it should be possible to decide whether the large body of data needed for an adequate modelling of cosmic a-interactions with matter can be sufficiently supplied by nuclear reaction theories or whether the data needs can only be fulfilled by detailed experimental work. Therefore, the new cross sections are analyzed in the framework of the hybrid model of preequilibrium reactions (Blann, 1971) using the code ALICE LIVERMORE 900 (Blann, 1990).

Experimental The stacked foil technique was used in this investigation. Irradiation experiments were performed at the injector cyclotron (Philips cyclotron) at PSI/Villigen (E~,ax= 119.7 MeV) and at the isochronous cyclotron JULIC at K F A JiJlich (Em,x= 170.5 MeV). The experiments covered a total of ten different elements (6 ~99.999% for Si and SiO2 and >99.5% for Si3N4). At PSI, 11 stacks were irradiated, each consisting of one target material and up to ten sets of single or triplicate 0.036 mm A1 foils for flux monitoring and energy control in front of and at different positions in the stacks. At K F A Jiilich, five stacks were irradiated. Three of them were of the same type (one target material plus A1 monitor foils) as those used at PSI. The fourth and fifth were made of combinations of C, Mn/Ni, Cu, A1 on the one hand and Mg, A1, Zr, Nb on the other. Also these stacks had the triplicate 0.036 mm A1 foils in front of each stack. The stacks were irradiated between 1.25 h and 7.5 h with beam currents between 26 and 60 nA. The constancy of the beam currents was controlled by Faraday cup measurements. The beam currents were determined by Faraday cup measurements at the JULIC accelerator. At PSI, no absolutely calibrated Faraday cup was available. Therefore, the a-fluxes were determined from 22Na activity in the middle foil

of the first set of three thin A1 foils in front of each stack, taking the reaction -~TAl(a,4p5n)2~-Naas monitor reaction and adopting a cross section of 36.5 mb at E = 119.7 MeV. This cross section was obtained by interpolating those recommended by Tobailem et al. (1971) and Tobailem and de Lassus St Genies (1981). The excitation functions determined from the irradiations at the two accelerators overlap between 120 and 80 MeV. Here, the cross sections are in excellent agreement, demonstrating the consistency of the flux determinations. As in our earlier work (Michel and Brinkmann, 1980b; Michel et al., 1980, 1983a, b) the a-energies in the individual target foils were calculated according to Williamson et al. (1966). The flux gradients inside the stacks were calculated taking into account nuclear absorption and angle straggling. The uncertainties given for the a-energies in the individual targets take into account the finite thickness of the foils as well as the energy straggling calculated according to Bohr's approximation (Bohr, 1915). After the irradiations, the stacks were transported to Cologne and Hannover within 24 h. There, they were repeatedly measured y-spectrometrically using several Ge(Li) and high-purity Ge detectors. The measurements and the evaluational procedure were the same as used earlier (Michel and Brinkmann, 1980b; Michel et al., 1980, 1983a, b). After the 7-spectrometrical investigations, ~°Beand 26A1were chemically extracted from the targets to be processed for AMS measurements. The separation schemes used are described elsewhere (Dittrich et al., 1990a, b; Bodemann et al., 1993). ~°Be/gBe and 26A1/ZTA1ratios were measured at the PSI-ETH AMS facility at Zfirich. A description of the AMS technique is given elsewhere (Suter et al., 1984). The AMS standards used were the same as in our earlier work (Dittrich et al., 1990a, b; Bodemann et al., 1993), i.e. the standard "$433" for ~°Bewith a l°Be/gBe ratio of (9.31 _+0.23) • 10-~ (Hofmann et al., 1987) and the standard "A19" for 26A1 with a 26A1/27A1 ratio of (1.19 _+0.06) • 10-9 (Sarafin, 1985). The nuclear data needed for the calculation of cross sections (Table 1) were taken from the following sources: half-lives from the Chart of Nuclides (Seelmann-Eggebert et al., 1981), energies and branching ratios of y-rays from the compilation of Reus and Westmeier (1983). Q-values were calculated using the data of Keller et al. (1973).

Table 1. Nuclear decay data used for the determinationof cross sections. Half-lifeswere taken from Chart of Nuclides(SeelmannEggebertet al., 1981). ~,-energiesand -intensitiesweretakenfromReus and Westmeier(1983) Nuclide Halfqife E (keV) I (%) E (keV) 1 (%) 28Mg 20.90h 400.6 35.9 941.7 35.9 1342.2 54.0 1778.8 100 -'4Na 14.96h 1368 100 2ZNa 2.602yr 1274 99.9 7Be 53.29d 477 10.4

Production of residual nuclei

Experimental Uncertainties Firstly, there were strong recoil losses in the stack c o n t a i n i n g c a r b o n foils which was irradiated at Jfilich. Single C foils with a thickness o f 0.1 m m h a d been placed between M n / N i a n d Cu foils. As suggested by B o u c h a r d a n d Fairhall (1959), we corrected the 7Be activity o f the C foil with the m e a s u r e d 7Be activity in the succeeding M n / N i respective Cu foil a s s u m i n g the p r o d u c t i o n of 7Be in M n , N i a n d C u to b e negligible. Recoil losses o f up to 3 0 % were found. W i t h this correction, the d a t a from stacks irradiated at PSI a n d at K F A agreed within experimental errors in the overlapping energy region. F o r the reaction C(a, 4pxn)I°Be in the stack irradiated at K F A , the recoil losses were calculated f r o m the cross sections in the overlapping energy region of the " P S I " a n d " K F A " stacks. T h e recoil loss o f ~°Be t u r n e d out to be a b o u t 20%. The cross sections o b t a i n e d for higher energies o f the " K F A " stack were corrected for this recoil loss. A n o t h e r t r a n s p o r t process was observed in the SiO~ stack irradiated at PSI. Strong discrepancies were observed between the cross sections m e a s u r e d for the reaction Si(ct, 5pxn)22Na f r o m this stack a n d f r o m the a n a l o g o u s " p u r e Si" stack, also irradiated at PSI. T h e cause was f o u n d to be thermodiffusion o f 22Na in SiO2 because o f t o o high a t e m p e r a t u r e in the SiO2 stack d u r i n g the irradiation. A detailed description o f the p r o b l e m o f thermodiffusion o f 22Na in q u a r t z d u r i n g i r r a d i a t i o n can be f o u n d elsewhere ( B o d e m a n n et al., 1993). F r o m the cross sections for Si(a, 5pxn)Z2Na o b t a i n e d from the SiO2 stack, a m a x i m u m t e m p e r a t u r e in the stack o f 400°C was estimated. The results o b t a i n e d f r o m this stack were therefore disregarded. The errors q u o t e d for the cross sections include the uncertainties in the d e t e r m i n a t i o n o f the n u m b e r o f target atoms, generally 2 % , a n d the reproducibility o f repeated m e a s u r e m e n t s o f m o n i t o r foils (1.5-3.5%). F o r the 7-spectrometrical measurements, uncertainties in the efficiency c a l i b r a t i o n o f the G e a n d Ge(Li) spectrometers o f 5 % , the statistical errors o f the net-peaks a n d the reproducibility o f repeated m e a s u r e m e n t s were t a k e n into account. T h e latter estimates the uncertainties o f peak evaluation a n d sample positioning at the detector. F o r ~°Be a n d 26A1, the errors o f the weight o f the carrier material (0.2%) a n d o f the g r a d u a t e d pipette (0.2%) a n d the errors o f the A M S measurements, i.e. statistical c o u n t i n g errors, reproducibility o f repeated m e a s u r e m e n t s as well as calibration uncertainties ( 3 - 1 3 % ) , were t a k e n into account. F o r the p r o d u c t i o n o f 7Be a n d ~°Be f r o m SiO_, a n d Si3N4 targets, the c o n t r i b u t i o n o f Si was corrected using the respective cross sections m e a s u r e d in this work. F o r some reactions, e.g. M g ( a , 3pxn)-'ZNa, interferences from fast secondary n e u t r o n s were observed, since the m e a s u r e d cross sections extend below the lowest thresholds o f a - i n d u c e d p r o d u c t i o n modes.

95

Table 2. Experimentalcross sections for the production of TBeand "~Be from carbon, nitrogen and oxygen by o-induced reactions Energy Cross section Energy Cross section (MeV) (rob) (MeV) (rob) C~. 4pxn)TBe N(~. 5pxnl~Be 78.7_ 1.0 20.8 __.1.5 44.2_+ 1 7 . 2 7.0_+0.5 83.6_+1.1 26.7+1.9 71.9-t-11.5 21.8___2.1 89.7 5:1.0 33.2-+2.4 92.0-I-_9.6 29.2 __.2.2 92.3 ! 1.0 33.5 5:2.4 108_+8.7 28.8 ___2.2 96.6_+0.9 33.2_+2.4 1095:8.3 31.0___2.3 98.9_+ 1.3 30.3 _+3.2 124_+7.9 29.0_+2.4 98.9_+0.9 31.9__.2.3 138x 7.2 27.0___2.0 103_+0.8 33.6-+ 2.4 151 _+6.7 26.2___2.2 105_+0.8 33.55:2.4 163 +6.3 26.7_+2.1 107_+1.2 31.6__.3.3 110+_0.8 32.5+_2.3 N(ot, 5pxnl~°Be 113+_ 1.2 32.4_+5.5 115-+0.7 32.6_+2.3 44.2_+ 17.2 0.17_+0.02 1175:0.7 28.9~ 2.0 71.9"1-11.5 1.235:0.09 120_+1.1 31.8_+3.4 92.0___9,6 2.93-+0.29 126_+1.0 32.1 _+3.3 109-+8.3 3.18_+0.72 132_+1.0 33.8! 3.4 124+ 7,9 4.36_+0.35 137_+0.9 36.7_+3.5 151 -+6.7 5.26_+0.41 143_+0.9 34.0 _+3.8 149_+0.8 31.75:3.5 O(~,6pxn)~Be 155_+0.7 38.3-+3.7 159+_0.7 38.0_+3.5 53.8 + 13.2 5.3 5:0.4 165-+0.6 35.95:3.7 76.1_+10.1 12.8_+1.4 81.1 + 9.9 16.1 _+1.6 C(a, 4pxn)l°Be 94.0 _+8.6 17.2___1.3 98.8 +9.0 18.55:1.5 78.7+ 1.0 3.47±0.32 110_+7.7 18.4+ 1.4 80.9_+1.0 5,03+0.46 115+8.0 21.1 -+ 1.7 82.2___1.1 4.585:0.32* 128__.6.9 21.5__.1.6 89.7+ 1.0 5.12-1-0.36" 141 _+6.4 21.9_+ 1.6 96.6_+0.9 6.50-t-0.60 153_+6.1 22.35:1.6 98.9_+ 1.2 6.44_+0.56 164_+5.5 21.35:1.7 103_+0.8 6.70_+0.61 107+ 1.2 7.14___0.61 0(o:, 6pxn)J°Be 110-t-0.8 7.28-t-0.67 112+0.7 5.63__.0.40* 53.8_+13.2 0.12_+0.01 113_+1.2 7.56_+0.65 76.1_+10.1 1.15+0.10 120_+1.1 7.335:0.63 94.0+8.6 2.13_+0.16 137_+0.9 8.68_+0.74 110_+7.7 2.46_+0.19 165_+0.6 9.38 _+0.76 141 _+6.5 4.05 _+0.39 153-+6.2 4.35 5:0.40 164_+5.6 3.81 _+0.31 *Not yet corrected for recoil loss.

These contributions, which significantly affected only the n e a r - t h r e s h o l d data, were subtracted f r o m the m e a s u r e d ones a s s u m i n g c o n s t a n t n e u t r o n backg r o u n d over the entire stacks. F o r all corrections, the p r o p a g a t i o n o f errors o f the m e a s u r e d cross section a n d of the corrections was properly t a k e n into account.

Experimental Results A total o f 24 detailed excitation functions is presented describing the p r o d u c t i o n by a-induced reactions o f 7Be a n d 1°Be from carbon, nitrogen a n d oxygen (Table 2), o f 7Be, 2-~Na, -~4Na a n d -'SMg from m a g n e s i u m (Table 3), a l u m i n u m (Table 4) a n d silicon (Table 5) a n d o f ~°Be a n d ~-6A1from Mg, A1 a n d Si (Table 6). T h e new d a t a (Tables 2-6) o f the different irradiation experiments are fully consistent results for the different i r r a d i a t i o n experiments. The individual excitation functions consist o f u p to 28 data points. They permit a detailed discussion o f all earlier

96

H.-J. L a n g e

measurements. The internal consistency of our new data with the earlier work of our group (Michel and Brinkmann, 1980b; Michel et al., 1980, 1983a, b) was checked using the data for the target element manganese which had been irradiated in the recent series of experiments as well as earlier (Michel et at., 1983b). Though these data are not presented here, we can state that the results agreed within experimental errors, at worst within 10%. Target Elements Carbon, Nitrogen and O x y g e n Generally, there are only a few earlier reports on cross section measurements for most of the reactions dealt with in this work, except for the target element aluminum. The data for this element permit a

Table 3. Experimentalcross sections for the production 7Be, 22Na, 24Na and 28Mg from magnesium by ~-induced reactions Energy (MeV) 34.6+__2.3 44.3 _+2.0 52.4_+ 1.9 62 ~ _+ 1.6 70.8_+ 1.3 78.3 *__1.4 86.7± 1.2 92.9 _+ 1.6 94.4 _+ 1.4 96.8__, 1.2 105+_ 1.4 106_+ 1.0 107 _+1.4 115+--0.7 117_+ 1.2 118_+ 1.3 130_+ 1.2 132 + 1.2 143__, 1.0 144_+ 1.0 152+-0.9 153 ! 0 . 9 163 +-0.8 164±0.7

11.3 ~4.3 17.9 m 3.4 23.0 _+2.9 34.6 _+2.3 44,3 _+2,0 62.8 -+_1.5 70.8 _+ 1.3 78.3_+ 1.4 88.3 _+ 1.0 92.9_+ 1.6 94.4± 1.4 96.8 _+ 1.1 105_+ 1.4 106_+0.9 107 _+1.4 115_+0.7 117_+ 1.2 118 _+ 1.3 130 +- 1.2 132 _+ 1.2 143 +- 1.0 144 +- 1.0 152_+0.9 153-+0.9 163-+0.8 164_+0.7

Cross section (mb)

Mg(o~, lOpxn]TBe

Mg(ct, 3pxn)22Na

0.076-+0.008 0.685 ! 0.054 1.79_+0.13 3.39 ___0.24 4.58_+0.33 5.42 _+0.38 6.39___0.46 7.55 _+0.76 7.55 _+0.76 7,94m0.57 8,97_+0.90 8,61 !0.61 8.97 -+.0.90 8.3720.60 8.38+-0.84 8.38+0.84 9.70___0.97 9.70 m 0.97 10.0_+ 1.0 I0.0+- 1.0 10.4m 1.0 10.4_+ 1.0 10.1 _+ 1.0 10.1 _+ 1.0

2.7!0.2 74.3 _+5.2 130_+9 116 _+8 100_+7 90.2 -r 6.0 91.9_+6.6 84.2 _+5.9 79.5 _+5.6 85.4_+6.0 78.3 _+5.5 79.1 _+5.6 78.5 --.T-5.5 73.7+_5.2 74,6_+5.3 74.7-+5.2 71,4_+ 5.1 68.4 _+4.8 70.4_+5.0 65.4+-4.6 68.1 +-4.8 64.1 _~4.5 64.8_~ 4.6 62.1 _+4.4

Mg(ct, 3pxn)Z4Na

Mg(~, 2pxn )2~Mg

0.581 _+0.043 0.666 __.0.048 2.10 ± 0.15 10.2 _+0.7 14.2 +- 1.0 21.7 _+ 1.5 22.6_+ 1.6 22.9_+ 1.6 24.2 ± 1.9 25.4_+ 1.8 25.8_+ 1.8 22.7 _+1.6 24,5--+ 1.8 22.1 _+ 1.5 25.8 _+1.8 21.1 ± 1.5 23.4+_ 1.7 24.9± 1.8 22,4_+ 1.6 24.0 _+ 1,7 22.0 ± 1.6 23.4 _+ 1.7 21.2_+ 1.5 22.5___ 1.6 19.5-+ 1.4 21.4_+ 1.5

--0.0264 +- 0.0062 0.278 _+0.026 0.300 m 0.028 0,228 _+0.041 0.252 _+0,045 0.226-.-0.041 0.236 7- 0.054 0,191 m 0.028' 0.19620.033 0.202 +- 0.038 0.145+-0.027 0.161 +-0.041 0.139 ! 0.029 0.127±0.035 0.113n-0.024 0.109+-0.023' 0.087 m 0.021 0,099 ! 0.02 I 0.066_+ 0.019 0.076 _+0,020 0.055 !0.018 0.059+-0.019 0.046_+0.017 0.037_+0.013

et al.

Table 4. Experimental crosssections for the production 7Be, 2-'Na. -~4Na and 28Mg from aluminum by s-induced reactions Energy

Cross section

(MeV)

(rob)

(mb)

27A/(ct, llpl3n)TBe

27A1(~,4p5n)22Na

-0.044 ± 0.007 0.217_+0.033 0.502 ! 0,057 0.883 ± 0.065 1.33-r0.10 1.80m0.13 2.20_+0.16 2.64_+0,19 2.97 _+0.21 3.16m0.23 3.43 -+ 0.24 3,85 ___0.27 4.20 ~0.30 3.93_+0.28 4.82-.-0.35 5.00 _+0.36 4.62 m 0.34 5.37 m 0.38 5.36_+0.39 4.44 ~ 0.32 4.67_+0.33 4.94___0.35 4.95 ~ 0.35 5.12+_0.37 5.66-+0.41 5.80-+0.43 4.31_+0.32

0.10+0.01 0.12_+0.01 0.84 ! 0.06 19.5_+ 1.4 39.3 -+ 2.8 44.6 -+ 3.1 37.5_+2.6 30.0+_2.1 25.9_+ 1.8 25.2_+ 1.8 28.6 _+2.0 31.2_+2.2 33.2 -+ 2.3 35.2+ 2.5 35.6-1- 2.5 37.2-+2.6 37.7 ~ 2.7 38,2 _+2.7 40,21-2.9 43,3 _+3.1 42.6_+3.0 40.3 _+2.9 39.9-+2.8 36.5-+2.6 41.2 -+ 3.0 44.1 -+3.1 42.8___3.1 -41.6-+3.0

27A1(o~,4p3n)24Na

27Allot, 3p)2~Mg

24,6+ 1.7 32.3__. 1.5 37.3 ___1.4 44.6_+ 1.2 49.8 +_ 1.2 55,4-+ 2.2 61.7_+2.0 67.4_+ 1.9 72.8+_ 1.8 77.9_+ 1.7 82.7 m 1~6 86,4_+ 1,9 87.4_+ 1.7 92.3 _+ 1.6 97.0-+ 1.5 99.7,1.7 104_+ 1.4 108 _+ 1.3 112__. 1.7 114 +_ 1.2 116_+ 1.1 118 -+0.4 118!0.4 119__.0.4 125 ___1.4 136___1.3 148.1.2 159-r 1.1 170_+0.3

86.4 ± 1.9 99.7_+ 1.7 112±1.7 125_+ 1.4 136+_ 1.3 148 _+ 1.2 159_+ 1.1 170 + 0.3

35.9 -+ 2.6 34.3_+2.5 32.5_+2.3 31.6+_2.3 31.7_+ 2.2 30.1 _+2.1 28.9_+2.1 31.0 -+ 2.2

Cross section

0.230 2 0.029 0.197!0.027 0.158-1-0.024 0.121 _+0.024 0.111 _+0.022 0.100__.0.021 0.087m0,019 0.080 +_0.029

consistency check with work of other authors. It has to be kept in mind that for some time a branching ratio of 12.0-12.3% for the 478 keV line of TBe was used by several authors. These data were renormalized for the more recent value of 10.4% as given by Reus and Westmeier (1983). This value was also used in this work. The target elements C, N and O were investigated earlier by a number of authors using counting techniques after radiochemical separation (Bouchard and Fairhall, 1959), track techniques (Vidal-Quadras and Ortega, 1979; Baixeras-Aiguabella et al., 1970; Jung et al., 1969) and mass spectrometry (Fontes et al., 1971; Fontes, 1977). For 7Be from carbon (Fig. 1), the cross section at 90.0 MeV measured by Jung et al. (1969) does not agree with our data. The measurements between 100 and 140 MeV by Fontes et al. (1971) and by Fontes (1977) agree within limits of errors with our results. The cross sections for 7Be [rom nitrogen and oxygen (Fig. 1) reported by Vidal-Quadras and Ortega (1979) are compatible within limits of error with the new data. For 7Be from oxygen, the data up to 40 MeV by Bouchard and Fairhall (1959) fit well to the excitation function measured in this work.

Production of residual nuclei For the production of ~°Be from C, N and O the earlier data (Vidal-Quadras and Ortega, 1979; Baixeras-Aiguabella, 1970; Jung et al., 1969) are in strong contradiction to our data with discrepancies of up to an order of magnitude (Fig. 2). The measurements of ~°Be from carbon by Fontes et al. (1971) agree with ours within limits of errors.

Target Elements Magnesium, Aluminum and Silicon Production of 7Be from magnesium (Fig. 3) was investigated earlier by Lindsay and Carr (1960b) up to 41.6 MeV and by Lindsay (1966) up to 63.4 MeV. Our new excitation function does not agree with either of these measurements, our cross sections lying between the two earlier data in the overlapping energy region. The target element aluminum has been investigated in detail in the past, for ~-induced reactions as well as for proton-induced ones. 7Be data from AI (Fig. 3) exist by Martens and Schweimer (1969) for energies up

Table 5. Experimental cross sections for the production 7Be, 22Na, 24Na and 2SMg from silicon by ~¢-induced reactions Energy (MeV) 45.9_+7.6 58.8±6.4 69.8±5.6 79.5--,5.1 80.6_+5.3 89.4_+4.9 90.8±4.6 97.5±4.6 98.9_+4.3 105+4.4 107_+4.0 112_+4.2 114±3.7 119_+4.0 126_+3.8 132_+3.6 138±3.5 t~±3.4 150_+3.2 156--,3.1 161±3.0 45.9 _~7.6 58.8 -+ 6.3 69.8 -+ 5.6 79.5-t-5.0 80.6 + 5.3 89.4_+4.9 90.8 _+4.5 97.5---4.6 98.9_4-4.2 105 4-4.4 107"1-3.9 112_~4.2 114_+3.7 119_4-4.0 126_+3.8 1324-_3.6 138_+3.5 144_+3.4 150__.3.2 1565-3.1 161 _+3.0 166-r 2.8

Cross section (mb)

Cross section (rob)

~(g,l~xn)TBe

~(g, Spxn)~Na

0.76~0.05 1.95~0.14 3.03_+0.21 3.96_+0.28 4.71±0.34 5.95_+0.43 5.17!0.36 6.71_+0.48 6.00_+0.42 6.97_+0.~ 6.60_+0.47 7.49~0.~ 6.84_+0.~ 7.80_+0.56 8.16_+0.58 8.50_+0.61 8.49!0.60 8.41-+0.60 9.~_+0.64 8.66±0.~ --

0.70_+0.05 11.9_+0.8 35.5_+2.5 41.3±2.9 42.6---3.0 ~.8_+3.0 37.6_+2.6 40.8_+3.0 39.6_+2.8 34.0_+2.4 41.3_+2.9 39.6_+2.8 42.4_+3.0 37.6_+2.7 34.5_+2.5 37.1--,2.6 33.9+2.4 33.8_+2.4 37.5±2.7 34.7±2.5 41.4±3.1

Si(~t, 5pxn)24Na

Si(ot, 4pxn)2SMg

0.513 _+0.036 1.56_+ 0.11 3.85 +- 0.27 8,22---0.58 12.2_+0.9 15.1 _+ 1.1 12.3 _+0.9 16.4_+ 1.2 13.7-+ 1.0 14.4_+ 1.0 14.7-+ 1.0 16.2_+1.] 15.84-1.1 15.9_+ 1.1 14.2-+ 1.0 15~0-+ 1.1 13.9-+ 1.0 13.9--, 1.0 14.6-1- 1.0 14.2_+ 1.0 15.6_+ 1.1 13.9-+ 1.0

0.0114 -+0.0015 0.0531 -+ 0.0047 0.0963 +- 0.0103 0.131 _+.0.015 0.150-+ 0.015 0.150-+0.016 0.136_+0.017 0.160 ~0.016 0.151 -+0,019 0.150--,0.016 0.165_+0.020 0.158-+0.017 0.t56__.0.019 0.157___0,016 0.158-+0.016 0.162_+0.017 0.162_+0,016 0.149_+0.015 0.163--,0.016 0.153_+0.016 0.168_+0.017 0.143--+0.015

97

Table 6. Experimental cross sections for the production of roBe and ~-~AI from magnesium, aluminum and silicon by ~-induced reactions Energy (MeV) 27.5__.2.7 34.6_+ 2.3 41.2_+2.1 62.8+ 1.6 78.3 ___1.4 92.1 -+ 1.1 92.9_+ 1.6 115+_0,7 117__. 1,2 1 3 0 ! 1.2 143 -+ 1.0 152 -+ 0.9 163 -+ 0.8 28.7-+ 1.6 35.7_+ 1.4 40.4-1- 1.3 58.6-+2.1 70.1 -+ 1.8 87.4-+ 1.7 87.9_+ 1.7 101 -+ 1.5 116_+ 1.7 127 _+ 1.3 149 _+ 1.2 170_+ 0.3

Cross section (mb)

Cross section (mb)

Mg(ot, lOpxn)'"Be

Mg(ct, pxn)'-~Al

0.0044-1-0.0008 0.0045 _ 0.00 I0 0.0140-+0.0015 0.153+0.012 0.352 -+ 0.030 0,598 -+0.053 0,641 __.0.036 1.01 -+0.09 0.999_+0.056 1.15_+0.07 -1.38 -1-0.08 1.40 _4-0.08

213_+35 255 + 18 135-+ 14 44.5_+3.8 40.1 _ 2.9 21.8_+ 1.7 I6.7+ 1.0 10.7_+0.8 8.61 -+0.49 6.87-+0.40 5.42 _+0.35 4.68 _+0.34 3.49 z 0.28

~TAl(~t, 1lp lOn)~°Be

27Al(~t,2p3n)26Al

--0.100---_0.006 0.274-+ 0.009 0.462_+0.012 0.378 _+0.022 0.508 ___0.029 0.890_+0.027 0.692 -+ 0.040 0.890 _+0.050 0.837 _+0.046

Si(ct, 12pxn)~°Be 58.8_+6.4 79.5_+5.1 90.8_+4.5 98.9_+4.3 114_+3.8 124_+7.9 138 _+3.5 141 -+6.5 150--, 3.2 151 _+6.7 153___6.2 161 _+2.9 164-+5.6

0.0147_+0.0012 0.0909_+0.0080 0.140_+0.011 0.193_+0.017 0.315+0.022 -0.309 -+ 0.028 0.326_+ 0.029 --0.547_+0.050 --

208-+ 16 223-+ 16 146--+ 11 56.1 -+4.9 70.2 +- 5.9 -75.6 -+ 4.6 75.3 __+4.4 -73.9 _+4.4 69.5 _ 4.2 67.0_+ 4.0

Si(¢t, 3pxn)Z6Al 156_+ 12 78.7!7.2 117_+9.4 64_+5.4 82.4_+7.4 50.4_+4.5 53.2 __.4.8 57.8 -c 5.0 52.0 _+4.6 4 7 . 0 ~ 3.7 59.8-+5.1 52.3 _+4.6 58.4__.4.2

to 103 MeV, by Lindsay and Carr (1960b) up to 41.4 MeV, by Bouchard and Fairhall (1959) up to 42 MeV, by Porile (1962) up to 41.5 MeV, by Gordon (1967) up to 77.4MeV, by Pape (1964) up to 74.8 MeV, by Probst et al. (1976) up to 152 MeV and by our group (Brinkmann. 1979; Michel et al., 1980) up to 172.5 MeV. Below 55 MeV there is general agreement. Exceptions are the data by Pape (1964) and Gordan (1967) which deviate from all other measurements systematically, the former being too high and the latter being too low. For energies above 55 MeV, our data are in general agreement with those by Probst et al. (1976), though the scatter of their data is much larger than ours. The only other earlier data above 55 MeV are by Martens and Schweimer (1969) with few data points between 100 and 110 MeV in disagreement with our data by a factor of two. For 7Be from silicon (Fig. 3) earlier measurements were reported by Mullie (1971) between 61 and 153 MeV and by Vysotsky et al. (1990) between 40.3 and 95 MeV. Mullie's cross sections are between 10 and 20% lower than our data, except for two data at

98

H.-J. Lange et al.

the lowest energies. Here, they are off by a factor of three. The data by Vysotsky et al. (1990) are systematically lower by a factor of ten than our data. Since the results by Vysotsky et aL (1990) for 22Na, 24Na and 2SMg from Si, obtained from the same experiments are in agreement with our results, this discrepancy looks more like a typesetting problem than like a physical one. For the production of ~°Be from Mg, A1 and Si (Fig. 4) no earlier measurements existed. The production of 22Na from Mg (Fig. 5) was measured only up to 63.2 MeV by Lindsay and Cart (1960a) and by Lindsay (1966). Our new data are nearly a factor of two higher than the earlier ones in the overlapping energy region. 22Na from A1 has been intensively investigated in the past (Probst et al., 1976; Martens and Schweimer, 1969; Porile, 1962; Lindsay and Cart, 1960a; Gordon and Hillman, 1966; Karpeles, 1969; Bouchard and Fairhall, 1959; Bowman and Blann, 1969; Gauvin, 1971; Mullie, 1971; Benzakin and Gauvin, 1970; Glascock et al., 1979; Brinkmann, 1979; Michel et al., 1980) and therefore is often used as a monitor reaction. The existing data were evaluated by Tobailem et al. (1971) and Tobailem and de Lassus St Genies (1981) up to 160MeV. From our recent measurements, absolute determinations of cross sections for this reaction were done between 115 and 170 MeV in the case of the irradiation at Jiilich. F r o m the PSI experiments our new data are relative to a cross section of 36.5 mb at 119.7 MeV for this reactions. In all the measurements there are just a few outliers (Bowmann and Blann, 1969; Karpeles, 1969; Glascock et al., 1979). But even these are not more than 40% off the mean of all other measurements. All other data are clustering closely together. There seems to be a discrepancy in the earlier data from our group. The data given by Brinkmann (1979) for 27Al(a, 4p5n)22Na are about 10% higher than those published one year later (Michel et al., 1980). Both these reports were based on the same irradiation experiments and the same measurements. The reason for the difference is that Brinkmann (1979) adopted a branching ratio of 89.95% for the 1274 keV y-line of 22Na taken from the compilation of Erdtmann and Soyka (1973), while Michel et al. (1980) adopted a branching ratio of 99.9% which is still accepted today (Table 1). It has to be pointed out that the revision of these cross sections from Brinkmann (1979) to Michel et al. (1980) does not affect the cross sections for any other a-induced reaction measured earlier by our group (Michel and Brinkmann, 1980b; Michel et al., 1980, 1983a, b), since the flux determinations were done by Faraday cup measurements in our earlier work. In Fig. 5, we compare our data from this work with the evaluated ones. All our data are in good agreement with the evaluated excitation function. However, in this work we find a 10% deeper minimum between 70 and 80 MeV than is seen in the evaluated data. Our

data from this work and those of Michel et al. (1980) are fully consistent and are in good agreement with the measurements by Probst et al. (1976). The production of-'-'Na from silicon (Fig. 5) was investigated earlier by Mullie (1971) and by Vysotsky et al. (1990). Five out of six data points by Mullie (1971) agree within limits of errors with ours. At the low energy end, the same discrepancies are seen between his work and ours that were observed for 7Be from silicon. The data by Vysotsky et al. (1990) are well in agreement with the new results. F o r 24Na from Mg (Fig: 6), only one earlier report of cross sections for a-energies between 24 and 35.8 MeV exists (Lindsay and Carr, 1960a). The new data agree fairly well with those of Lindsay and Carr (1960a) at 33-35 MeV, but more slowly with energy than the earlier data. F o r 24Na from A1 quite a number of data exists (Fung Si-Chang, 1949; Lindner and Osborne, 1953; Crandall et al., 1956; Bouchard and Fairhall, 1959; Lindsay and Carr, 1960a; Hower, 1962; Porile, 1962; Gordon, 1967; Bowmann and Blann, 1969; Martens and Schweimer, 1969; Probst et al., 1976; Glascock et al., 1979; Brinkmann, 1979; Benzakin and Gauvin, 1970; Michel et al., !980). The earlier references were evaluated by Tobailem et al. (1971) and by Tobailem and de Lassus St Genies (1981). Our new data agree with the earlier ones of our group (Brinkmann, 1979; Michel et al., 1980) within 3-6%. Except for some strong discrepancies (Gordon, 1967; Bowman and Blann, 1969; Benzakin and Gauvin, 1970; Glascock et al., 1979) the data are fairly consistent. Except for the data from those authors, those from all other authors form a very narrow band, excellently describing this excitation function. The excitation function for the 27Al(a, 4p3n)24Na reaction is the most complete of all a-induced reactions (Fig. 6). The range of cross sections from the various consistent measurements is about 5% for energies above 60 MeV. Below 60 MeV, the data of Probst et al. (1976) differ from a number of other measurements (Hower, 1962; Martens and Schweimer, 1969; Brinkmann, 1979; Michel et al., 1980). This discrepancy is probably caused by an energy shift rather than by problems in the absolute normalization, since the data by Probst et al. agree well with the other ones above 60 MeV. For 24Na from Si (Fig. 6), earlier data only were reported by Mullie (1971) for energies of 61, 70.3, 82 and 104MeV and by Vysotsky et al. (1990) for energies between 49.4 and 95 MeV. Again the data of the latter authors are well in agreement with our new results. Our measurements agree within experimental errors with Mullie's data at 104 MeV. However, with decreasing energy, the two data sets become increasingly discrepant. At 61 MeV Mullie's data are higher than ours by about a factor of 6. For the production of-'SMg from Mg and Si (Fig. 7) no earlier data exist, For 28Mg from A1 (Fig. 7) measurements by (Anonymous, 1956; Lindsay and Cart,

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Fig. 1. Production of 7Be by ~-induced reactions on carbon, nitrogen and oxygen. Errors are only plotted in this work if they exceed symbol size. Data from this work are given as full squares. Earlier measurements are from Vidal-Quadraz and Ortega (1979) [VI79], Jung et al. (1969) [JU69], Fontcs (1977) [FO77] and Bouchard and Fairhall (1959) [BO59]. Hybrid model Calculations are based on nuclear masses according to the Myers and Swiatecki mass formula (MS); no=4 full line, no=5 dashed line, no=6 dot-dashed line. 99 ARI 46/2--C

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are given as full squares. Earlier measurements are from Bouchard and Fairhall (1959)[BO59], Lindsay and Carr (1960a, b) [LI60];Lindsay and Carr (1966)[LI66], Martens and Schweimer(1969, 1970)[MA69],Porile (1962) [PO62],Gordon (1967) [GO67],Pape (1964) [PA64],Probst et aL (1976) [PR76],Mullie(1971) [MU71] and Vysotsky et al. (1990) [VY90]. 101

102

H.-J. Lange et al.

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Fig. 4. Production of '°Be by S-induced reactions on magnesium, aluminum and silicon. There are only data from this work (open squares).

Production of residual nuclei 1960a; Martens and Schweimer, 1969; Nozaki et al., 1975; Probst et al., 1976) were reported earlier, the investigations by Probst et al. (1976) being the most comprehensive ones. Generally, there is good agreement between all the different reports with the exception of some data by Martens and Schweimer (1969) between 90 and 100 MeV. Our data are slightly lower than those by Probst et al. (1976), but agree within limits of errors. F o r 28Mg from Si (Fig. 7), earlier data exist only from Vysotsky et al. (1990) between 57.6MeV and 95MeV, which are in agreement with ours. Finally, for the production of 26A1 from these elements only measurements below 45 MeV existed by Tanaka et al. (1975) (Fig. 8). Generally, our data tend to be somewhat higher, though they agree within limits of errors for aluminum. For magnesium and silicon, however, there are still some discrepancies which have to be further investigated. F o r Si, there is no overlap in energy between our measurements and those of Tanaka et al. (1975). However, the shape of the composite excitation function is fairly smooth, except for some scatter of data in our data set between 60 MeV and 100 MeV.

Hybrid Model Calculations Considering the lack of detailed excitation functions for s-induced reactions, the question whether nuclear models are capable of reliably predicting unknown excitation functions becomes crucial. F o r nucleoninduced reactions a priori calculations of production cross sections using the hybrid model of preequilibrium reactions (Blann, 1971) in combination with the statistical model of equilibrium reactions (Weisskopf and Ewing, 1940) in the form of various versions of the code ALICE, e.g. (Blann, 1978; Blann and Bisplinghoff, 1982; Blann and Vonach, 1983; Blann, 1987, 1990), have been very successful, e.g. Michel et al. (1985), Blann (1988) and references therein. However, our recent work on proton-induced reactions up to 100 MeV for the same target elements as discussed here (Bodemann et al., 1993) showed that the capability of the hybrid model to predict unknown excitation functions is not as good for light elements as for medium mass targe t elements. The calculations show that modelling of the reactions is possible in the framework of equilibrium and preequilibrium theories even for the lightest elements used here. But it was not possible to recommend a global set of calcuiational options which allows for adequate a priori calculations. F o r s-induced reactions, a further complication arises. Earlier investigations by our group had revealed some shortcomings of the hybrid model when calculating integral excitation functions for the production of radionuclides from target elements 22 ~
103

energy part of the excitation functions was observed. This was attributed to incorrect treatment of s-break-up in the initial phase of the reactions. In order to test the applicability of this model to or-induced reactions on light elements, a hybrid model analysis was performed on the reactions investigated in this work using the code ALICE 900 (Blann, 1990). Various combinations of input parameters were chosen in order to investigate the variability of results as well as to search for a best set of parameters with respect to global a priori calculations of nuclide production by c~-induced reactions. The code A L I C E 900 (Blann, 1990) is an extended version of the code ALICE LIVERMORE 82 (Blann and Bisplinghoff, 1982). It contains a number of new features. Firstly, it permits the use of experimental nuclide masses according to the Wapstra and Gove mass table (Wapstra and Gove, 1971). If this option is chosen, the Myers and Swiatecki mass formula (Myers and Swiatecki, 1966) is applied only to those nuclides for which no experimental masses exist. Secondly, it allows the choice of broken exciton numbers, thus taking into account the statistical distribution of different possible initial exciton configurations. A detailed discussion of this feature was given by Blann and Vonach (1983). Thirdly, in contrast to ALICE L I V E R M O R E 82, the new ALICE 900 takes into account multiple preequilibrium decay, allowing for both the emission of more than one nucleon from a single exciton configuration and for the preequilibrium emission of several nucleons in sequential exciton configurations. Further, an option was implemented allowing for correction of shell effects onto the nuclear level densities (Kataria et al., 1990).

Choice of Parameters In the present work, three different combinations of options and parameters were used in the calculations. The following features were common to all three: for the equilibrium reactions standard Weisskopf and Ewing (1940) evaporation calculations with multiple particle emission (p, n, d, ct) were performed. F o r preequilibrium reactions, the geometry dependent hybrid model (GDH) (Blann, 1972) was used. Preequilibrium emission of protons and neutrons, but not of complex particles was taken into account. Inverse cross sections were calculated from the optical model subroutine of the ALICE codes, which uses the Becchetti and Greenlees (1969) optical model parameters. A constant level density parameter of A/9 was adopted. Intranuclear transition rates were calculated using the Pauli corrected nucleon scattering cross sections, since the optical model parameters are valid only up to 55 MeV (Becchetti and Greenlees, 1969). However, the mean free paths for intranuclear transitions based upon nucleon cross sections are in quite reasonable agreement with optical model analyses of proton-induced reactions up to 200 MeV (Michel et al., 1985). In accordance with our earlier

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et al.

H.-J. Lange et al.

108

work on proton-induced reactions (Michel et al., 1978a, 1979a, b; Michel and Stiick, 1984; Bodemann et al., 1993), a mean free path multiplier k = 1 was adopted. For the excitation energies, energy bins of 0.5 MeV were used up to 45 MeV and of 1 MeV for higher energies in all calculations. For e-induced reactions, the initial exciton number is not uniquely defined as it is for nucleon-induced reactions. Initial configurations with exciton numbers between 4 and 6 contribute to ~-induced reactions with various combinations of particle-hole combinations. In this work, we distinguished calculations with no= 4 (p, n, h = 2, 2, 0), no=5 (50% p , n , h = 2 , 3 , 0 ; 50% p, n, h = 3 , 2, 0) and no=6 (50% p, n, h = 2 , 3, 1; 50% p, n, h = 3 , 2, 1). Since a strong dependency of the calculational results on the adopted nuclear masses was observed for proton-induced reactions on C, N, O, Mg, A1 and Si up to 100 MeV (Bodemann et al., 1993), the influence of different calculational options with respect to the choice of nuclear masses was also investigated in this work L Calculations were performed using: (1) MS: nuclear masses according to the mass formula of Myers and Swiatecki (1966) without shell or pairing corrections; (2) EX-MS: experimental Wapstra and Gove (1971) masses as far as available, Myers and Swiatecki masses otherwise, but without shell and pairing corrections; and (3) EX-MS-C: experimental masses as far as available, otherwise Myers and Swiatecki masses with shell and pairing corrections and shell-corrected level densities according to Kataria et al. (1990). Excitation functions were calculated in 1 MeV steps up to 50 MeV, 5 MeV steps between 50 and 150 MeV and 10 MeV steps above 150 MeV. Hybrid model calculations of the production of 7Be and 1°Be from Mg, A1 and Si are not feasible with ALICE 900, because it does not allow such large charge differences between target and product because of limitations on storage space. There exists, however, an improved version ALIBIG (Blann, 1990), which also allows to calculate evaporation of complex particles A > 4 . Using this code ALIBIG, first calculations were done to describe the production of 7Be and ~°Be from Mg, A1 and Si in this work. However, because of the enormous computing time needed by these calculations, the ALIBIG calculations were not continued.

Discussion As was already observed for proton-induced reactions on the same target elements as in this work (Bodemann et al., 1993), the calculations of e-induced reactions on the light elements C, N and O turned out to be much more problematic than the ones on Mg, AI and Si. It must be questioned, in general, whether the

statistical concepts of equilibrium and preequilibrium reactions can be extended to target nuclei with A ~<16. For the target elements C, N and O the three mass options used showed drastic differences in the results. As for the proton-induced reactions, the MS calculations gave the best but still unsatisfactory results. The calculations based on experimental nuclear masses (EX-MS and EX-MS-C) generally were about an order of magnitude lower than MS ones and failed completely to describe the experimental data. Thus, it seems that equilibrium and preequilibrium calculations can be extended to the lightest target elements, but only when adopting the general systematics o f nuclear masses, and not when taking into account the actual masses. As in our earlier calculations, we attribute this to problems with either the statistical approach of the mass formula to small masses or with the transition from empirical to calculated masses in quite narrow parts of the valley of stability. In particular, the transition from experimental to theoretical mass data might cause discontinuities in the excitation energies. Generally, EX-MS-C gives the least adequate results for the target elements carbon, nitrogen and oxygen. This may in addition point to problems with the shell and pairing corrections for nuclides far from stability. For the target elements Mg, A1 and Si, all three mass options investigated give meaningful results, EX-MS and EX-MS-C calculations being somewhat superior to MS ones. The quality differences between EX-MS and EX-MS-C varied a little for the various target-product combinations, but on average EX-MSC turned out to be the best option. Thus, with respect to a p r i o r i calculations it is not possible to recommend a general choice of nuclear masses in the calculations. A further ambiguity with respect to a priori calculations comes from the influence of the different initial exciton numbers possible in a-reactions. Initial configurations with 4, 5 and 6 excitons describe different scenarios of the first stage of e-induced reactions which in reality are all occurring. If the ~-particle breaks up in the target nuclide potential, a 4 exciton state of the type (p, n, h = 2, 2, 0) has to be adopted. If the break-up of the e-particle occurs as a consequence of a scattering process with an individual nucleon at about the Fermi energy, a 5 exciton state is produced, which when assuming zero neutron excess has equal chances to be a ( p , n , h = 2 , 3,0) or (p, n, h = 3 , 2, 0) state. Thirdly, a break-up after a collision with a nucleon of an energy well below the Fermi energy will create a 6 exciton state with about equal chances to be a ( p , n , h = 2 , 3 , 1 ) or a (p, n, h = 3, 2, 1) state. All these configurations assume that the e-particle breaks up completely and that all its nucleons participate in the reaction. There is no configuration describing peripheral collisions with partial break-up of the e-particle. Such reactions yield relatively low excitation energies, if a part of the e-particle acts only as spectator. As a consequence, reactions with few

Production of residual nuclei nucleons in the exit channels will tend to be underestimated. Also, there is no configuration that accounts for reactions of the types (~, axpyn) or (a, a + complex particles) in the preequilibrium phase. Therefore, in general, it cannot be assumed that the same quality of the calculations can be obtained for s-induced reactions as for nucleon-induced ones. Since the differences caused by the different possible initial configurations accounted for by the hybrid model are significant, we decided in this work to perform the discussion of the individual reactions in such a manner that theoretical data are presented for all 3 initial configurations for each reaction. As a consequence, we have to limit the following discussion to one mass option for each target element. We decided in favour of the MS option for the target elements C, N, O and in favour of the EX-MS-C option for Mg, A1 and Si. 7Be is produced mainly from ~2C,14N and I60 via the reactions 12C(~,4p5n)TBe, Z4N(~,5p6n)TBe and 160(~, 6p7n)TBe, which all can occur via nucleon and complex particle emission. However, significant maxima pointing to an important a-contribution in the exit channels is not seen in the experimental data (Fig. 1). The calculations predict such evaporation maxima for the target elements carbon and oxygen. For both elements, the experimental and theoretical excitation functions disagree with respect to shape and magnitude. For nitrogen, the calculated shape of the excitation functions for 7Be production agrees better with the experimental one. But again, the absolute cross sections are not reproduced, the experimental data being higher by about a factor of two. Also for the production of l°Be from C, N and O (Fig. 2), which is dominated by the reactions 12C(a, 4p2n)l°Be, ~4N(a, 5p3n)~°Be and ~60(~t,6p4n)l°Be, no significant contribution of a-particles in the exit channel is seen. The agreement between experiment and theory is somewhat better than for 7Be from C, N and O, but there are still differences of a factor of two to be recognized. The disagreement between theory and experiment is not unexpected, since the nuclear reaction models used in the code do not take into account direct reactions, which most probably are responsible for the observed underestimation of the excitation functions. There are no restrictions on the applicability of the calculational methods for the production of ~Na, 24Na, 28Mg and 26A1from Mg, A1 and Si. The models should also be valid for the production of 7Be and '°Be with two reaction modes to be considered. Both nuclei can be produced as residual nuclei of the reaction or they can be evaporated as ejectile as was discussed in detail by Lindsay and Carr (1960a, b) and by Lindsay (1966). In all older versions of ALICE the evaporation of complex particles A > 4 could not be calculated. The evaporation of 7Be and I°Be from Mg, A1 and Si (Figs 3 and 4) could be calculated with the recent code ALIBIG (Blann. 1990). Such calculations were performed up to 100 MeV for these target elements in

109

this work. But these calculations neither describe adequately the experimental data. Discrepancies of factors up to five exist and too high apparent thresholds show in the theoretical excitation functions. For the products 22Na, 24Na, 28Mg and -~6A1. the hybrid model calculations are much better. However, the agreement is not as good as observed earlier for nucleon-induced reactions (Michel et al., 1985: Bodemann et al., 1993). In the case of 22Na from Mg, A1 and Si, the experimental excitation functions are less structured than the theoretical ones (Fig. 5). The calculations predict pronounced maxima in the low energy parts of the excitation functions as a consequence of a-evaporation. Then follow slight minima before the emission of individual nucleons dominates and causes a further increase of the excitation functions with increasing a-energy. For the target elements AI and Si, theory predicts a steady increase of cross sections with energy in this final part of the excitation functions. The experimental data, in contrast, all show slight maxima in the low-energy part followed by nearly constant plateaus. The missing minima in the experimental data can be explained by preequilibrium emission of a-particle, a reaction mode which is not included in the calculations. Except for this shortcoming, the calculated data describe the measured one reasonably well in case of Z2Na from Mg. The differences caused in the theoretical data by the different initial configurations are small, i.e. less than a factor of 2. However, in case of 22Na from A1 and Si the calculations strongly underestimate the low-energy parts of the excitation functions up to about 100 MeV and above this energy the increase of the calculated excitation functions is also m contradiction to the experiment. Again, the different initial exciton configurations do not show significant differences. For 24Na from Mg, AI and Si. agreement between theory and experiment is again not satisfying (Fig. 6). For 24Na from Mg, the threshold is well described, but the a-evaporation is underestimated by almost a factor of ten. The calculated maximum at 80 MeV matches the height of the experimental cross sections, but the decrease with energy predicted by theory for energies above 80 MeV is in contrast to the nearly constant plateau of the experimental data. In case of 24Na from A1, the calculations match the threshold data reported by Bowman and Blann (1969). However, all other experimental data show the threshold and the increase of the excitation function at about 10 MeV lower, m contrast to the calculations. The theory predicts a nearly constant plateau for this reaction, best described by no = 4, which is. however, lower than the experimental data by factors between 2 and 5. For 24Na from Si, the theoretical data deviate from the experimental ones with respect to both shape and size. Relatively good calculational results were obtained for 2SMg from Mg and AI. while the theory failed

110

H.-J. Lange et al.

completely for 28Mg from Si (Fig. 7). The production of 28Mg from magnesium and aluminum is exclusively due to the reactions 26Mg(c~,2p)28Mg and 27A1(~, 3p)-nMg. Both reactions are well described by hybrid model calculations with initial exciton configurations between no= 4 and no = 5. Calculations based on no= 6 strongly underestimate the experimental data, thus pointing to the importance of surface reactions for the (c~,2p) and (~, 3p) reactions. In case of ZSMgfrom silicon, the reaction type is not uniquely defined, (~, 4p), (~,4pn) and (~, 4p2n) reactions contribute to its production. The experimental data show nearly constant cross sections between 80 and 170 MeV, quite in contrast to all calculated data, which give a decrease by factors between two and ten in this energy region depending on the initial exciton configuration. Also in case of 26A1from Mg, A1 and Si (Fig. 8), the calculations are not satisfying. For Mg(~, pxn)26A1the maximum of the excitation function is overestimated by more than a factor of 2, but the decrease to higher energies is reasonably described by initial configurations with no between four and five. For 27A1(c~,2p3n)26A1, the discrepancies between 50 and 70 MeV are due to the neglect of preequilibrium ~-emission. There are general problems with the shape of the excitation function for Si(~, 3pxn)26A1, the reasons for which are not yet clear. Surely, the hybrid model analysis of all the reactions measured in this work deserves a more detailed discussion than is possible within the limited space available here. But it can be concluded that the calculations based on current codes show discrepancies too large to allow their application to predictions of integral excitation functions. Consequently, systematic measurements are presently the only means to satisfy the data needs of cosmochemistry and astrophysics. From the experimental data and the discrepancies with the calculated data, deficiencies in the codes can be extracted as described above. Including such reaction modes as preequilibrium emission of complex particles and incomplete break-up of the incoming ~-particles should produce improved codes with higher predictive power. Based on the new data of the production of J°Be and 26A1 in ~-induced reactions, a first estimate of the importance of ~-particles in model calculations of SCR interactions with stony meteorites and lunar surface materials can be made. The energy dependence of solar proton and ~-spectra is the same when the energies are taken as energy per nucleon. The production thresholds due to proton- and o-reactions are, however, dependent on the total energies of the impinging particles. Thus, the s-fluxes are effectively higher than the proton fluxes near thresholds as would be expected from the overall ratios of SCR o-particles to proton fluxes of 0.02 to 0.1. Moreover, the cross sections for the production of ~°Befrom C, N, O, Mg, A1 and Si by ~-induced reactions are higher by factors

between four and ten at 100MeV than for proton-induced ones, Consequently, a significant contribution by SCR s-particles can be expected, which has to be properly taken into account in SCR model calculations. For product nuclides such as -~2Na and 26A1, the excitation functions of proton- and c~-induced reactions differ considerably with respect to their shapes. The total cross sections reached in o-induced reactions are higher. The effect of c~-particles is further amplified by the fact that o-induced reactions in contrast to the proton-induced reactions have excitation functions with constant plateaus at high energies, It can be concluded that for adequate modelling of the SCR production of cosmogenic nuclides and of their production by primary GCR particles, o-induced reactions have to be taken into account. This work should be seen as a first step to provide the necessary nuclear reaction data for this purpose, authors are grateful to the authorities of PSI/Villigen and KFA/Jfilich for the beam-time and to the staffs of the accelerators for their good cooperation. We thank M. Blann for making available the most recent versions of the ALICE code. The silicon targets were kindly provided by Wacker Chemitronic, Burghausen. This work was supported by the Deutsche Forschungsgemeinschaft and by the Swiss National Science Foundation. Acknowledgements--The

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