Production of radionuclides by cosmic rays at mountain altitudes

Earth and Planetary Science Letters, 36 (1977) 44-50 © Elsevier Scientific Publishing Company, Amsterdam - Printed in The Netherlands

44

PRODUCTION OF RADIONUCLIDES BY COSMIC RAYS AT MOUNTAIN ALTITUDES YUJI YOKOYAMA, JEAN-LOUIS REYSS and FRANCOIS GUICHARD

Centre des Faibles Radioactioitds, Laboratoire mixte CNRS-CEA, Gif-sur-Yvette (France) Revised version received April 15, 1977 Production rates of 22Na (T1/2 = 2.6 years) from aluminium by the action of cosmic rays are measured at the Mont Blanc (altitude 4600 m), the Aiguille du Midi (3840 m), and the Col du Lautaret (2070 m). They are 2.3 +0.5, 1.8 -+ 0.3, and 0.77 ± 0.18 atoms rain -1 kg -1 , respectively, in good agreement with the calculated production rates, 2.4, 1.7 and 0.6 atoms min -1 kg -1, respectively, at the three stations. Production rates of 24Na (T1/2 = 15 hours) from aluminium and magnesium axe also measured at the Aiguille du Midi; the observed rates of 3.4 +- 0.4 and 6.0 ± 1.7 atoms min -1 kg -1 , respectively, agree well with the theoretically expected rates of 3.7 and 5.6 atoms min -1 kg -1. The production rates of 3H, 7Be, 10Be, 14C, 22Na, 26A1, 36C1,3TAr, 39At, S3Mn, S4Mn, and 5SFe in terrestrial rocks by the action of cosmic rays are calculated in order to show the possibility of applying the measurements of these cosmogenic radionuclides to the earth science.

1. Introduction

2. Experimental procedures and results

Interactions o f cosmic rays with the terrestrial atmosphere producing radionuclides such as 3H, 7Be, l°Be, and 14C are weU known, and these products, especially 14C, have useful applications in the earth science. Most o f these nuclides are produced in the stratosphere (maximum production occurring at an altitude o f about 20 km). Since the flux of cosmic rays decreases rapidly with atmospheric depth, the production o f radionuclides at the solid surface o f the earth is lower by two or three orders of magnitude than at the o p t i m u m altitude. That is why practically no studies were carded out, up to the present, on the cosmonuclides produced in terrestrial rocks. The progress made in counting techniques as prompted by studies o f lunar samples, makes it possible to undertake such researches. To explore this possibility, we have made a theoretical estimation o f the production rates o f principal radionuclides in terrestrial rocks, and performed experimental measurements of the production rates of 22Na and 24Na from aluminium targets exposed at mountain altitudes to cosmic rays (aluminium was chosen because its atomic mass is close to that of silicon, the most abundant element in rocks except oxygen).

2.1. Production o f 22Na from Al A duralumin plate (94% A1, 4% Cu, 0.5% Mg) o f about 200 g, which had been exposed for eight years in the television tower at the summit o f the Aiguille du Midi, was placed at our disposal. Before dissolution, a direct measurement o f 22Na was carried out with a gamma-gamma coincidence spectrometer, consisting o f two 12.7 cm X 12.7 cm NaI (1"1) scintillators shielded by successive layers of 1.5 cm Hg, 5 cm plastic anti-coincidence scintillator, 2 cm Cu, 12 cm Fe, and 15 cm Pb. The sample was dissolved in hot 6 N HC1 (1 liter per 100 g o f sample). Sodium was separated from the solution by two successive extractions using an inorganic ion-exchanger, hydrated antimony p e n t o x y d e (HAP) [1 ]. The extractions were carded o u t by the batch method, each time with a new exchanger o f 7 g per liter o f solution. Since a preliminary experiment with 24Na tracer showed that the extraction yield is better in the case where no Na carder was added than in the case with Na carrier, we did not add Na carrier. The chemical yield from separate experiments with 24Na tracer was 85 -+ 3% (as a mean o f three runs:

45 88%, 87% and 80%). The measurement of radioactivities was carried out with the above-mentioned gammagamma coincidence spectrometer. Since the production rate of 22Na from Mg is twice that from A1, we assume the duralumin contained 95% A1 (94% + 2 × 0.5%). The production of 22Na from Cu is negligible. Results are summarized in Table 1. An agreement within the experimental error is obtained between the result obtained from the radiochemical determination and that from the direct measurement. The second sample is an aluminium pot-cover (99% A1) which had been exposed more than ten years in a chalet on the Col du Lautaret. We made two independent runs of the radiochemical determination of 22Na from each 400 g sample. The results are also given in Table 1. A good agreement is obtained between the results of the two runs. The third sample, a duralumin piece (94% A1, 3.5% Cu, 0.5% Mg) of about 360 g was taken from the wreck of an aeroplane fallen about 20 years ago near the summit of the Mont Blanc. The sample was collected from a smooth snow slope (<20°), about 20 m beneath the mountain ridge. The shielding effect of cosmic rays by the ridge was estimated to be less than 1% by assuming a zenith angle distribution of cos20. The results of radiochemical analyses on this sample are also given in Table 1. Snow covers are negligible for the Aiguille du Midi Television Tower samples and the Col du Lautaret sample. For the Mont Blanc aeroplane wreck, we estimate that snow cover was not important and no correction of its effect was made.

2.2. Production of 24Nafrom Al Two packs of aluminium plates (-~99.5%) 5 mm thick, weighing 12 and 21 kg, respectively, were exposed to cosmic rays in the television tower of the Aiguille du Midi for 72 hours. After the exposure, the plates were brought to our laboratory, placed around the above-mentioned gamma-ray spectrometer in the place of the mercury shield, and measured in noncoincidence mode of the 2.76-MeV gamma-rays of 24Na. The counting yield was determined by placing a 24Na standard of known activity in different positions of the pack of aluminium plates and by averaging the efficiencies measured at these positions. The

I dpm / Kg

0.1

lO I

~0 I

Time

30 I

from

40

the

end

50 I

of irradiation

{h)

Fig. 1.24Na activities in the aluminium plates as a function of time after exposition to cosmic rays at the Aiguille du Midi. The observed activities (dpm kg-1 AI) are shown as open circles (the first irradiation with 12 kg AI), solid circles (the second one with 21 kg A1) and squares (the third one with 1.6 kg A1).The least-squares fit curve was calculated with a half-life of 15 hours.

background counting rates were measured with the same aluminium plates after the decay of 24Na. Another irradiation of 24 hours was made at the Aiguille du Midi with an aluminium plate (99.99% A1) of 1.6 kg. The sample was counted in coincidence mode for 1.37-2.76-MeV gamma-rays with a gammaray spectrometer which consists of two semi-cylindrical NaI (T1) scintillators of 30 cm × 25 cm in size. The observed decay of the combination of these three experiments (Fig. 1) is consistent with the halflife of 24Na, 15 hours; the results are summarized in Table 1. A good agreement is obtained between the results of the three irradiations.

2.3. Production of 24Nafrom Mg Magnesium oxide (>95%, most of impurities being H20 and CO2) was exposed to cosmic rays at the Aiguille du Midi. 24Na was measured radiochemically with the HAP extraction. Two irradiations of magnesium oxides of 1 and 1.6 kg, respectively, were made. A good agreement is obtained between the results of the two irradiations (Table 1).

865 916

Aluminium - Col du Lautaret 404 g; chemical, 511-511 keV (6.2%) 402 g; chemical, 511-511 keV (6.2%)

3.3 + 1.0 2.4 -+ 0.9

Th + U

-+ 14 -+ 14

-+ 15 -+ 8

-+ 14 -+ 8 -+ 17

^

0.3 -+ 0.1 0.3 -+ 0.1

222 -+ 5 321 -+ 2 0.2 -+ 0.1

^

2 1 1

353 -+ 16 364 -+ 17

135 -+ 9 35-+ 2

28-+ 8-+ 14-+

-

-

counting rate in 1 0 - 2 c p m

382 382

436 123

424 131 360

counting rate in 10 - 4 c p m

background

contribution o f

-+ 45 -+ 48

-+ 38 -+20

-+ 31 -+16 -+ 27

.

3.0 -+ 1.0 2.1 -+ 0.9

66 -+ 13 98 -+ 13 3.2 -+ 0.6

130 170

164 56

146 50 49

net at t = 0

-+ 0.6 -+0.7

-+ 0.5 -+0.6 -+ 0.9

6.2 5.8

3.2 3.7 3.2

± 2.2 -+ 2.6

-+ 0.7 -+0.6 -+ 0.7

0.67 -+ 0.24 0.88 -+ 0.26

2.5 2.0

2.0 1.7 1.6

Production rate *** (atoms rain - 1 kg - 1 )

are -+5% and -+10% for 22Na and 24Na, respectively. Saturation factors are 0.88 -+ 0.05, 1.00 +0.00 and 1.00 +0.00 for the productions of 22Na at the Aiguille -0.01 -0.07 du Midi, at the Mont Blanc and at the Col d u Lantaret, respectively. For the production of 24Na, saturation factors are 0.964, 0.67, 1.00 and 0.67 for the first two irradiations of A1, the third one o f AI, t h e first one of MgO and the second one of MgO, respectively. Chemical yields for 22Na are 85 -+ 3%, 78 -+ 5% and 78 -+ 5% for Aiguille du Midi, Mont Blanc a n d Col du Lautaret, respectively, and 80 -+ 5% for 24Na from MgO. The duralumin plate o f Aiguille du Midi was shielded by 1 cm Fe and a correction of 5% was applied to this effect.

The errors include all k n o w n sources of errors (i.e., counting statistics, counting yield, chemical yield, and correction for saturation). Errors o f counting yield

* Chemical = gamma-ray m e a s u r e m e n t after chemical separation; direct = non-destructive gamma-ray m e a s u r e m e n t ; 511-511 keV (6.2%) indicates that the measurement was made on the coincidence peak o f 511-511 keV with a counting efficiency o f 6.2%. ** The measurements were made with 5 0 0 0 - 2 0 , 0 0 0 minutes of counting for 22Na, and with runs o f 1000 minutes for 24Na. The errors are counting statistical errors on the basis of 1 standard deviation. *** The production rates are given in atoms min - 1 kg - 1 A1 (or Mg).

MgO - AiguiUe du Midi 1.0 kg;ehemical, 1370-2760 keV (1.0%) 1.6 kg;chemical, 1370-2760 keV (0.75%)

Aluminium - Aiguille du Midi 12 kg; direct, 2760 keV (1.8%) 2 1 k g ; direct, 2760 keV (1.3%) 1.6 kg;direct, 1370-2760 k e V (0.92%)

-+ 39 -+ 43

-+ 34 -+18

-+ 27 -+14 -+ 21

288 -+ 12 419 -+ 13 3.4 -+ 0.6

735 214

Duralumin - Mont Blanc 142 g; chemical, 511-511 keV(6.2%) 511-1786 keV (2.6%)

Production of 24Na from AI and Mg

r 598 189 423

gross at t = 0

Counting rate **

Duralumin - Aiguille du Midi 172 g; chemical, 511-511 keV (6.2%) 511-1786 keV (2.6%) l 1 2 g; direct, 511-511 k e V ( 3 . 4 % )

Production of 22Na from Al

Sample and location weight, determination method *

Rates of production of 22Na and 24Na from a l u m i n i u m and magnesium by cosmic rays measured at the AiguiUe du Midi (altitude of 3840 m), Mont Blanc (4600 m) and Col du Lantaret (2070 m)

TABLE 1

4~ O~

47 3. Theoretical calculation of production rates We consider here only the interaction of galactic cosmic rays. The calculation of the production rates was carried out by using a three-step cascade model, which was used for lunar samples. Since the details were given in a previous paper [2], only a brief description which is necessary to the discussion, will be given here. From the assumption of exponential decrease of the primary cosmic ray flux with the traversed length, D/cos 0, we obtain: 7r/2 Nl,D = NI,O f

exp(-/alD/cos 0) sin 0 d0

O

= N1 ,o [exp(-/alD) + ~1D Ei(-btlD)]

(1)

where Nl,o is the flux of the incident energetic primary particles (2.5 nucleon cm -2 s -1 (21r) -1 at the polar region), N l , o is the flux of the high-energy component at an atmospheric depth D (g cm-2), 0 is the incident zenith angle,/a 1 is the attenuation coefficient, and Ei designates the exponential integral function. Fluxes of medium- and low-energy particles, N2, D and N3, D, are supposed to be in equilibrium with the flux of the high-energy component, and estimated to be respectively 2.0 N 1,D and 8.0 N 1,D (for the choice of these numerical factors, see the previous paper [2]). The energy domains of the three components are respectively E > 1 BeV, 1 BeV > E > 100 MeV, and 100 MeV > E > 2 MeV. A 1/E decrease of the differential energy spectrum of the third component was assumed (it is a good approximation between 3 and 100 MeV). Since the cross-section does not vary much for energies of more than 100 MeV, the shape of the energy spectrum is not important for the highand the medium-energy components. As it is seen in equation (1), the decrease of the flux as a function of depth is not a simple exponential decrease, as long as we assume an exponential decrease of the flux with the traversed length, D/cos 0, which seems physically more probable. Nevertheless, for a limited interval of depth, for example, from 650 to 1030 g c m -2, equation (1) can be approximated by an exponential decrease with the depth, D:

N1 , D

=

kNl ,o e x p ( - P l ' D )

(2)

where/a 1' is the apparent attenuation coefficient and k is a correction factor. Mabuchi et al. [3] measured the production rates of 32p by the action of cosmic rays on sulphur at the atmospheric depth between 664 and 1030 g cm -2, and found an apparent attenuation coefficient of 1/(160 -+ 5) cm 2 g - l . From the comparison of equations (1) and (2), we found it corresponding to a true attenuation coefficient of 1/(192 --- 6) cm 2 g - l . On the other hand, Imamura et al. [4] measured the depth profile of SaMn in a lunar soil core down to 416 g cm -2 and found a true attenuation coefficient of 1/(220 +- 55) cm 2 g - l , which is in good agreement with the result of Mabuchi et al. We adopt here an attenuation coefficient of 1/192 cm 2 g-1 and use this to calculate the fluxes with equation (1). The effect of the geomagnetic field on the cosmic ray flux was estimated, as a function of cut-off rigidity, from Merker et al. [5] and Light et al. [6]. In the region of Mont Blanc (cut-off rigidity of 4.7 GV), the fluxes are estimated to be 67% of the fluxes at the polar region. The excitation functions of the formation of radionuclides were taken from the following papers: 3H, 14C, 36Cl, 37At and 39A£ [7]; 22Na and 26A1 ([8-12], see also Appendix in Yokoyama et al. [2]); 53Mn, S4Mn and SSFe [13]; 7Be [14]; 24Na [11,15]. A ratio of 0.123, average of 0.08 [14], 0.14 [16] and 0.15 [17], is adopted for the production of l°Be/TBe, using the new half-life of 1°Be [18]. The excitation functions of the production of 22Na and 26A1 from Ca are calculated by the formula of Silberberg and Tsao [19]. The ratio of the production of 26gAl/26mAl is assumed to be 3.

4. Results of calculation and discussion The calculated production rates of 22Na and 24Na from ahiminium are given in Fig. 2 as a function of atmospheric depth. A good agreement is obtained between the experimentally measured production rates and the calculated ones. The calculated production rate of 24Na from magnesium, 5.6 atoms min -1 kg -1 is also in good agreement with the measured production rate of 6.0 + 1.7 atoms min -1 kg -1. The productions of 24Na from aluminium and from magnesium are due to very low-energy reactions, 27A1-

48 i

i

TABLE 2

f

Calculated production rates of radionuclides in rocks by cosmic rays at the Aiguille du Midi (altitude 3840 m, atmospheric depth 640 g cm -2, geomagnetic latitude 47.4°N, cut-off rigidity 4.7 GV)

o ~

~

E to

:3 "0

~ ,_1

_--

m_=

=

_=

o._=

~

.

Nuclide t

tt

E

1

E 0

;

1

AI 2_ 4Na 1

AI _..Na 22

cO

"(3 0

e~

atmospheric depth (g i

I

I

J

26A1 36C1 3TAr 39Ar 53Mn 54Mn SSFe

12.3 53.3 days 1.6 × 106 5730 2.6 7.16 × 105 3.01 X 105 35 days 269 3.7 × 106 312.5 days 2.7

Production rate (atoms min -1 kg-1) granite

basalt

limestone

2.1 0.45 0.06 0.37 0.72 1.24 0.21 0.04 0.40 0.04 0.04 0.11

2.0 0.41 0.05 0.34 0.72 1.12 0.19 0.65 0.24 0.24 0.27 0.74

2.0 0.48 0.06 0.37 0.03 0.04 0.84 4.1 0.80 -

Chemical compositions used for calculation are: SiO2 73.0%, A1203 14.0%, FeO + Fe203 1.5%, MgO 0.2%, CaO 0.5%, Na20 4.0%, K20 3.5% for granite; SiO2 52.5%, AI203 16.0%, FeO + Fe203 10.0%, MgO 6.0%, CaO 9.0%, Na20 3.0%, K20 1.0% for basalt; and CaCO3 100% for limestone.

, 1000~,

500 I

/c m2" ",,

3H 7Be t0Be 14C 22Na

Half-life (years, unless otherwise stated)

I

I

i

Fig. 2. Production rates of 22Na and 24Na from aluminium as a function of atmospheric depth. The experimental values are shown as solid circles with error bars (22Na) and ppen circle with error bars (24Na). The'curves show the theoretically calculated production rates.

(n, a) 24Naand 24Mg(n, p) 24Na, o f which the excitation functions show maximums at 13.0 MeV and 13.4 MeV, respectively. The production o f 22Na from aluminium is due to relatively low-energy reactions, of which excitation function has a pronounced maximum at 35 MeV. Therefore, the good agreements o f the theoretical estimations with the experimental data for these two nuclides can be a fair indication of the validity o f our model, especially for low-energy reactions. As for high-energy reactions, we calculated the production rates o f 7Be from oxygen, and compared

its results with the experimentally measured production rates by Lal et al. [20] at Echo Lake (cut-off rigidity o f 3.0 GV and atmospheric depth o f 685 g cm - 2 ) and by Nakamura et al. [21] at Mt. Fuji (11.8 GV, 772 g c m - 2 ) , at Tokyo (11.6 GV, 1033 g c m - 2 ) and at Gif-sur-Yvette (3.6 GV, 1030 g cm-Z). Good agreements are obtained between their observed production rates and our calculated rates: Echo Lake, 0.58 + 0.06 (calculated rate 0.63); Mt. Fuji, 0.144 -+ 0.024 (calculated rate 0.142); Tokyo, 0.025 -+-0.004 (calculated rate 0.030); and Gif-sur-Yvette, 0.06 -+0.012 (calculated rate 0 . 0 7 2 ) i n units o f atoms min -1 kg -1 oxygen. The production rates o f principal radionuclides in rocks were calculated as a function o f altitude. The results for the AiguiUe du Midi (altitude 3840 m, vertical cut-off rigidity 4.7 GV) are summarized in Table 2. These calculated production rates include the productions due to pions, but not the productions due to muons such as 39K(,u-,/))39Ay, 285i0J-, u2n)-

49 TABLE 3 Relative production rates of cosmonuclides (1) As a function of altitude Altitude (m)

0

Atmospheric depth (g cm - 2 ) Relative production rate

1033 0.09

Altitude (m)

3500

Atmospheric depth (g cm - 2 ) Relative production rate

500

1000

973 0.13 3840

670 0.83

1500

916 0.18

862 0.25

4000

640 set 1.00

2000 810 0.35

5000

628 1.08

6000

551 1.76

481 2.8

2500

3000

761 0.47

714 0.63

7000

8000

419 4.2

363 6.0

(2) As a function of cut-off rigidity Cut-off rigidity (GV) Geomagnetic latitude ( o ) . Europe, North Africa South Africa North America South America Asia Australia Relative production rate **

0

1

2

3

4

6

8

80 -80 80 -80 80 -80

62 -60 58 -64 56 -57

56 -50 52 -58 49 -51

52 -43 47 -53 44 -47

49 -38 44 -49 40 -44

43 -31 38 -41 35 -39

39 -25 32 -34 31 -34

1.49

1.49

1.39

1.23

1.09

0.86

0.70

10

12

15

35 -18 28 -28 28 -30

30 -11 20 -14 25 -26

15 0 17 -17

0.56

0.45

0.37

* Geomagnetic latitudes are those which approximately correspond to the cut-off rigidities on each continent. ** Set 1.00 for a cut-off rigidity of 4.7 GV.

26A1 and 27Al(,u-, vt)24Na. Contributions of muon reactions are negligible for near surface samples: for example, at sea level they are ~<10% of the productions due to nucleons except the production of 3TAr from K (about 40%). For a depth of several meters underground the productions by muons, however, become predominant [22,23]. The precision of the calculated production rates are estimated to be about +-20% for 7Be, 22Na, 24Na, 26A1, 36C1, 37At, 53Mn, 54Mn and SSFe, and +35% for 3H, l ° B e , 14C and 39At. The production rates for other altitudes and/or for other cut-off rigidities can be obtained by multiplying the value of Table 2 with the factors indicated in Table 3. Snow cover can attenuate the cosmic ray flux. Since the attenuations per g cm - 2 are practically independent of the nature of matter (air, ice, or rock), the correction can be made by taking into account an additional depth (g cm -2) due to snow to the real

atmospheric depth. A snow cover of 110 g c m - 2 diminishes the production rates to half. The expected activities of these radionuclides in rocks are equal to the production rates, if we assume saturation. This condition can be satisfied only for the short-lived nuclides. For long-lived nuclides, if we assume a constant erosion rate a (g cm -2 y - l ) , the activities can be estimated to be A0/(1 +/a'orr) where A 0 is the production rate,/2' is 1/180 cm 2 g-1, and r is the mean life of the nuclide (in years). The expected activities summarized in Table 2 are in the range of what can be measured with present techniques. It is therefore possible to use the measure. ments of these cosmonuclides as a tool to study geophysical processes such as the erosion of rocks. The wide variety of half-lives of these nuclides permits one to choose among them to suit each particular problem. In some favorable cases, the method can also be applied to the dating of volcanic lava or archaeological objects.

50 Acknowledgements We are grateful to Dr. Jacques Labeyrie for his c o n s t a n t e n c o u r a g e m e n t . We wish to t h a n k the staff o f the l a b o r a t o r y o f Dr. Claude Lorius, in particular Dr. Pourchet, o f the Laboratoire de Glaciologie Alpine du C N R S for making samples available to us. The use o f the facilities at the O R T F Television T o w e r o f the AiguiUe du Midi is gratefully acknowledged.

References 1 N. Bourrelly and N. Deschamps, Etude du comportement des m6taux alcalins sur le pentoxyde d'antimoine hydrat6, J. Radioanal. Chem. 8 (1971) 303-312. 2 Y. Yokoyama, J. Sato, J.L. Reyss and F. Guichard, Variation of solar cosmic-ray flux deduced from 22Na-26A1 data in lunar samples, Proc. 4th. Lunar Sci. Conf., Geochim. Cosmochim. Acta, Suppl. 4, 2 (1973) 2209-2227. 3 H. Mabuchi, R. Gensho, Y. Wada and H. Hamaguchi, Phosphorus-32 induced by atmospheric cosmic rays in laboratory chemicals, Geochem. J. 4 (1971) 105-110. 4 M. lmamura, R.C. Finkel and M. Wahlen, Depth profile of 53Mn in the lunar surface, Earth Planet. Sci. Lett. 20 (1973) 107-112. 5 M. Merker, E.S. Light, H.J. Verschell, R.B. Mendell and S.A. Korff, Time dependent world-wide distribution of atmospheric neutrons and of their products, 1. Fast neutron observations, J. Geophys. Res. 78 (1973) 2727-2740. 6 E.S. Light, M. Merker, H.J. Verschell, R.B. Mendell and S.A. Korff, Time dependent world-wide distribution of atmospheric neutrons and of their products, 2. Calculation, J. Geophys. Res. 78 (1973) 2741-2762. 7 R.C. Reedy and J.R. Arnold, Interaction of solar and galactic cosmic-ray particles with the moon, J. Geophys. Res., 77 (1972) 537-555. 8 M. Furukawa, K. Shizuri, K. Komura, K. Sakamoto and S. Tanaka, Production of 26A1 and 22Na from proton bombardment of Si, AI, and Mg, Nucl. Phys. A174 (1971) 539-544. 9 S. Regnier, M. Lagarde, G.N. Simonoff and Y. Yokoyama, Production de 26A1dans F e e t Si par protons de 0.6 et 24 GeV, Earth Planet. Sci. Lett. 18 (1973), 9-12.

10 C.H. de Lassus St-Genies and J. Tobailem, Sections efficaces des r6actions nucl6aires induites par protons, deutons, particules alpha, II. Fluor, n6on, sodium, magn6sium, Note CEA-N-1466 (2), CEA-France (1972). 11 J. Tobailem, C.H. de Lassus St-Genies and L. Leveque, Sections efficaces des r6actions nucl6aires induites par protons, deutons, particules alpha, I. R6actions nucl6aires moniteurs, Note CEA-N-1466 (1), CEA-France (1971). 12 J. Tobailem and C.H. de Lassus St-Genies, Sections efficaces des r6actions nucl6aires induites par protons, deutons, particules alpha, IV. Si (in preparation). 13 J. Tobailem and C.H. de Lassus St-Genies, Sections efficaces des r6actions nucl6aires induites par protons, deutons, particules alpha, II1. Fer, Note CEArN-1466 (3), CEA-France (1975). 14 F. Yiou, C. Seide and R. Bernas, Formation cross sections of lithium, beryllium and boron isotopes produced by the spallation of oxygen by high-energy protons, J. Geophys. Res. 74 (1969) 2447-2448. 15 J.R. Stehn, M.D. Goldberg, B.A. Magurno and R. WienerChasman, Neutron cross sections, 1. Z = 1 to 20, BNL325 (Brookhaven National Laboratory, 1964) 2nd ed., Suppl. 2. 16 R.C. Finkel, M. Imamura, M. Honda, K. Nishiizumi, C.P. Kohl, S.M. Kocimski and J.R. Arnold, Cosmic-rayproduced Mn and Be radionuclides in the lunar regolith (abstract), in: Lunar Science V (Lunar Science Institute, Houston, Texas, 1974) 228-229. 17 B.S. Amin, S. Biswas, D. Lal and B.L.K. Somayajulu, Radiochemical measurements of 10Be and 7Be formation cross-sections in oxygen by 135- and 550-MeV protons, Nucl. Phys. A195 (1972) 311-320. 18 F. Yiou and G.M. Raisbeck, Half-life of lOBe, Phys. Rev. Lett. 29 (1972) 372-375. 19 R. Silberberg and C.H. Tsao, Partial cross-sections in high-energy nuclear reactions and astrophysical applications, 1. Targets with Z < 28, Astrophys. J., Suppl. Set. 25, No. 220 (1973) 315-335. 20 D. Lal, J.R. Arnold and M. Honda, Cosmic-ray production rate of Be-7 in oxygen, P-32, P-33, S-35 in argon at mountain altitude, Phys. Rev. 118 (1960) 1626-1632. 21 Y. Nakamura, H. Mabuchi and H. Hamaguchi, Beryllium-7 production from oxygen by atmospheric cosmic rays, Geochem. J. 6 (1972) 43-47. 22 W. Hampel, J. Takagi, K. Sakamoto and S. Tanaka, Measurement of muonqnduced 26A1 in terrestrial silicate rock, J. Geophys. Res. 80 (1975) 3757-3760. 23 Rama and M. Honda, Cosmic-ray-induced radioactivity in terrestrial materials, J. Geophys. Res. 66 (1961) 3533-3539.