- Email: [email protected]
Production rates of 7Be and 10Be in the atmosphere
Nuclear Instruments and Methods in Physics Research B 172 (2000) 796±801
Production rates of 7 Be and
10
www.elsevier.nl/locate/nimb
Be in the atmosphere
Hisao Nagai *, Wataru Tada, Takayuki Kobayashi Department of Chemistry, College of Humanities and Sciences, Nihon University, 3-25-40 Sakura-Josui, Setagaya, Tokyo 156-8550, Japan
Abstract We have estimated the production rates of cosmogenic 7 Be and 10 Be in the stratosphere and troposphere using the neutron and proton cross-sections for 14 N and 16 O. The global average production rates (atoms cmÿ2 sÿ1 ) are 0.041 (7 Be) and 0.018 (10 Be) in the stratosphere and 0.027 (7 Be) and 0.018 (10 Be) in the troposphere for the solar minimum. To convert to long-term average production rates, these values are multiplied by 0.8±0.9. The correlation between these production rates and the observed 10 Be/7 Be ratio in the atmosphere and its seasonal variation is shown using a simple box model calculation with adequate parameters. Ó 2000 Elsevier Science B.V. All rights reserved. PACS: 96.40.Vw Keywords: Production rate; Cosmogenic nuclide; 7 Be;
10
1. Introduction The radionuclides 7 Be (53.35 d half-life) and Be (1.5 ´ 106 yr) are produced by cosmic rays in the atmosphere. Although the ratio of the production rates for these two nuclides in the atmosphere is assumed to be constant, the atomic ratio changes with time for the relatively short half-life of 7 Be. We have already reported that the 10 Be/7 Be ratio in the atmosphere changes from 1.3 in the northern hemisphere (0±40°N) to 1.9 in the southern hemisphere (0±60°S) over the Western Paci®c Ocean and adjacent areas during December 10
*
Corresponding author. Tel.: +81-3-5317-9738; fax: +81-35317-9433. E-mail address: [email protected] (H. Nagai).
Be; Atmosphere
to February [1]. To interpret this result, two factors are required. One is a transport mechanism which is related to time; the other is the initial ratio, i.e., the ratio of the production rates of 10 Be to 7 Be. The observation of the 7 Be and 10 Be concentrations in the atmosphere gives important information about the production and behavior of these nuclides in the atmosphere, as pointed out by Raisbeck et al. [2] and Dibb et al. [3]. We present calculations of the production rates, which involve a modi®cation of the nuclide production model presented by Lal and Peters [4], using the neutron and proton cross-sections for 7 Be and 10 Be production from N and O, and the neutron and proton ¯uxes in the atmosphere. In addition, we discuss the correlation between the calculated production rates and the observed 10 Be/ 7 Be ratio at sea level using a box model.
0168-583X/00/$ - see front matter Ó 2000 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 5 8 3 X ( 0 0 ) 0 0 1 2 4 - 5
H. Nagai et al. / Nucl. Instr. and Meth. in Phys. Res. B 172 (2000) 796±801
2. Production rates 2.1. Cross-sections The excitation functions used to calculate the production rates for 7 Be and 10 Be are shown in Fig. 1. These curves were drawn mostly based on the experimental data for the 7 Be and 10 Be productions from: (i) 14 N, 16 O + n by Imamura et al. [5]; (ii) 16 O + p by Sisterson et al. [6]; (iii) 14 N + p compiled by Read and Viola Jr. [7]. In the energy region over 100 MeV, the neutron excitation functions were extrapolated to the corresponding proton excitation functions. The uncertainties in the excitation functions depend mainly on the experimental errors. 2.2. Vertical pro®les of the production rates
797
nation of product nuclide, target nuclide and incident particle. We used the neutron spectra calculated for various atmospheric depths by Armstrong et al. [8], Fig. 2. The vertical distribution of the total proton ¯ux was approximated as ftot d ftot 0 eÿ0:00714d , and the same spectral shape was applied to all depths. The total proton ¯ux was normalized to the total neutron ¯ux using the relation given by Lal and Peters [4]. Fig. 3 shows the vertical distributions of the 7 Be and 10 Be production rates. It is clear that most of the nuclides are produced by neutron-induced reactions, except for 7 Be production by 14 N + p in the stratosphere. In addition, most of the 7 Be atoms produced in the stratosphere do not reach sea level. Thus, the neutron ¯ux and its spectral shape are the dominant factors for the 10 Be/7 Be ratio in the atmosphere at sea level.
Production rates P(d) (7 Be or 10 Be) at eight atmospheric depths d (in g cmÿ2 ) were calculated using Z P d
E2 E1
Nf E; dr E dE
E1 10 MeV; E2 10 GeV; where N is the number of target atoms (14 N or 16 O), f the neutron or proton ¯ux and r(E) is the excitation function for the corresponding combi-
Fig. 1. Excitation functions for the 7 Be and from 14 N and 16 O by neutrons and protons.
10
Be productions
Fig. 2. Calculated neutron spectra for various atmospheric depths at k 42°N in the solar minimum (after Armstrong et al. [8]). These ¯uxes are multiplied by 10ÿ1 for 5 and 400 (g cmÿ2 ), 10ÿ2 for 10 and 600 (g cmÿ2 ), 10ÿ3 for 50 and 800 (g cmÿ2 ) and 10ÿ4 for 100 and 1033 (g cmÿ2 ).
798
H. Nagai et al. / Nucl. Instr. and Meth. in Phys. Res. B 172 (2000) 796±801
Fig. 3. Depth pro®les of the 7 Be and the atmosphere.
10
Be production rates in
2.3. Global distributions of the production rates The global distributions of the 7 Be and 10 Be production rates were calculated based on the global distribution of the nuclear disintegration rate presented by Lal and Peters [4]. Our calculation included some modi®cation to the original distribution. For each latitude, the 7 Be and 10 Be production rates for each altitude were calculated from the corresponding nuclear disintegration rate multiplied by the normalization factor obtained by our vertical distributions of the 7 Be and 10 Be production rates. Figs. 4(a) and (b) show the latitudinal distributions of the 7 Be and 10 Be production rates per unit area and the integrated value along each latitude, respectively. If the produced nuclides do not move along the longitude, south or north, the distributions of these nuclides would be the same as shown in Fig. 4(a). On the other hand, if the air over a certain latitudinal range is mixed well, the total number of produced nuclides is obtained by integrating the distributions of total number of production rates per each latitude (Fig. 4(b)), and the
Fig. 4. Latitudinal distributions of the 7 Be and 10 Be production rates in the atmosphere: (a) per unit area; (b) integrated for each latitude.
average production rates are calculated from these values and the surface area of the corresponding latitudinal range. The global average production rates of 7 Be and 10 Be listed in Table 1 are calculated in this way. Since our calculation was based on the neutron ¯ux during solar minimum, the long-term average production rates may be 10±20% lower than those listed in Table 1. Following this estimation, the long-term average production rate of 10 Be was calculated to 0.028±0.032 atoms cmÿ2 sÿ1 , which is Table 1 Global average production rates of atmosphere for the solar minimum
7
Be and
10
Be in the
Production rate (atoms cmÿ2 sÿ1 ) 7
Stratosphere Troposphere Total a
Be
0.041 0.027
a
10
Be
0.018 0.018 0.036
Calculated to be 0.068, but there is no meaning for this value.
H. Nagai et al. / Nucl. Instr. and Meth. in Phys. Res. B 172 (2000) 796±801
higher than 0.0184 atoms cmÿ2 sÿ1 calculated by Masarik and Beer [9] and lower than 0.038 atoms cmÿ2 sÿ1 determined from a wet precipitation measurement by Monaghan et al. [10]. 3. Box model 3.1. Distribution of
10
Be/7Be in the atmosphere
The average 10 Be/7 Be ratios observed in the atmosphere near sea level were 2:00 0:46 and 1:89 0:42 for the northern and southern hemisphere during the ``summer'', respectively, and 1:24 0:27 for the northern hemisphere during the ``winter''. The summer corresponds to December to February for the southern hemisphere and July to August for the northern hemisphere and the winter corresponds to December to February for the northern hemisphere in Table 2. In addition, the summer and the winter indicate the periods in the year in which the 10 Be/7 Be ratios are high and low in the atmosphere near sea level, respectively. These data are the average of the 10 Be/7 Be ratio observed in the atmosphere over the Western Paci®c, Indian and Southern Ocean and adjacent areas, which range from 60°S to 50°N during the mentioned six cruises from 1994 to 1998. The details of the experiments will be reported elsewhere.
799
dN10 S or T =dt P10 S or T ÿ k S or T N10 S or T kS N10S ; dN7 S or T =dt P7 S or T ÿ k S or T kN7 S or T kS N7S ;
where N and P are the concentrations and production rates of the Be isotopes, respectively, in the atmosphere; k is the 7 Be decay constant; k the removal rate constant, which is expressed as k 1=s (s is the mean residence time); subscripts 7 and 10 denote 7 Be and 10 Be, respectively; subscripts S and T denote the stratosphere and troposphere, respectively; the last terms in the equations are used only for the troposphere. To induce a seasonal variation of the 10 Be/7 Be ratio in the atmosphere on the box model calculation, kS is set to k1 during the summer for the period DT (yr) and k2 during the winter (k1 > k2 ). The residence times for the stratosphere (sS ) and troposphere (sT ) are assumed to be 1.5 yr and 30 d, respectively, which are typical values obtained from the study on fall-out nuclides (90 Sr, 137 Cs and 239; 240 Pu) [11] and the study on 7 Be [3,12]. Then, two parameters, DT and k1 /k2 , are left as variables. In Fig. 5, the calculated 10 Be/7 Be
3.2. Box model calculation We adopted a simple two-box model consisting of a stratosphere and a troposphere box in order to correlate the calculated production rates and the observed data. The equations are written as follows: Table 2 Seasonal variation of
10
Northern hemisphere Southern hemisphere Average a
Be/7 Be in the atmospherea Summer
Winter
2:00 0:46 1:89 0:42 1:92 0:44b
1:24 0:27 ± 1:24 0:27
The errors indicate standard deviation (1r). This value is not the average of the northern and southern hemisphere, but the average of all data for summer.
b
Fig. 5. 10 Be/7 Be ratio during the summer versus 10 Be/7 Be ratio during the winter by a two-box model calculation. The residence time for the stratosphere, sS 1:5 yr, and for the troposphere, sT 30 d (see text). The solid lines indicate constant DT. The ®gures located at each end of the line indicate the period (DT) of high exchange rate (k1 ). The ®gures located below the dot indicate the k1 /k2 ratio.
800
H. Nagai et al. / Nucl. Instr. and Meth. in Phys. Res. B 172 (2000) 796±801
ratios during the summer (maximum value) are plotted against the 10 Be/7 Be ratios during the winter (minimum value), and all data points for the same DT are connected by a line. On each line, k1 / k2 varies from 1 to 1000, which means a constant exchange rate throughout the year, and restricted exchange only during the summer between the stratosphere and troposphere, respectively. The average of the observed data is plotted as a cross (+); also, the standard deviations are indicated by the dotted lines. Although various conditions are included in the dotted square, one can interpret the result of the calculations more clearly if the low probability conditions plotted near to the dotted lines are excluded. For the typical average condition, DT 0:4 yr and k1 =k2 5, the seasonal variation for the 7 Be and 10 Be concentrations and 10 Be/7 Be ratios are shown in Fig. 6. The 10 Be concentration and 10 Be/7 Be ratio in the troposphere show large seasonal variations. On the other hand, the 7 Be concentrations in the stratosphere and troposphere and the 10 Be concentration and 10 Be/ 7 Be ratio in the stratosphere show small seasonal variations.
4. Summary The production rates of 7 Be and 10 Be in the stratosphere and troposphere, which were calculated using the neutron and proton cross-sections for N and O, are not so far from the estimations given by the previous studies [9,10]. The uncertainty in our estimation will be decreased when more accurate information about the distribution of the neutron ¯ux and the spectral shape in the atmosphere are obtained. The 7 Be and 10 Be concentrations and 10 Be/7 Be ratios in the atmosphere near sea level give important information about the production and transportation of these nuclides in the atmosphere. By adopting a simple box model, the production rate and the parameters for the transportation of the nuclides in the atmosphere, such as residence time and air exchange rate through the tropopause, are limited by the 7 Be and 10 Be concentrations and their ratios measured in the atmosphere. Acknowledgements This work was partly supported by a grantin-aid for Scienti®c Research (No. 11440168, H. Nagai, Principal Investigator) from the Ministry of Education, Science, Sports and Culture, Japan. References
Fig. 6. Seasonal variation of the 7 Be and 10 Be concentrations and 10 Be/7 Be ratios in the stratosphere and troposphere, starting from the beginning of summer (Time 0) to the end of winter (Time 1 yr).
[1] H. Nagai, M. Uchida, M. Murayama, N. Ahagon, M. Ikehara, M. Imamura, S. Hatori, K. Kobayashi, (AMS 7 abstracts) Radiocarbon 38 (1996) 94. [2] G.M. Raisbeck, F. Yiou, M. Fruneau, J.M. Loiseaux, M. Lieuvin, J.C. Ravel, Geophys. Res. Lett. 8 (1981) 1015. [3] J.E. Dibb, L.D. Meeker, R.C. Finkel, J.R. Southon, M.W. Caee, L.A. Barrie, J. Geophys. Res. 99 (D6) (1994) 12855. [4] D. Lal, B. Peters, in: S. Fl ugge, K. Sitte (Eds.), Handbuch der Physik, Vol. 46/2, Springer, Berlin, 1967, p. 551. [5] M. Imamura et al., Private communication. [6] J.M. Sisterson, K. Kim, A. Beverding, P.A.J. Englert, M. Caee, A.J.T. Jull, D.J. Donahue, L. McHargue, C. Castaneda, J. Vincent, R.C. Reedy, Nucl. Instr. and Meth. B 123 (1997) 324. [7] S.M. Read, V.E. Viola Jr., At. Data Nucl. Data Tables 31 (1984) 359. [8] T.W. Armstrong, K.C. Chandler, J. Barish, J. Geophys. Res. 78 (1973) 2715.
H. Nagai et al. / Nucl. Instr. and Meth. in Phys. Res. B 172 (2000) 796±801 [9] J. Masarik, J. Beer, J. Geophys. Res. 104 (D10) (1999) 12099. [10] M.C. Monaghan, S. Krishnaswami, K.K. Turekian, Earth Planet. Sci. Lett. 76 (1985/86) 279.
801
[11] K. Hirose, M. Aoyama, Y. Katsuragi, Y. Sugimura, J. Meteorol. Soc. Japan 65 (1987) 259. [12] M.A. Shapiro, J.L. Forbes-Resha, J. Geophys. Res. 81 (1976) 2647.
Production rates of 7 Be and
10
www.elsevier.nl/locate/nimb
Be in the atmosphere
Hisao Nagai *, Wataru Tada, Takayuki Kobayashi Department of Chemistry, College of Humanities and Sciences, Nihon University, 3-25-40 Sakura-Josui, Setagaya, Tokyo 156-8550, Japan
Abstract We have estimated the production rates of cosmogenic 7 Be and 10 Be in the stratosphere and troposphere using the neutron and proton cross-sections for 14 N and 16 O. The global average production rates (atoms cmÿ2 sÿ1 ) are 0.041 (7 Be) and 0.018 (10 Be) in the stratosphere and 0.027 (7 Be) and 0.018 (10 Be) in the troposphere for the solar minimum. To convert to long-term average production rates, these values are multiplied by 0.8±0.9. The correlation between these production rates and the observed 10 Be/7 Be ratio in the atmosphere and its seasonal variation is shown using a simple box model calculation with adequate parameters. Ó 2000 Elsevier Science B.V. All rights reserved. PACS: 96.40.Vw Keywords: Production rate; Cosmogenic nuclide; 7 Be;
10
1. Introduction The radionuclides 7 Be (53.35 d half-life) and Be (1.5 ´ 106 yr) are produced by cosmic rays in the atmosphere. Although the ratio of the production rates for these two nuclides in the atmosphere is assumed to be constant, the atomic ratio changes with time for the relatively short half-life of 7 Be. We have already reported that the 10 Be/7 Be ratio in the atmosphere changes from 1.3 in the northern hemisphere (0±40°N) to 1.9 in the southern hemisphere (0±60°S) over the Western Paci®c Ocean and adjacent areas during December 10
*
Corresponding author. Tel.: +81-3-5317-9738; fax: +81-35317-9433. E-mail address: [email protected] (H. Nagai).
Be; Atmosphere
to February [1]. To interpret this result, two factors are required. One is a transport mechanism which is related to time; the other is the initial ratio, i.e., the ratio of the production rates of 10 Be to 7 Be. The observation of the 7 Be and 10 Be concentrations in the atmosphere gives important information about the production and behavior of these nuclides in the atmosphere, as pointed out by Raisbeck et al. [2] and Dibb et al. [3]. We present calculations of the production rates, which involve a modi®cation of the nuclide production model presented by Lal and Peters [4], using the neutron and proton cross-sections for 7 Be and 10 Be production from N and O, and the neutron and proton ¯uxes in the atmosphere. In addition, we discuss the correlation between the calculated production rates and the observed 10 Be/ 7 Be ratio at sea level using a box model.
0168-583X/00/$ - see front matter Ó 2000 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 5 8 3 X ( 0 0 ) 0 0 1 2 4 - 5
H. Nagai et al. / Nucl. Instr. and Meth. in Phys. Res. B 172 (2000) 796±801
2. Production rates 2.1. Cross-sections The excitation functions used to calculate the production rates for 7 Be and 10 Be are shown in Fig. 1. These curves were drawn mostly based on the experimental data for the 7 Be and 10 Be productions from: (i) 14 N, 16 O + n by Imamura et al. [5]; (ii) 16 O + p by Sisterson et al. [6]; (iii) 14 N + p compiled by Read and Viola Jr. [7]. In the energy region over 100 MeV, the neutron excitation functions were extrapolated to the corresponding proton excitation functions. The uncertainties in the excitation functions depend mainly on the experimental errors. 2.2. Vertical pro®les of the production rates
797
nation of product nuclide, target nuclide and incident particle. We used the neutron spectra calculated for various atmospheric depths by Armstrong et al. [8], Fig. 2. The vertical distribution of the total proton ¯ux was approximated as ftot d ftot 0 eÿ0:00714d , and the same spectral shape was applied to all depths. The total proton ¯ux was normalized to the total neutron ¯ux using the relation given by Lal and Peters [4]. Fig. 3 shows the vertical distributions of the 7 Be and 10 Be production rates. It is clear that most of the nuclides are produced by neutron-induced reactions, except for 7 Be production by 14 N + p in the stratosphere. In addition, most of the 7 Be atoms produced in the stratosphere do not reach sea level. Thus, the neutron ¯ux and its spectral shape are the dominant factors for the 10 Be/7 Be ratio in the atmosphere at sea level.
Production rates P(d) (7 Be or 10 Be) at eight atmospheric depths d (in g cmÿ2 ) were calculated using Z P d
E2 E1
Nf E; dr E dE
E1 10 MeV; E2 10 GeV; where N is the number of target atoms (14 N or 16 O), f the neutron or proton ¯ux and r(E) is the excitation function for the corresponding combi-
Fig. 1. Excitation functions for the 7 Be and from 14 N and 16 O by neutrons and protons.
10
Be productions
Fig. 2. Calculated neutron spectra for various atmospheric depths at k 42°N in the solar minimum (after Armstrong et al. [8]). These ¯uxes are multiplied by 10ÿ1 for 5 and 400 (g cmÿ2 ), 10ÿ2 for 10 and 600 (g cmÿ2 ), 10ÿ3 for 50 and 800 (g cmÿ2 ) and 10ÿ4 for 100 and 1033 (g cmÿ2 ).
798
H. Nagai et al. / Nucl. Instr. and Meth. in Phys. Res. B 172 (2000) 796±801
Fig. 3. Depth pro®les of the 7 Be and the atmosphere.
10
Be production rates in
2.3. Global distributions of the production rates The global distributions of the 7 Be and 10 Be production rates were calculated based on the global distribution of the nuclear disintegration rate presented by Lal and Peters [4]. Our calculation included some modi®cation to the original distribution. For each latitude, the 7 Be and 10 Be production rates for each altitude were calculated from the corresponding nuclear disintegration rate multiplied by the normalization factor obtained by our vertical distributions of the 7 Be and 10 Be production rates. Figs. 4(a) and (b) show the latitudinal distributions of the 7 Be and 10 Be production rates per unit area and the integrated value along each latitude, respectively. If the produced nuclides do not move along the longitude, south or north, the distributions of these nuclides would be the same as shown in Fig. 4(a). On the other hand, if the air over a certain latitudinal range is mixed well, the total number of produced nuclides is obtained by integrating the distributions of total number of production rates per each latitude (Fig. 4(b)), and the
Fig. 4. Latitudinal distributions of the 7 Be and 10 Be production rates in the atmosphere: (a) per unit area; (b) integrated for each latitude.
average production rates are calculated from these values and the surface area of the corresponding latitudinal range. The global average production rates of 7 Be and 10 Be listed in Table 1 are calculated in this way. Since our calculation was based on the neutron ¯ux during solar minimum, the long-term average production rates may be 10±20% lower than those listed in Table 1. Following this estimation, the long-term average production rate of 10 Be was calculated to 0.028±0.032 atoms cmÿ2 sÿ1 , which is Table 1 Global average production rates of atmosphere for the solar minimum
7
Be and
10
Be in the
Production rate (atoms cmÿ2 sÿ1 ) 7
Stratosphere Troposphere Total a
Be
0.041 0.027
a
10
Be
0.018 0.018 0.036
Calculated to be 0.068, but there is no meaning for this value.
H. Nagai et al. / Nucl. Instr. and Meth. in Phys. Res. B 172 (2000) 796±801
higher than 0.0184 atoms cmÿ2 sÿ1 calculated by Masarik and Beer [9] and lower than 0.038 atoms cmÿ2 sÿ1 determined from a wet precipitation measurement by Monaghan et al. [10]. 3. Box model 3.1. Distribution of
10
Be/7Be in the atmosphere
The average 10 Be/7 Be ratios observed in the atmosphere near sea level were 2:00 0:46 and 1:89 0:42 for the northern and southern hemisphere during the ``summer'', respectively, and 1:24 0:27 for the northern hemisphere during the ``winter''. The summer corresponds to December to February for the southern hemisphere and July to August for the northern hemisphere and the winter corresponds to December to February for the northern hemisphere in Table 2. In addition, the summer and the winter indicate the periods in the year in which the 10 Be/7 Be ratios are high and low in the atmosphere near sea level, respectively. These data are the average of the 10 Be/7 Be ratio observed in the atmosphere over the Western Paci®c, Indian and Southern Ocean and adjacent areas, which range from 60°S to 50°N during the mentioned six cruises from 1994 to 1998. The details of the experiments will be reported elsewhere.
799
dN10 S or T =dt P10 S or T ÿ k S or T N10 S or T kS N10S ; dN7 S or T =dt P7 S or T ÿ k S or T kN7 S or T kS N7S ;
where N and P are the concentrations and production rates of the Be isotopes, respectively, in the atmosphere; k is the 7 Be decay constant; k the removal rate constant, which is expressed as k 1=s (s is the mean residence time); subscripts 7 and 10 denote 7 Be and 10 Be, respectively; subscripts S and T denote the stratosphere and troposphere, respectively; the last terms in the equations are used only for the troposphere. To induce a seasonal variation of the 10 Be/7 Be ratio in the atmosphere on the box model calculation, kS is set to k1 during the summer for the period DT (yr) and k2 during the winter (k1 > k2 ). The residence times for the stratosphere (sS ) and troposphere (sT ) are assumed to be 1.5 yr and 30 d, respectively, which are typical values obtained from the study on fall-out nuclides (90 Sr, 137 Cs and 239; 240 Pu) [11] and the study on 7 Be [3,12]. Then, two parameters, DT and k1 /k2 , are left as variables. In Fig. 5, the calculated 10 Be/7 Be
3.2. Box model calculation We adopted a simple two-box model consisting of a stratosphere and a troposphere box in order to correlate the calculated production rates and the observed data. The equations are written as follows: Table 2 Seasonal variation of
10
Northern hemisphere Southern hemisphere Average a
Be/7 Be in the atmospherea Summer
Winter
2:00 0:46 1:89 0:42 1:92 0:44b
1:24 0:27 ± 1:24 0:27
The errors indicate standard deviation (1r). This value is not the average of the northern and southern hemisphere, but the average of all data for summer.
b
Fig. 5. 10 Be/7 Be ratio during the summer versus 10 Be/7 Be ratio during the winter by a two-box model calculation. The residence time for the stratosphere, sS 1:5 yr, and for the troposphere, sT 30 d (see text). The solid lines indicate constant DT. The ®gures located at each end of the line indicate the period (DT) of high exchange rate (k1 ). The ®gures located below the dot indicate the k1 /k2 ratio.
800
H. Nagai et al. / Nucl. Instr. and Meth. in Phys. Res. B 172 (2000) 796±801
ratios during the summer (maximum value) are plotted against the 10 Be/7 Be ratios during the winter (minimum value), and all data points for the same DT are connected by a line. On each line, k1 / k2 varies from 1 to 1000, which means a constant exchange rate throughout the year, and restricted exchange only during the summer between the stratosphere and troposphere, respectively. The average of the observed data is plotted as a cross (+); also, the standard deviations are indicated by the dotted lines. Although various conditions are included in the dotted square, one can interpret the result of the calculations more clearly if the low probability conditions plotted near to the dotted lines are excluded. For the typical average condition, DT 0:4 yr and k1 =k2 5, the seasonal variation for the 7 Be and 10 Be concentrations and 10 Be/7 Be ratios are shown in Fig. 6. The 10 Be concentration and 10 Be/7 Be ratio in the troposphere show large seasonal variations. On the other hand, the 7 Be concentrations in the stratosphere and troposphere and the 10 Be concentration and 10 Be/ 7 Be ratio in the stratosphere show small seasonal variations.
4. Summary The production rates of 7 Be and 10 Be in the stratosphere and troposphere, which were calculated using the neutron and proton cross-sections for N and O, are not so far from the estimations given by the previous studies [9,10]. The uncertainty in our estimation will be decreased when more accurate information about the distribution of the neutron ¯ux and the spectral shape in the atmosphere are obtained. The 7 Be and 10 Be concentrations and 10 Be/7 Be ratios in the atmosphere near sea level give important information about the production and transportation of these nuclides in the atmosphere. By adopting a simple box model, the production rate and the parameters for the transportation of the nuclides in the atmosphere, such as residence time and air exchange rate through the tropopause, are limited by the 7 Be and 10 Be concentrations and their ratios measured in the atmosphere. Acknowledgements This work was partly supported by a grantin-aid for Scienti®c Research (No. 11440168, H. Nagai, Principal Investigator) from the Ministry of Education, Science, Sports and Culture, Japan. References
Fig. 6. Seasonal variation of the 7 Be and 10 Be concentrations and 10 Be/7 Be ratios in the stratosphere and troposphere, starting from the beginning of summer (Time 0) to the end of winter (Time 1 yr).
[1] H. Nagai, M. Uchida, M. Murayama, N. Ahagon, M. Ikehara, M. Imamura, S. Hatori, K. Kobayashi, (AMS 7 abstracts) Radiocarbon 38 (1996) 94. [2] G.M. Raisbeck, F. Yiou, M. Fruneau, J.M. Loiseaux, M. Lieuvin, J.C. Ravel, Geophys. Res. Lett. 8 (1981) 1015. [3] J.E. Dibb, L.D. Meeker, R.C. Finkel, J.R. Southon, M.W. Caee, L.A. Barrie, J. Geophys. Res. 99 (D6) (1994) 12855. [4] D. Lal, B. Peters, in: S. Fl ugge, K. Sitte (Eds.), Handbuch der Physik, Vol. 46/2, Springer, Berlin, 1967, p. 551. [5] M. Imamura et al., Private communication. [6] J.M. Sisterson, K. Kim, A. Beverding, P.A.J. Englert, M. Caee, A.J.T. Jull, D.J. Donahue, L. McHargue, C. Castaneda, J. Vincent, R.C. Reedy, Nucl. Instr. and Meth. B 123 (1997) 324. [7] S.M. Read, V.E. Viola Jr., At. Data Nucl. Data Tables 31 (1984) 359. [8] T.W. Armstrong, K.C. Chandler, J. Barish, J. Geophys. Res. 78 (1973) 2715.
H. Nagai et al. / Nucl. Instr. and Meth. in Phys. Res. B 172 (2000) 796±801 [9] J. Masarik, J. Beer, J. Geophys. Res. 104 (D10) (1999) 12099. [10] M.C. Monaghan, S. Krishnaswami, K.K. Turekian, Earth Planet. Sci. Lett. 76 (1985/86) 279.
801
[11] K. Hirose, M. Aoyama, Y. Katsuragi, Y. Sugimura, J. Meteorol. Soc. Japan 65 (1987) 259. [12] M.A. Shapiro, J.L. Forbes-Resha, J. Geophys. Res. 81 (1976) 2647.