Cosmic-Ray Production Rate and Mean Removal Time of Beryllium-7 from the Atmosphere

Abstract

The ${\mathrm{Be}}^{7}$ production rate is given by the product of the nucleon flux (${E}_{\mathrm{nucleon}}>~40$ Mev), the ${\mathrm{Be}}^{7}$ production cross section, and an appropriate constant. The nucleon flux (as a function of altitude and latitude) is determined for ${E}_{\mathrm{nucleon}}>~500$ Mev from the fairly complete theoretical treatment available in the literature. For nucleons with energy between 40 Mev and 500 Mev, an approximate theory given in the literature is used. The sum of these two gives the nucleon flux applicable to ${\mathrm{Be}}^{7}$ production. The ${\mathrm{Be}}^{7}$ production cross section is obtained by multiplying the $\mathrm{C}(p, X){\mathrm{Be}}^{7}$ excitation function available in the literature by the $\frac{\mathrm{N}(p, X){\mathrm{Be}}^{7}}{\mathrm{C}(p, X){\mathrm{Be}}^{7}}$ ratio obtained at Bev energies.The ${\mathrm{Be}}^{7}$ production rate in the atmosphere as a function of latitude and altitude is then obtained. Since the main errors lie in the determination of the nucleon flux, the derived flux curves are compared to literature data on the latitude effect and star production rate. The agreement is found to be satisfactory and error limits are placed at \ifmmode\pm\else\textpm\fi{}50%.The mixing and washout processes in the atmosphere are then considered. The production rate of ${\mathrm{Be}}^{7}$ in the stratosphere is found to be 5.0 atoms/${\mathrm{cm}}^{2}$ min, and 1.3 atoms/${\mathrm{cm}}^{2}$ min for the troposphere (assumed tropopause=35 000 ft). The production rates are used with the rain water removal rate to determine the stratosphere mean removal time as a function of the troposphere mean removal time. Curves of this function are presented for three different average tropopause elevations (30 500 ft, 35 000 ft, 40 000 ft). Compared to these curves, the approximate literature values of 120 days and 14 days for ${\mathrm{Be}}^{7}$ mean removal times from the stratosphere and troposphere respectively, seem too short. Longer times are indicated, of the order of years for the stratosphere, and three weeks or more for the troposphere. Recent experimental evidence in the literature appears to confirm this.