Cosmic-Ray Air Showers at Sea Level

An investigation at sea level of cosmic-ray showers with sizes from 5×${10}^5$ to over ${10}^9$ particles is described. The core locations, arrival directions, and particle density distributions of several thousand showers whose cores landed within an area of ${10}^5$ ${\mathrm{m}}^2$ were determined by the techniques of fast-timing and density sampling. The most important results are as follows: (1) The existence of primary particles with energies greater than ${10}^{18}$ ev is established by the observation of one shower with more than ${10}^9$ particles. (2) The function $f\left(r\right)=0.45\left(\frac{N}{{R_0}^2}\right)r^{-0.7\mathrm{}}{\mathrm{}(1+r)\mathrm{}}^{-3.2\mathrm{}}$, where $r=\frac{R}{R_0}$ and $R_0=79\mathrm{}$ m, describes the lateral distribution of particles at distances in the range $50 \mathrm{m}<R<\mathrm{}400\mathrm{} \mathrm{m}$ and for showers with sizes in the range $5\times {10}^5<N<\mathrm{}{10}^8$. (3) At distances greater than 50 m from the core the density fluctuations in individual showers have a Poisson distribution. (4) The size and zenith angle distribution can be represented by the formula $s(N, x)=s_0{\left(\frac{{10}^6}{N}\right)}^{\Gamma +1\mathrm{}}\exp [-\frac{(x-x_0)}{\Lambda }]$, where $x=x_{0}sec\theta$, $x_0=1040\mathrm{}$ g ${\mathrm{cm}}^{-2\mathrm{}}$, $s_0=(6.6\mathrm{}\pm 1.0)\times {10}^{-8\mathrm{}}$ ${\mathrm{cm}}^{-2\mathrm{}}$ ${\sec }^{-1\mathrm{}}$ ${\mathrm{sterad}}^{-1\mathrm{}}$, $\Gamma =1.9\mathrm{}\pm 0.1$, $\Lambda =(113\mathrm{}\pm 9)$ g ${\mathrm{cm}}^{-2\mathrm{}}$, $x_0<x<\mathrm{}1.3\mathrm{}{x}_0$, and $7\times {10}^5<N<\mathrm{}7\mathrm{}\times {10}^8$. (5) No evidence is found of anisotropy in the arrival directions or of a break in the energy spectrum of the primaries up to the largest energies observed. (6) Assuming a specific model for shower development and taking into account fluctuations in the depth of the first interaction, the integral energy spectrum of the primaries is $J\left(E\right)=J_0{\left(\frac{{10}^{15}}{E}\right)}^{\gamma }$, where $J_0=(8.1\mathrm{}\pm 3.1)\times {10}^{-11\mathrm{}}$ ${\mathrm{cm}}^{-2\mathrm{}}$ ${\sec }^{-1\mathrm{}}$ ${\mathrm{sterad}}^{-1\mathrm{}}$, $\gamma =2.17\mathrm{}\pm 0.1$, and $3\times {10}^{15} \mathrm{ev}<E<\mathrm{}{10}^{18} \mathrm{ev}$.