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ON THE INTENSITY AND SPECTRUM OF PRIMARY COSMIC RADIATION
It is known that the latitude effect of cosmic radiation, consisting in a decrease in the intensity of cosmic radiation with decreasing geomagnetic latitude of the place of observation, is caused by the deflecting action of the Earth’s magnetic field on primary cosmic radiation. From the theory of this effect it is known that, at a given latitude \(\varphi\), beyond the limits of the Earth’s atmosphere only those primary particles can arrive whose momenta are greater than a certain critical momentum \(P_\varphi\), related to the latitude in the following way:
\[ \frac{P_\varphi c}{Ze}=1.5\cdot 10^{10}\cos^4\varphi\ \text{v}, \tag{1} \]
where \(Ze\) is the charge of the particle. This formula is valid for particles incident normally to the Earth’s surface. The measurement of the vertical intensity of cosmic radiation \(I\) beyond the limits of the Earth’s atmosphere at latitude \(\varphi\) consists, according to (1), in measuring the intensity of primary radiation with
\[ \frac{Pc}{Ze}>\frac{P_\varphi c}{Ze}. \]
Thus, by measuring \(I\) at different latitudes and knowing the dependence (1), which relates \(\frac{P_\varphi c}{Ze}\) to \(\varphi\), one can obtain the integral spectrum of cosmic-ray particles in \(\frac{P_\varphi c}{Ze}\). The composition of the primary radiation is at present sufficiently well known—it consists mainly of protons, \(\alpha\)-particles (about 10–20% of the total radiation), and a small quantity of heavier nuclei. Therefore, without great error it may be considered that the integral spectrum of cosmic-ray particles obtained from the study of the latitude effect at the boundary of the atmosphere gives the spectrum of primary protons. The study of the latitude effect, as is seen from (1), makes it possible to obtain the integral spectrum down to values of
\[ \frac{P_\varphi c}{Ze} \]
of the order of \(1.5\cdot 10^{10}\ \text{v}\). One of the recent works devoted to measuring the latitude effect at the boundary of the atmosphere belongs to Winkler et al.,\(^1\) who measured the intensity of cosmic rays with telescopes made of Geiger counters lifted by balloons.
up to altitudes of about 27 km at 0, 20, 30, and 40° north geomagnetic latitude. A photograph of the ascending apparatus is shown in Fig. 1.
The data obtained from measurements at the maximum altitude on the vertical intensity of cosmic radiation are shown in Fig. 2, where the vertical axis gives the vertical intensity in particles per 1 cm² per second per steradian, and the horizontal axis gives the particle energy in Bev, on the assumption that all these particles are protons. Thus the straight line in Fig. 2 gives the integral energy spectrum of primary cosmic radiation.
Fig. 1.
spectrum of primary cosmic radiation. It should be noted that: 1) in these measurements a three-centimeter layer of lead was placed between the rows of the telescope scintillators, and 2) the balloons did not reach the boundary of the atmosphere. For both reasons the measured intensity is somewhat less than the actual intensity of the primary radiation. However, apparently, this difference is not very large and, according to the authors’ estimate, does not exceed 10–20%. This follows, in particular, from comparison of the presented data with data obtained by launching apparatus on rocket projectiles rising to altitudes greater than 150 km. From Fig. 3, where the data are presented in logarith-
Fig. 2.
Text in the figure:
- Vertical intensity (particles/cm²·sec·sterad)
- Protons
- \( \mathrm{GeV} \)
Fig. 3.
Text in the figure:
- Vertical intensity (particles/cm²·sec·sterad)
- Geomagnetic latitude
- Mean particle charge [[unclear: axis label]],
\[ \frac{pc}{Ze}\,(10^8) \] - Geomagnetic latitude
- Protons \((\mathrm{GeV})\)
Legend:
- ● rocket measurements
- \(+\) Pickering (1949)
- × Pickering (1950)
- ○ Winkler et al. (1949)
Formula shown in the figure:
\[ \sin\theta = \frac{\left(\dfrac{dI}{d\Omega}\right)} {\left(\dfrac{dI}{d\Omega}\right)_{90}} < 1 \]
mic scale, it is evident that they lie well on a straight line. The authors indicate that this straight line is described by the following power law:
\[ I(>E)=0.30\cdot E^{-0.90\pm0.05}, \tag{2} \]
where \(I(>E)\) is the vertical intensity of primary protons with energies greater than \(E\). Analogous measurements in recent years were made by several investigators who raised Geiger-counter telescopes on rockets or balloons. Note 2 gives the spectrum of the primary radiation obtained from the totality of all these data. This spectrum is shown in Fig. 3, where along the abscissa is plotted the magnetic rigidity \(\frac{pc}{Ze}\), or the kinetic energy, or the geomagnetic latitude, and along the ordinate—the vertical flux of particles with momentum greater than that determined by the abscissa. The authors indicate that in the interval of values of \(\frac{pc}{Ze}\) from 2 to \(15\cdot10^9\) V the integral spectrum is described by the formula
\[ I\left(>\frac{pc}{Ze}\right)=0.48\left(\frac{pc}{Ze}\right)^{-1.1}\ \text{particles}/\text{sec}\cdot\text{cm}^2\cdot\text{sterad}. \tag{3} \]
This spectrum, although differing in its analytical expression from spectrum (2) (Fig. 2), gives intensity values that agree quite well with (2). Thus, for example, the intensity of primary protons calculated by formula (2) for latitude \(\varphi=30^\circ\) \(\left(E=7\ \text{BeV};\ \frac{pc}{Ze}=8.5\cdot10^9\ \text{V}\right)\) is \(0.045\ \text{particles}/\text{cm}^2\cdot\text{sec}\cdot\text{sterad}\), while that calculated by formula (3) for the same latitude is \(0.050\ \text{particles}/\text{cm}^2\cdot\text{sec}\cdot\text{sterad}\). The same intensities calculated for latitude \(55^\circ\) by formulas (2) and (3) are, in the same units, 0.30 and 0.28, respectively. Both empirical formulas agree sufficiently well with each other and with the experimental data in the energy interval of primary protons from 1.5 to 15 BeV.
From the curve in Fig. 3 it follows that the intensity of cosmic radiation almost does not change for latitudes greater than \(55^\circ\). It is quite probable that this is explained by the absorption, at these latitudes, by the residual atmosphere above the apparatus, of particles of small energy responsible for the latitude effect (the last point on the curve, corresponding to a latitude of about \(70^\circ\), was obtained in balloon ascents). To test this assumption, it is necessary to measure the intensity of the primary radiation at high latitudes by means of rockets carrying the apparatus far beyond the limits of the Earth’s atmosphere.
A. V.
CITED LITERATURE
- J. R. Winckler, T. Stix et al., Phys. Rev. 79, 656 (1950).
- J. A. Van Allen and S. F. Singer, Phys. Rev. 78, 819 (1950).