Cherenkov Selector of Heavy Particles

A Cherenkov counter¹ is a type of scintillation counter in which the fluorescent phosphor is replaced by a transparent substance with a sufficiently high refractive index. Passing through this substance, charged particles produce Cherenkov radiation, which is then registered by a photomultiplier. The difference between the properties of a Cherenkov counter and an ordinary scintillation counter is thus due to the difference in the radiations produced by the particles.

Thus, the duration of Cherenkov scintillations is shorter than the glow duration of the phosphors usually employed by at least one order of magnitude; in principle, this speed of response opens up the possibility of direct measurement of particle velocities.

Another feature of Cherenkov radiation is the directionality of the rays. As is known, light is emitted at an angle \(\vartheta\) to the direction of motion of the particle, where the angle \(\vartheta\) is determined by the particle velocity \(v\) and the refractive index of the medium \(n\):

\[ \cos \vartheta = \frac{1}{\beta n}, \]

where \(\beta = v/c\). This property has not yet found application in counters, although it has been successfully used for photographic determination of the velocities of protons of monochromatic directed radiation from a cyclotron.²

In the paper under review³, another interesting property of Cherenkov radiation is used, namely that, for it to arise, the particle velocity must exceed the phase velocity of light in the medium: \(v > \frac{c}{n} = v_c\). Thus, a Cherenkov counter is a threshold counter: it registers only those particles whose velocity is greater than \(v_c\).

In the present work, particles were registered that did not cause the counter to operate and for which, consequently, \(v < v_c\). In addition, in order to be registered, a particle had to pass through a lead

filter of thickness \(R\). Only particles having a sufficiently large mass \(M\) can satisfy these two conditions simultaneously. The minimum mass \(M\) can be determined as follows.

The range of a particle possessing kinetic energy \(W_k\) and rest mass \(M\) is approximately equal to

\[ R=\frac{W_k^2}{A(W_k+Mc^2)} \]

or

\[ R=\frac{Mc^2}{A}\, \frac{\left(1-\sqrt{1-\beta^2}\right)^2}{\sqrt{1-\beta^2}}. \]

If \(R\) is expressed in \(\mathrm{g/cm^2}\) and \(W_k\) and \(Mc^2\) in MeV, then \(A=1.2\).

Let us consider the case in which the scintillations occur in water, and let us express the range in units of water equivalent; then, through a filter of thickness \(R_c\), only those particles will pass for which \(v\leq v_c\), and for which

\[ Mc^2 \geq 6.85\,R_c, \]

since in water

\[ \beta_c=\frac{v_c}{c}=\frac{1}{n_{\mathrm{H_2O}}}=\frac{1}{1.33}. \]

In Fig. 1 the theoretical dependence is shown of the intensity of Cherenkov radiation (referred to one centimeter of particle path) on the residual range of the particle. The formation of energetic \(\delta\)-particles leads to the fact that, even at velocities smaller than the critical one, the occurrence of Cherenkov scintillations is possible. This circumstance, as well as the fluctuation character of the formation of fast \(\delta\)-particles, worsens the resolving power of the counter.

Fig. 1. The theoretical curve of the intensity of Cherenkov radiation \((400\,m\mu<\lambda<750\,m\mu)\), referred to a unit path length of a heavy particle, as a function of the residual range in water. The curves \(I_0+I_e\) are the total radiation from the heavy particle and from the \(\delta\)-particles produced by it. The dashed straight line \(I_c\) is the maximum intensity of radiation (for a particle having velocity \(c\)) without taking \(\delta\)-particles into account.

A Cherenkov selector of heavy particles, based on the principle described above, is shown in Fig. 2. A metal box with sides each \(24\ \mathrm{cm}\) long was coated on the inside with a layer of \(\mathrm{MgCO_3}\) and filled with distilled water. A photomultiplier was inserted into the box from the side. \(A^1, A, B, B^1\) are boxes of Geiger counters. Between the Cherenkov box \(D\) and the counters \(B\) there was placed a lead filter of thick-

3 cm thick, which stops the electrons from the decay of mesons stopping in water. For control experiments, an additional lead absorber 20 cm thick and a box of Geiger counters \(C\) were also placed below.

The total thickness of the working part of the apparatus (without the additional filter) is equal to \(40 \text{ g}/\text{cm}^2\) of water equivalent. From the condition \(Mc^2 > 6.8 R_c\) it follows that only particles with a mass greater than 540 electron masses can pass through such a layer without producing a Cherenkov scintillation.

The ratio of the number of anticoincidences \((A^1 + A + B + B^1 - D)\) to the number of fourfold coincidences \((A^1 + A + B + B^1)\) was found to be

\[ \frac{N_A}{N_4} = (2.15 \pm 0.15)\cdot 10^{-3}. \]

The ratio of the number of anticoincidences \((A^1 + A + B + B^1 + C - D)\) to the number of fivefold coincidences was found to be \((0.32 \pm 0.1)\cdot 10^{-3}\). These anticoincidences cannot be caused by individual protons, since protons with \(v < v_c\) cannot pass through a lead filter more than 23 cm thick. These residual anticoincidences may be due to showers, random coincidences, inefficiency of the Cherenkov counter, etc.

For checking that the main fraction of the anticoincidences measured without the additional lead filter is indeed caused by protons, experiments were carried out with a Wilson chamber controlled by a Cherenkov selector and placed above the chamber. In all, 134 photographs were taken. On the basis of the photographs obtained, the authors conclude that in 80% of the cases the anticoincidences were caused by protons that stopped in one of the 6 lead plates (2 cm thick) placed inside the chamber.

Fig. 2.
Labels in the figure: \(A^1\); \(A\); \(D\); \(B\); \(B^1\); \(C\); light-tight box; optical photomultiplier; distilled water; lead (3 cm); lead (23 cm).

The momenta of the protons recorded by the apparatus lie in the interval 700–1100 MeV/\(c\). The absolute intensity of protons with momenta lying in the indicated interval can be determined from the known experimental value of the meson intensity and from the ratio of the intensities of protons and mesons measured in the present work \(\left(= \frac{N_A}{N_4}\right)\).

The resulting value is in good agreement with data obtained by other methods.

L. B.

References

1. Uspekhi Fizicheskikh Nauk, XXXIX, 402 (1949); Uspekhi Fizicheskikh Nauk, XLIV, 443 (1951).
2. Uspekhi Fizicheskikh Nauk, XLVI, 413 (1952).
3. T. Duerden, B. Hyams, Phil. Mag., 43, 717 (1952).