Propagation of Cherenkov radiation of cosmic ray particles through water

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Nuclear Instruments and Methods in Physics Research A248 (1986) 219-220 North-Holland, Amsterdam

PROPAGATION OF CHERENKOV RADIATION OF COSMIC RAY PARTICLES THROUGH WATER E.V . BUGAEV, J .A .M . DJILKIBAEV and M.D . GALPERIN

Institute for Nuclear Research of the Academy of Sciences of the USSR, 60th October anmoersary prospect, 7A, Moscow, 117312, USSR

The spatial distribution of Cherenkov radiation emitted by a relativistic muon passing through the water is calculated by the Monte Carlo method . The absorption and scattering of photons in the medium are taken into account. Analytical expressions are obtained for asymptotically large distances from the particle trajectory to the detector.

1 . Introduction The spatial distribution of Cherenkov radiation created by a relativistic particle propagating through a continuous medium can be easily calculated only if one can neglect the scattering of radiation. This scattering occurs on density fluctuations and admixtures which are available to a certain extent in any real medium . When one has to take into account simultaneously the absorption and scattering of photons the calculation of the intensity distribution becomes a complicated problem in transport theory. Our main interest is the distribution of Cherenkov light emitted by a high-energy cosmic-ray muon passing through the water of some lake or sea. This problem has been appeared in connection with the rapid development in recent years of a new branch of experimental high-energy physics. We have in mind the experiments on deep underwater detection of cosmic neutrinos and muons. The arrays which are planned and created for this experiments have large dimensions and consist of a large number of Cherenkov detectors. The distances between these detectors depend on their type and on the properties of the water but surely they will be very large (about several tens of even a hundred meters). So these distances will have the same order of magnitude as the absorption- and scattering length of light in water has. Hence it is impossible in all cases to neglect the scattering of light in water. It is known that for the calculation of photon distributions numerical methods should be used because the analytical solutions of similar problems exist only for asymptotically large distances from the photon source to a point of observation . It is most natural in our case to use for the calculation the Monte Carlo method because the number of collisions on the way of photons from the source to the detector is not too large. For 0168-9002/86/$03 .50 © Elsevier Science Publishers B.V . (North-Holland Physics Publishing Division)

large distances in which case the Monte Carlo method becomes ineffective, the numerical solution should be joined to the asymptotic solution . 2. The method of calculation In present work we are interested in the flux of photons from a source (which is a muon trajectory) at arbitrary points of space but with the important restriction that we integrate this flux over all directions and times of arrival of the photons at this points . So we solve the stationary problem and look for the total photon flux through a sphere with unit cross section area which is located at a certain distance p from the trajectory of the passing particle . It is evident that the problem has cylindrical symmetry and the flux depends only on p . This symmetry was used for reducing of the computation time in the following way. The plane was uniformly filled up by centres of unintersecting spheres. The Cherenkov photons being emitted by each bit of the trajectory during their flight intersect the surfaces of these spheres and all events with intersection of the spheres having their centres located on circles of radius p =d(n - z) (d is the sphere diameter, n = 1, 2. . . . ) are separately summed . In order to determine the number of photons hitting the spherical detector of unit cross section it is necessary to divide the total number of intersections of all spheres by pn on the number of such spheres m which is given by formula m = Entier

( arcsin d/2 pn

)

and on the area of cross section of the sphere . In our concrete Monte Carlo calculation the sphere diameter was taken equal to 30 cm . IV . COSMIC RAY PHYSICS

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