Download The Discovery and Interpretation of the Cerenkov effect

The Discovery and Interpretation of the Cerenkov effect
The observance of the Cerenkov effect in 1934 and the subsequent work Pavel
Cerenkov performed in order to characterize the electromagnetic radiation of the same
name has proven to be of substantial use in the fields of high energy and nuclear physics
in later years. The apparent “blue glow” that develops in modern detectors when charged
particles move through a substance at a speed greater than the phase velocity of light in
the same medium provides information as to the nature of the particles as well as their
supposed origin. Because of the practical applications for his work, Cerenkov was
awarded the Nobel Prize in Physics in 1958 along with fellow researchers Frank and
Tamm who developed the theory relating the required speeds with the unidirectional
nature of the emitted radiation.
Although Pavel Cerenkov is often credited with the discovery of this particular
form of asymmetric radiation, decades of research into the luminescence of known lightemitting substances had been conducted by many scientists including Pierre and Marie
Curie. Due to the induced luminescence marked by excited states lasting approximately
10-10 seconds, the desired phenomena was masked throughout the dying-out process;
associates of Cerenkov, most notably S.I. Vavilov, were first to detect the aforementioned
type of radiation via visual photometry. To examine the physical properties of the fluids,
the “quenching method” was employed so as to reduce the amount of familiar
luminescence by contamination with foreign reagents or by heating, consequently
altering the polarization of the emitted light as well. A diagram of one of Cerenkov‟s
original quenching photometers can be found in the appendix (see Figure 1); the enlarged
image produced by the ocular lens, L, from reflected light of vessel A was slowly
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distorted by the movement of a grey wedge until light was no longer capable of forming a
visual image on the retina of their eyes. It was observed, however, that all of the fluids
studied radiated a “blue glow” which may still have been attributed to luminescence.
Whereas all known fluorescing solutions reacted in accordance with expectations
predicted by experimental data, the intensity and polarization of the desired radioactive
emissions in solution remained unchanged such that “the main direction of the vector of
the electric vibrations did not run perpendicularly to the exciting beam, as in the case
with polarized fluorescence, but parallel to it”.1 This principle was established from
further testing by means of magnetic fields to characterize the behavior and propagation
of this secondary radiation. In order to study the directionality of this effect, Cerenkov
designed the experimental setup illustrated in Figure 2 using a conical mirror that
reflected incoming radiation against a photographic plate located above a fluid-filled
vessel. Photographs of the reflected light represent cases of ordinary luminescence
(producing a closed ring) in addition to radiation described by two unique patches
separated by an angle of 2 (see Figure 3). Experimentation with four known fluids of
varying degrees of n, refractive indices, gave rise to the graphs in Figure 4 whose curves
correspond to the emissions of Compton electrons that were excited by ThC and Ra
gamma ray sources. These results, specifically the angular distributions of light
intensities, were consistent with the proposed Tamm-Frank model for Cerenkov radiation
outlined below.
Based solely on electromagnetic theory as opposed to a quantum mechanical
explanation provided by V.L. Ginsburg some years later, the Tamm-Frank formula
1
Cerenkov, P.A. Radiation of particles moving at a velocity exceeding that of light, and some of the
possibilities for their use in experimental physics. Nobel Lecture, December 11, 1958 pp. 429 [online]
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relates the number of photons emitted by a charged particle per unit path length and per
interval unit of photon energy2:
such that the angle, , according to the “mechanism of radiation” depicted
in Figure 5 is defined by: cos = 1/n
(2)
where n is the refractive index of a particular fluid and  is the
standard ratio between the velocity of a particle and the speed of light as it
pertains to relativistic kinetic energies. A threshold condition exists at
 = 1/n and  = 0 in which no radiation occurs.
The angle found by applying Equation 2 to known energetic particles corresponds
to the observed values for theta recorded in Figure 4. A corollary to Equation 2 dictates
that Cerenkov radiation is only emitted when the velocity of a charged particle in a
medium with n > 1 exceeds the phase velocity of light (vp):
vp = c/n
(3)
When the refractive index is independent of frequency as in a vacuum and for that
reason a constant (dn/dk = 0), the group velocity (vg) is equal to the phase velocity
whereby both values are related to one another by the formula:
vg*vp = c2
(4)
Accordingly, the dispersive properties within a medium maintains vg < vp. The
electromagnetic field of a moving particle delocalizes nearby electrons causing them to
release photons in order to achieve equilibrium following the event. Given that the
2
Govorkov, B.B. “Cherenkov detectors in Cherenkov‟s laboratory.” Lebedev Physical Institute pp. 15
[online]
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triggered photon cascade travels slower than the field akin to a „sonic boom‟, these
polarized photons will undergo constructive interference thereby contributing to the
observed radiation.3 Furthermore, Frank exemplified that the direction of the radiation as
determined by theta coincides with the wave model predicted by the Huygens principle
such that partial waves of spherical radius equal to ct/n will “quench each other
everywhere except for their common envelope”.4 The resulting wave therefore creates a
cone of radiation that propagates in the same direction as the particle‟s motion with
distinctive polarization characteristics initially discovered by Cerenkov post his efforts to
quench luminescence and are defined by a magnetic field vector, H, tangent to the cone‟s
surface as well as an electric field vector orthogonal to the light‟s direction (see Figure 6).
While O. Heaviside was first to suggest „conical radiation‟ forming at the angle
determined by Equation 2 nearly half a century earlier, much of his work was neglected.
Orienting the graphs of Figure 4 with respect to three dimensions elucidates the structure
of the cone which when projected onto a plane is a circle formed by rings of different
intensities. The area of the outermost ring is composed of spectrally blue-shifted light
from radiation by Compton electrons at their maximal threshold energy. Conversely, the
innermost sections surrounding the center of the Cerenkov cone‟s base appear red when
considering normal dispersion within the visible spectrum. To mathematically address
this issue, it is necessary to consider Equation 1 in terms of the rate at which light energy,
W, is produced per unit path length (note the equation cited by Cerenkov in his Nobel
lecture paper is inaccurate with respect to the degree of n):
3
“Cherenkov effect” Wikipedia [online]
Govorkov, B.B. “Cherenkov detectors in Cherenkov‟s laboratory.” Lebedev Physical Institute pp. 18
[online]
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Applying the relationship: w = kc/n
(6)
since the spectrum is continuous:
dW/dl = e2/c2(w2/2 – 1)
(7)
the final term, allowing for n to be constant, reduces to 1; differentiating with
respect to the angular frequency, w:
dW/dw = (e2lw)/c2
(8)
which is proportional to w itself and by comparison can be expressed in
wavelengths respectively as:
From equation 9, it is apparent that although radiation with frequencies
throughout most of the electromagnetic spectrum are theoretically assessable, shorter
wavelengths begin to decrease exponentially prior to 1 and are subsequently not
permitted according to relativistic kinetic energies when n is less than unity.5 Because the
short wavelength cut-off for Cerenkov radiation excludes x-rays and it is probable that
low frequency radiation is absorbed within solution due to atomic collisions, the “blue
glow” associated with Cerenkov detectors is therefore justified.
Cerenkov had calculated the threshold energies for electrons and other particles
radiating for different values of n. Provided with a table of known nuclei and related
energies, one can differentiate between a number of particles since the intensity of the
observed radiation is “proportional to the square of the charge carried by the radiating
5
Jelley, J.V. “Cerenkov radiation and its applications.” British Journal of
Applied Physics 6, 227-232 (1955) pp. 228
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particle”. 6 The practical uses of Cerenkov radiation arise due to its unique selection for
relativistic particles consequently allowing undesirable background radiation below the
energy threshold to remain undetected. The added development of photomultiplier tubes
(PMTs) which are capable of converting light signals into measurable electrical pulses
augment the resolving power afforded with Cerenkov radiation by specifying exact
particle energies and trajectories. In contrast to Cerenkov‟s original design which was a
forerunner of the simple RICH detector, a modified focusing Cerenkov counter is
illustrated in Figure 7 such that the velocity threshold for incoming particles is
determined by the emission angle as opposed to the refractive index linked with
nonfocusing counters. Of particular significance, the option of sequencing two counters
sensitive for two energy thresholds has allowed scientists to identify the antiproton and
other particles found within specified energy regions. 7
Despite the energy threshold required to produce directed radiation which
stipulates particle selection in conjunction with the detectors later proposed by Jelley, the
editors of Nature found fault with Cerenkov‟s research and declined to publish his
original paper (Hubbell 1).8 Current applications for Cerenkov counters have included the
detection of solar neutrinos and the investigation into cosmic ray phenomena. Large-scale
detectors including the Super-Kamiokande and the Sudbury Neutrino Observatory (SNO)
utilize a series of PMTs positioned around pools of „heavy water‟ to establish the origin
and intensity of high energy particles via Cerenkov radiation; these particles, apart from
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Snell, A.H. Nuclear instruments and their uses. Vol. 1. John Wiley & Sons,
Inc., New York 1962 pp. 166
7
Cerenkov, P.A. Radiation of particles moving at a velocity exceeding that of light, and some of the
possibilities for their use in experimental physics. Nobel Lecture, December 11, 1958 pp. 439 [online]
8
Hubbell, John H. “Faster than a speeding photon.” National Institute of Standards and Technology,
August 26, 1991 pp. 1 [online]
6
secondary shower products, are chiefly comprised of electrons and positrons created
when cosmic rays interact with the earth‟s atmosphere and undergo pair production.
Whereas common scintillation counters are plagued by proton recoils and do not limit the
amount of luminescence generated by background radiation, the extensive deployment of
Cerenkov detectors is marked by their ability to characterize charged particles with
respect to energy as well as path determination.
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References
Cerenkov, P.A. “Visible Radiation Produced by Electrons Moving in a Medium with
Velocities Exceeding that of Light.” Phys. Review 52, 378-379 (1937) pp. 378-379.
[online] 28 February 2005 <http://prola.aps.org/pdf/PR/v52/i4/p378_1>
Cerenkov, P.A. Radiation of particles moving at a velocity exceeding that of light, and
some of the possibilities for their use in experimental physics. Nobel Lecture, December
11, 1958 pp. 426-440. [online] 18 February 2005
<http://nobelprize.org/physics/laureates/1958/cerenkov-lecture.pdf>
“Cherenkov effect” Wikipedia [online] 28 February 2005
<http://en.wikipedia.org/wiki/Cerenkov_effect>
Govorkov, B.B. “Cherenkov detectors in Cherenkov‟s laboratory.” Lebedev Physical
Institute pp. 1-36. [online] 28 February 2005
<http://www.ifisica.uaslp.mx/rich2004/talks/0003/Cherenkov_Present.ppt>
Hubbell, John H. “Faster than a speeding photon.” National Institute of Standards and
Technology, August 26, 1991 pp. 10. [online] 3 March 2005
<http://www.garfield.library.upenn.edu/classics1991/A1991GA09200001.pdf>
Jelley, J.V. “Cerenkov radiation and its applications.” British Journal of
Applied Physics 6, (1955) pp. 227-232.
Snell, A.H. Nuclear instruments and their uses. Vol. 1. John Wiley & Sons,
Inc., New York 1962 pp. 166-184.
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