2235:, developed in the 1980s. In a RICH detector, a cone of Cherenkov light is produced when a high-speed charged particle traverses a suitable medium, often called radiator. This light cone is detected on a position sensitive planar photon detector, which allows reconstructing a ring or disc, whose radius is a measure for the Cherenkov emission angle. Both focusing and proximity-focusing detectors are in use. In a focusing RICH detector, the photons are collected by a spherical mirror and focused onto the photon detector placed at the focal plane. The result is a circle with a radius independent of the emission point along the particle track. This scheme is suitable for low refractive index radiators—i.e. gases—due to the larger radiator length needed to create enough photons. In the more compact proximity-focusing design, a thin radiator volume emits a cone of Cherenkov light which traverses a small distance—the proximity gap—and is detected on the photon detector plane. The image is a ring of light whose radius is defined by the Cherenkov emission angle and the proximity gap. The ring thickness is determined by the thickness of the radiator. An example of a proximity gap RICH detector is the High Momentum Particle Identification Detector (HMPID), a detector currently under construction for ALICE (
538:
1196:). This means that, when a charged particle (usually electrons) passes through a medium at a speed greater than the phase velocity of light in that medium, that particle emits trailing radiation from its progress through the medium rather than in front of it (as is the case in normal materials with, both permittivity and permeability positive). One can also obtain such reverse-cone Cherenkov radiation in non-metamaterial periodic media where the periodic structure is on the same scale as the wavelength, so it cannot be treated as an effectively homogeneous metamaterial.
307:
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emission, where the detected signal can be imaged at the entry and exit surfaces of the tissue. The
Cherenkov light emitted from patient's tissue during radiation therapy is a very low light level signal but can be detected by specially designed cameras that synchronize their acquisition to the linear accelerator pulses. The ability to see this signal shows the shape of the radiation beam as it is incident upon the tissue in real time.
1971:
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238:. The light was observed using a camera imaging system called a CDose, which is specially designed to view light emissions from biological systems. For decades, patients had reported phenomena such as "flashes of bright or blue light" when receiving radiation treatments for brain cancer, but the effects had never been experimentally observed.
1905:. Radioactive atoms such as phosphorus-32 are readily introduced into biomolecules by enzymatic and synthetic means and subsequently may be easily detected in small quantities for the purpose of elucidating biological pathways and in characterizing the interaction of biological molecules such as affinity constants and dissociation rates.
549:
nuclei. On the other hand, the phenomenon can be explained both qualitatively and quantitatively if one takes into account the fact that an electron moving in a medium does radiate light even if it is moving uniformly provided that its velocity is greater than the velocity of light in the medium."
548:
In their original work on the theoretical foundations of
Cherenkov radiation, Tamm and Frank wrote, "This peculiar radiation can evidently not be explained by any common mechanism such as the interaction of the fast electron with individual atom or as radiative scattering of electrons on atomic
1961:
External beam radiation therapy has been shown to induce a substantial amount of
Cherenkov light in the tissue being treated, due to electron beams or photon beams with energy in the 6 MV to 18 MV ranges. The secondary electrons induced by these high energy x-rays result in the Cherenkov light
1872:
is directly related to the velocity of the disruption. The
Cherenkov angle is zero at the threshold velocity for the emission of Cherenkov radiation. The angle takes on a maximum as the particle speed approaches the speed of light. Hence, observed angles of incidence can be used to compute the
1535:
1925:
More recently, Cherenkov light has been used to image substances in the body. These discoveries have led to intense interest around the idea of using this light signal to quantify and/or detect radiation in the body, either from internal sources such as injected
3609:
Jarvis, Lesley A; Zhang, Rongxiao; Gladstone, David J; Jiang, Shudong; Hitchcock, Whitney; Friedman, Oscar D; Glaser, Adam K; Jermyn, Michael; Pogue, Brian W (2014). "Cherenkov Video
Imaging Allows for the First Visualization of Radiation Therapy in Real Time".
3154:
Tendler, Irwin I.; Hartford, Alan; Jermyn, Michael; LaRochelle, Ethan; Cao, Xu; Borza, Victor; Alexander, Daniel; Bruza, Petr; Hoopes, Jack; Moodie, Karen; Marr, Brian P.; Williams, Benjamin B.; Pogue, Brian W.; Gladstone, David J.; Jarvis, Lesley A. (2020).
1853:) would be observed. However, X-rays can be generated at special frequencies just below the frequencies corresponding to core electronic transitions in a material, as the index of refraction is often greater than 1 just below a resonant frequency (see
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field is asymmetric along the direction of motion of the particle, as the particles of the medium do not have enough time to recover to their "normal" randomized states. This results in overlapping waveforms (as in the animation) and
1747:
that have characteristic spectral peaks, Cherenkov radiation is continuous. Around the visible spectrum, the relative intensity per unit frequency is approximately proportional to the frequency. That is, higher frequencies (shorter
1386:
2227:
of the medium) by looking at whether this particle emits
Cherenkov light in a certain medium. Knowing particle momentum, one can separate particles lighter than a certain threshold from those heavier than the threshold.
427:, that is the velocity of the charged particle is less than that of the speed of light in the medium, then the polarization field which forms around the moving particle is usually symmetric. The corresponding emitted
2137:
The simplest type of particle identification device based on a
Cherenkov radiation technique is the threshold counter, which answers whether the velocity of a charged particle is lower or higher than a certain value
2032:
with enormous velocities. The
Cherenkov radiation emitted in the atmosphere by these charged particles is used to determine the direction and energy of the cosmic ray or gamma ray, which is used for example in the
382:). When any charged particle passes through a medium, the particles of the medium will polarize around it in response. The charged particle excites the molecules in the polarizable medium and on returning to their
534:, one can also obtain a variety of other anomalous Cherenkov effects, such as radiation in a backwards direction (see below) whereas ordinary Cherenkov radiation forms an acute angle with the particle velocity.
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observed a pale blue light in a highly concentrated radium solution in 1910, but did not investigate its source. In 1926, the French radiotherapist Lucien Mallet described the luminous radiation of
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spectrum—it is only with sufficiently accelerated charges that it even becomes visible; the sensitivity of the human eye peaks at green, and is very low in the violet portion of the spectrum.
1025:
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Astrophysics observatories using the
Cherenkov technique to measure air showers are key to determining the properties of astronomical objects that emit very-high-energy gamma rays, such as
3550:
848:
159:. Cherenkov saw a faint bluish light around a radioactive preparation in water during experiments. His doctorate thesis was on luminescence of uranium salt solutions that were excited by
386:, the molecules re-emit the energy given to them to achieve excitation as photons. These photons form the spherical wavefronts which can be seen originating from the moving particle. If
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1831:
varies with frequency (and hence with wavelength) in such a way that the intensity cannot continue to increase at ever shorter wavelengths, even for very relativistic particles (where
3071:
1806:
1329:
Radiation with the same properties of typical
Cherenkov radiation can be created by structures of electric current that travel faster than light. By manipulating density profiles in
3098:
Malaca, Bernardo; Pardal, Miguel; Ramsey, Dillon; Pierce, Jacob R.; Weichman, Kale; Andryiash, Igor A.; Mori, Warren B.; Palastro, John P.; Fonseca, Ricardo; Vieira, Jorge (2023).
1075:
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425:
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Genevet, P.; Wintz, D.; Ambrosio, A.; She, A.; Blanchard, R.; Capasso, F. (2015). "Controlled steering of Cherenkov surface plasmon wakes with a one-dimensional metamaterial".
3499:
1263:
1188:(materials with a subwavelength microstructure that gives them an effective "average" property very different from their constituent materials, in this case having negative
1626:
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waves generated by the aircraft travel at the speed of sound, which is slower than the aircraft, and cannot propagate forward from the aircraft, instead forming a conical
1659:
2177:
1319:
1070:
3257:
Liu, H.; Zhang, X.; Xing, B.; Han, P.; Gambhir, S. S.; Cheng, Z. (21 May 2010). "Radiation-luminescence-excited quantum dots for in vivo multiplexed optical imaging".
3549:
Spinelli, Antonello Enrico; Ferdeghini, Marco; Cavedon, Carlo; Zivelonghi, Emanuele; Calandrino, Riccardo; Fenzi, Alberto; Sbarbati, Andrea; Boschi, Federico (2013).
1597:
1997:
decay. The glow continues after the chain reaction stops, dimming as the shorter-lived products decay. Similarly, Cherenkov radiation can characterize the remaining
1283:
2053:. Cherenkov radiation emitted in tanks filled with water by those charged particles reaching earth is used for the same goal by the Extensive Air Shower experiment
356:
1752:) are more intense in Cherenkov radiation. This is why visible Cherenkov radiation is observed to be brilliant blue. In fact, most Cherenkov radiation is in the
542:
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2197:
1829:
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of light. The phase velocity can be altered dramatically by using a periodic medium, and in that case one can even achieve Cherenkov radiation with
922:
431:
may be bunched up, but they do not coincide or cross, and there are therefore no interference effects to consider. In the reverse situation, i.e.
2001:
of spent fuel rods. This phenomenon is used to verify the presence of spent nuclear fuel in spent fuel pools for nuclear safeguards purposes.
1530:{\displaystyle {\frac {d^{2}E}{dx\,d\omega }}={\frac {q^{2}}{4\pi }}\mu (\omega )\omega {\left(1-{\frac {c^{2}}{v^{2}n^{2}(\omega )}}\right)}}
4298:
2440:
3670:"Initial Clinical Experience of Cherenkov Imaging in External Beam Radiation Therapy Identifies Opportunities to Improve Treatment Delivery"
866:
318:
The effect can be intuitively described in the following way. From classical physics, it is known that accelerating charged particles emit
595:
4283:
1341:
and emit optical shocks at the Cherenkov angle. Electrons are still subluminal, hence the electrons that compose the structure at a time
3069:
Bugaev, S. P.; Kanavets, V. I.; Klimov, A. I.; Koshelev, V. I.; Cherepenin, V. A. (1983). "Relativistic multiwave Cerenkov generator".
986:
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2432:
93 (1967) 385. V sbornike: Pavel Alekseyevich Čerenkov: Chelovek i Otkrytie pod redaktsiej A. N. Gorbunova i E. P. Čerenkovoj, M.,
2054:
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of an electrically charged elementary particle by the properties of the Cherenkov light it emits in a certain medium. If the
2943:
1038:. The latter is designed to introduce a gradient of phase retardation along the trajectory of the fast travelling particle (
4278:
4247:
4192:
3911:
2365:
511:. In a similar way, a charged particle can generate a "shock wave" of visible light as it travels through an insulator.
4227:
3515:
2395:
272:), the speed in a material may be significantly less, as it is perceived to be slowed by the medium. For example, in
1232:. In such a system, this effect can be derived from conservation of the energy and momentum where the momentum of a
4293:
2236:
2232:
2109:
1629:
1193:
2973:
Macleod, Alexander J.; Noble, Adam; Jaroszynski, Dino A. (2019). "Cherenkov radiation from the quantum vacuum".
692:
127:, the sharp sound heard when faster-than-sound movement occurs. The phenomenon is named after Soviet physicist
1917:
Cherenkov light emission imaged from the chest wall of a patient undergoing whole breast irradiation, using 6
1762:
4359:
3795:
Smith, S. J.; Purcell, E. M. (1953). "Visible Light from Localized Surface Charges Moving across a Grating".
2947:
852:
The left corner of the triangle represents the location of the superluminal particle at some initial moment (
323:
859:). The right corner of the triangle is the location of the particle at some later time t. In the given time
2411:
2070:
119:
in that medium. A classic example of Cherenkov radiation is the characteristic blue glow of an underwater
3294:
Liu, Hongguang; Ren, Gang; Liu, Shuanglong; Zhang, Xiaofen; Chen, Luxi; Han, Peizhen; Cheng, Zhen (2010).
1901:
Cherenkov radiation is widely used to facilitate the detection of small amounts and low concentrations of
4389:
4379:
4115:
2752:
1881:
1855:
1845:
frequencies, the refractive index becomes less than 1 (note that in media, the phase velocity may exceed
1212:
decreases and the velocity of charged particles can exceed the phase velocity while remaining lower than
1034:
Cherenkov radiation can also radiate in an arbitrary direction using properly engineered one dimensional
434:
389:
227:
2081:, a former solar tower refurbished to work as a non-imaging Cherenkov observatory, which was located in
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without violating relativity) and hence no X-ray emission (or shorter wavelength emissions such as
1744:
1602:
1072:), reversing or steering Cherenkov emission at arbitrary angles given by the generalized relation:
734:
662:
527:
167:
of the radiation and came to the conclusion that the bluish glow was not a fluorescent phenomenon.
2541:
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
2437:
568:
4110:
3904:
1635:
537:
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3936:
2826:
2295:
2279:
2141:
1380:
1295:
1041:
303:(can be polarized electrically) medium with a speed greater than light's speed in that medium.
144:
1152:{\displaystyle \cos \theta ={\frac {1}{n\beta }}+{\frac {n}{k_{0}}}\cdot {\frac {d\phi }{dx}}}
203:
in 1904, but both had been quickly dismissed following the relativity theory's restriction of
4355:
4090:
2891:
2457:
2290:
2240:
2022:
1943:
1582:
1165:. The angle stays the same, meaning that subsequent waves generated between the initial time
1162:
24:
3647:"Technical Note: Time-gating to medical linear accelerator pulses: Stray radiation detector"
3646:
2262:
1268:
1161:
Note that since this ratio is independent of time, one can take arbitrary times and achieve
4212:
4100:
4057:
4007:
3806:
3704:
3565:
3450:
3307:
3223:
3212:
Bolotovskii, B. M. (2009). "Vavilov – Cherenkov radiation: Its discovery and application".
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311:
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8:
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3692:
2667:"For the first time, scientists capture light flashes from human eye during radiotherapy"
1927:
1741:
1330:
1290:
1205:
333:
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3810:
3781:
3708:
3569:
3454:
3351:
Zhong, Jianghong; Qin, Chenghu; Yang, Xin; Zhu, Shuping; Zhang, Xing; Tian, Jie (2011).
3311:
3296:"Optical imaging of reporter gene expression using a positron-emission-tomography probe"
3227:
3157:"Experimentally Observed Cherenkov Light Generation in the Eye During Radiation Therapy"
3084:
2996:
2904:
2822:
2697:"Experimentally Observed Cherenkov Light Generation in the Eye During Radiation Therapy"
2556:
2484:
Oliver Heaviside: The Life, Work, and Times of an Electrical Genius of the Victorian Age
481:
leads to an observed cone-like light signal at a characteristic angle: Cherenkov light.
4324:
4145:
4125:
4105:
3989:
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3755:
3720:
3591:
3526:
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3129:
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3051:
3016:
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2924:
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2721:
2695:
Tendler, Irwin I.; Hartford, Alan; Jermyn, Michael; Pogue, Brian W. (25 October 2019).
2586:
2276:, about conjectural propagation of information or matter faster than the speed of light
2256:
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2182:
2105:
1814:
1712:
1692:
1668:
1562:
1542:
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1215:
668:
644:
565:
In the figure on the geometry, the particle (red arrow) travels in a medium with speed
361:
262:
175:
2801:
2270:, radiation produced when charged particles are decelerated by other charged particles
4217:
4095:
4032:
3997:
3766:
3724:
3627:
3583:
3531:
3511:
3476:
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3243:
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3099:
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2621:
2611:
2578:
2570:
2548:
2515:
2488:
2433:
2391:
2300:
2273:
2089:
2050:
1986:
1978:
1931:
478:
219:
204:
200:
3020:
2928:
2870:
Tamm, I.E.; Frank, I.M. (1937), "Coherent radiation of fast electrons in a medium",
2856:
2590:
1184:
A reverse Cherenkov effect can be experienced using materials called negative-index
4222:
3814:
3712:
3619:
3595:
3573:
3521:
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3458:
3382:
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3043:
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3000:
2908:
2836:
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2716:
2708:
2560:
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2224:
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2066:
1994:
1809:
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686:
531:
379:
196:
108:
88:
40:
3691:
Branger, E; Grape, S; Jacobsson Svärd, S; Jansson, P; Andersson Sundén, E (2017).
1908:
561:
The geometry of the Cherenkov radiation shown for the ideal case of no dispersion.
189:
Cherenkov radiation as conical wavefronts had been theoretically predicted by the
4334:
4319:
4135:
4047:
4037:
3889:
3797:
3623:
3259:
3214:
3172:
2951:
2768:
2712:
2640:
2509:
2482:
2444:
2029:
1877:
1876:
Cherenkov radiation can be generated in the eye by charged particles hitting the
1869:
1686:
919:
whereas the emitted electromagnetic waves are constricted to travel the distance
760:
We define the ratio between the speed of the particle and the speed of light as
171:
128:
120:
100:
484:
4182:
4140:
4130:
4052:
4042:
4012:
3787:
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1990:
1837:
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1209:
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winner, who was the first to detect it experimentally under the supervision of
116:
104:
3844:
3833:
3578:
3047:
3034:
Wang, Zhong-Yue (2016). "Generalized momentum equation of quantum mechanics".
2329:
1204:
The Cherenkov effect can occur in vacuum. In a slow-wave structure, like in a
1176:
will form similar triangles with coinciding right endpoints to the one shown.
4373:
4257:
4017:
4002:
3180:
2625:
2574:
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1998:
1947:
163:
instead of less energetic visible light, as done commonly. He discovered the
3818:
2840:
2673:. American Association for the Advancement of Science (AAAS). 7 January 2020
170:
A theory of this effect was later developed in 1937 within the framework of
4237:
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4062:
3631:
3587:
3535:
3480:
3462:
3396:
3337:
3280:
3272:
3198:
3100:"Coherence and superradiance from a plasma-based quasiparticle accelerator"
3012:
2920:
2912:
2848:
2776:
2730:
2582:
2565:
2536:
2077:. Other projects operated in the past applying related techniques, such as
2014:
1737:
1189:
1185:
1035:
383:
235:
140:
3423:
3410:
Sinoff, C. L (1991). "Radical irradiation for carcinoma of the prostate".
3377:
2605:
1930:
or from external beam radiotherapy in oncology. Radioisotopes such as the
1321:. This type of radiation (VCR) is used to generate high-power microwaves.
3979:
3439:"In vivo Cerenkov luminescence imaging: A new tool for molecular imaging"
2751:
Blumenthal, Deborah T.; Corn, Benjamin W.; Shtraus, Natan (August 2015).
1939:
1935:
1902:
1753:
310:
Cherenkov radiation during Scheduled Refueling and Maintenance Outage of
208:
3412:
South African Medical Journal = Suid-Afrikaanse Tydskrif vir Geneeskunde
1985:
Cherenkov radiation is used to detect high-energy charged particles. In
295:. Cherenkov radiation results when a charged particle, most commonly an
287:
can accelerate to a velocity higher than this (although still less than
19:
4027:
3974:
3437:
Mitchell, G. S; Gill, R. K; Boucher, D. L; Li, C; Cherry, S. R (2011).
2285:
2082:
2018:
1955:
1951:
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508:
497:
493:
300:
183:
164:
124:
96:
3319:
2414:(1934). "Visible emission of clean liquids by action of γ radiation".
2118:
for particle identification. One could measure (or put limits on) the
4314:
4187:
4022:
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3959:
3920:
1850:
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179:
160:
112:
1970:
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these waves will form spherical wavefronts which propagate with the
3964:
3949:
3548:
3116:
2987:
2800:
Luo, C.; Ibanescu, M.; Johnson, S. G.; Joannopoulos, J. D. (2003).
2511:
Radioactivity: Introduction and History, From the Quantum to Quarks
2123:
2119:
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2046:
2026:
1913:
500:
296:
193:
92:
3690:
4242:
3737:
3494:
Das, S.; Thorek, D. L. J.; Grimm, J. (2014). "Cerenkov Imaging".
2305:
2126:
of the particle is measured independently, one could compute the
2074:
2042:
190:
1958:
have been imaged in humans for diagnostic value demonstration.
330:
of that medium (i.e. the speed of light in that medium given by
291:, the speed of light in vacuum) during nuclear reactions and in
3693:"On Cherenkov light production by irradiated nuclear fuel rods"
3153:
2610:(1st ed.). New Delhi: New Age International. p. 189.
2093:
2078:
1909:
Medical imaging of radioisotopes and external beam radiotherapy
1873:
direction and speed of a Cherenkov radiation-producing charge.
1233:
284:
257:
212:
2799:
4067:
3954:
3674:
International Journal of Radiation Oncology, Biology, Physics
3612:
International Journal of Radiation Oncology, Biology, Physics
3161:
International Journal of Radiation Oncology, Biology, Physics
2701:
International Journal of Radiation Oncology, Biology, Physics
1975:
1842:
974:{\displaystyle x_{\text{em}}=v_{\text{em}}t={\frac {c}{n}}t.}
504:
273:
43:
16:
Electromagnetic radiation from a charged particle in a medium
3068:
1354:
are different from the electrons in the structure at a time
557:
3753:
Landau, L. D.; Liftshitz, E. M.; Pitaevskii, L. P. (1984).
3443:
Philosophical Transactions of the Royal Society of London A
2244:
2127:
2061:
and other projects. Similar methods are used in very large
2038:
2034:
1559:
emitted from Cherenkov radiation, per unit length traveled
58:
55:
46:
3738:
The High Momentum Particle Identification Detector at CERN
2694:
64:
3752:
3608:
2010:
1918:
1868:
As in sonic booms and bow shocks, the angle of the shock
3097:
2259:, similar radiation produced by fast uncharged particles
689:
of the medium. If the medium is water, the condition is
2972:
2888:
543:
University of Massachusetts Lowell Radiation Laboratory
3496:
Emerging Applications of Molecular Imaging to Oncology
1954:
have measurable Cherenkov emission and isotopes F and
1759:
There is a cut-off frequency above which the equation
1539:
The Frank–Tamm formula describes the amount of energy
3436:
2750:
2231:
The most advanced type of a detector is the RICH, or
2209:
2185:
2144:
2114:
Cherenkov radiation is commonly used in experimental
1896:
1817:
1765:
1715:
1695:
1671:
1638:
1605:
1585:
1565:
1545:
1389:
1379:
of Cherenkov radiation by a particle is given by the
1298:
1271:
1242:
1218:
1078:
1044:
989:
925:
912:{\displaystyle x_{\text{p}}=v_{\text{p}}t=\beta \,ct}
869:
813:
766:
737:
695:
671:
647:
598:
571:
526:
minimum particle velocity, a phenomenon known as the
437:
392:
364:
336:
67:
61:
2944:"Topsy turvy: The first true "left handed" material"
1665:
of the material the charged particle moves through.
634:{\displaystyle {\frac {c}{n}}<v_{\text{p}}<c,}
52:
2426:Reprinted in Selected Papers of Soviet Physicists,
2390:(3rd ed.). New York: Wiley. pp. 637–638.
49:
3919:
3754:
2215:
2191:
2171:
2130:of the particle by its momentum and velocity (see
1823:
1800:
1721:
1701:
1677:
1653:
1620:
1591:
1571:
1551:
1529:
1313:
1277:
1257:
1224:
1151:
1064:
1019:
973:
911:
842:
795:
749:
723:
677:
653:
633:
584:
464:
419:
370:
350:
230:discovered Cherenkov light being generated in the
2753:"Flashes of light-radiation therapy to the brain"
1020:{\displaystyle \cos \theta ={\frac {1}{n\beta }}}
796:{\displaystyle \beta ={\frac {v_{\text{p}}}{c}}.}
199:in papers published between 1888 and 1889 and by
4371:
2537:"Oliver Heaviside: an accidental time traveller"
2507:
215:irradiating water having a continuous spectrum.
3350:
3256:
2099:
1921:beam from a linear accelerator in radiotherapy.
530:. In a more complex periodic medium, such as a
23:Cherenkov radiation glowing in the core of the
3493:
3293:
3905:
843:{\displaystyle v_{\text{em}}={\frac {c}{n}}.}
3846:Nuclear Reactor starting up (alternate link)
3794:
2282:, giving the spectrum of Cherenkov radiation
1993:(high-energy electrons) are released as the
3365:International Journal of Biomedical Imaging
3211:
2941:
2004:
1337:are created and may travel faster than the
1179:
1029:
3912:
3898:
2942:Schewe, P. F.; Stein, B. (24 March 2004).
2690:
2688:
2239:), one of the six experiments at the LHC (
1880:, giving the impression of flashes, as in
807:(denoted by blue arrows) travel at speed
724:{\displaystyle 0.75c<v_{\text{p}}<c}
514:The velocity that must be exceeded is the
3577:
3525:
3470:
3386:
3376:
3327:
3188:
3115:
2986:
2869:
2830:
2802:"Cerenkov Radiation in Photonic Crystals"
2720:
2564:
2410:
1414:
1333:setups, structures up to nanocoulombs of
902:
123:. Its cause is similar to the cause of a
2795:
2793:
2603:
1969:
1912:
1801:{\displaystyle \cos \theta =1/(n\beta )}
556:
536:
483:
305:
186:, who also shared the 1958 Nobel Prize.
155:in 1934. Therefore, it is also known as
18:
3855:
3783:Cerenkov Radiation and Its Applications
2685:
2638:
2385:
2358:"Cerenkov – Search | ScienceDirect.com"
2035:Imaging Atmospheric Cherenkov Technique
1324:
4372:
4253:Wireless electronic devices and health
3779:
3667:
3644:
3409:
3353:"Cerenkov Luminescence Tomography for
2659:
3893:
2790:
2534:
2480:
4279:List of civilian radiation accidents
4248:Wireless device radiation and health
4243:Biological dose units and quantities
4193:Electromagnetic radiation and health
3858:"Cherenkov's Particles as Magnetons"
3033:
2134:), and hence identify the particle.
863:, the particle travels the distance
218:In 2019, a team of researchers from
143:scientist Pavel Cherenkov, the 1958
3757:Electrodynamics of Continuous Media
1965:
465:{\displaystyle v_{\text{p}}>c/n}
420:{\displaystyle v_{\text{p}}<c/n}
13:
4228:Radioactivity in the life sciences
3508:10.1016/B978-0-12-411638-2.00006-9
3502:. Vol. 124. pp. 213–34.
2071:Sudbury Neutrino Observatory (SNO)
1897:Detection of labelled biomolecules
1884:and possibly some observations of
1709:is the speed of the particle, and
1370:
241:
14:
4411:
3827:
2508:L'Annunziata, Michael F. (2016).
2458:"The Nobel Prize in Physics 1958"
1305:
1249:
983:So the emission angle results in
552:
178:theory by Cherenkov's colleagues
139:The radiation is named after the
3072:Soviet Technical Physics Letters
1808:can no longer be satisfied. The
488:Animation of Cherenkov radiation
39:
3731:
3684:
3668:Jarvis, L. A. (April 1, 2021).
3661:
3638:
3602:
3542:
3487:
3430:
3403:
3344:
3287:
3250:
3205:
3091:
3062:
3036:Optical and Quantum Electronics
3027:
2966:
2935:
2882:
2863:
2744:
2642:The Physics of Nuclear Reactors
2632:
2487:. JHU Press. pp. 125–126.
2368:from the original on 2024-01-22
2237:A Large Ion Collider Experiment
2233:ring-imaging Cherenkov detector
2110:Ring imaging Cherenkov detector
3717:10.1088/1748-0221/12/06/T06001
3236:10.3367/UFNe.0179.200911c.1161
3005:10.1103/PhysRevLett.122.161601
2597:
2528:
2514:. Elsevier. pp. 547–548.
2501:
2474:
2450:
2404:
2379:
2350:
2322:
1795:
1786:
1648:
1642:
1615:
1609:
1515:
1509:
1458:
1452:
1258:{\displaystyle p=\hbar \beta }
103:) at a speed greater than the
1:
4395:Experimental particle physics
3645:Ashraf, M.R. (Dec 14, 2018).
2948:American Institute of Physics
2025:, it may produce an electron–
1621:{\displaystyle \mu (\omega )}
750:{\displaystyle n\approx 1.33}
3624:10.1016/j.ijrobp.2014.01.046
3558:Journal of Biomedical Optics
3300:Journal of Biomedical Optics
3173:10.1016/j.ijrobp.2019.10.031
2769:10.1016/j.radonc.2015.07.034
2713:10.1016/j.ijrobp.2019.10.031
2386:Jackson, John David (1999).
2316:
2100:Particle physics experiments
1199:
585:{\displaystyle v_{\text{p}}}
7:
4116:Cosmic background radiation
3551:"First human Cerenkography"
3500:Advances in Cancer Research
2250:
1882:cosmic ray visual phenomena
541:Cherenkov radiation in the
228:Norris Cotton Cancer Center
207:particles until the 1970s.
157:Vavilov–Cherenkov radiation
10:
4416:
4345:
4203:Lasers and aviation safety
3745:
3697:Journal of Instrumentation
3126:10.1038/s41566-023-01311-z
2417:Doklady Akademii Nauk SSSR
2103:
2041:), by experiments such as
1654:{\displaystyle n(\omega )}
134:
4343:
4307:
4271:
4233:Radioactive contamination
4158:
4086:Electromagnetic radiation
4076:
3988:
3935:
3928:
3856:Radović, Andrija (2002).
3579:10.1117/1.JBO.18.2.020502
3048:10.1007/s11082-015-0261-8
2757:Radiotherapy and Oncology
2645:. Springer. p. 191.
2607:Classical electrodynamics
2443:October 22, 2007, at the
2388:Classical electrodynamics
2335:Dictionary.com Unabridged
2172:{\displaystyle v_{0}=c/n}
1974:Cherenkov radiation in a
1314:{\displaystyle p=\hbar k}
1065:{\displaystyle d\phi /dx}
757:for water at 20 °C.
518:of light rather than the
479:constructive interference
246:
85:electromagnetic radiation
29:Idaho National Laboratory
4346:See also the categories
4284:1996 Costa Rica accident
3945:Acoustic radiation force
3871:(4): 1–5. Archived from
3835:Nuclear Reactor start up
3699:(Submitted manuscript).
2059:Pierre Auger Observatory
2005:Astrophysics experiments
1180:Reverse Cherenkov effect
1030:Arbitrary emission angle
663:speed of light in vacuum
492:A common analogy is the
4258:Radiation heat-transfer
4111:Gravitational radiation
3819:10.1103/PhysRev.92.1069
2975:Physical Review Letters
2841:10.1126/science.1079549
2639:Marguet, Serge (2017).
2535:Nahin, Paul J. (2018).
2296:Non-radiation condition
2065:detectors, such as the
1891:
1856:Kramers–Kronig relation
1592:{\displaystyle \omega }
234:of patients undergoing
4299:1990 Zaragoza accident
4294:1984 Moroccan accident
4263:Linear energy transfer
3937:Non-ionizing radiation
3780:Jelley, J. V. (1958).
3463:10.1098/rsta.2011.0271
3306:(6): 060505–060505–3.
3273:10.1002/smll.200902408
2913:10.1038/nnano.2015.137
2566:10.1098/rsta.2017.0448
2217:
2193:
2173:
1982:
1922:
1825:
1802:
1723:
1703:
1679:
1655:
1622:
1593:
1573:
1553:
1531:
1315:
1279:
1278:{\displaystyle \beta }
1259:
1226:
1153:
1066:
1021:
975:
913:
844:
797:
751:
725:
679:
655:
635:
586:
562:
545:
489:
466:
421:
372:
352:
315:
31:
4289:1987 Goiânia accident
4091:Synchrotron radiation
4081:Earth's energy budget
4063:Radioactive materials
4058:Particle accelerators
3865:Journal of Theoretics
2892:Nature Nanotechnology
2872:Dokl. Akad. Nauk SSSR
2604:Sengupta, P. (2000).
2481:Nahin, P. J. (1988).
2436:, 1999, s. 149–153. (
2291:List of light sources
2241:Large Hadron Collider
2218:
2194:
2174:
1973:
1916:
1886:criticality accidents
1826:
1803:
1724:
1704:
1680:
1656:
1623:
1594:
1574:
1554:
1532:
1316:
1280:
1260:
1227:
1154:
1067:
1022:
976:
914:
845:
798:
752:
726:
680:
656:
636:
587:
560:
540:
487:
467:
422:
373:
353:
309:
293:particle accelerators
25:Advanced Test Reactor
22:
4360:Radiation protection
4213:Radiation protection
4101:Black-body radiation
4008:Background radiation
3923:(physics and health)
2311:Transition radiation
2207:
2183:
2142:
2009:When a high-energy (
1928:radiopharmaceuticals
1862:Anomalous dispersion
1815:
1763:
1713:
1693:
1669:
1636:
1603:
1583:
1563:
1543:
1387:
1325:Collective Cherenkov
1296:
1269:
1240:
1216:
1076:
1042:
987:
923:
867:
811:
764:
735:
693:
669:
645:
596:
569:
528:Smith–Purcell effect
435:
390:
362:
334:
312:Arkansas Nuclear One
299:, travels through a
4330:Radiation hardening
4272:Radiation incidents
4208:Medical radiography
4167:Radiation syndrome
4121:Cherenkov radiation
3811:1953PhRv...92.1069S
3709:2017JInst..12.6001B
3570:2013JBO....18b0502S
3455:2011RSPTA.369.4605M
3378:10.1155/2011/641618
3359:Radiopharmaceutical
3312:2010JBO....15f0505L
3228:2009PhyU...52.1099B
3085:1983PZhTF...9.1385B
2997:2019PhRvL.122p1601M
2905:2015NatNa..10..804G
2823:2003Sci...299..368L
2557:2018RSPTA.37670448N
2021:interacts with the
1841:is close to 1). At
1663:index of refraction
1331:plasma acceleration
1291:de Broglie relation
1206:traveling-wave tube
351:{\displaystyle c/n}
224:Dartmouth-Hitchcock
95:) passes through a
35:Cherenkov radiation
4390:Special relativity
4380:Physical phenomena
4325:Radioactive source
4146:Radiation exposure
4126:Askaryan radiation
4106:Particle radiation
3990:Ionizing radiation
2280:Frank–Tamm formula
2257:Askaryan radiation
2213:
2189:
2169:
2106:Cherenkov detector
2090:supernova remnants
2023:Earth's atmosphere
1987:open pool reactors
1983:
1923:
1821:
1798:
1719:
1699:
1675:
1651:
1618:
1589:
1579:and per frequency
1569:
1549:
1527:
1381:Frank–Tamm formula
1377:frequency spectrum
1311:
1289:) rather than the
1275:
1255:
1222:
1149:
1062:
1017:
971:
909:
840:
793:
747:
721:
675:
651:
631:
582:
563:
546:
490:
462:
417:
368:
348:
324:Huygens' principle
316:
263:universal constant
176:special relativity
81:Cerenkov radiation
32:
4367:
4366:
4348:Radiation effects
4218:Radiation therapy
4154:
4153:
4096:Thermal radiation
4033:Neutron radiation
3998:Radioactive decay
3772:978-0-08-030275-1
3449:(1955): 4605–19.
3320:10.1117/1.3514659
3222:(11): 1099–1110.
2652:978-3-319-59559-7
2617:978-81-224-1249-9
2549:The Royal Society
2521:978-0-444-63489-4
2494:978-0-8018-6909-9
2301:Radioluminescence
2274:Faster-than-light
2216:{\displaystyle n}
2192:{\displaystyle c}
1824:{\displaystyle n}
1722:{\displaystyle c}
1702:{\displaystyle v}
1689:of the particle,
1678:{\displaystyle q}
1572:{\displaystyle x}
1552:{\displaystyle E}
1519:
1447:
1422:
1225:{\displaystyle c}
1163:similar triangles
1147:
1124:
1104:
1015:
963:
946:
933:
890:
877:
835:
821:
788:
782:
712:
678:{\displaystyle n}
654:{\displaystyle c}
619:
607:
579:
445:
400:
371:{\displaystyle n}
270:= 299,792,458 m/s
201:Arnold Sommerfeld
153:Lebedev Institute
75:) (also known as
4407:
4385:Particle physics
4308:Related articles
4223:Radiation damage
4048:Nuclear reactors
3933:
3932:
3914:
3907:
3900:
3891:
3890:
3886:
3884:
3883:
3877:
3862:
3847:
3836:
3822:
3791:
3776:
3760:
3740:
3735:
3729:
3728:
3688:
3682:
3681:
3665:
3659:
3658:
3642:
3636:
3635:
3606:
3600:
3599:
3581:
3555:
3546:
3540:
3539:
3529:
3491:
3485:
3484:
3474:
3434:
3428:
3427:
3407:
3401:
3400:
3390:
3380:
3348:
3342:
3341:
3331:
3291:
3285:
3284:
3254:
3248:
3247:
3209:
3203:
3202:
3192:
3151:
3145:
3144:
3142:
3140:
3119:
3104:Nature Photonics
3095:
3089:
3088:
3066:
3060:
3059:
3031:
3025:
3024:
2990:
2970:
2964:
2963:
2961:
2959:
2950:. Archived from
2939:
2933:
2932:
2886:
2880:
2879:
2867:
2861:
2860:
2834:
2817:(5605): 368–71.
2806:
2797:
2788:
2787:
2785:
2783:
2748:
2742:
2741:
2739:
2737:
2724:
2692:
2683:
2682:
2680:
2678:
2663:
2657:
2656:
2636:
2630:
2629:
2601:
2595:
2594:
2568:
2532:
2526:
2525:
2505:
2499:
2498:
2478:
2472:
2471:
2469:
2468:
2454:
2448:
2425:
2412:Cherenkov, P. A.
2408:
2402:
2401:
2383:
2377:
2376:
2374:
2373:
2354:
2348:
2347:
2345:
2343:
2326:
2225:refractive index
2222:
2220:
2219:
2214:
2198:
2196:
2195:
2190:
2178:
2176:
2175:
2170:
2165:
2154:
2153:
2116:particle physics
2067:Super-Kamiokande
1995:fission products
1966:Nuclear reactors
1830:
1828:
1827:
1822:
1810:refractive index
1807:
1805:
1804:
1799:
1785:
1728:
1726:
1725:
1720:
1708:
1706:
1705:
1700:
1684:
1682:
1681:
1676:
1660:
1658:
1657:
1652:
1627:
1625:
1624:
1619:
1598:
1596:
1595:
1590:
1578:
1576:
1575:
1570:
1558:
1556:
1555:
1550:
1536:
1534:
1533:
1528:
1526:
1525:
1521:
1520:
1518:
1508:
1507:
1498:
1497:
1487:
1486:
1477:
1448:
1446:
1438:
1437:
1428:
1423:
1421:
1406:
1402:
1401:
1391:
1366:
1353:
1320:
1318:
1317:
1312:
1284:
1282:
1281:
1276:
1264:
1262:
1261:
1256:
1231:
1229:
1228:
1223:
1171:
1158:
1156:
1155:
1150:
1148:
1146:
1138:
1130:
1125:
1123:
1122:
1110:
1105:
1103:
1092:
1071:
1069:
1068:
1063:
1055:
1026:
1024:
1023:
1018:
1016:
1014:
1003:
980:
978:
977:
972:
964:
956:
948:
947:
944:
935:
934:
931:
918:
916:
915:
910:
892:
891:
888:
879:
878:
875:
858:
849:
847:
846:
841:
836:
828:
823:
822:
819:
802:
800:
799:
794:
789:
784:
783:
780:
774:
756:
754:
753:
748:
730:
728:
727:
722:
714:
713:
710:
687:refractive index
684:
682:
681:
676:
660:
658:
657:
652:
640:
638:
637:
632:
621:
620:
617:
608:
600:
591:
589:
588:
583:
581:
580:
577:
532:photonic crystal
471:
469:
468:
463:
458:
447:
446:
443:
426:
424:
423:
418:
413:
402:
401:
398:
380:refractive index
377:
375:
374:
369:
357:
355:
354:
349:
344:
279:
271:
197:Oliver Heaviside
115:in a medium) of
99:medium (such as
89:charged particle
74:
73:
70:
69:
66:
63:
60:
57:
54:
51:
48:
45:
4415:
4414:
4410:
4409:
4408:
4406:
4405:
4404:
4370:
4369:
4368:
4363:
4362:
4339:
4335:Havana syndrome
4320:Nuclear physics
4303:
4267:
4160:
4150:
4136:Unruh radiation
4072:
4053:Nuclear weapons
4038:Nuclear fission
3984:
3924:
3918:
3881:
3879:
3875:
3860:
3845:
3834:
3830:
3825:
3798:Physical Review
3773:
3748:
3743:
3736:
3732:
3689:
3685:
3680:(5): 1627–1637.
3666:
3662:
3657:(2): 1044–1048.
3651:Medical Physics
3643:
3639:
3607:
3603:
3553:
3547:
3543:
3518:
3492:
3488:
3435:
3431:
3408:
3404:
3349:
3345:
3292:
3288:
3267:(10): 1087–91.
3255:
3251:
3215:Physics-Uspekhi
3210:
3206:
3152:
3148:
3138:
3136:
3096:
3092:
3067:
3063:
3032:
3028:
2971:
2967:
2957:
2955:
2940:
2936:
2887:
2883:
2868:
2864:
2832:10.1.1.540.8969
2804:
2798:
2791:
2781:
2779:
2749:
2745:
2735:
2733:
2693:
2686:
2676:
2674:
2665:
2664:
2660:
2653:
2637:
2633:
2618:
2602:
2598:
2533:
2529:
2522:
2506:
2502:
2495:
2479:
2475:
2466:
2464:
2456:
2455:
2451:
2445:Wayback Machine
2409:
2405:
2398:
2384:
2380:
2371:
2369:
2356:
2355:
2351:
2341:
2339:
2328:
2327:
2323:
2319:
2253:
2208:
2205:
2204:
2184:
2181:
2180:
2161:
2149:
2145:
2143:
2140:
2139:
2112:
2102:
2007:
1968:
1911:
1899:
1894:
1878:vitreous humour
1816:
1813:
1812:
1781:
1764:
1761:
1760:
1714:
1711:
1710:
1694:
1691:
1690:
1687:electric charge
1670:
1667:
1666:
1637:
1634:
1633:
1604:
1601:
1600:
1584:
1581:
1580:
1564:
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1560:
1544:
1541:
1540:
1503:
1499:
1493:
1489:
1488:
1482:
1478:
1476:
1469:
1465:
1464:
1439:
1433:
1429:
1427:
1407:
1397:
1393:
1392:
1390:
1388:
1385:
1384:
1373:
1371:Characteristics
1365:
1355:
1352:
1342:
1327:
1297:
1294:
1293:
1270:
1267:
1266:
1241:
1238:
1237:
1217:
1214:
1213:
1202:
1182:
1172:and final time
1166:
1139:
1131:
1129:
1118:
1114:
1109:
1096:
1091:
1077:
1074:
1073:
1051:
1043:
1040:
1039:
1032:
1007:
1002:
988:
985:
984:
955:
943:
939:
930:
926:
924:
921:
920:
887:
883:
874:
870:
868:
865:
864:
853:
827:
818:
814:
812:
809:
808:
779:
775:
773:
765:
762:
761:
736:
733:
732:
709:
705:
694:
691:
690:
670:
667:
666:
646:
643:
642:
616:
612:
599:
597:
594:
593:
576:
572:
570:
567:
566:
555:
454:
442:
438:
436:
433:
432:
409:
397:
393:
391:
388:
387:
363:
360:
359:
340:
335:
332:
331:
277:
276:it is only 0.75
266:
249:
244:
242:Physical origin
137:
129:Pavel Cherenkov
121:nuclear reactor
101:distilled water
87:emitted when a
42:
38:
17:
12:
11:
5:
4413:
4403:
4402:
4397:
4392:
4387:
4382:
4365:
4364:
4344:
4341:
4340:
4338:
4337:
4332:
4327:
4322:
4317:
4311:
4309:
4305:
4304:
4302:
4301:
4296:
4291:
4286:
4281:
4275:
4273:
4269:
4268:
4266:
4265:
4260:
4255:
4250:
4245:
4240:
4235:
4230:
4225:
4220:
4215:
4210:
4205:
4200:
4195:
4190:
4185:
4183:Health physics
4180:
4179:
4178:
4173:
4164:
4162:
4156:
4155:
4152:
4151:
4149:
4148:
4143:
4141:Dark radiation
4138:
4133:
4131:Bremsstrahlung
4128:
4123:
4118:
4113:
4108:
4103:
4098:
4093:
4088:
4083:
4077:
4074:
4073:
4071:
4070:
4065:
4060:
4055:
4050:
4045:
4043:Nuclear fusion
4040:
4035:
4030:
4025:
4020:
4015:
4013:Alpha particle
4010:
4005:
4000:
3994:
3992:
3986:
3985:
3983:
3982:
3977:
3972:
3967:
3962:
3957:
3952:
3947:
3941:
3939:
3930:
3926:
3925:
3917:
3916:
3909:
3902:
3894:
3888:
3887:
3853:
3842:
3829:
3828:External links
3826:
3824:
3823:
3792:
3788:Pergamon Press
3777:
3771:
3763:Pergamon Press
3749:
3747:
3744:
3742:
3741:
3730:
3683:
3660:
3637:
3618:(3): 615–622.
3601:
3541:
3516:
3486:
3429:
3402:
3343:
3286:
3249:
3204:
3167:(2): 422–429.
3146:
3090:
3061:
3026:
2981:(16): 161601.
2965:
2934:
2899:(9): 804–809.
2881:
2862:
2789:
2763:(2): 331–333.
2743:
2707:(2): 422–429.
2684:
2658:
2651:
2631:
2616:
2596:
2527:
2520:
2500:
2493:
2473:
2462:NobelPrize.org
2449:
2429:Usp. Fiz. Nauk
2403:
2396:
2378:
2362:Science Direct
2349:
2320:
2318:
2315:
2314:
2313:
2308:
2303:
2298:
2293:
2288:
2283:
2277:
2271:
2268:Bremsstrahlung
2265:
2260:
2252:
2249:
2212:
2201:speed of light
2188:
2168:
2164:
2160:
2157:
2152:
2148:
2101:
2098:
2006:
2003:
1991:beta particles
1967:
1964:
1910:
1907:
1898:
1895:
1893:
1890:
1820:
1797:
1794:
1791:
1788:
1784:
1780:
1777:
1774:
1771:
1768:
1731:speed of light
1718:
1698:
1674:
1650:
1647:
1644:
1641:
1617:
1614:
1611:
1608:
1588:
1568:
1548:
1524:
1517:
1514:
1511:
1506:
1502:
1496:
1492:
1485:
1481:
1475:
1472:
1468:
1463:
1460:
1457:
1454:
1451:
1445:
1442:
1436:
1432:
1426:
1420:
1417:
1413:
1410:
1405:
1400:
1396:
1372:
1369:
1363:
1350:
1339:speed of light
1326:
1323:
1310:
1307:
1304:
1301:
1287:phase constant
1274:
1254:
1251:
1248:
1245:
1221:
1210:phase velocity
1201:
1198:
1181:
1178:
1145:
1142:
1137:
1134:
1128:
1121:
1117:
1113:
1108:
1102:
1099:
1095:
1090:
1087:
1084:
1081:
1061:
1058:
1054:
1050:
1047:
1031:
1028:
1013:
1010:
1006:
1001:
998:
995:
992:
970:
967:
962:
959:
954:
951:
942:
938:
929:
908:
905:
901:
898:
895:
886:
882:
873:
839:
834:
831:
826:
817:
792:
787:
778:
772:
769:
746:
743:
740:
720:
717:
708:
704:
701:
698:
674:
650:
630:
627:
624:
615:
611:
606:
603:
575:
554:
553:Emission angle
551:
520:group velocity
516:phase velocity
461:
457:
453:
450:
441:
416:
412:
408:
405:
396:
367:
347:
343:
339:
328:phase velocity
322:waves and via
314:Unit 2 (ANO-2)
253:speed of light
248:
245:
243:
240:
232:vitreous humor
149:Sergey Vavilov
136:
133:
105:phase velocity
15:
9:
6:
4:
3:
2:
4412:
4401:
4400:Light sources
4398:
4396:
4393:
4391:
4388:
4386:
4383:
4381:
4378:
4377:
4375:
4361:
4357:
4353:
4352:Radioactivity
4349:
4342:
4336:
4333:
4331:
4328:
4326:
4323:
4321:
4318:
4316:
4313:
4312:
4310:
4306:
4300:
4297:
4295:
4292:
4290:
4287:
4285:
4282:
4280:
4277:
4276:
4274:
4270:
4264:
4261:
4259:
4256:
4254:
4251:
4249:
4246:
4244:
4241:
4239:
4236:
4234:
4231:
4229:
4226:
4224:
4221:
4219:
4216:
4214:
4211:
4209:
4206:
4204:
4201:
4199:
4196:
4194:
4191:
4189:
4186:
4184:
4181:
4177:
4174:
4172:
4169:
4168:
4166:
4165:
4163:
4157:
4147:
4144:
4142:
4139:
4137:
4134:
4132:
4129:
4127:
4124:
4122:
4119:
4117:
4114:
4112:
4109:
4107:
4104:
4102:
4099:
4097:
4094:
4092:
4089:
4087:
4084:
4082:
4079:
4078:
4075:
4069:
4066:
4064:
4061:
4059:
4056:
4054:
4051:
4049:
4046:
4044:
4041:
4039:
4036:
4034:
4031:
4029:
4026:
4024:
4021:
4019:
4018:Beta particle
4016:
4014:
4011:
4009:
4006:
4004:
4003:Cluster decay
4001:
3999:
3996:
3995:
3993:
3991:
3987:
3981:
3978:
3976:
3973:
3971:
3968:
3966:
3963:
3961:
3958:
3956:
3953:
3951:
3948:
3946:
3943:
3942:
3940:
3938:
3934:
3931:
3929:Main articles
3927:
3922:
3915:
3910:
3908:
3903:
3901:
3896:
3895:
3892:
3878:on 2016-03-04
3874:
3870:
3866:
3859:
3854:
3852:
3848:
3843:
3841:
3837:
3832:
3831:
3820:
3816:
3812:
3808:
3804:
3800:
3799:
3793:
3789:
3785:
3784:
3778:
3774:
3768:
3764:
3759:
3758:
3751:
3750:
3739:
3734:
3726:
3722:
3718:
3714:
3710:
3706:
3703:(6): T06001.
3702:
3698:
3694:
3687:
3679:
3675:
3671:
3664:
3656:
3652:
3648:
3641:
3633:
3629:
3625:
3621:
3617:
3613:
3605:
3597:
3593:
3589:
3585:
3580:
3575:
3571:
3567:
3564:(2): 020502.
3563:
3559:
3552:
3545:
3537:
3533:
3528:
3523:
3519:
3517:9780124116382
3513:
3509:
3505:
3501:
3497:
3490:
3482:
3478:
3473:
3468:
3464:
3460:
3456:
3452:
3448:
3444:
3440:
3433:
3425:
3421:
3417:
3413:
3406:
3398:
3394:
3389:
3384:
3379:
3374:
3370:
3366:
3362:
3360:
3356:
3347:
3339:
3335:
3330:
3325:
3321:
3317:
3313:
3309:
3305:
3301:
3297:
3290:
3282:
3278:
3274:
3270:
3266:
3262:
3261:
3253:
3245:
3241:
3237:
3233:
3229:
3225:
3221:
3217:
3216:
3208:
3200:
3196:
3191:
3186:
3182:
3178:
3174:
3170:
3166:
3162:
3158:
3150:
3135:
3131:
3127:
3123:
3118:
3113:
3109:
3105:
3101:
3094:
3086:
3082:
3079:: 1385–1389.
3078:
3074:
3073:
3065:
3057:
3053:
3049:
3045:
3041:
3037:
3030:
3022:
3018:
3014:
3010:
3006:
3002:
2998:
2994:
2989:
2984:
2980:
2976:
2969:
2954:on 2009-01-31
2953:
2949:
2945:
2938:
2930:
2926:
2922:
2918:
2914:
2910:
2906:
2902:
2898:
2894:
2893:
2885:
2877:
2873:
2866:
2858:
2854:
2850:
2846:
2842:
2838:
2833:
2828:
2824:
2820:
2816:
2812:
2811:
2803:
2796:
2794:
2778:
2774:
2770:
2766:
2762:
2758:
2754:
2747:
2732:
2728:
2723:
2718:
2714:
2710:
2706:
2702:
2698:
2691:
2689:
2672:
2668:
2662:
2654:
2648:
2644:
2643:
2635:
2627:
2623:
2619:
2613:
2609:
2608:
2600:
2592:
2588:
2584:
2580:
2576:
2572:
2567:
2562:
2558:
2554:
2550:
2546:
2542:
2538:
2531:
2523:
2517:
2513:
2512:
2504:
2496:
2490:
2486:
2485:
2477:
2463:
2459:
2453:
2446:
2442:
2439:
2435:
2431:
2430:
2423:
2419:
2418:
2413:
2407:
2399:
2397:0-471-30932-X
2393:
2389:
2382:
2367:
2363:
2359:
2353:
2338:(Online). n.d
2337:
2336:
2331:
2325:
2321:
2312:
2309:
2307:
2304:
2302:
2299:
2297:
2294:
2292:
2289:
2287:
2284:
2281:
2278:
2275:
2272:
2269:
2266:
2264:
2261:
2258:
2255:
2254:
2248:
2246:
2242:
2238:
2234:
2229:
2226:
2210:
2202:
2186:
2166:
2162:
2158:
2155:
2150:
2146:
2135:
2133:
2132:four-momentum
2129:
2125:
2121:
2117:
2111:
2107:
2097:
2095:
2091:
2086:
2084:
2080:
2076:
2072:
2068:
2064:
2060:
2056:
2052:
2048:
2044:
2040:
2036:
2031:
2028:
2024:
2020:
2016:
2012:
2002:
2000:
1999:radioactivity
1996:
1992:
1988:
1980:
1977:
1972:
1963:
1959:
1957:
1953:
1949:
1945:
1941:
1937:
1933:
1929:
1920:
1915:
1906:
1904:
1889:
1887:
1883:
1879:
1874:
1871:
1866:
1864:
1863:
1858:
1857:
1852:
1848:
1844:
1840:
1839:
1834:
1818:
1811:
1792:
1789:
1782:
1778:
1775:
1772:
1769:
1766:
1757:
1755:
1751:
1746:
1743:
1739:
1734:
1732:
1716:
1696:
1688:
1672:
1664:
1645:
1639:
1631:
1612:
1606:
1586:
1566:
1546:
1537:
1522:
1512:
1504:
1500:
1494:
1490:
1483:
1479:
1473:
1470:
1466:
1461:
1455:
1449:
1443:
1440:
1434:
1430:
1424:
1418:
1415:
1411:
1408:
1403:
1398:
1394:
1382:
1378:
1368:
1362:
1358:
1349:
1345:
1340:
1336:
1332:
1322:
1308:
1302:
1299:
1292:
1288:
1272:
1252:
1246:
1243:
1235:
1219:
1211:
1207:
1197:
1195:
1192:and negative
1191:
1187:
1186:metamaterials
1177:
1175:
1169:
1164:
1159:
1143:
1140:
1135:
1132:
1126:
1119:
1115:
1111:
1106:
1100:
1097:
1093:
1088:
1085:
1082:
1079:
1059:
1056:
1052:
1048:
1045:
1037:
1036:metamaterials
1027:
1011:
1008:
1004:
999:
996:
993:
990:
981:
968:
965:
960:
957:
952:
949:
940:
936:
927:
906:
903:
899:
896:
893:
884:
880:
871:
862:
856:
850:
837:
832:
829:
824:
815:
806:
790:
785:
776:
770:
767:
758:
744:
741:
738:
718:
715:
706:
702:
699:
696:
688:
672:
664:
648:
628:
625:
622:
613:
609:
604:
601:
573:
559:
550:
544:
539:
535:
533:
529:
525:
521:
517:
512:
510:
506:
502:
499:
495:
486:
482:
480:
475:
459:
455:
451:
448:
439:
430:
414:
410:
406:
403:
394:
385:
381:
365:
345:
341:
337:
329:
325:
321:
313:
308:
304:
302:
298:
294:
290:
286:
282:
275:
269:
264:
260:
259:
254:
239:
237:
233:
229:
225:
221:
216:
214:
210:
206:
202:
198:
195:
192:
187:
185:
181:
177:
173:
168:
166:
162:
158:
154:
150:
146:
142:
132:
130:
126:
122:
118:
114:
110:
106:
102:
98:
94:
90:
86:
82:
78:
72:
36:
30:
26:
21:
4356:Radiobiology
4238:Radiobiology
4198:Laser safety
4120:
3880:. Retrieved
3873:the original
3868:
3864:
3802:
3796:
3782:
3761:. New York:
3756:
3733:
3700:
3696:
3686:
3677:
3673:
3663:
3654:
3650:
3640:
3615:
3611:
3604:
3561:
3557:
3544:
3495:
3489:
3446:
3442:
3432:
3415:
3411:
3405:
3368:
3364:
3358:
3354:
3346:
3303:
3299:
3289:
3264:
3258:
3252:
3219:
3213:
3207:
3164:
3160:
3149:
3137:. Retrieved
3107:
3103:
3093:
3076:
3070:
3064:
3039:
3035:
3029:
2978:
2974:
2968:
2956:. Retrieved
2952:the original
2937:
2896:
2890:
2884:
2875:
2871:
2865:
2814:
2808:
2780:. Retrieved
2760:
2756:
2746:
2734:. Retrieved
2704:
2700:
2675:. Retrieved
2671:EurekaAlert!
2670:
2661:
2641:
2634:
2606:
2599:
2551:: 20170448.
2544:
2540:
2530:
2510:
2503:
2483:
2476:
2465:. Retrieved
2461:
2452:
2427:
2421:
2415:
2406:
2387:
2381:
2370:. Retrieved
2361:
2352:
2340:. Retrieved
2333:
2324:
2230:
2136:
2113:
2087:
2015:gamma photon
2008:
1984:
1979:reactor pool
1960:
1924:
1903:biomolecules
1900:
1875:
1867:
1860:
1854:
1846:
1836:
1832:
1758:
1738:fluorescence
1735:
1630:permeability
1538:
1374:
1360:
1356:
1347:
1343:
1328:
1203:
1194:permeability
1190:permittivity
1183:
1173:
1167:
1160:
1033:
982:
860:
854:
851:
803:The emitted
759:
564:
547:
523:
513:
491:
474:polarization
384:ground state
317:
288:
280:
267:
255:
250:
236:radiotherapy
217:
205:superluminal
188:
169:
156:
138:
91:(such as an
80:
76:
34:
33:
3980:Ultraviolet
3975:Radio waves
3805:(4): 1069.
2330:"Cherenkov"
1754:ultraviolet
1750:wavelengths
1733:in vacuum.
1208:(TWT), the
805:light waves
592:such that
509:shock front
220:Dartmouth's
209:Marie Curie
145:Nobel Prize
109:propagation
4374:Categories
4161:and health
4159:Radiation
4028:Cosmic ray
3882:2015-09-30
3786:. London:
3418:(8): 514.
3139:28 October
3117:2301.11082
2988:1810.05027
2958:1 December
2467:2021-05-06
2372:2024-01-22
2286:Light echo
2263:Blue noise
2104:See also:
2083:New Mexico
2019:cosmic ray
1851:gamma rays
1236:should be
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