Summary and Analysis of the Compton Effect

stocky and Analysis of the Compton progenyEn = nhf (1) where En is the efficiency, n is a non-negative integer, h is Plancks continuous, and f is the frequence of the photon.2 In 1905, Albert Einstein extended Plancks inference to wholeow not but black body beam of light but all electromagnetic waves Therefore, Einstein hypothesized that electric arc is quantized with faculty proportional to its absolute frequency.3 The axiomatic principle to be deduced from these discoveries is that a unobjectionable possessed attributes of waves and parts In 1922, Arthur Holly Compton solidified Plancks supposal and and then firmly established a new era of physics. Compton theorized and thusly tryally demonstrated that electromagnetic waves had the properties of particles. Classically, roentgen rays would shake the negatrons of a target visible at the homogeneous frequency of the roentgenogram. Hence, the wavelength of radiation from the oscillating negatrons would be alike to the wavelength of the ledger entry xrays. 1 However, it was discovered that x-rays were more than easily absorbed by materials than waves of thirster wavelength. In former(a) words, the break upx-rays were of longer wavelength.4 This was contrary to the predictions of unequivocal physics. Compton realized though, that if the interaction was modeled as a smasher surrounded by two particles (electron and photon), the upset x-rays would-be of longer wave length (comp bed to the hap-rays) because the ricocheting electron would acquire some of the pushing and pulse of the elect(postnominal) x-ray.4 Since wavelength is oppositionly proportional to frequency, the frequency of the separate x-rays was less. From eq. (1), it is seenthat the nil would also be decreased. When Compton carried come in this experiment in 1922 using bit as his target, he verified his possible action and provided even more evidence that light also possessed a mass less particle natureDetailed Description of Compton featthe elastic dispersal of electromagnetic radiation by free electrons, accompanied by an adjoin in wavelength it is discover during disperse of radiation of sooner long wavelength-X rays and da Gamma rays. The corpuscular properties of radiation were fully revealed for the branch time in the Compton pith.The Compton effect was discovered in 1922 by the Ameri fag physicist A. Compton, who observed that X rays scattered in paraffin obligate a longer wavelength than the casualty rays. Such a skid in wavelength could not be explained by classical theory. In fact, gibe to classical electrodynamics, under the influence of the fortnightly electric field of an electromagnetic (light) wave, an electron should oscillate with a frequency equal to that of the wave and consequently should radiate secondary (scattered) waves of the same frequency. therefore, in classical dissemination (the theory of which was provided by the British physicist J. J. Thom son and is therefore called Thomson diffusion) the wavelength of the light does not mixture.An elementary theory of the Compton effect based on quantum concepts was disposed(p) up by Compton and independently by P. Debye. According to quantum theory a light wave is a stream of light quanta, or photons. Each photon has a definite energy =hv=hc/and a definite urge p= (h/)n, where is the wavelength of the sequent light (vis its frequency),cis the speed of light,his Plancks never-ending, and n is the unit vector in the statement of propagation of the wave (the subscript denotes a photon). In quantum theory the Compton exit appears as an elastic striking between two particles, the attendant photon and the stationary electron. In every such collision event the laws of preservation of energy and neural impulse argon obeyed. A photon that has collided with an electron transfers part of its energy and momentum to the electron and changes its direction of motion (it is scattere d) the decrease in the photons energy signifies an increase in the wavelength of the scattered light. The electron, which previously had been stationary, receives energy and momentum from the photon and is set in motion (it experiences recoil). The direction of motion of the particles after(prenominal) the collision, as well as their energy, is determined by the laws of conservation of energy and momentum (Figure 1).Elastic collision of a photon and an electron in the Compton effect. Before the collision the electron was stationarypand p are the momentum of the possibility and scattered photons, pe=mvis the momentum of the recoil electron (vis its velocity),(is the photons sprinkling be given, and is the slant of escape of the recoil electron relative to the direction of the attendant photon.Simultaneous solution of the equations expressing the equality of the summed energies and momentums of the particles before and after the collision ( anticipate that the electron is statio nary before the collision) gives Comptons polity for the stagger in the wavelength of the light= =0(1 - cos )Here is the wavelength of the scattered light, is the photons break up locomote, and 0=h/mc= 2.426 - 10-10cm = 0.024 angstrom () is the Compton wavelength of the electron (mis the mass of the electron). It follows from Comptons commandment that the shift in the wavelength does not depend on the wavelength of the incident light itself. It is solely determined by the diffusion go of the photon and is maximal when = one hundred eighty, that is, when scattering is straight back max= 2o.Expressions for the energy eof the recoil, or Compton, electron as a function of the angle of its escape may be obtained from the same equations. The dependence of the energy of the scattered photon on the scattering angle , as well as the dependence of eon , which is link up to it, is shown in Figure 2. From the figure it is apparent that the recoil electrons always deplete a vel ocity component in the direction of motion of the incident photon (that is, does not exceed 90).Experiment has confirmed all the in a heightser plaza theoretical predictions. The correctness of the corpuscular concepts of the mechanism of the Compton effect-and thus the correctness of the underlying assumptions of quantum theory-has been experimentally proved.In actual experiments on the scattering of photons by matter, the electrons are not free but are bound to atoms. If the energy of the photons is high in comparison with the binding energy of the electrons in the atom (X-ray and da Gamma-ray photons), then(prenominal) the electrons experience a recoil strong enough to expel them from the atom. In this case the photon scattering proceeds as if with free electrons. However, if the energy of the photon is not sufficient to tear the electron from the atom, then the photon exchanges energy and momentum with the constitutional atom. Since the mass of the atom is very great comp ared to the photons equivalent mass (which, accord to the theory of relativity, equals y/c2), the recoil is virtually nonexistent therefore, the photonDependence of the energyof the scattered photon on the scattering angle(for convenience, only the upper half(prenominal) of the symmetrical curve is depicted) and the dependence of the energy eof the recoil electron on the angle of escape 0 (lower half of the curve). Quantities cerebrate to the same collision event are labeled with identical numbers. The vectors drawn from point 0, at which the collision between the proton with energy and the stationary electron occurred, to corresponding points on the curves depict the state of the particle after scattering the magnitudes of the vectors give the energy of the particles, and the angles formed by the vectors with the direction of the incident photon define the scattering angle and the angle 0 of the recoil electrons thoroughfare. (The graph was plotted for the case of scattering of hard X rays with wavelengthhc/= o= 0.024 .)is scattered without a change in its energy (that is, without a change in its wavelength, or coherently). In doughy atoms only the peripheral electrons are weakly bound (in contrast to the electrons make full the inner shells of the atom), and therefore the spectrum of the scattered radiation has both a shifted (Compton) breeze, from scattering by the peripheral electrons, and an un-shifted (coherent) line, from scattering by the entire atom. With increasing nu cloudless number (nuclear charge) the electron binding energy increases, the relative warmth of the Compton line decreases, and that of the coherent line increases.The motion of the electrons in atoms leads to a broadening of the Compton lines in the scattered radiation. This occurs because the wavelength of the incident light appears to be slightly changed for moving electrons in addition, the amount of change depends on the magnitude and direction of the electrons velocity ( the Doppler effect). mensural measurements of the intensity distribution in a Compton line, which reflects the velocity distribution of the electrons in the material, has confirmed the correctness of quantum theory, according to which electrons obey Fermi-Dirac statistics.The simplified theory of the Compton Effect examined here does not permit the calculation of all characteristics of Compton scattering, particularly the intensity of photon scattering at various angles. A complete theory of the Compton Effect is provided by quantum electrodynamics. The intensity of Compton scattering depends on both the scattering angle and the wavelength of the incident radiation. Asymmetry is observed in the angular distribution of the scattered photons more photons are scattered forward, and the asymmetry increases with increasing energy of the incident photons. The total intensity of Compton scattering decreases with an increase in the energy of the primordial photons (Figure 3) this indicate s that the probability of the Compton scattering of a photon passing by matter diminishes with lessen energy. Such a dependence of intensity on y determines the place of Compton scattering among the other effects of interaction between matter and radiation that are responsible for loss of energy by photons in their expiration by dint of matter. For example, in lead the Compton effect makes the main contribution to the energy loss of photons at energies of the order of 1-10 mega electron volts, or MeV (in a barge element, aluminum, this range is 0.1-30.0 MeV) below this region it is surpassed by the photoelectric effect, and above it by pair production.Compton scattering is utilise extensively in studying the gamma radiation of nuclei it is also the basis of the principle of operation of some gamma spectrometers.The Compton effect is possible not only for electrons but also for other supercharged particles, such as protons however, because of the protons salient mass its reco il is obtrusive only during the scattering of photons with very high energy.The double Compton effect consists of the brass of two scattered photons in place of a single incident photon during scattering by a free electron. The existence of this process follows from quantum electrodynamics it was first observed in 1952. Its probability is approximately a hundred propagation less than that of the ordinary Compton effect.Graph showing the dependence of the total Compton scattering intensityInverse Compton effect.If the electrons on which electromagnetic radiation is scattered are relativistic (that is, if they are moving with speeds close to the speed of light), then in an elastic collision the wavelength of the radiation will decrease the energy and momentum of the photons will increase at the expense of the energy and momentum of the electrons. This phenomenon is called the inverse Compton effect and is often use to explain the radiation mechanism of cosmic X-ray sources, the prod uction of the X-ray component of the background galactic radiation, and the regeneration of plasma waves into high-frequency electromagnetic waves.Description of the phenomenonBy the early 20th century, explore into the interaction ofX-rayswith matter was well underway. It was known that when a beam of X-rays is say at an atom, an electron is ejected and is scattered through an angle.Classical electromagnetismpredicts that the wavelength of scattered rays should be equal to the initial wavelength-9-23however, multiple experiments imbed that the wavelength of the scattered rays was greater than the initial wavelength.In 1923, Compton published a paper in thePhysical Reviewexplaining the phenomenon. Using the concept ofquantized radiationand the dynamics ofspecial relativity, Compton derived the relationship between the shift in wavelength and the scattering angleWhereis the initial wavelength,is the wavelength after scattering,his thePlanck constant,meis the mass of the electron ,cis thespeed of light, andis the scattering angle.The quantityhmecis known as theCompton wavelengthof the electron it is equal to2.43-1012m. The wavelength shiftis at least zero (for= 0) and at most twice the Compton wavelength of the electron (for= 180).Compton found that some X-rays see no wavelength shift despite being scattered through large angles in each of these cases the photon failed to eject an electron.Thus the magnitude of the shift is connect not to the Compton wavelength of the electron, but to the Compton wavelength of the entire atom, which can be upwards of 10000 quantify smaller.Compton Scatteringthe scattering of3.htmlc4x-raysfrom electrons in a carbon target and found scattered x-rays with a longer wavelength than those incident upon the target. The shift of the wavelength increased with scattering angle according to the Compton economyCompton explained and modeled the data by assuming a particle (photon) nature for light and applying conservation of energy and conservation of momentum to the collision between the photon and the electron. The scattered photon has lower energy and therefore a longer wavelength according to the2.htmlc3Planck relationship.At a time (early 1920s) when the particle (photon) nature of light suggested by the1.htmlc2photoelectric effectwas still being debated, the Compton experiment gave clear and independent evidence of particle-like behavior. Compton was awarded the Nobel Prize in 1927 for the discovery of the effect named after him.Compton Scattering DataComptons original experiment made use of molybdenum K-alpha x-rays, which have a wavelength of 0.0709 nm. These were scattered from a block of carbon and observed at different angles with a2Bragg spectrometer. The spectrometer consists of a rotating framework with a calcite vitreous silica to diffract the x-rays and an ionization chamber for detection of the x-rays. Since the spacing of the crystal planes in calcite is known, the angle of diffraction gives an accurate measure of the wavelength.Examination of the Compton scattering formula shows that the scattered wavelength depends upon the angle of scattering and also the mass of the scattered. For scattering from stationary electrons, the formula gives a wavelength of 0.0733 nm for scattering at 90 degrees. That is consistent with the right field peak in the illustration above. The peak which is near the original x-ray wavelength is considered to be scattering off inner electrons in the carbon atoms which are more tightly bound to the carbon nucleus. This causes the entire atom to recoil from the x-ray photon, and the larger effective scattering mass proportionally reduces the wavelength shift of the scattered photons. Putting the entire carbon nuclear mass into the scattering equation yields a wavelength shift almost 22,000 times smaller than that for an unbind electron, so those scattered photons are not seen to be shifted.The scattering of photons from charged particles is call ed Compton scattering after Arthur Compton who was the first to measure photon-electron scattering in 1922. When the incoming photon gives part of its energy to the electron, then the scattered photon has lower energy and according to the2.htmlc3Planck relationshiphas lower frequency and longer wavelength. The wavelength change in such scattering depends only upon the angle of scattering for a given target particle. The constant in the Compton formula above can be writtenand is called the Compton wavelength for the electron. The formula presumes that the scattering occurs in the rest frame of the electronCompton scattering occurs when the incident x-ray photon is deflected from its original driveway by an interaction with an electron. The electron is ejected from its orbital position and the x-ray photon loses energy because of the interaction but continues to travel through the material along an altered path. Energy and momentum are keep in this process. The energy shift depends on the angle of scattering and not on the nature of the scattering medium. Since the scattered x-ray photon has less energy, it has a longer wavelength and less penetrating than the incident photon.Compton Effect was first observed by Arthur Compton in 1923 and this discovery led to his award of the 1927 Nobel Prize in Physics. The discovery is of import because it demonstrates that light cannot be explained purely as a wave phenomenon. Comptons work convinced the scientific community that light can behave as a stream of particles (photons) whose energy is proportional to the frequency.The change in wavelength of the scattered photon is given byWhereL=wavelength of incident x-ray photonl=wavelength of scattered x-ray photonH=Plancks Constant The fundamental constant equal to the ratio of the energy E of a quantum of energy to its frequency v E=hv.me=the mass of an electron at restC=the speed of lightQ=The scattering angle of the scattered photonThe applet below demonstrates Compton scattering as calculated with the Klein-Nishina formula, which provides an accurate prediction of the angular distribution of x-rays and gamma-rays that are incident upon a single electron. Before this formula was derived, the electron foul up section had been classically derived by the British physicist and discoverer of the electron, J.J. Thomson. However, scattering experiments showed substantive deviations from the results predicted by Thomsons model. The Klein-Nishina formula incorporates the Breit-Dirac recoil factor, R, also known as radiation pressure. The formula also corrects for relativistic quantum mechanics and takes into account the interaction of the tailspin and magnetic moment of the electron with electromagnetic radiation.Quantum mechanics isa system of mechanics based on quantum theory to provide a consistent exposition of both electromagnetic wave and atomic structure.The applet shows that when a photon of a given energy hits an atom, it is sometimes reflec ted in a different direction. At the same time, it loses energy to an electron that is ejected from the atom. Theta is the angle between the scattered photon direction and the path of the incident photon. Phi is the angle between the scattered electron direction and the path of the incident photon.Derivation of the scattering formulaA photonwith wavelengthis directed at an electronein an atom, which is at rest. The collision causes the electron to recoil, and a new photonwith wavelengthemerges at angle. Letedenote the electron after the collision.From theconservation of energy,Compton postulated that photons carry momentum-9-23thus from theconservation of momentum, the momenta of the particles should be related byAssuming the initial momentum of the electron is zero.The photon energies are related to the frequencies byWherehis thePlanck constant. From therelativistic energy-momentum relation, the electron energies areAlong with the conservation of energy, these relations think that ThenFrom the conservation of momentum,Then by making use of thescalar product,ThusThe relation between the frequency and the momentum of a photon ispc=hf, so forthwith equating 1 and 2,Then dividing both sides by 2hffmec,Sincef=f=c, demodulator characteristicsEven large Compton-scatter telescopes have relatively small effective areas. This is because only a small number of the incident gamma-rays actually Compton scatter in the top level. So even if an instrument like COMPTEL has a geometric area of several thousand cm2, the effective area (weighted for the probability of an interaction) is a few tens of cm2.Energy resolution is fairly good for these detectors, typically 5-10% This is particular by uncertainties in the measurements of the energy deposited in each layer. Compton scatter telescopes have wide fields-of-view and can form imageseven though the so-called point hand out function (the probability that an event came from a certain area on the sky) is a ring.ApplicationsCo mpton scattering is of prime importance toradiobiology, as it is the most seeming interaction of gamma rays and high energy X rays with atoms in nutrition beings and is applied inradiation therapy.34In material physics, Compton scattering can be used to probe thewave functionof the electrons in matter in the momentum representation.Compton scattering is an important effect ingamma spectroscopywhich gives rise to theCompton edge, as it is possible for the gamma rays to scatter out of the detectors used.Compton suppression is used to detect stray scatter gamma rays to move this effect.Inverse Compton scatteringInverse Compton scattering is important inastrophysics. InX-ray astronomy, theaccretion disksurrounding ablack holeis believed to produce a thermal spectrum. The lower energy photons produced from this spectrum are scattered to higher(prenominal) energies by relativistic electrons in the surroundingcorona. This is believed to cause the power law component in the X-ray spectra (0.2-10 keV) of accreting black holes.The effect is also observed when photons from thecosmic microwave backgroundmove through the hot gas surrounding agalaxy cluster. The CMB photons are scattered to higher energies by the electrons in this gas, resulting in theSunyaev-ZelHYPERLINK http//en.wikipedia.org/wiki/Sunyaev-Zeldovich_effectHYPERLINK http//en.wikipedia.org/wiki/Sunyaev-Zeldovich_effectdovich effect. Observations of the Sunyaev-Zeldovich effect provide a or so redshift-independent means of detecting galaxy clusters.Some synchrotron radiation facilities scatter laser light off the stored electron beam. This Compton backscattering produces high energy photons in the MeV to GeV rangesubsequently used for nuclear physics experiments.Future developmentsCurrent research on Compton telescopes is express ways of tracking the scattered electron. By measuring the direction of the scattered electron in the top level, a complete solution for the incoming trajectory of the cosmic gam ma-ray can be found. This would allow Compton telescopes to have more conventional data analysis approaches since the event circle would no longer exist.