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11.3Comptoneffect
X-raysimpinges(冲击,撞击)onmatter,someoftheradiationisscattered(散射),justasthevisiblelightfallingonaroughsurfaceundergoesdiffusereflection(漫射，diffusion).Scatteredradiationhassmallerfrequencyandlongerwavelengththantheincidentradiation.Thewavelengthofscatteredradiationdependsonthescatteredangleφ.
ClassicalexplanationBasedontheclassicalprinciples,thescatteringmechanismisinducedbythemotionofelectronsinthematerial,causedbytheincidentradiation.Thismotionmusthavethesamefrequencyasthatofincidentwavebecauseofforcedvibration,andsothescatteredwaveradiatedbytheoscillatingchargesshouldhavethesamefrequency.Thereisnoreasonthatthefrequencycanbeshiftedbythismechanism.
··P?0,p0?pφQuantumexplanationThequantumtheory,bycontrast,providesabeautifullysimpleexplanation.SchematicdiagramofComptonscattering.
Quantumexplanation:modelThescatteringprocessistakenasacollisionoftwoparticles,theincidentphotonandanelectronatrest.Thephotongivesupsomeofitsenergyandmomentumtotheelectron,whichrecoilsasaresultofthisimpact;andthefinalphotonhaslessenergy,smallerfrequencyandlongerwavelengththantheinitialone.
TheoreticalderivationSupposethat?0and?arethewavelengthoftheincidentandscatteredradiation,respectively.TheComptoneffectcouldbedescribedbythefollowingprocedures:Usingrelativistictheory;Energyconservation;Momentumconservation;
Thekeypointsofderivationprocedure:(1)Relativistictheory:Whenm0=0,themomentumisequalto
(2)EnergyconservationForelectron,wehave(1)(2)Wherep=mV
(3)Themomentumconservationh/?h/?0mV?Andweknow:(3)
(4)Squaring(1),wehave(5)(4)-(5)(1)
Theaboveequationcanberewrittenas(6)
wherem0istheelectronmass.calledComptonwavelength.(7)(8)
Lightshowsthepropertyofwavesinitsinterferenceanddiffracti
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