国际物理林匹克竞赛试题Th.doc

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1、Th3NEUTRONSINAGRAVITATIONALFIELDInthefamiliarclassicalworld,anelasticbouncingballontheEarth’ssurfaceisanidealexampleforperpetualmotion.Theballistrapped:itcannotgobelowthesurfaceoraboveitsturningpoint.Itwillremainboundedinthisstate,turningdownandbouncinguponceandagain,

2、forever.Onlyairdragorinelasticbouncescouldstoptheprocessandwillbeignoredinthefollowing.AgroupofphysicistsfromtheInstituteLaueLangevininGrenoblereportedV.V.Nesvizhevskyetal.“QuantumstatesofneutronsintheEarth’sgravitationalfield.”Nature,415(2002>297.PhysRevD67,102002(2

3、003>.in2002experimentalevidenceonthebehaviourofneutronsinthegravitationalfieldoftheEarth.Intheexperiment,neutronsmovingtotherightwereallowedtofalltowardsahorizontalcrystalsurfaceactingasaneutronmirror,wheretheybouncedbackelasticallyuptotheinitialheightonceandagain.b5E

4、2RGbCAPgDMAWXZvxvzzHLAMDF-1ThesetupoftheexperimentissketchedinFigureF-1.ItconsistsoftheopeningW,theneutronmirrorM(atheightz=0>,theneutronabsorberA(atheightz=HandwithlengthL>andtheneutrondetectorD.ThebeamofneutronsflieswithconstanthorizontalvelocitycomponentvxfromWtoDt

5、hroughthecavitybetweenAandM.AlltheneutronsthatreachthesurfaceofAareabsorbedanddisappearfromtheexperiment.ThosethatreachthesurfaceofMarereflectedelastically.ThedetectorDcountsthetransmissionrateN(H>,thatis,thetotalnumberofneutronsthatreachDperunittime.p1EanqFDPwMarksar

6、eindicatedatthebeginningofeachsubquestion,inparenthesis.DXDiTa9E3dTheneutronsenterthecavitywithawiderangeofpositiveandnegativeverticalvelocities,vz.Onceinthecavity,theyflybetweenthemirrorbelowandtheabsorberabove.RTCrpUDGiT1.(1.5>Computeclassicallytherangeofverticalvel

7、ocitiesvz(z>oftheneutronsthat,enteringataheightz,canarriveatthedetectorD.AssumethatLismuchlargerthananyotherlengthintheproblem.5PCzVD7HxA2.(1.5>CalculateclassicallytheminimumlengthLcofthecavitytoensurethatallneutronsoutsidethepreviousvelocityrange,regardlessofthevalue

8、sofz,areabsorbedbyA.Usevx=10ms-1andH=50µm.jLBHrnAILgTheneutrontransmissionrateN(H>ismeasuredatD.Weexpectthatitincreasesmonot