Volume 44A, number 2 PHYSICS LETTERS 21 May 1973

THE PHOTOMOBILITY OF ELECTRON BUBBLES IN LIQUID HELIUM

J.R. FLETCHERandR.M. BOWLEYDepartmentof Physics, UniversityofNottingham,University Park, Nottingham,UK

Received4 April 1973

An explanation is given for the changein the drift properties of negativeions in liquid helium when they areexposedto near infra-red radiation.

In an experimentstudyingthe mobility of electrons Averagerateof momentumlossin liquid helium, Northby andSanders[1] have

(1)reportedthatexposureto near infra-redradiation 2ir �~klM(k)I2(n(k)+l)ö(h~—L~�--E(k)÷hk.u)producesan increasein mobility. Theyexplainedthis k

result by assumingthat the radiationejectselectronsfrom bubblesin the heliuminto continuumstatesof wherehw is the energy of the photon,& is the differ-highermobility. Thepurposeof this letteris to pro- encein the energyof the ‘p’ and ‘s’ states,E(k) is theposeanalternativemechanismfor themobility in- energyof the phonon(roton)of momentumhk,crease. liku is the kinetic energylost by theelectronbubble,

Thereareseveraldifficulties with the Northby and andn(k) is the usual Bosedistribution functionsbf

Sandersexplanation,aspointedoutin their paper. phononsThemostseriousis thatphotonshavingenergiesof n(k) = {exp(~3E(k))—l}_1only 0.7 eV causeincreasedmobility, whereasthedepthof thepotentialwell is believedto be ‘-l eV. Thespontaneousemissionterm ineq.(1) averagesThesephotonsare unableto ejectelectronsfrom to zerowhereasthe stimulatedemissiontermgivesthe bubbles. to first orderin u,

Whena photonis absorbedby an electronbubblethe electroncanmakea transitionfrom the ground +u2ir ~ 12 ~‘s’ stateto a ‘p’ statewithout any changeof bubble k ~ IM(k) dE(k)radius.After the electronictransitionthe bubblerelaxesto a newequilibrium size andshapefor the This rateof momentumloss is in the oppositedirec-new electronicstate,releasingenergyin the process. tions to u(dn(k)/dE(k)is negative)sothat the ionFrom the calculationsof Fowler andDexter [2] we is accelerated.Onecanobtaina similarexpressioncan estimatethe energyreleasedfor the ls ~ for the rateof momentumlossdue to two phonontransitionto be -‘0.2 eV. If this energycreates andmultiphononemission.phonons,theyare radiatedpreferentiallyin the ~ It is easyto estimatean upperlimit for theextrapositedirectionto the motionof thebubbledue to momentumgiven to theelectronbUbble for eachstimulatedemissionby thermalphonons.Thereis photonabsorbed.The maximumpossibleeffectthereforea net loss of momentumby the bubble would occurif all the phononswere radiatedin thein the oppositedirectionto themotion,andit must backwarddirectiongiving a momentumincreasebe accelerated.A similaraccelerationoccursduring of WIswhere W is the energyreleasedin relaxationfluorescence. ands thevelocity of sound.Usingthe mobility

For simplicity let us calculatethe rateof momen- measuredby SchwarzandStark [3] this momentumturn lossby the ion due to onephononradiation causetheelectronbubble tomove an extradistancewhen it drifts atvelocity u. If the matrix element of 2 X i0~m at 0.5°K.for thisprocessisM(k), then Thisupperlimit would notbe reachedin practice

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Volume 44A, number 2 PHYSICS LETTERS 21 M~1973

because the phononsare not a]! radiatedin the inteiisity ratio on the temperatureandthe driftbackwarddirection. Theangulardistribution of velocity of the bubble. The signal to intensity ratioemit tedphononsis a complicatedfunction of tern- probablyvariesslightly with the anglebetweentheperatureandvelocity. For low velocitiestheeffective planeof polarisationof thelight andthe velocity olnumber of phononsradiatedin the backwarddirection theelectronbubbles.The reasonis that the radiationis proportionalto u. of phononsis anisotropic.sincein the ‘p’ statethe

The number of electronbubblesacceleratedby cavity is not spherical,aswell asbeing anisotropicthe light is proportionalto theintensity of thelight dueto thedrift velocity of theelectronbubble.and the absorptioncrosssection.If all theelectron Measurementsof the fluorescencespectrumof thebubbleswhich absorb a photon areaccelerated excitedelectronbubblewould also be of interest.sufficiently to be detected,then the signal detectedby Northby andSanderswill be proportionalto thelight intensity. The signal to intensity ratio is then Referencesproportionalto the optical absorptionspectrurn

If theelectronbubbleswhichabsorba photon are Ill l.A. Northby andTM. Sanders.Jr..Phys.Rev. Lctt.

not all acceleratedsufficiently to be detected,then 18(1967)1184.

the signal to intensity ratio will not beproportional 121 W.t3. Fowlerand1).L. Dexter,Phys. Rev. 176 (1968)

to the optical absorptio:~spectrum,althoughit should [31 k.W.SchwarzandR.W. Stark. l’hys. Rev. Let). 21

reflect the structureof thatspectrum.This could he (1968)967.

theexplanationfor thedependenceof the signal to

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