Level Crossing Spectroscopy

Transcription

1 Level Crossng Spectroscopy October 8, 2008 Contents 1 Theory 1 2 Test set-up 4 3 Laboratory Exercses Hanle-effect for fne structure Hanle-effect for hyperfne structure Level crossng n a feld Theory Hyperfne structure The hyperfne structure s a splttng of the energy levels n an atomc system. It s caused by the nteracton of the hull electrons and hgher moments of the nucleus. The total splttng s made up by three effects: a) The magnetc moment of the nucleus µ I couples wth the magnetc feld caused by the movement of the electrons B J. The resultng energy s E = µ I B J = g Iµ K B J [F (F + 1) I(I + 1) J(J + 1)] 2 J(J + 1) b) As the nucleus represents a charge dstrbuton, t wll acqure a secound energy splttng n an electrc feld gradent of the electrons. The energy splttng depends on the orentaton of the nuclear spn n relaton to the electrc feld gradent. c) The last effect s the so called sotopc shft caused by the dfferent masses of sotops(mass effect) and the volume of the nucleus(volume effect) whch leads to a correcton of the Coulomb potental. The hyperfne structure s very small compared to the shftment of electronc levels and s about 10 5 ev. Hyperfne structure n magnetc felds In an external magnetc feld a splttng of the hyperfne levels wll occur. Dependng on the strength of the feld ether the Zeeman, Paschen-Back or a mxture of both effects wll be seen. 1

2 a) The Zeeman effect s seen when the external feld s weak compared to the magnetc feld of the electrons. In ths case the spn S and the angular momentum L of the electrons wll stll couple and we fnd: E = µ B Bg F M F b) The Paschen-Back effect wll result n a strong magnetc feld. The couplng between L and S s broken and from quantum mechanc calculatons we get: Radaton and Lfetmes E = µ B B(g J M J g I M I ) + am I M J Fgure 1: Radatve processes between two energy levels There are 3 processes nvolved n the radaton between two energy levels. The spontaneous emsson A 21 that can not be explaned n quantum mechancs,but n quantum electrodynamcs(qed) where a couplng between the atom and the vacuum state of the feld s responsble for the emsson. The stmulated emsson B 21 and absorpton B 12 are caused by a pertubaton from an electromagnetc feld. You fnd that B 21 = B 12. Due to stmulated and spontaneous emsson an exted state of an atom has a certan lfetme. After ths tme the atom wll return to the groundstate by radaton of a photon. The lfetme τ s gven by τ = 1 A and, f there are several possble ways to decay, τ = P 1 A. Level Crossng Spectroscopy Level Crossng Spectroscopy makes use of the effect that an alteraton of the polarzaton and angular dstrbuton of lght emtted by an atom occurs when an external magnetc feld s scanned across an area where magnetc sublevels cross. There s a classcal explanaton made by Hanle n 1924 whch only explans the effect f the magnetc feld equals zero and a quantum mechancal explanaton whch descrbes the effect for B 0,too. The Hanle effect A lght source emtts lght whch s lnear polarzed n the x-drecton. When an atom absorbs the lght, t becomes a dpol oscllatng n x-drecton. As a dpol 2

3 Fgure 2: Hanle effect does not emtt lght n ts drecton of oscllaton, no lght wll be detected by the detector. Now we apply a magnetc feld perpendcular to the oscllaton. The electrons wll start to precess wth the lamor frequency ω l = gjµ0b. The dpole wll twst and the tensty measured by the detector wll change wth sn 2 (ω l t). The ntensty of the dpole radaton wll declne wth e t τ and to get the measured tensty you have to calcute: I(B) = C 0 = Cτ 2 sn 2 (ω l t)e t τ ( 2gjµ B τb Ths s an nverted lorentz curve wth a FWHM of B = g jµ B τ. So by measurng the FWHM the natural lfetme τ can be derved. Quantum mechancal Explanaton Imagne an atom wth the shown energy levels and a geometry lke n fgure 2. If we excte ths atom by shnng n lnear polarzed lght(whch means σ lght), t wll be coherently excted nto a lnear combnaton of the two states wth M=3 and M=1. Ths process s only allowed n the overlap regon of both levels, because of the uncertanty n ther energy. Otherwse only ncoherent agtaton to one of the mentoned energy levels wll occur. After a certan amount of tme the excted state wll decay emttng σ lght. The detected tensty wll have a tme dependency of sn 2 (ωt) wth ω = E3 E1 ) 2 (quantum beats), because of the dfference n ther phase e E j t.of course ths effect wll be seen at every crossng of two energy levels wth M = 2. A good analogy may be the Young douple slt experment. The slts are represented by the energy levels and the dstance of the slts s gven by the uncertanty of the energy levels. Interference can be seen only f both slts are llumnated coherently. 3

4 Fgure 3: Explanaton of Level Crossng Usng ths effect on the detected tensty t s possble to localze the poston of level crossngs and thereby learn somethng about the fne or hyperfne structure of the atoms n queston. Quantum beats If two energy levels that ly close together are populated at the same tme(for example by a short laser pulse), the resultng wave functon can be wrtten as a superposton of the egentates of the two energy levels. After a whle the excted state wll decay wth an tensty I(t) = I 0 e t τ wth a oscllatng modulaton whch s due to the fact that nterference between the emsson of the two egenstates wll occur. 2 Test set-up As lght sources lamp cells flled wth mercury or rubdum were used. The rght transtons were selected by usng nterference flters and the polarzaton of the used lght was adjusted wth a polarzaton flter. The resonance cells flled wth mercury or rubdum were placed between magnetc cols n order to elmnate the earth magnetc feld and to produce a magnetc feld n order to acheve level crossng. The emtted photons were detected by photomultplers whch wasplaced n some dstance above the lght cell to prevent detecton of scattered lght. Whle the mercury cell was cooled by lqud ntrogen durng the lab, because of the hgh vapour pressure, the rubdum cell had to be heated n order to get suffcent vapour pressure n the cell. 3 Laboratory Exercses 3.1 Hanle-effect for fne structure Turn on the Hg-lamp and ncrease the voltage to 700V. Place the Hg-resonance cell n the angled arm and adjust the thermoelement that t has contact wth the cell. Fll a thermos wth a mxture of alcohol and lqud ntrogen and place 4

5 the thermos under the arm. Calbrate the lnear polarzer and mount t t n the tunable flter contaner. An nterference flter has to placed n the detecton ppe n front of the fotomultpler. To elmnate the earths magnetc feld Helmholtzcols are used. Check the drecton of ther feld wth a compass. Scan the feld manually untl the Hanle-sgnal arrves. Record the sgnal wth a prnter. Fne tune the polarzer so that the sgnal becomes Lorentz-formed. Study the appearance of the sgnal form when the polarzer s turned to 90,45 and -45 and explan the appearance. Note whch current regon you must scan. Cool the resonance cell to -60. Record the Hanle-sgnal by scannng the feld. Contnue to scan the feld to and from and note the thermoelements voltage each tme the centre of the Hanle-Curve s passed. Measure the half value wdth and draw a dagramm of B as a functon of temperature. Calculate τ and A. 3.2 Hanle-effect for hyperfne structure The lamp cell contans rubdum and must be heated to 120 n order to get enough atomc densty n the cell. Use a nterference flter wth 4203 Å n order to measure on the state 6p 2 P 3/2. Modulaton cols and a photomultpler are connected wth a lock-n amplfer. Record the Hanle-sgnal for 4 dfferent modulaton currents mod =0.8,0.6,0.4 and 0.2 ma. Draw a dagramm of the wdth d as functon of mod and ft a straght lne. You get the undsturbed wdth d 0 = B 3 from ntersecton wth the y-axs. Calculate g F and the lfetme τ. 3.3 Level crossng n a feld Measure the hyperfne structure splttng n the state 6p 2 P 3/2.Scan the magnetc feld through the Hanle-sgnal and further upward. Make marks contnously for the current. When you have recorded 3 level crossngs, evaluate the postons of the magnetc felds and calculate the a-factor. Dscuss possble errors. 5