INTRODUCTORY PAPER ON HANLE EFFECT, LEVEL CROSSING AND DOUBLE RESONANCE EXPERIMENTS

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INTRODUCTORY PAPER ON HANLE EFFECT, LEVEL CROSSING AND DOUBLE RESONANCE

EXPERIMENTS

H. Bucka

To cite this version:

H. Bucka. INTRODUCTORY PAPER ON HANLE EFFECT, LEVEL CROSSING AND DOU- BLE RESONANCE EXPERIMENTS. Journal de Physique Colloques, 1969, 30 (C1), pp.C1-3-C1-9.

�10.1051/jphyscol:1969101�. �jpa-00213632�

Colloque

C

1, supplkment all no 1, Tome

30,

Janvier 1969, page

C 1 - 3

INTRODUCTORY PAPER ON HANLE EFFECT, LEVEL CROSSING AND DOUBLE RESONANCE EXPERIMENTS

H. BUCKA

Technische Universitat Berlin, Institut fiir Kernphysik

R&umC. -

L'auteur passe en revue un certain nombre de techniques expcrimentales :qui uti- lisent les proprietes de la diffusion de la lumiere par des atomes libres au voisinage d'une frequence de resonance pour etudier des niveaux atomiques excites

:

-

L'effet Hanle et ses divers dtveloppements recents (effet Hanle moleculaire, effet Hanle en prbence d'un champ Clectrostatique, effet Hanle de niveaux excites par echelons, effet Hanle par fluorescence sensibilisk).

-

La doublc resonance et ses variantes (effets de

⁽⁽

battements lumineux

^D,

excitation en lumitre modulec

...).

-

Les croisements et anticroisements de niveaux (y compris 1Vtude de l'effet Stark par croise- ments de niveaux).

Abstract. -The author reviews experimental techniques which use the properties of the scattering of light by free atoms in the neighborhood of a resonant frequency for invest~gation of excited atomic energy levels

:

-

Hanle effect and its recent developments

:

(Hanle effect in an electrostatic field, molecular Hanle efrect, Hanle effect of stepwise excited levels, sensitized fluorescence Hanle effect).

-

Double resonance experiments and its variations

(((

light beats

)I),

excitation with modulated light...).

-

Level crossings and anticrossings (including of the study Stark effect by level crossings).

1. Experimental aspects concerning scattering of

light

on free atoms.

-

In level-crossing and double resonance experiments photons are scattered on frec atoms which are exposed to static as well as alterna- ting electromagnetic fields. These investigations are performed to study the interaction of the light with the atoms, to find the experimental consequences of this interaction and also t o deduce spectroscopic data of the atoms involved from the experimental results.

Due to the interaction between the radiation and the atoms one photon of the incoming light is absorbed and another photon emitted. With respect to experi- ments for example the angular distribution of the scattered photon may be studied including measu- rements of polarisation, or the time dependence of the scattering process investigated. Regarding the excitation of the intermediate state thereby more than one level may be excited coherently by the first photon. Because the scattered photons connect the intermediate state with the final state, the behavior of the state function of the intermediate state during the lifetime is of importance. Taking in mind that the matrix elements containe the eigenfunctions of the atomic states involved a much deeper insight can be gained if changes in the state functions are induced by

applying additional perturbations. For example the atoms are investigated in static or alternating elec- tromagnetic fields. In addition second excitations may be studied or the influence of perturbations by colli- sions investigated. In collision experiments questions of transfer of coherence are of special interest. Because two photons are also involved, if an excited level decays in a cascade through an intermediate state, some effects in resonance scattering of light corres- ponds to effects in

y y

angular correlation.

Regarding the scattering of photons on free atoms the cross-section is normally very small and of the order of the square of the classical electron radius

r i .

However if the energy of the photons corresponds to the energy differences of the states connected by dip01 radiation, large cross sections are gained by virtue of resonance scattering. If the atoms would be at rest and the exciting light would have the exact resonance energy, the classical cross section would be of the order of A2.

In many experiments the spectral width of the exciting light o is larger than the radiation width y, and there- fore the effective cross section for excitation isdecreased by a factor of the order

y l o .

For the investigation of excited states which are connected with the ground- state with oscillator-strength between

1

and a

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1969101

C 1 - 4

H.

BUCKA

density of about 108-1012 atom/ccm is often sufficient with regard to the intensity of the resonance fiuores- cence. Atoms with high vapour pressure can often been studied in resonance bulbs, while for the inves- tigation of atoms for which a sufficient vapour pres- sure can be produced only at very high temperature the light is scattered on atomic beams. As a source for the exciting photons low pressure discharges in hollow cathodes are used very often operated with direct current or radio frequency power.

2. Perturbation of resonance scattering of light by static external electromagnetic fields. - In experi- ments on resonance scattering of light or on cascade decay of excited states like

^{y y}

angular correlations the initial state is connected with the intermediate state by the radiation field of one photon and again the intermediate state is connected with the final state by the radiation field of the second photon. In the case of resonance scattering of light the first transi- tion corresponds to the absorption of an incoming photon while the second photon is caused by the interaction with the radiation field corresponding to spontaneous emission. In the case of cascade decay both transitions correspond to spontaneous emission.

The probability to observe the photon which is emitted in the second transition depends on the exci- tation of the intermediate state and on the evolution during the time until the emission process takes place.

For the description of the process the axis of quanti- sation for the atom as well as a direction which specifies the photon is of interest. The scattering process may be regarded for the simple case with an intermediate leva1 with angular momentum I

=

1, a ground state with I

=

0 and linear polarisation of the exciting photon. Tf one chooses for example the axis of quan- tisation z perpendicular to the polarisation of the exciting radiation, two sublevels of the intermediate state with magnetic quantum numbers

^p, = i-

1 and y,

= -

1 are excited coherently from the ground state with magnetic quantum number m

= 0.

The application of an external magnetic field causes that both levels of the intermediate state are no more degenerated and have now a finite difference in energy.

Because the scattering amplitude of the photon with energy hv has only an appreciable amplitude if the difference between photon energy hv and the energy difference E,

-

Em is not larger than the radiation with y, the influence of coherent excitation of two levels in the excited states cannot play an important part, if the levels under discussion have energy diffe- rences which are much larger than the radiation width.

If one takes into account a continuous frequency dis-

tribution of the incoming photons, which is the case in many experiments, the frequency of a single photon does of course no more appear in the expression for the scattering probability I, which was first derived by Breit [I]

whereby x and 5 designe the component of the radius vector r in the direction of the polarisation of incident and scattered light.

Instead of choosing the axis of quantisation z perpendicular to the polarisation of the exciting light one may take the axis of quantisation z' parallel to the polarisation. Corresponding to the direction z' the linear polarized light connects the ground state m

= 0

with the excited level

^{p,, =} 0

of the interme- diate state. If one applies a magnetic field again per- pendicular to the polarisation of the exciting radiation the eigen functions of the intermediate levels will be mixed due to the magnetic field perturbation during the lifetime of the intermediate state. If the perturbing static field is strong enough that during the lifetime the amplitudes of

^p,, =

+ 1 and

^p,, = -

1 are getting considerable amounts, the angular distribution of the scattered radiation is changed substantially. This change first detected by Hanle [2] is reached if the magnetic field perturbation

^p~

H/h will be comparable with the radiation width

y

of the intermediate state, as it was the case in the first description.

Very similar processes are observed in experiments on perturbed

y y

angular correlation. Because the multipole character of the photons involved is not only of type E 1 but may also correspond to electric multipole radiation E 2, E 3, ... or magnetic multipole radiation M 1, M 2, ... the situation is of course more general. The probability for observing the photons k, and k, after time t is [3]

whereby mi,

p

and mf designe the magnetic quantum

numbers of the initial, intermediate and final state,

H, and

H z

are the operators corresponding to the

emission of k , and k,, and

INTRODUCTORY PAPER ON HANLE EFFECT C 1 - 5

describes the time evolution of the eigen-function in the intermediate state during the lifetime according to the external perturbation. If one does not make measurements which take into account the time t the observations are described by the time integrated pro- bability function and yiels as in the case of resonance scattering of light a change of the angular correlation and a decrease of the factor which describes the not isotropic part of the coincidence rate 141. A substantial change is obtained again if the magnetic field pertur- bation y, H/h is of the order of the radiation width, where y, is the magnetic nuclear moment of the interme- diate state. If one distinguishes the two photons with the aid of energy measurement a rotation of the angular y y correlation fonction is observed [5 a]. Using time delayed coincidence technic in y y angular correlation experiments the probability W ( k , , k,, t ) is observed as a function of the delay time and the effect of the time evolution of the intermediate states can be obser- ved directly. For example with fixed positions of the counters and constant magnetic field strength a modu- lation of the coincidence rate with approximately twice the Lamor frequency of the intermediate state as a function of the delay time is reported [5 b]. Mea- surements are possible for a time interval which amounts a few times of the lifetime of the interme- diate state.

In experiments on Hanle effect [2] the perturbation of the resonance scattering of light on free atoms is studied if static magnetic or electric fields are applied which remove the degeneracy of states in zero magne- tic and electric fields with angular momentum J or F. For the case of experiments in magnetic fields the magnetic field perturbation y,.g.H.mZ removes the degeneracy according to the Zeeman effect in first order. If an electric field is applied atomic levels of opposite parity are connected to the state under inves- tigation. The degeneracy of levels with different abso- lute value of magnetic quantum number I y I is removed according to second order perturbation theory corres- ponding to quadratic Stark-effect. For an electric field parallel to the axis of quantisation the change of the energy of sublevels may be obtained from the perturbation (a + ^PJ:) E~' [ 6 ] .

The measurement of the attenuation of the coherent contributions of resonance scattering gives therefore informations for the ratio g/y or Ply where

g

and P

determine the effect of magnetic and electric fields on the energy levels. Because in many simple atomic spectra the g-values of excited levels are well known from theoretical considerations, Hanle effect measure- ments are used to deduce the radiation width of

excited states 171. In the case where several emission lines, coming from excited levels with different

g,-

or g,-values, cannot be resolved in the resonance fluorescence further assumptions for the intensities of the excitation process are necessary. If higher den- sity of the atoms investigated are used, effects of coherence narrowing as well as collision phenomena (also for example if additional foreign gases are present) may be of importance. If one applies a n electric field [8] simultaneously with a magnetic field the Hanle effect is modificated in such a way that the amplitude of signal becomes smaller and the width of the signal larger. From the measured values of

y

or p informations on sums of radial matrix elements of the atom may be obtained and in suitable cases values for oscillator strength can be deduced. Besides measurements on neutral atoms experiments on ions are reported. In connection with the charge of the ions additional care must be taken that the density of the ions is not disturbed by changing the magnetic field [9]. Further experiments on resonance scatte- ring of light on free atoms measurements on molecules are reported showing for example Hanle-effect in an excited state of the diatomic molecule NO [lo].

In addition to the investigations of the two photon processes in static external electromagnetic fields further perturbations may be studied. If one is able to get enough atoms in an excited state a second absorp- tion from this intermediate state may be performed corresponding to stepwise excitations and the radia- tion following second excitation may be observed.

For properly chosen polarisations for the excitation and the observation coherence effects of the first or second state may be observed. Experiments are repor- ted involving stepwise excitation of the 3Sl-state in Cd I-spectrum via the first excited state 3P, [ll].

Regarding collision phenomena problems of cohe- rence transfer from one excited atom to another atom by collision are explored with theoretical and experi- mental investigations. For example in a vapour which consists of a mixture of Hg- and Cd-atoms the levels of the 3 ~ , - s t a t e of Hg were excited coherently and the observation of coherence processes for the cor- responding excited state 5 3P1 in Cd I-spectrum is reported [12].

3. Resonance scattering of light in presence of

an

alternating magnetic field with regard to double reso-

nance experiments.

-

The application of a magnetic

field perpendicular to the axis of quantisation causes

a connection of levels with difference in magnetic

quantum number Am

=

i- 1. If the frequency of this

C 1 - 6 H. BUCKA

magnetic field does not correspond to the energy difference of the levels involved and if the perturbation caused by this field is small compared with the energy difference of the regarded levels, no conside- rable admixture of the connected levels can be achie- ved. But if the frequency of the alternating magnetic field is very near to the energy difference of the regarded sublevels the mixing of the states is very strong, even for small perturbing magnetic fields by virtue of resonance. Magnetic resonance technics are applied in many fields of physics and differ in the detection mechanism of the induced transition. If an alternating magnetic field is applied to an atom, which is in an excited state with different populated magnetic sublevels the mixing of these sublevels during the lifetime may result in a change of the polarisation of the resonance radiation as was first shown by Bitter, Brossel and Kastler [13]. The mixing of states due to the radio frequency field will be considerable if in a rotating frame the correspon- ding magnetic field perturbation is of the order of the radiation width. With increasing field strength double resonance multiquantum transitions are observed [13 a] in similar way as in the atomic beam resonance method. The line width of the double resonance signal is given by the radiation width of the excited state in the limit of vanishing field strength of the pertur- bing magnetic field and shows for the case of multiple scattering of light coherence narrowing [14]. Besides the change of polarisation due to the radio frequency transitions in the excited state, also changes in the population number of the ground state result and may be used for the detection [15].

Double resonance experiments give informations on absolute values of level distances yielding for example absolute values of hyperfine structure cons- tants or g,-values. Figure 1 shows for example double resonance signals for the transitions between the hyperfinestructure levels P

=

5 and P

=

4 of the excited 7 'P3,,-state in Cs I-spectrum for the isotopes C S ~ ~ ~ , C S ~ ~ ~ , Cs13' 1161. Investigations of hyperfi- nestructures for excited states which differ only in the principle quantum number may be used for example to investigate Sternheimer [17] corrections. Many experiments have been performed for energy diffe- rences of levels up to several 1000 Mc/s [17 a].

Excited states with lifetime much shorter than lo-' s are nor easy to investigate, because large magnetic field strength for the radio frequency fields are neces- sary. Double resonance signals may be used for spe- cial detectors for certain isotopes in scanning expe- riments. If the levels involved belong to states with

FIG. 1. - Level scheme and double resonance signals bet- ween hyperfinestructure levels F = 5 and F = 4 for the 7 2P3/2-state of Cs I-spectrum.

different parity an alternating electric field pertur- bation may result in transitions.

With regard to the time dependence of the reso- nance radiation modulation effects of resonance fluorescence were detected in double resonance expe- riments by Series [18]. The additional radio frequency field mixes the levels involved coherently. Modula- tions of the intensity of the resonance fluorescence are reported not only at resonance frequency but also for other frequencies which are deduced from the time evolution of the coherently connected levels.

The excitation of resonance fluorescence by modu-

lated light, reported by Corney and Series [18 a] pro-

vides a further experimental method for studying

excited atomic states.

INTRODUCrOKY PAPER O N HANLE EFFECT C I - 7 4.

Influence of change of coupling of angular

momenta on resonance scattering of light. - For atomic states in which finestructure or hyperfinestruc- ture interactions causes finestructure or hyperfinestruc- ture multipletts the application of a suficient large magnetic field gives rise to a change of the coupling of angular momenta. A substential change of the eigen-function results if the external magnetic field perturbation becomes of the order of the multiplett splitting in zero magnetic field. The corresponding change of the eigen-functions causes a change of the polarisation degree of the resonance fluorescence.

This effect was first used by Heydenburg [I91 and co-workers to investigate the strength of the hyper- finestructure interaction of excited states in alkali- spectra. This effect ceases if the coupling for strong magnetic field is reached. But also without external perturbation the polarisation degree of the resonance fluorescence mirrors the coefficients which describe for a certain sublevel of the excited state the contribu- tions of the different orbital angular momentum eigenfunctions with different magnetic quantum numbers. Therefore the value of the polarisation degree gives information on the coupling of spins, if the finestructurc or hyperfinestructure interaction is larger than the radiation width.

In the intermediate region between Zeeman-effect and Paschen-Back-effect at certain magnetic field strength the energy of sublevels may become equal.

If the difference of the magnetic quantum numbers of these levels are Am

=

1 or Am

=

2 these levels can be cxcited coherently with electric dipol radiation in the vicinity of the magnetic field strength of the level-crossings. The resulting change in the resonance fluorescence corresponds to the change of the reso- nance fluorcsccnce due to Hanle-effect in the vici- nity of zero magnetic field. These interference signals due to level-crossings in the course of the change of coupling of angular momenta caused by external magnetic field perturbation were first detected by Colegrove, Franken, Lewis and Sands [20] in the excited 2 3P-states of He I-spectrum. Because the magnetic field strength at which level-crossings occur is determined by the Hamiltonian which contains as parameter the finestructure- or hyperfinestructure interaction constants, and by the strength of the external field perturbation, described by g-values and the magnetic field strength H , the level-crossing tech- nique corresponds to an comparison of these two interactions. Therefore values for the ratio of inter- action constants devided by the g-value are deduced from the level-crossing-signals. For example in the

case that the finestructure splitting is much larger than the hyperfinestructure, the crossings for hyper- finestructure levels may be calculated from the Hamiltonian

1211

Because the linewidth is again determined by the radiation width arid a factor (of the order of the g-value) which describes the increase of the energy difference of the crossing levels for increasing or decrea- sing magnetic field strength with regard to the cros- sing point the level-crossing-signals may provide spectroscopic data with high resolution. The signal width becomes smaller with increasing lifetime, but because long lifetimes are connected with small oscil- latorenstrength for the transition between the ground state and the excited state, it becomes more difficult to investigate excited states with lifetimes longer than for example lo-' s by means of resonance scatte- ring of light.

For hyperfinestructure investigations level-cros- sing-experiments have been performed in the alkali and alkali-like elements for the alkali-earth-elements, trivalent elements and complex spectra [22]. In figure 2 an atomic beam apparatus for level-cros-

FIG. 2. - Experimental arrangement for Icvel-crossing expe- riments, using scattering of light on atomic beams. A atomic beam, 0 electron bombardment oven, P proton resonance probe, V holes for conncction of pumps, L and R direction of incoming lightbcam and of observed scattered light. Magnetic field parallel to z-direction.

H.

BUCKA

cur

1- J

2

FIG. 3.

-

Level scheme and lcvel crossing signals of Cu 65 for the hyperfinestructure of thc 4 zPy2-state in Cu I-spectrum.

sing investigations is shown. Figure 3 shows for example level-crossings in the first excited 4 p

2P-312-

state of Cu I-spectrum. If the hypefine structure inte- raction is large due to s-leectrons, the accuracy for the measurement of the magnetic hyperfinestructure interaction constant is in suited cases of the order of

and better and hyperfinestructure anomalies may be determined. If as another extreme the excited state has only a small hyperfinestructure interaction which may occur if the hyperfinestructure is determined by p- and d-electrons with small magnetic field at the nucleus, the radiation width is often no more small compared with the hyperfinestructure interaction.

For this case detailed investigations of the line shape of overlapping level-crossing-signals must be perfor- med. Even for the case that the radiation width is of the same order than the hyperfinestructure interac- tion values for the hyperfinestructure constants can be deduced with some accuracy [23].

For level-crossings of sublevels of a finestructure

multiplett only the lightest elements can be investi- gated at the moment, because for other elements the finestructure splitting is too large. In the event of fine- structure crossings for isotops with nuclear spin not zero, the additional interaction with the nucleus may give rise to anticrossings which involve the change of eigen-functions near the level-crossing. This effect was first detected by Eck [24] for the first finestructure level-crossing of the 2 2 P states of Li I-spectrum.

Investigations of the shift of level-crossing field

strength caused by the additional application of an

electric ficld yields again information on the Stark-

parameter p, which describes for example for electric

field parallel to the magnetic field the electric field

interaction proportional to 5 , ' . The change of the

magnetic field strength of the crossing point results

if the energy shift of the two sublevels involved are

different. For the investigations of the interaction

constant p the measurement of the shift of a level

crossing at H # 0 may be more suited than the mea-

INTRODUCTORY PAPER ON HANLE EFFECT C 1 - 9

surement of the influence of a n electric field o n the zero field level-crossing, because only two levels are involved. In experiments with a n additional elec- tric field the hamiltonian contains besides the hyper- finestructure interaction a n d the magnetic field inter- action in addition the interaction with the electric field. Therefore from the experimental results a rela- tion between the Stark-parameter P and the hyperfi- nestructure interaction constants may be deduced.

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