LEVEL CROSSING EXPERIMENTS IN THE Tm I AND Sm I SPECTRA

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LEVEL CROSSING EXPERIMENTS IN THE Tm I AND Sm I SPECTRA

E. Handrich, A. Steudel, R. Wallenstein, H. Walther

To cite this version:

E. Handrich, A. Steudel, R. Wallenstein, H. Walther. LEVEL CROSSING EXPERIMENTS IN THE Tm I AND Sm I SPECTRA. Journal de Physique Colloques, 1969, 30 (C1), pp.C1-18-C1-23.

�10.1051/jphyscol:1969104�. �jpa-00213635�

JOURNAL DE PHYSIQUE Colloque C I ? ~upplknzent au no I , Tome 30, Janvier 1969, page C 1 - 18

LEVEL CROSSING EXPERIMENTS IN THE Tm I AND Sm I SPECTRA

E. HANDRICH, A. STEUDEL, R. WALLENSTEIN AND H. WALTHER

Institut f u r Experimentalphysik A der Technischen Universitat, Hannover, Germany

RbumB. - Nous avons mesure par la technique des croisements de niveaux en champ nu1 (effet Hanle) la duree de vie de 12 niveaux de Tm I et de 4 niveaux de Sm I. Nous avons Cgale- ment mesurk la structure hyperfine de 16'Tm en Ctudiant les croisements de deux niveaux de Tm I en champ non nul. Nous discutons les durkes de vie des niveaux de Tm I en utilisant les vecteurs propres calcules rkcemment par Camus.

Abstract. - The lifetimes of 12 levels of the Tm I and of 4 levels of the Sm I spectrum have been measured using the technique of zero field level crossing (Hanle effect). For two Tm I levels the hyperfine splitting of '69Tm was also measured by investigating the level crossings at finite magnetic fields. The lifetimes of the Tm I levels are discussed using the eigenvectors recently derived by Camus.

New computational methods and the great efforts quantities will be described which have been per- which have been made during the last years have formed in the T m I and S m I spectra using the level yielded rather good eigenvectors for the lower excited crossing method (I).

atomic states of some of the rare earths. In order t o

test these results it is useful to provide accurate expe- l . Experimental set up. - A schematic diagram rimental data. F o r this purpose the hyperfine splitting of the experimental set u p is shown in figure I . F o r constants and the lifetimes of the energy levels are the experiments the free atoms of a n atomic beam appropriate. I n the following, measurements of these were used. They were excited by the light of a n intense

(IN o saw tooth modu-

Tanperahre cmtrolled resrstor

FIG. 1. -Schematic diagram of the cxperirnental set up.

( I ) At the ⁽⁽ Colloque de Spectroscopie Atomique ⁾⁾ also measurements in thc MnII and Eu lspectra have been reportcd. These

results ^will be published elsewhere.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1969104

LEVEL CROSSING EXPERIMENTS IN THE Tm I AND Sm I SPECTRA C 1 - 1 9

hollow cathode. To assure that only a single excited state was populated, the different spectral lines of the light source had to be separated by a grating mono- chromator (Bausch and Lomb, Model1 500, grating 1 200 grooveslmm). The external magnetic field which was perpendicular to both the direction of the atomic beam and the direction of the exciting light was pro- duced by two pairs of Helmholtz coils. The bigger one was used to generate the constant part of the field, whereas the smaller one was applied to sweep the field over the region of the level crossing. The scattered light was observed in the direction of the magnetic field. In general an incoherent mixture of of and o- light is emitted in this direction. But, if a Am = 4 2 level crossing occurs, the fluorescent light also consists partly of a coherent superposition of ^o+ and ^o- light which can be detected by a linear polarization of the fluorescent light. If, therefore, the scattered light is observed through a rotating linear polarizer, the alternating part of the signal (at twice the rotational frequency of the filter) gives the information on the level crossing, whereas the DC part is proportional to the incoherently scattered light intensity (2).

The DC part of the signal is amplified and recorded for control purposes. The AC part is fed to a lock-in amplifier, and rectified phase sensitively. The refe- rence voltage for the lock-in amplifier is taken from the rotating polarizer. By changing the reference phase the signal shape observed can be changed : either a pure Lorentzian, a pure dispersion shaped signal, or a mixture of both can be obtained. For the mea- surements described here the phase was so adjusted that a Lorentzian was observed. The rectified signal is further averaged in a transient averaging computer (ND 800 Enhancetron). In order to synchronize the channel variation of the Enhancetron to the sweep of the magnetic field, the control voltage sup- plied by the instrument was used. The time for a single signal transient (1 024 data points) was 64 seconds for most of the measurements. The integrating time constant in the lock-in amplifier was 0.3 or 1 seconds.

The magnetic field was calibrated using a proton resonance probe. For this purpose the current of the Helmholtz coils was measured by means of a tem- perature controlled resistor and a differential volt- meter. The details of this part of the apparatus are described in [2].

The signal data stored in the Enhancetron during a measurement were plotted on a xy-recorder and pun-

( 2 ) The advantage of this arrangement is discussed in detail in [I].

ched into paper tape. The signal was evaluated by fitting a linear combination of a Lorentzian and a dispersion shaped curve to the 1 024 data points.

It turned out that the dispersion part, resulting mainly from errors in the adjustment of the reference phase, was always smaller than 4 %.

2. Measurements in the Tm I spectrum (3). - The ground state of Tm I is a 'F,,, level which belongs to the configuration 4 f l 3 6 s2. The lowest levels of even parity which can combine with the ground state by electric dipole radiation belong to 4 f ^{l 3} 6 s 6 p and 4 f ^{l 2} 5 d 6 s2. Recently Camus [4] calculated the energy eigenvalues of these levels considering the interaction between the two configurations. By this, the identification of 68 levels between 15 000 and 35 000 cm- was possible with a mean error of 93 cm-l.

The deduced eigenvectors of the levels, which have been given in the J, J2 coupling scheme, show that there is a strong mixing between 4 f ^{l 3} 6 s 6 p and

4 f ^{l 2} 5 d 6 s2. The extensive calculations of Camus

stimulated our level crossing experiments in the Tm I spectrum.

At a large number of levels Hanle effect measure- ments have been performed. Natural Tm consists of the single isotope lb9Tm which has the nuclear spin I = 112. The hyperfine splitting influences the half- width of the Hanle signal. As the hyperfine splitting of a11 measured levels is known by high resolution spectroscopy [5] [6], it could be taken into account.

For this purpose the signal form for different assumed lifetimes was calculated by means of the Breit formula considering the eigenfunctions of the Zeeman levels for intermediate magnetic fields (4). The g, values for the Tm levels necessary for these calculations were taken from [4]. By these calculations the connection between the halfwidth of the Hanle signal and the assumed lifetimes was obtained for each level, so that the real lifetime of the level could be interpolated using the halfwidth determined in the experiment.

The results are compiled in table 1. The values given are the mean values of at least 6 independent measu- rements. The errors quoted are about three times larger than the mean square errors of the measure- ments. These errors include systematic influences on the halfwidth of the Hanle signal caused by the spectral profile of the exciting light [I].

(3) First results of the measurements in the Tm I and Sm I spectra have been published in [3].

(4) The program used for this calculation is similiar to that used by Khadjavi, Happer and Lurio [7]. We thank to Professor W. Happer for sending us the list and the deck of this program.

C I - 2 0 E. HANDRICH, A. STEUDEL, R. WALLENSTEIN A N D H. WALTHER

TABLE I made by considering the consistency of the results Lifetimes of the investigated Tml-Levels

Designation of the levels according to reference [4]

Levels Lifetimes sec]

From the levels compiled in table I, the first five levels can only decay to the ground state multiplet

4 f ^{j 3} 6 s 2 2F512, 712. For these levels the reciprocal

of the lifetime is only determined by the sum of the transition probabilities to the 2F712 and 2F,12 levels :

where o,,, and a S l 2 are the wavenumbers of the tran- sitions to the 2 ~ 7 1 2 and 'F,,, levels respectiveIy.

Furthermore is

-- -

fi,; = C ( S L J, j;, J') x

and

A(n1, n' 1') = - e ~ $ ( r ) rRnCt,(r) d r

.

The factors C ( J , , S, L2 J,, J) and C ( S L J , j i , J') --- describe the mixture of 4 f l 3 6 s 6 p and 4 f ^{l 2} 5 d 6 s 2 in the level considered. If this level consists of several _--- components of the kind ( J , , S2 L2 J2, J ) or of ( S L J , j;: J'), a summation over the different components

must be carried out in order to get a ~ ; and PJi.

The determination of two r values allows the calcula- tion of the integrals A(6 p, 6 s ) and A(5 d, 4 f ) using equation (1). If more than two .r values are known a check on the eigenvectors of the levels can be

obtained when the equations ( I ) belonging to diffe- rent levels are combined in a different way. This test becomes especially simple, if the levels considered can only decay in the 2F7,2 ground state. In this case equation (1) gives a linear connection between A(6 p, 6 s) and A(5 d, 4 f ), which means that in a diagram where A(6 p, 6 s) is plotted against A(5 d, 4 f ) a straight line is obtained for each investigated level.

Figure 2 shows this diagram for the (712, ' P , ) 9/2, (712, P , ) 512, (3H6, 512) 912 and (3F4, 312) 712 levels (').

The slope of the straight lines is given by the eigen- vectors of the levels. Owing to the uncertainty of the lifetime measurements, each line can be shifted parallel to itself within the bars indicated on the figure 2. It can be seen that the lines nearly cross in one point, if the experimental errors are taken into account. This shows that the eigenvectors of Camus must be rather good, at least for the levels considered in figure 2.

Unfortunately only the sign of the ratio

1

FIG. 2. - Evaluation o f A(5 d, 4f) and A(6 p, 6 s) from the experimental lifetimes of some Tm I levels. The indicated error bars result from the experimental uncertainties. For further explanation of the diagram see section 2.

( 5 ) From the first five levels in table 1 the level ^('H6, 512)

712 was omitted in the diagram as this level can also decay in the 2 F 5 / 2 level and therefore no linear connection exists between A(6p, 6 s) and A(5 d, 4f). But this presents no fun- damcntal difficulty for including this level in the plot. The level (3F4,3/2) 712 can also decay in the 2F5/2 level, but the probability for this transition is very small compared to that for the tran- sition to the 2F7/* level (see table 4 of reference [4]), and was, therefore, neglected.

LEVEL CROSSING EXPERIMENTS IN THE Tm I AND Sm I SPECTRA C 1 - 2 1

can be determined from the figure and not the signs of A(6 p, 6 s ) and A(5 d, 4 f ) separately. This is due to the fact that the lifetime is connected to the square of the matrix elements. Therefore, another solution for A(6p, 6 s) and A(5 d, 4 f ) exists which is obtained from that shown in figure 2 by a reflection at the origin.

The straight lines which belong to this solution are omitted in figure 2 for simplicity.

For the levels ( 3 ~ s , 312) 912 and ( 3 ~ 4 9 512) 712 also level crossings at finite magnetic fields have been investigated in order to determine the hyperfine split- ting of 16'Tm more accurately. As an example figure 3 shows the Zeeman splitting of the 4 f 5 d 6 s2 (3F4, 512) 712 level. The nuclear spin of 1 6 ' ~ m is 1 = 112, thus two hyperfine levels exist at zero field which split into 16 sublevels at finite field. The Am =

+

For this evaluation a computer program was used which was set up by the atomic beam group in Berke- ley, and which was slightly changed for our special purpose (6). The present errors of the A factors result from the uncertainties of the gJ values used for the evaluation. These can be reduced by more than a factor 10 as soon as our double resonance experiments (AF = 0, Am =

+

FIG. 3. - Zeeman splitting of the hyperfine levels of the 4 f 12 5 d 6 s2 (3F4, 512) 712 level of 169Tm. The Am = f 2 crossings which can be observed in the experiment are marked by circles.

Erratum. - The designation of the level given in the figure should be read as (3F4, 512) 712. ,

Results of the level crossing measurements for the 4 f l2 5 d 6 s2 ( 3 ~ s , 312) 912 and (3F4, 512) 712 levels at finite magnetic fields. The values for the positions of the crossings are mean values of at least 6 independent mea- surements. The errors quoted are the mean square errors. The sign of the A factor is taken from [5] and [6]. The errors for A quoted in round brackets follow from the errors quoted in column 3, and those quoted in square brackets are due to the present error of the gJ values for the (3H5, 312) 912 and (3F49 512) 712 levels.

level designation of the position of the

crossings crossings (gauss) A (MHz)

(F, m) - (J", m')

(6) The program is called Hyperfine 4. We thank Prof. H. A. Shugart for sending the list of this program.

E. HANDRICH, A. STEUDEL, R. WALLENSTEIN AND H. WALTHER

U

FIG. 4. - (F, m) - (F, m') = (3,l) - (4,l) level crossing signal for the 4 f12 5 d 6 s2 (3F4, 512) 712 level. The shown signal curve consists of 1024 data points which have been stored in the Enhancetron. The signal was averaged for 1 1/2 hours.

Erratum. - The designation of the level given in the figure should be read as (3F4, 512) 712.

Unfortunately the eigenvectors of Camus are not As the matrix elements of the first transition have yet used in order to calculate the A factors of the another sign than those of the second transition, the investigated levels. Therefore no comparison between signal is inversed.

theory and experiment can be made at the moment.

+

3. Measurements in the Sm l spectrum. - The _4f 66s 6p ground state in the Sm I spectrum is 4 f 6 s 2 7F'0.

The splitting of the 7F multiplet is smaller than

5 000 cm-l. That means that most of these levels are ^{2s om}

state than to the 7 ~ level. , If, therefore, the line gated levels. The numbers at the left side of the levels are the disignations according to Albertson [8]. The identification

= 419 A is used for of the levels given is taken from Blaise, Carlier and Schweighofer light is obtained in A = 4 363 A than in 1 = 4 419 A. 191.

thermally populated in the atomic beam. Therefore, the atoms can be excited by lines starting from levels

different from the ground state. The lowest levels of 2 0 m . .

odd parity belong to the configurations 4 f 6 6 s 6 p and 4 f 5 d 6 s2. Figure 5 shows part of the level

scheme of the Sm I spectrum. Hanle effect measure- ISOOO

ments have been performed on the four excited levels 4 f 6 6 s 6 p 7G1, 7D1 and 4 f 5 5 d 6 s 2 7G,, 5F1. The

transitions, which have been used in order to excite _10000..

the investigated levels, are indicated on figure 5. As an example, figure 6 shows two Hanle signals obtained for the 4 f 6 6 s 6 p 7G1 level. The upper curve is

5000.

obtained if the line A = 4 363 A is used for excitation, and the lower signal if the atoms are excited by 1 = 4 419 A. That an inversed Hanle signal is observed

in the latter case is due to the fact that from the atoms ^{0 A}

80 6.5

.-

excited in the 7G, level more decay to the 7F0 ground FIG. 5. - Part of the level scheme of Sm I with the investi-

LEVEL CROSSING EXPERIMENTS IN THE Tm I AND Sm I SPECTRA C 1 - 2 3

FIG. 6. - Hanle signal measured for the 4 ^{f 6} 6 ^s 6 p 7G1 level of Sm I. The upper signal was obtained if the line IZ = 4 419 A was used in order to excite the atoms, and the lower signal if ^{1 =} 4 363

a

Lifetimes of the investigated Sm I levels. The

~ ( l ~ ~ S m ) factors in the last column are obtained by Kuhl [lo] by high resolution spectroscopy.

Level lifetime (sec) A ( ' ~ ' s ~ ) MHz

- -

4 f 5 d 6 s2 5F1 0.44 (4).

-

4 f 5 d 6 s2 7G4 0.34 (3).

4 f 6 s 6 p 7G1 0.71 (7).10-*

4 f 6 s 6 p 7D1 0.79 (7). lo-'

- ⁺

From the halfwidth of the Hanle signals the life- times of the investigated levels have been evaluated.

The g, values necessary for this evaluation have been taken from [9]. The natural Sm, which was used for the level crossing experiments, consists of about 30 %

of odd isotopes (147Sm and 14'Sm) with hyperfine splitting. Therefore, corrections are necessary which turn out to be about 10 %. The corrections for the levels 4 f 5 d 6 s2 5 ~ 1 and 4 f 6 s 6 p ^{7 ~} were ¹ calculated with the A('47Sm) factors given in table 3.

The A ( ' 4 9 ~ m ) factors have been calculated from A(147Sm) using the ratio p(147~m)/p(149Sm) = 1.21 (see e. g. [ll]). For the levels 4 f 5 d 6 s2 7G4 and 4 ^{f 6} 6 s 6 p 7G1 the hyperfine splitting is not known, thus the corrections have been calculated only under the assumption that the Hanle experiments have been performed in the range of linear Zeeman effect for the hyperfine levels.

As the abundance of the odd isotopes 147Sm and 149Sm is low in the natural mixture, it is extremly difficult to measure level crossings at finite magnetic fields, but, with enriched isotopes such an experiment should be possible.

We are indebted to the Deutsche Forschungsge- meinschaft for support of this work.

References

[I] KRETZEN (H.), LANGE (W.), STEUDEL (A.) and WAL-

THER (H.), Z. Physik, to be published.

[2] WALTHER (H.), Z. Physik. to be published.

[3] HANDRICH (E.), KRETZEN (H.), LANGE (A.), STEU-

DEL (A.), WALLENSTEIN (R.), and WALTHER (H.), Proceedings of the Conference on Optical Pumping and Line Shape, Warszawa 1968, to be published.

[4] CAMUS (P.), J. Physique, 1966,27, 717.

[5] BLAISE - - (J.), and VET~ER (R.), C. R . Acad. Sci., 1963, 256, 630.

[6] BORDARIER ^(Y.), VETTER (R.), and BLAISE (J.), J. Phy- sique, 1963, 24, 1107.

[7] KHADJAVI (A.), HAPPER (W.), and LURIO (A.), Phys.

Rev. Letters, 1966, 17, 463.

[8] ALBERTSON (W.), Phys. Rev., 1935, 47, 370.

[9] BLAISE (J.), CARLIER (A.), and SCHWEIGHOFER (M. G.), J. Physique, 1968, 29, 729.

[lo] KUHL (J.), private communication.

[I 11 WOODGATE (G. K.), Proc. Roy. SOC., 1966 A 293,117.