HFS MEASUREMENTS IN THE 4 s4p 1P1 STATE OF 43Ca BY THE LEVEL CROSSING TECHNIQUE

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HFS MEASUREMENTS IN THE 4 s4p 1P1 STATE OF 43Ca BY THE LEVEL CROSSING TECHNIQUE

H.-J. Kluge, E.-W. Otten, G. Zimmermann

To cite this version:

H.-J. Kluge, E.-W. Otten, G. Zimmermann. HFS MEASUREMENTS IN THE 4 s4p 1P1 STATE OF 43Ca BY THE LEVEL CROSSING TECHNIQUE. Journal de Physique Colloques, 1969, 30 (C1), pp.C1-15-C1-17. �10.1051/jphyscol:1969103�. �jpa-00213634�

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Colloque C I , supplkment au no I , Tome 30, Janvier 1969, page C 1

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15

HFS MEASUREMENTS IN THE 4 s 4 p ' P I STATE OF 43Ca BY THE LEVEL CROSSING TECHNIQUE

H.-J. KLUGE, E.-W. OTTEN ^ANDG. ZIMMERMANN (*) I. Physikalisches Institut der Universitat Heidelberg

RBsum6. - Nous avons mesure par la technique des croisements de niveaux, la structure hyperfine du niveau 4 s 4 p lP, de 43Ca. Nous avons trouve pour la constante dipolaire de 43Ca A = - 15,3 (4) MHz. Ceresultat est compar6 B celui de la theorie de Breit Wills. La limite supkieure du moment quadrupolaire est 1 Q I < 0,23 b.

Abstract. - The hyperfine structure of the 4 s 4 p [ P I state of 43Ca has been measured by the level crossing technique. The dipole interaction constant of 43Ca was determined to be A = - 15.3 (4) Mc/sec. This result is compared with that obtained by the Breit Wills-theory. An upper limit for the quadrupole moment can be given as 1 Q I < 0.23 b.

A systematic investigation of the hyperfine structure (hfs) of the excited sp-configuration of alkaline earth spectra seems to be very desirable, since compa- risons between recent results in singlet states with those in the triplet states revealed a breakdown of the conventional Breit Wills theory [I]. They showed that the one electron wave functions in the singlet and triplet system differ substantially and that therefore in hfs calculations the < r - 3 > values cannot be considered to be equal [2]. It was the aim of this experiment to extend these investigations to a case of pure Russel Saunders coupling which is fulfilled in 43Ca for instance. The hfs in the 4 s 4 p 'PI state of this isotope was determined by level crossing (LC) technique.

helmholtz

-

^coil

holloy cathode

\

diaphragm

w

MgO

-

resonance-;ell filter light- pipe photomultiplier fo multichannel analyzer

FIG. 1. -Schematic diagram of the experimental setup.

The experimental setup shown in figure 1 was chosen in the conventional way with the direction of the incident and scattered light at right angles to the magnetic field of the Helmholtz coils and at right angles to each other. A hollow cathode served as a light source for the resonance line

Since the abundance of 43Ca is only 0.14 % of the natural isotopic mixture, the experiment had to be conducted with quantities of about 1 mg of separated isotope. This was possible by use of a resonance vessel cut out of chemically resistent single crystals of MgO. The magnetic field which was calibrated by optical pumping of 23Na to 8.086 (7) gausslampere was varied periodically from - 20.00 to

+

179.00 gauss in steps of 1.00 gauss. The intensity of the resonance light was stored in the memory of a multichannel analyzer, 200 channels of which were locked to the corresponding number of field points.

In order to avoid radiation trapping and the resul- ting coherence narrowing, the line shape and width of the Hanle signal of natural calcium (99.86 % even isotopes) was investigated as a function of vapor density as shown in figure 2. The levelcrossing experiment was therefore conducted at temperatures below 360 O C , where the effect of coherence narrowing is neglible and a distortion of the symmetry of the resonance light curve does not occur.

Figure 3a shows the energy level diagram of 4 3 ~ a (I = 712, p, = - 1.317 p,), calculated for

(*) Now at Institut fiir Kernphysik, TU, Berlin. A = - 15.3 MHzand B = 0 M H z .

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1969103

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C 1 - 1 6 H.-J. KLUGE. E.-W. OTTEN AND G. ZIMMERMANN

1.10~' F~O~~,&ITOMS/CC]

250 300 ^I 350 400 4;0

CELL TEMPERATURE

FIG. 2. -Apparent lifetime of the (4 s 4 p lPl) state of 40Ca as a function of vapor density measured by narrowing of the Hanle signal. The density region in which LC experiments of 43Ca were performed is indicated.

.._ --_.

MAGNETIC FIELD

FIG. 3a. -Energy level diagram of the (4 s 4 p 'PI) state of 43Ca ( I = 712, ,UI = - 1.317 p ~ ) , calculated for

A = -15,3 MHz and B = 0.OMHz.

Erratum. - In fig. 3a, the length for Avnat is to be shortened by a factor 2.

FIG. 3b. - Plot of scattered intensity and its derivative as functions of magnetic field obtained under conditions for observing Am = 2 crossings. Only every second of the 200 steps is plotted in the diagram up to 90 gauss. The solid curve is as computer fit of the experimental points.

Since the natural linewidth (Av = 35 MHz) is compa- rable with the hfs splitting itself, only the steep crossing ( F = 912, m, = 912) x (F = 712, m, = 512) can be expected to show a pronounced LC-structure.

The fold over crossings of the (F = 712) states however will not appear at all, since these states remain almost completly degenerate in this field region. The experimental points in figure 3b show that even this steep crossing is not clearly resolved but is perturbed by the slopes of the Hanle signals. In this situation it is appropriate to compute the resonance light curve strictly from the Breit formula [3] using the programm of Happer [4] (I). According to this formula, the resonance light is a function of the following parameters : polarization vectors and geometry of incident and detected light, angular momentum of ground and excited state, z, g,.H,, A and B. From these only the last two are unknown. The program was therefore extended to perform a least squares fit of these two parameters. The fit included a constant back- ground and the isotopic concentration as additional parameters. It is typical for crossings (AF ⁼1) that their positions depend primarily on the A factor alone and are extremely insensitive to the B factor. The latter has only a weak influence on the shape of this crossing. As a result of the computation one gets a range of parameter combinations fitting the experimental curve within the limits of error. The limits of this area determine the A factor

A(lP,) = - 15.3 (4) MHz and

I

^B(lP,)

I

^<^{12 MHz.}

This corresponds to an upper limit of the electric quadrupole moment of

I

^Q(43Ca)

I

^<0,23.10-24 cm2.

The A factor of the singlet state can be calculated by the theory of Breit and Wills, if one uses the value of < ( r ( 4 ~ ) ) - ~ > obtained from the 3P, state, which can be estimated from the fine structure splitting.

Because of the almost pure Russel Saunders coupling the A factor is determined primarily by the a factor of the 4 p electron, while the a factor of the 4 s electron, which has the opposite sign, only causes a cor- rection of 10 %. Thus one expects the theoretical value to be A(lP,) = - 36.8 MHz in contradiction with the experiment. This disagreement has been observed in the spectra of Ba, Cd and Hg as well and is usually understood by introducing a parameter R which accounts for the difference of the 4 p wave func-

( 1 ) The authors are indebted to D r Happer for making the computer program available to them.

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HFS MEASUREMENTS IN THE 4 s4 p 1P1 STATE OF 43CA C 1 - 1 7 tions in the singlet and in the triplet state [2]. This

experiment yields

L = ( < (r(4p))-3 >,I< ( r ( 4 ~ ) ) - ~ >.)'I2 = 0.69.

King and Van Vleck [5] originally calculated L from the fine structure splitting to be L = 0.81. Theoretical calculations of L from Hartree wave functions [6]

(A = 0.46) and recently from Hartree Fock wave functions [7] (A = 0.47) predict even a stronger difference in the < r U 3 > values. As in other cases of groupe I1 elements the agreement between the experimental and the theoretical result is still poor.

This work was supported by the Deutsche For- schungsgemeinschaft.

References

[I] BREIT (G.) and WILLS (L. A.), Phys. Rev., 1933, 44, 470.

[2] LURIO (A.), Phys. Rev., 1965, 142, 46.

D] BREIT (G.), Rev. Mod. Phys., 1933, 5 , 91.

PRAN'&N-(P. A.), Phys. Rev., 1961, 121, 508.

[4] HAPPER (W.), Conference on ⁽⁽The Physics of Free Atoms ⁾⁾Berkeley 1966.

[5] KING (C. W.) and VLECK (J. H.), Phys. Rev., 1939, 56, 464.

[6] HARTREE (D. R.) and HARTREE (W.), Proc. Roy. Soc., 1938, A 164, 167.

[7] KLAPISCH (M.), ⁽⁽La structure hyperfine des atomes et des molecules D, IParis, 1966, editions du C.N.R.S., No 164, 1967.