SPECIAL PROBLEMS CONCERNING THE MEASUREMENT OF THE ISOTOPE SHIFT IN THE CESIUM I, BARIUM II, AND SILVER I SPECTRUM

HAL Id: jpa-00213650

https://hal.archives-ouvertes.fr/jpa-00213650

Submitted on 1 Jan 1969

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

SPECIAL PROBLEMS CONCERNING THE

MEASUREMENT OF THE ISOTOPE SHIFT IN THE CESIUM I, BARIUM II, AND SILVER I SPECTRUM

W. Fischer, H. Hühnermann

To cite this version:

W. Fischer, H. Hühnermann. SPECIAL PROBLEMS CONCERNING THE MEASUREMENT OF

THE ISOTOPE SHIFT IN THE CESIUM I, BARIUM II, AND SILVER I SPECTRUM. Journal de

Physique Colloques, 1969, 30 (C1), pp.C1-59-C1-63. �10.1051/jphyscol:1969119�. �jpa-00213650�

JOURNAL

Colloque C I, suppl&nent au no I , Tome 30, Janvier 1969, page C 1 - 59

SPECIAL PROBLEMS CONCERNING THE MEASUREMENT OF THE ISOTOPE SHIFT IN THE CESIUM I, BARIUM 11, AND SILVER I SPECTRUM

W. FISCHER and H. HUHNERMANN Physikalisches Institut der Universitiit Marburg

Resume.

- Des erreurs systematiques qui influencent les mesures de deplacement isotopique des raies spectrzles peuvent Stre CvitCes en excitant les diffkrents isotopes dans une seule source et non dans plusieurs. Nous montrons sur trois exemples comment une analyse numQique des courbes aide

rQoudre les difficultes de depouillement dues au nombre ainsi accru de raies dans la structure hyperfine.

Abstract.

- Systematical errors frequently influencing the measurements of the isotopic shift of spectral lines can be avoided by exciting the different nuclides in one light source instead of several ones. In which way a digital curve analysis helps to overcome the difficulties of evaluation arising from the thus increased number of lines in the hyperfine structure is shown by three examples.

A convenient method of determining the isotope shift (IS) in spectral lines is to measure the differences of the wavelength emitted by pure nuclides in different light sources. This method, however, may involve two kinds of possible systematical errors.

I. The light of the two sources may pass an imper- fect interferometer in different ways and affect the value of the IS.

11.

Pressure-and Stark-shift may influence the I

frequencies of the emitted spectral lines. The first error source is well known, but we assume ,I[ ^{j u ,} i / I 1

d I

that the possible errors caused by pressure-and - v

Stark shift are widely underestimated. In the first part expected measured of this paper the results of two little experiments hyperfine structure

CsI

concerning these shifts will be discussed. The second with

-absorption

part may show a way how one may overcome these

FIG. 1.

- Self-absorption

the line Cs

error sources when measuring the IS.

A. The line was excited

a radio-frequency electro-

deless

filled with two torr argon. Stark-effects are believed I. to

the reason of the shift between

emission- and absorption Two common light sources were tested in res-

pect to pressure and Stark-shift, a radio-frequency excited electrodeless tube, and a hollow cathode.

In both cases we investigated the hyperfine-structure (hfs) of the resonance line Cs I

-

The rf-tube was filled with two torr argon and the hollow cathode burned with four torr helium. The light of the rf-tube showed self absorption (Fig. 1). These absorption lines, however, do not coincide with the center of the four emission lines as one would expect (Fig. 1, left side). The measured curve on the right and the graph at the top of figure 1 shows that the absorption lines are shifted to lower frequencies o r

line.

right :

measured curve

left

expected curve without any shift top

centers of absorption- and emission lines.

that the emission lines are shifted to higher frequen- cies, respectively. Stark-effect in the discharge and at the wall are believed to be the reason of this shift being in the order of some mK. Pressure shift we may exclude by the argument that the gas density will be nearly the same at each point in the tube.

The crossing of light with an atomic beam gives an unshifted absorption line, as the density in a beam is very low so that no pressure shift is possible, and the

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1969119

absence of electric fields prohibits any Stark-effect.

In the second experiment we crossed the light of the Cs resonance line - excited in a hollow cathode lamp

with a Cs atomic beam to show the shift of the emission line. Figure 2 shows the result of the measurement. At the top there is the hfs of the Cs resonance line without absorption (I). The absorption reduces the light. The center of the absorption line does not coincide with the center of the emission line and causes the non symmetric line shape of curve No 11. The emission line is shifted to higher frequencies.

emitted light ( 1 )

, , , .

C s

I

. ' light transmitted

A

=

A

.

.-.

.'

.. . . ^.. . . . . . . .

:.

'.

.. .. _.

, .. ..

..

.

.

_

i . .

, !

; , .

I

.-

-

,-.-

.-

. . . ! .

:

!

, . . .

. I . . absorbed

. , . : I

10 m K . . . . ' . I '. Light ( I -11)

! ¹ --.

- -

--.-

FIG. 2. - Shift of the transition Cs 1, 6 2PlI2

-

t

A ,

The emission line (I) was shifted, the absorption line of a Cs-atomic beam remained unshifted. The pressure shift A v is shown by the curve 0-10 and causes the non symmetric line shape of the curve 01).

The amount of this shift Av

0.6, ..., 0.8 mK approxi- mately is indicated a t the lower curve which shows the absorption line broadened by the apparatus width.

Several authors have published shift measurements at pressures of a half to 50 atm and more [I]. The extrapolation of their shift-values down to 4 torr gives the same value Av

0.7 mK. Their measure- ments also show that shifts of transitions of high excited atoms (for example the transition 12 P - 6 S of Cs) may be larger by a factor of 45 or 30 mK under same conditions of experiment

Let us conclude. Line shifts up to 10 mK and more may appear in hollow cathodes and spectral lamps.

If one uses two different constructed light sources to measure the IS the line shifts will not compensate each other and large systematic errors may appear.

For the same reason one should not compare emission lines with absorption lines. Such an experiment had

been performed for instance by Marrus when measu- ring the IS of Cs 134m. In his first electric scanning experiment [2] he compared the Cs 133 emission line with a Stark-shifted Cs 134m absorption line. Perhaps pressure- and Stark-shifts in the spectral lamp are the reason for the discrepancy with his later value, obtained with an improved apparatus [3].

Even if the spectral lines of different nuclides were produced in light sources of the same kind and under the same conditions it is possible, that the lamps will burn slightly different, especially, if only few micro- grams of substances were excited. If we assume that the frequency shifting effects are different by an amount of only 5, ..., 10 %, isotope shifts in the order of 0.5 mK may be simulated.

In view of this error sources measuring the IS in Marburg we always excite nearly equal amounts of two nuclides simultaneously in one hollow cathode.

In which way a digital curve analysis helps to over- come the difficulties of evaluation arising from the thus increased number of lines in the hfs shall be shown by three examples.

The analysis of hfs is easy to perform if the hfs-splitting and the IS is large compared with the line width. It will be complicated with decreasing splitting factors and IS. But even when the spin of one or both nuclides is equal zero and there is no hfs and only very little IS so that the two spectral lines overlap completely it is possible to get accurat and pressure-shift-error-free data of the IS in some cases.

Figure 3 shows the hfs of an intercombination line in the silver I spectrum at 19 372 A. The resolution of the hfs was attained by a photoelectric digi- tal registrating Fabry-PCrot-interferometer. With the exception of the isotopic mixture ratio of the natural silver neither the IS nor the splitting factors of both levels were known. The digital analysis previously reported in the Colloque de Spectroscopie Instru- mentale Paris 1966 by the authors [4] has given not a single but three possible sets of values for the spec- troscopic data which are listend in Table 1. With the aid of these data three curves (Fig. 3

a, b, c), their differences with the experimental curve A and the positions of the hfs components were calculated.

The difference curve below curve b, a nearly straight

line, and its mean quadratic value (Table I, last

column) show that only the set belonging to curve b

can be the right one.

SPECIAL PROBLEMS CONCERNING THE MEASUREMENT OF THE ISOTOPE SHIFT C 1 - 6 1

Three curves a, b, c, calculated with the

<

1 Ica~c

ii -; ^{. .,}

i '.

I . ;! _1; A(2D3/2), A(2Pl12), AVIS (tab. 1) fit the

, I

;:

> . ^{: :}

! : a : :

. . .

_{. . . .}

. . . .

*? *

.;

.,,.

.

i

TABLE I

Results of the fits of curve A in figure 3 and final values (summary of all experiments) of the A-factors of "J9Ag and the IS

- -

-

Curve 3 a . . . . . - 10.2

16.9 34.6 Curve 3b . . .

12.2 - 7.0 35.8 Curve 3c . . .

1.9 + ^{16.4 35.3}

Final values . . .

12.18 (23) - 7.0 (5) 35.77 (12) Of course the accuracy of the IS value is limited

by the uncertainty of the A-factors. Therefore, the A-factors shall be determined later more exactly with separated nuclides. Nevertheless, the value of the IS [5] of

Av,,(l09

107

Ag I, 3.

19 372 A)

35.77 (12) mK is sufficiently accurate due to the fact that the isotope shift is large compared to the line width.

The second example deals with the IS of the reso- nance lines of the 9.7 day isotope Cs 131 and the stable Cs 133. In this case the IS is very small [6]

but the hfs is large compared to the line width. The A-factors and B-factors are well known from radio- frequency measurements. Unknown, however, was the isotopic abundance of the reactor produced Cs 131. The best way to measure the abundance and to prepare the hollow cathode was to use the Marburg

electromagnetic isotope separator [7]. We can inject the ion current directly into the hollow cathode so that no further chemical preparation is necessary.

The result of the measurement of the isotope abun- dance was that the Cs-sample contained only 4 % Cs 133. Adding stable Cs 133 a suited isotopic mixture was obtained so that no mass separation was necessary.

Therefore, the Cs ion current could be collected behind the ion source without having passed the separating magnetic field.

Figure 4 shows the hfs of the resonance line

1 3 1 , 1 3 3 ~ ~

1 . , 6 2P,12

6

2 S 1 / 2 , 1

8 943 A. The positions of the hfs components are shown on the left side of figure 4. Drawn lines represent Cs 131, dotted lines represent Cs 133. The connections show the splitting of the 2P,,, levels. The difference I,,,,

I,,, shows that the calculated curve I,,,, fits the measured curve I,,, well and that no sign of a disturbing line or self absorption is to be seen.

Perhaps it is interesting how exact the IS is measu-

rable if all splitting factors are known. To get an

+I- -

lOmK

v

I c a ~ c

-

Fig. 4. - Hfs of 13l9133Cs I ; 6 p 2P112 ^- 6 ^s 2S112, A=8 943

if.

Zex, : experimental curve,

ZCa1, : curve calculated with the best fitted IS-value AVIS = - 0,39 mK

.

The connections between the 13lCs-components (-) or the 13 3Cs-components (---.-- ) show the splitting of the ZPll2-levels.

impression of the exactness of digital data proces- sing we have analyzed the measured curve I,,, in figure 4 with the right and with two wrong values of the IS. The assumed wrong IS deviate from the real one by - 0.8 m K or + ^{1.6 mK.}

Av,, = -1.2 mK

I c a ~ c

-

FIG. 5. - Hfs of 131,133C~ I ; 6 p 2Pi/2-6 ^s 2Si/2, IZ=8 943

A.

Zexp : experimental curve,

Zcal, - Zexp : differences of lexp and three curves I,,l,, calculated with three assumed values A v ~ s of the IS. The difference curves show that the exact value of the IS cannot deviate much from the assumed valued AVIS = - 0.4 mK.

The results of the three fits are shown in figure 5.

At the top there is the experimental curve I,,, of the figure 4 again. Below there are the differences of the three calculated and the experimental curve. Two

of them show strong systematic deviations, expecially when the assumed IS is too large by + 1.6 mK. These deviations have the same order of magnitude as the weak hfs-component of Cs 131. With naked eyes one may see errors in the IS of perhaps 0.3 mK, the computer

sees

more accurate and detects errors of 0.1 mK in this special case of signal to noise ratio.

In the first two examples, Ag and Cs, the IS was so large or the hfs of the nuclides differed so much, that the hfs-components were separated at least partly. In the case of nuclides without hfs, for instance even-even nuclides, and with an IS small compared with the line width the method of simultaneous exci- tation fails. If one cannot see any structure in the hfs one cannot get any information about the IS.

However, one can excite nuclides in dzflerent light sources and avoid the errors caused by Stark- and pressure shift nevertheless. But then the positions of the spectral lines are to be measured with respect to a reference line. Of course this reference line should have the same Stark- and pressure shift as the unre- solved lines of the investigated nuclides. Most suitable for reference lines are nuclides of the same element but with resolved hfs or with an IS which is large compared with the line width.

The last example may iIIustrate this method. We have started to remeasure the IS of barium nuclides in the Ba I1 resonance lines 6 p 2P312,112 - 6

2 S 1 , 2 . The IS of the seven stable Ba-nuclides were already repeatedly investigated [8]. But there are little diffe- rences between the results. We used as reference lines the odd Ba-nuclides 135 and 137, because they have a suitable hfs. Yet their splitting factors were not known as exactly as necessary.

Therefore, we had to remeasure them. For the measurements of the IS we used again mixtures in the ratio 1 :l. Quantities of about 100 yg were elec- trolytically deposited in hollow cathodes.

Figure 6 shows four measured curves of the hfs of the transition 6 P I , , - ^{6 S,:,, 1}

^{4 934} A obtained with pure Ba 135, pure Ba 137, and with mixtures of these nuclides with Ba 138. From the upper curves we got the splitting factors of the levels of Ba 135 and Ba 137, from the lower ones the IS, indicated at the abscissa of the upper curves where one may see peaks of Ba 138, too. The hfs components are indi- cated with their relative intensities. Furthermore, the splitting of the 2PI,2 - levels is shown. We believe that our preliminary values of the IS

Avis(138 - 135 Ba I1

1

4 934 A)

12.16 (34) mK

Av,,(138 - 137 Ba I1

1

4 934 A)

9.34 (32) mK

SPECIAL PROBLEMS CONCERNING THE MEASUREMENT OF THE ISOTOPE SHIFT C

1-63

FIG.

6.

Hfs of Ba

6

2S1/2,

A measured

enriched 13sBa and I37Ba (top), and

mixtures of l35Ba and 138Ba and of 137Ba and

(below). From the first two curves one may deter- mine the splitting factors, the isotope-mixture-curvcs are well suited to determine the

The hfs-components, the splitting of the ~ P ~ ~ ~ - l c v c l s (connections between the hfs-components), and the

are shown.

are more accurate than the preceeding ones. A hint to the attained accuracy may be given by our measured splitting factors A and B. The ratio of the magnetic splitting factors A of the two o d d nuclides a n d the known ratio of the magnetic nuclear moments agree within 10

a t the 'P,,, - level and within 4 x l o p 4 a t the 's,,,

level. The accuracy of our measurements has the same order of magnitude.

The same fact is true for the ratio of the electric splitting factors B(6 P3,,) and the known ratio of the electric quadrupole moments

If one would make the same experiment with the even-even nuclide Ba 136 instead of Ba 138 one would determine the IS 136-138 without any systematic error caused by Stark- and pressure shift.

In the last described experiment we mixed pure Ba 138 o r pure Ba 136 with the reference nuclide Ba 137 although it is not absolutely necessary to use

nuclides. The reference-line method should allow t o determine the IS with

of two nuclides even if their IS is small and the hfs is missing.

F o r instance it is nearly impossible t o get isotopic pure radioactive Ba 140 to measure the IS of Ba 140 referring to Ba 138. But is should be possible to deter- mine the positions of the unresolved lines of Ba 138 and Ba 140, since

I. The line profile is measureable form the reference line Ba 137,

11. The IS of Ba 138 is known in respect to the reference line, and

111.

The change of the isotopic mixture ratio due to the radioactive decay can be calculated.

The aim of this paper was to show the possibilities of avoiding systematical errors in measuring the IS.

The discussion of the results of our measurements shall follow elsewhere [5] [6] [9].

Acknowledgement. - The authors are much indeb- ted t o Prof. Dr. W. Walcher for many helpful sugges- tions and t o the

Deutsche Forschungsgemeinschaft >>

for providing the apparatus.

References

[I] GARRETT (R. C.), SHANG YI CH'EN,

1966,

66.

[2] MARRUS (R.), MCCOLM (D.),

1965,

813.

[3] MARRUS (R.), WANG (E.), YELLM (J.),

Letters,

1967, 19, 1.

[4]

HUHNERMANN (H.),

1967,

C 2-260.

[5] KRUGER

Diplomarbeit, 1968, Marburg.

FISCHER (W.), HUHNERMANN (H.), KRUGER (E.),

1968, 216, 136.

[6] HWHNERMANN (H.), WAGNER (H.),

1968,

216. 28

[7] W A L ~ ; ; ~

(W.),

1938,108,376.

KOCH (J.), DAWTON (R. H. V. M.)? SMITH (M. L.), W A L C H ~ K

Electromagnet~c Isotope Sepa- rators and Applications of Electromagnetically Enriched Isotopes, North-Holland Publishing Company, Amsterdam, 1958.

WAGNER (H.),

1965, 38, 69.

[8] KELLY (F. M.), TOMCHUK (E.),

1967,

3931.

[9] BECKER (W.), Diplomarbeit, 1968, Marburg.

BECKER (W.), FISCHER

HUHNERMANN

1968, 216, 142.