MEASUREMENT OF RELATIVE TRANSITION PROBABILITIES AND X-RAY WIDTHS FOR THE K SHELL

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MEASUREMENT OF RELATIVE TRANSITION PROBABILITIES AND X-RAY WIDTHS FOR THE K

SHELL

G. Nelson, B. Saunders

To cite this version:

G. Nelson, B. Saunders. MEASUREMENT OF RELATIVE TRANSITION PROBABILITIES AND

X-RAY WIDTHS FOR THE K SHELL. Journal de Physique Colloques, 1971, 32 (C4), pp.C4-97-C4-

104. �10.1051/jphyscol:1971419�. �jpa-00214620�

JOURNAL DE PHYSIQUE

Colloque C4, supplkment au no 10, Tome 32, Octobre 1971, page C4-97

MEASUREMENT OF RELATIVE TRANSITION PROBABILITIES AND X-RAY WIDTHS FOR THE K SHELL (*)

G. C . NELSON (**)

Sandia Laboratories, Albuquerque, N. M.

B. G. SAUNDERS (**) Encyclopaedia Britannica, Chicago, Ill.

Rhum6. - Les largeurs des raies X Kul, Ka2, KB1 et KB3 ont et6 determinbs pour les elements au-del8 de 1'6tain

50). Les effets instrumentaux ont it6 corriges. Lavariation de la largeur instrumentale a ete mesurk dans tout le domaine d'energie etudi6. Ces mesures ont permis de deter- miner le rendement de fluorescence des couches L*, L3, M2 et M3, en utilisant le rendement de fluorescence experimental de la couche Ket les probabilites de transition theoriques pour les couches K, L et M. Les rendements de fluorescence obtenus pour L2 et L3 sont en accord avec ceux de Price et al. dans la limite des erreurs exp6rimentales. Les rendements de fluorescence determines pour M2 et M3 peuvent 6tre utilises comme estimation de ces quantites.

Une table des meilleures valeurs des probabilitks de transition relatives de la couche K a et6 etablie B partir de ces mesures. Ces valeurs ne sont pas en accord avec celles de la table de Wapstra et al.

Abstract. - Widths of the Kal, Kaz, KBI, and K83 X rays have been determined for elements above 50Sn. Corrections have been made for instrumental effects. The variation of the instrumental width was measured over the entire energy range of interest. Fluorescent yields of the L2, L3, M2, and M3 shells have been determined from these measurements, the experimental k shell fluorescent yields, and the theoretical radiative transition probabilities for the K, L and Mshells. The L2 and L3 fluorescent yields were found to agree within the present experimental error with the values reported by Price et al. The M2 and

fluorescent yields determined from these measurements can be used as estimates for these quantities.

A table of best values for the K shell relative transition probabilities has been formed from recent measurements. The values are not in agreement with those reported in the table of Wapstra et al.

Introduction. - In the past few years, improve- ments in experimental techniques have enabled more precise measurements of X-ray widths and relative transition probabilities. Also, more reliable theore- tical calculations of decay rates have been reported.

Scofield [l] and Rosner and Bhalla [2] have reported relativistic calculations of the radiative transition probabilities for the K and L sh.ells. Rosner and Bhalla also included the M shell. Both calculations include the effect of retardation. Scofield used the central potential given by the relativistic Hartree-Slater theory while Rosner and Bhalla used the self-consis- tent relativistic Hartree-Fock-Slater model. The results of these calculations are in excellent agreement.

I am going to report on the measurement of the KLZ,, KM,, KP, and KP, X-ray widths for elements above 5oSn. I will also discuss a table of relative transition probabilities which we have formed from recent measurements. I will compare these results

(*)

Work performed under the auspices of the U. S. Atomic Energy Commission.

(**)

Work performed while at Lawrence Radiation Labora- tory, Livermore, California.

with the previously reported values and the theoretical calculations.

K X-RAY WIDTHS. -In the cases under study, the shape of the spectral line, Y, is determined primarily by the natural widths. The Weisskopf-Wigner [3]

theory gives the frequency distribution as Lorentzian.

However, the observed distribution f (v) is a fold of the true distribution, Y, and the instrumental res- ponse, @.

In the present measurements it was experimentally determined that an excellent fit of the instrumental profile could be made by assuming

to be Gaussian.

We have used these functions to solve Equation 1 numerically on a CDC 6600 computer and have used f (v) to fit our experimental data.

A schematic drawing of our 2-m Cauchois-type transmission bent-crystal spectrometer is shown in figure 1. An 80 C i l S 2 ~ a source is used to fluoresce

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1971419

C4-98 G. C .

NELSON, B.

SAUNDERS

FIG.

- Schematic top view of the bent-crystal spectrometer.

Shaded areas are lead.

the X rays of the element of interest. The X-rays diffracted by the (310) planes of a quartz crystal are automatically scanned in steps of 0.01-mm by a 0,177-mm slit and are detected in a 2-cc Ge(Li) detector. A single channel analyzer selects out the energy region of interest. Figure 2 shows a scan over the Ir Kal X-ray.

response which has been folded in the detector slit, The function we use is

where c is the instrumental width, S is the slit width and X, is the peak position. Figure 3 is a scan over the 241Am 59.537 keV gamma-ray line. The solid line is a computer fit to the experimental data. The successful fit can be considered as confirmation of the proper choice of instrumental shape.

Ir K n l X ' O y

E = 6 4 . 8 9 5 6 k c V

0.01 I I

6.764 7 . 2 M 7 . 7 M 8.764

S l i t Polifion (mm)

FIG.

Least-squares computer fit to the 59.537 keV241 Am gamma-ray diffraction peak.

0.01 I l I

67.034 67.504 68.034 68.504

Slit Position (mm,

FIG. 2.

Least-squares computer

to the Ir

X-ray diffraction peak.

Since gamma rays have natural widths which are negligible in comparision with the instrumental widths, their profiles can be used as a measure of the instrumental response. In fitting the garnma- ray peaks, we have found that the observed data can be fit well by assuming a Gaussian instrumental

Previously we reported [4] measurements of the Kg, and Ka2 widths wbich were higher than would be expected on semi-theoretical grounds. In these measurements we assumed a constant instrumental width as a function of energy. This assumption was based on our measurements between 59 keV and 100 keV and the results of Edwards [5]. Since then we have measured the instrumental width from 26 keV to 100 keV and have found that while the width remains relatively constant from 55 keV to 100 key, it varies as below 55 keV. Figure 4 is a plot of the instrumental width as a function of wavelength.

The variation of the width as a function of wavelength

is not completely understood. Sumbayev [6] has pre-

dicted a behavior similar to this for both ideal and

mosaic crystals. However, the wavelength at which

the change in slope takes place and the magnitude of

the change do not coincide. Sumbayev predicts a

variation proportional to the first power of the wave-

MEASUREMENT

RELATIVE TRANSITION PROBABILITIES A N D X- RAY length, 1, while we observe

While further expe-

riments are necessary to resolve these differences, the empirical results necessary for the present measure- ments appear in figure 4.

Wavelength

( X ) - ^A

FIG. 4. - Variation of the instrumental width as a function of wavelength.

In the present measurements we assume a Lorent- zian distribution for the natural X-ray shape and a Gaussian for the instrumental response. The observed spectrum is obtained by folding these functions into the detector slit. The function used in the fitting pro- cedure is

where S and cr are defined as before and r is the natu- ral X-ray width. The solid line in Figure 2 is a compu- ter fit of equation 3 to the experimental data.

The widths, r, in millimeters obtained from the least-squares fits are converted to energy by differen- tiating the position versus energy equation.

We have measured the Ka, widths using figure 4 for the variation of the instrumental width with energy.

The Kg, widths for 26 elements between ,,Sb and ,,Np are listed in Table I and are plotted in figure 5.

The errors are estimated to be 6 %. The solid line in figure 5 is a straight line fit to the experimental data points. This line varies as

When extended to lower atomic numbers this line falls below the data of Gokhale [7]. The agreement between the value of 43.0 0.9 eV reported by Richtmyer and Barnes [8]

for ,,W and our measured value of 43.2 + ^{2.5 eV}

is excellent.

Widths of the Kg2 X-rays have been obtained by correcting our previously reported [4] Ka, widths for the variation of instrumental width. These values are

The Ka, and

Ka, X-ray Widths for Elements above 5oSn

FIG.

-Width of the Kal X-rays as a function of atomic number.

also listed in Table I. In this case the errors are esti- mated to be 15 %.

The method we have used to check our measure-

ments follows a suggestion of Professor Bhalla. The

X-ray widths, Ka, for example, are given by

C4- 100 G. C . NELSON, B. G. SAUNDERS

where r; is the radiative width of the K level and TABLE I1

TP is the non-radiative width of the K level. The L, _The KP1 and

terms are defined similarly. Using the definition of KP, X-ray Widths for Elements above ,$n fluorescent yield, o, equation 4 becomes.

Z KPl KP, z KPl KP3

rK"

rKN,

+ -. ^{( 5 )} - ( 0 -

(eV> -

OK U L ~

50 11.7 11.5 65 33.2 33.0

We have used the theoretical radiative widths and 55 17.7 14.6 67 33.5 34.0 best values of m, obtained from experimental data 58 18.8 17.3 70 44.0 37.8 in conjunction with our measurements of the Ka, 62 27.5 24.7 73 49.9 49.3

0.0 I I I I

P 60 m 6 90 m

A l a u c oon

FIG.

-The

fluorescent yield as a function of atomic number.

widths to determine

Figure 6 shows the results of these calculations. The open circles are the values obtained from our measurements while the solid line was obtained when the straight line fit to the measured widths was used. The points are the measured values of Price et al. [9]. Considering the 6 % error in the X-ray widths, we feel that the present results for

are in good agreement with the values of Price et al.

The Ka, widths were analyzed in a similar manner.

The general agreement with Price et al. [9] is again quite good. However, the points are more scattered due to the larger uncertainties in the widths.

We have recently extended these measurements to the KP, and KP, X-rays. Due to the small energy separation between the lines, it was necessary to measure and analyze the KP1 and KP, lines simulta- neously. Figure 7 is a computer fit to the KP1 and KP3 diffraction peaks of ,,Ta. The KP, and K/?, widths are listed in Table I1 and are plotted in figures 8 and 9.

The errors are estimated to be 6 %. Richtmyer and Barnes [8] have reported values of 48.6 f 1.5 and 50.0 f 1.5 eV, respectively, for the KP1 and KP, widths of 74W. These values are in good agreement with the present results. As before, the solid lines are straight line fits to the data points. The KP, line varies as z ~ while the KP, line varies as z~.'*. . ~ ~

0

L

I

66.404 67.404 68.404

Slit position

-

FIG. 7. - Least-squares computer fit to the Ta Kpl and Kba diffraction peaks.

The KP1 and K@, widths were analyzed in the same manner as the Ka, data and values were obtained for

C C ) ~ 2

and m,,. These values are plotted as a function of

atomic number in figures 10 and 11. In this case there

are no previously reported values with which to

compare our results. However, considering the agree-

ment between the m,, and mLj values determined

MEASUREMENT O F RELATIVE TRANSITION PROBABILITIES AND X-RAY

FIG. 8. -Width of the KB1 X-rays as a function of atomic number.

FIG. 9. -Width of the

X-rays as a function of atomic number.

0.m 54 70

Amac mBP(

FIG. 10. - The

fluorescent yield as a function of atomic number.

FIG.

-The

fluorescent yield as a function of atomic number.

from our width measurements and those measured by Price et al. [9] we feel that these values can be used as good estimates of the M, and M, fluorescent yields.

Relative K X-Ray transition probabilities.

In addition to measuring K X-ray widths, we have deter- mined relative radiative decay rates for the K shell.

These ratios provide additional tests of the theoretical calculations and have important applications in both nuclear and atomic physics.

Prior to 1969, systematic measurements of relative decay rates had been made by Meyer [l01 (23 ,< Z ,< 49), Williams [l11 (24 Z 52) and Beckman [l21 (73 d Z d 92). The values obtained in these measurements formed the basis of the table of Wapstra et al. [l31 which has been the standard table of relative radiative transition probabilities.

Since 1969 four groups [14-201 have reported systematic measurements of relative radiative transition probabili- ties. Because of improved instrumentation these results are more precise than the previous measurements.

We have used these new measurements to form a new table of best values of relative transition probabilities.

Each of the groups mentioned above used a diffe-

rent method in making their measurements. Hansen

et al. [l41 used Ge(Li) and Si(Li) detectors to look at

X-rays produced by radioactive decay. By unfolding

the pulse-height spectra, they have obtained values of

K/3/Ka for 17 ,< Z 82. They have also measured

K/3;/Ka1, KP;/Ka, and Ka,/Kcl,, for atomic numbers

81 and 82. Salem et al. [15], [l61 have used an X-ray

C4-102 G. C. NELSON, B. G. SAUNDERS spectrometer and a proportional counter to measure

(KP, + KP3)/Ka1 for 22 Z G 47 and Ka2/Kal for 21 < ^Z 50. Ebert and Slivinsky [17, 181 unfolded the X-ray pulse-height spectra obtained with a high resolution Ge(Li) detector to obtain values for KPIKa for 40 6 Z 6 92, K/?;/Kal, Kj?;/Ka,, and Ka, for 62 6 Z 6 92. They used an X-ray tube to fluoresce the X-rays of interest. We 1191, [20] used a bent-crystal spectrometer and a Ge(Li) detector to obtain the relative transition probabilities for Ka2/Kal for 51 6 Z G 95 and Kb3/KPl for 50 6 Z 6 92.

We wed a gamma ray source to fluoresce the X-rays.

The results of our tabulation are shown in figures 12-17. In these figures we have plotted the various expe-

0.65

-

Solem and Wimmer

0 Nelson and Sounders 0.60- A Ebert and Slivinrky

a- 0.55 -

Y

b

I

I

0 . 4 5 t

---

----

I -.-.-.

l

Atomic "umbel

Frc.

- Transition probability ratio KazlKal as a function of atomic number.

'-0.4 , 0 Solem, e t al.

C

Y Smooth curve through experimental data

---

Atomic nvmbe~

FIG.

- Transition probability ratio KB3/KD1 as a function of atomic number.

Y

o Ebert ond Slivinsky A Solem and Johnron

-

- - -

.-,- Theoretical calculation of Baburhkin

0.1 I I I

20 40 60 80 100

Atomic number

FIG. 14.

Transition probability ratio (KP1 +

as a function of atomic number.

rimental data, the curve of best values, the theoretical calculation of Scofield, and where applicable, the values of Wapstra

al. [13]. The values obtained from

0 Ebert and Slivinsky A Solem and Jahnron

Honsen, et al.

Smooth curve through experimental data

---

.-.-

0.1 l I I

20 40 60 8 0 100

Atomic number

FIG. 15. - Transition probability ratio K/?i/Kal as a function of atomic number.

Smooth curve through experiment01 data Theoretical colculotion of Scofield

0.15

.-.-.-.

/'

Atomic number

FIG.

- Transition probability ratio KBi/Kal as a function of atomic number.

I ^---

I

0 l I l

1

20 40 60 8 0 100

Atomic number

FIG.

- Transition probability ratio KAKa as a function of

atomic number.

MEASUREMENT OF RELATIVE TRANSITION PROBABILITIES AND X-RAY C4-103 these new measurements and those of Wapstra et al.

differ by as much as 30 %. The theoretical calculation of Scofield is in good agreement with the experiments in the case of the Ka,/Ka, doublet. For the KP,/KP, doublet, Scofield's calculation drops below the experi- mental values at high 2. For the ratios of the other transitions, Scofield's calculation is consistently below the experimental results. However, he does reproduce the shapes of the curves quite well.

As a more sensitive test of the theoretical calcula- tions, we have recently measured the ratio of the L, - K to Kol, X-rays for five elements. The L,

K transition is a magnetic dipole transition and thus much weaker than the Kol, transition. The L ,

K transition occurs in Scofield's calculation due to retar- dation and relativistic effects and is thus sensitive to these corrections. The preliminary results of our mea- surements are shown in figure 18. The present values are in good agreement with the results of Beckman [l21 but are 1.5 to 3 times larger than the calculation of Scofield.

Acknowledgments. - We would like to thank Professor Bhalla, Jim Scofield, and Simon Salem for their helpful discussions. We especially want to thank Walter John for his help and encouragement during

these measurements. ^{FIG. 18.} - Ratio of the ( L I - K ) to Kul X-rays as a function of atomic number.

References SCOFIELD (J. H.), Phys. Rev., 1969, 179, 9.

ROSNER (H. R.) and BHALLA (C. P.),

Physik, 1970, 231,347.

WEISSKOPF (V.) and WIGNER (E.),

Physik, 1930,63,

54.

NE;& (G. C.), JOHN (W.) and SAUNDERS (B. G.), Phys. Rev., 1969, 187, 1.

EDWARDS (W. F.), Ph. D. thesis, California Institute of Technology, Pasadena, Calif., 1960 (unpublished).

SUMBAYEV (0. I.), Government Publishers of Litera- ture on Atomic Science and Technology, Govern- ment Committee on the Uses of Atomic Energy, Moscow, 1963.

GOKHALE (B.), Ann. de Phys., Paris, 1952,

852.

RICHTMYER (F. K.) and BARNES (S. W.), Phys. Rev., 1934, 46, 352.

PRICE (R. E.), MARK (H.) and SWIFT (C. D.), Phys.

Rev., 1968, 176, 3.

MEYERS (H. T.), Wissenschaftliche Verofentlichungen Siemens-Konzern, 1929, 7, 108.

[l l ] WILLIAMS (J. H.), Phys. Rev., 1933, 44, 146.

[l21 BECKMAN (O.), Arkiv Fysik, 1955, 9, 495.

[l31 WAPSTRA (A. H.), NIJGH (G. J.) and VAN LIESHOUT (R.), Nuclear Spectroscopy Tables (North-Holland Publishing Co., Amsterdam, 1959).

[l41 HANSEN (J. S.), FREUND (H. U.) and FINK (R. W.), Nucl. Phys., 1970, A 142, 604.

1151 SALEM (S. I.) and JOHNSON (J. P.), Phys. Letters, 1969, 30A,

[l61 SALEM (S. I.) and WIMMER (R. J.), Phys. Rev. to be published.

[l71 SLIVINSKY (V. W.) and EBERT (P. J.), Phys. Letters, 1969,29A, 463.

[l81 EBERT (P. J.) and SLIVINSKY (V. W.), Phys. Rev., 1969, 188, 1.

[l91 NELSON (G. C.) and SAUNDERS (B. G.), Phys. Rev., 1969, 188, 108.

[20] SALEM (S. I.), SAUNDERS (B. G.) and NELSON (G. C.), Phys. Rev., 1970, 1, 1563.

DISCUSSION

~ l l e

CAUCHOIS. - Comment tenez-vous reelle- ment compte de la largeur instrumentale que vous avez obtenue g l'aide d'Cmissions

dont la largeur vraie est consideree comme negligeable ? Vos figures portent en ordonnte :

iargeur instrumentale-r (eV) >). Si la determination de la largeur vraie de la raie X Ctait ainsi deduite, cela reviendrait 2 supposer certaines formes mathkmatiques pour les differentes raies (formes vraies et formes experimentales) qu'il faudrait justifier.

-+

RCponse du Conferencier.

RCponse Y. CAUCHOIS. - I1 y a donc dans vos determinations, entre autres une hypothihe ou approxi- mation qui assimile la forme experimentale d'une raie y a une gaussienne, la forme vraie d'une raie X ttant lorentzienne.

Answer to M"" CAUCHOIS. - We assume a Gaus-

sian for the instrumental response. The width of the

Gaussian is determined by fitting gamma ray data.

C4-104 G. C. NELSON, B. G. SAUNDERS To fit the X-ray data the Gaussian is folded into a

Lorentzian distribution which we assume represents the X-ray shape. These in turn are folded into the detector slit. The function used is

where y(xi) is the counting rate at position Xi, X,, is the peak position, ^o is the width of the Gaus- sian, S is the slit width and r is the X-ray width.

C . KUNZ. - Could you explain your Am spectrum in the light of your reply to Prof. Cauchois' question ? Answer to KUNZ. - We fold a Gaussian instru- mental response into the slit-which is rectangular.

The function we use is

The resulting function looks something like a Gaussian.

Mr. DAS GUPTA.

HOW the line width with Cau- chois spectrometer compares with 2 crystal spectro- meter ?

How to account for small angle scattering from slit?

Answer to DAS GUPTA. - ^{The only} 2 crystal data reported in this range of atomic numbers is for W.

For Ka, the reported value is 43.0 k 0.9 and we measure 43.2 f 2.5. The KP, and KP, agreement is also quite good.

We had some problems with scattering at the slit and had to redesign the slit.

Mr. JORGENSEN.

Since the Chairman talks about super-heavy elements, what wouId be the expected half-width for the element 126 ?

Answer

about 250 eV.

CARLSON, comments with NELSON.

I should like to comment that unpublished results of Ditner and Bernir on the relative X-ray transition rates in tran ...

elements appear to agree with yours rather than the

earlier results reported by Wapstru. Also I am very

happy to see improved experimental results in this

field because of the usefulness of these data for help

in identifying superheavy elements.