Determination of relative intensities of M internal conversion lines in pure E2 transitions

Nuclear Physics A120 (1968) 569--575; (~) North,Holland Publishin# Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher

DETERMINATION OF RELATIVE INTENSITIES OF M INTERNAL CONVERSION LINES IN PURE E2 TRANSITIONS S. H O G B E R G , J.-E. B E R G M A R K , G. MALMSTEN and 0 . NILSSON Institute of Physics, University of Uppsala, Sweden Received 1 July 1968 Abstract: Accurate measurements have been performed on the relative intensities of the M internal conversion lines of three pure E2 transitions in nuclei in the rare-earth region. The results are compared with theoretical values obtained from the calculations by Bhalla and by Hager and Seltzer. Discrepancies of about 6 % between experiment aad theory are reported for the MJMH and Mx/M m ratios of the 80.57 keV transition in 1SeEr. The MH/M m ratios of the 84.26 keV transition in lv°Yb and of the 100.09 keV transition in ls~w are significantly lower than predicted by theory. I E

RADIOACTIVITY le6Ho [from le6Ho(n,y)], 17°Tm [from leSTm(n,7)], ~S2Ta [from 1SiTs(n, ~,)]; measured lee. Natural targets.

1. Introduction

By the use of high-resolution beta spectrometers, it is possible to measure very accurately the internal conversion electron intensities. In studies of the relative intensities of the L subshell internal conversion lines of pure E2 transitions performed at Brookhaven and Stockholm 1), Chalk River 2) and Uppsala 3,4), the precision was high enough to reveal discrepancies of about 6 9/0 between the theoretical and experimental ratios. At the time of these L conversion studies, only the internal conversion coefficient tabulations by Rose 5) and by Sliv and Band 6) were published. Later calculations of internal conversion coefficients have been performed by Hager and Seltzer 7), Pauli s) and Bhalla 9). All theoretical calculations give about the same L subshell ratios for the transitions studied, and since the different experimental determinations all agree, the discrepancies between experiment and theory seem to be well confirmed. A comparison between the experimentally obtained L subshell ratios 3) and those obtained from the different theoretical calculations 5-9) is given in ref. 1o). Up to 1967, theoretical M subshell internal conversion coefficients were available only from the tabulation by Rose 5). These coefficients were calculated with the assumption of a point nucleus and without correction for screening. The tabulation is accordingly not very accurate and can be used merely as a rough guide. Later an empirical screening correction to Rose's M subshell conversion coefficients has been described by Chu and Perlman 11). 569

570

s. HOGBERGet

al.

The M internal conversion coefficients are included in the recent publications by Hager and Seltzer, Pauli and Bhalla. Hager and Seltzer 7) performed their calculations with wave functions obtained from a modified Hartree-Fock-Slater method and with several significant improvements over earlier calculations. The coefficients were computed for every Z-value between 30 and 103. Pauli's calculations were performed with the use of a Thomas-Fermi-Dirac potential. In the preliminary report s) available at the time of the present investigation, the dynamic effects of the finite nuclear size were omitted. The tabulation contains M subshell coefficients for every fourth Z-value between 72 and 96. The calculations by Bhalla 9) were performed with the use of a Hartree-FockSlater method with the inclusion of the static finite nuclear-size effects. The coefficients were computed directly for E2 transitions earlier studied in L conversion measurements, and hence no errors due to interpolation in energy or Z are introduced when using Bhalla's values. The interpolation uncertainties have been confusing when establishing discrepancies between experimental intensity ratios and those derived by interpolation in theoretical tabulations. The aim of the present work was to provide accurate measurements of M subshell ratios for comparison with the new theoretical values. The result of these measurements might also give information for the explanation of the discrepancies between theoretical and experimental L subshell ratios as suggested by Bhalla 9). A verification of the ratios between the theoretical M subshell internal conversion coefficients would imply that not only L but also M subsheU intensity ratios can be used for multipolarity assignments.

2. Source preparation To obtain a resolution sufficiently high for the present investigation, the source thickness must be low. At the same time, however, a considerable source strength is desired and in order to fulfill both requirements, multi-strip sources lz) were used. The source materials of metallic Ta and oxides of T m and Ho were evaporated in thin layers ( ~ 3/~g/cm 2) onto aluminium foils. These were then irradiated in a neutron flux of about 2 • 1014 n/cm 2 • s to obtain 182Ta, 17°Tm and 166Ho, respectively. For the lS2Ta (T~r = 115 d) and 17°Tin (T, = 127 d), the irradiations lasted between 10 and 50 d. The 166Ho sources (T~r = 27.0 h) were produced by irradiation for 3 d. After the irradiations, the foils were glued onto plexiglass backings, and each source was then cut into 15 strips, each 16 x 0.5 m m 2. The measurements with the Ta sources were started more than three months after the irradiation. Conversion lines from the decay of lS3Ta (T~r = 5.0 d), which is produced together with lS2Ta, did then not disturb the measurements. At least three sources of each isotope were used. The results obtained with the different sources all agreed, and no influence due to source effects was found.

INTERNAL CONVERSION RATIOS (II)

571

3. Instrumentation and measurement

The 50 cm iron-free spectrometer at Uppsala 13) was used in the measurements. The momentum resolution of the M lines varied between 0.045 % and 0.060 %, which means that the M a and Mn[ conversion lines were almost completely separated (see fig. 1). The spectra were recorded with current increments of about 0.004 % yielding about 30 points on each line above 10 % of the peak intensity. The current through the spectrometer coils was checked for each point by measuring the voltage drop over a precision resistor with a precision potentiometer. During the earliest part of the investigation, the precision in the current increments was not very high, and corrections for different step lengths had to be applied in the analysis. Later the current control was improved and during the main part of the work no such corrections had to be applied. L

i

I

=

I

i

166

15

6aE r

80.57 H

¢' 10 =,

0.051% D

I

O

5

J 0

12.52

12.54

'

12156

12.58

12.60

SPECTROMETER CURRENT (A)

Fig. 1. T h e M internal conversion lines o f the 80.57 keV transition in 16eEr.

The temperatures at ten different places of the spectrometer were continuously registered, and the variations were kept within __0.1 ° C. The elimination of the vertical component of the earth magnetic field and other disturbing magnetic fields was continuously controlled during the measurements. The two horizontal components were checked before and after the recording of a line and also when large changes in the vertical component were observed. A side window G M counter was used for electron detection. The entrance slit of 25 x 0.3 mm 2 was covered with thin layers of formvar with a typical value for the cut-off energy of 5 keV. Accordingly the transmission is expected to be 100 % for the

572

s. HOGBERG et al.

electrons studied, and even if there is some absorption, no correction is necessary since then the transmission variation over an M spectrum is negligible. Careful measurements were performed of the tails from the N and O conversion lines and of the background on the high-energy side of these lines. The constant counter background ( ~ 25 counts/60 s) was measured in connection with each run.

4. Analysis and results The analyses were performed in essentially the same manner as described by Karlsson et al. 3). A computer was used to subtract the constant counter background and 104

166

68Er

80.57 M

103 ~D In

o ¢J 10 2

10

121s2

'

12.'5~

'

12!$6

'

12158

'

lz.'6o

SPECTROMETER CURRENT (A) Fig. 2. A semilogarithmic plot o f the analysed M lines o f the 80.57 keV transition in Z66Er. The same recording as in fig. 1 is shown. Horizontal lines indicate 10 ~o of the peak intensities.

to make corrections for the counter deadtime and for decay. After subtraction of the beta background and the tails originating from the N and O lines, the logarithm of the counting rate was plotted versus current. The components of the spectrum were separated with the assumption of identical line shapes for all M lines and with the basic shape obtained from the M m line. The low-energy tail was first estimated and then adjusted through an iterative procedure until the sum of the components became consistent with the experimental data. To obtain a measure of the line intensities, the sum of counts for currents where the counting rate exceeded 10 ~o of the peak intensity was calculated. This sum was then divided by the peak position current.

experiment theory Hager and Seltzer a) Hager and Seltzer b)

II~W 100.09 keV 8.30 7.99

8.0-t=0.5

7.11 7.26 (9.24)

7.24-0.4

7.46 7.62 (10.05)

7.90-t-0.18

MI

110.2 109.7

103.24-1.4

98.1 99.0 98.1

95.54-1.1

94.6 94.9 94.5

93.4±0.8

Miz

100 100

100

100 100 100

100

100 100 100

100

MIH

1.13 1.11

1.15=t=0.09

1.09 1.09 1.07

1.04i0.12

1.05 1.04 1.04

1.05±0.04

Mxv

0.93 0.92

1.06±0.09

0.97 0.98 0.97

0.994-0.11

0.97 0.97 0.98

1.054-0.05

My

2.06 2.03

2.21 :L0.13

2.06 2.07 2.04

2.044-0.07

2.02 2.01 2.02

2.104-0.05

Mxv + My

s) Deduced using the graphical interpolation method described in ref. 8). b) Obtained using the computer program given by Hager and Seltzer v). This program may yield wrong M i values as pointed out in ref. 7).

170

experiment theory Bhalla Hager and Seltzer ~) Hager and Seltzer b)

experiment theory Bhalla Hager and Seltzer ~) Hager and Seltzer b)

~oYb 84.26 keV

80.57 keV

ssEr

186

Isotope and transition energy

TABLE 1 Relative M internal conversion line intensities

O

¢3 O

574

s. HOGBERGe t

al.

In the L subshell measurements reported in ref. a), an extra check of the tail extrapolation was made by comparing the intensities in the regions 3-10 ~o and above 10 ~o of the peak intensity. The determination of the intensities in the region 3-10 was in the present study very uncertain, and the extra check of the tail extrapolation was not performed. A semilogarithmic plot of the analysed M spectrum of the 80.57 keV transition in 166Er is shown in fig. 2. A doubtful part of the analysis was the separation of the Miv and M v lines, and the intensities determined for these lines are rather uncertain. The filled circles in fig. 2 are attributed to the Mn, line and were obtained by subtraction of the high-energy tail of the Mia line and the low-energy flank of the M v line from the experimental data. By subtraction of the high-energy flank of the M~v line from the experimental data, the open circles, which are attributed to the M v line, were obtained. A more accurate intensity value can be calculated for the sum of the M~v and M v lines, since this sum is rather independent of the separation of the individual parts. TABLE 2

Experimentally obtained M and L subshell ratios for the 80.57 keV transition in leeEr compared with theoretical values calculated by Bhalla 8) M~/Mxx present experiment a) theory Bhalla 8) exp./theory, present work Ref. 1~) experiment 3) b) theory Bhalla s) exp./theory

0.085 4-0.002 0.0789 1.07 -4-0.03 1.13

Mx/Mnx 0.079 t0.002 0.0746 1.06 - I - 0 . 0 2 1.10 4 - 0 . 1 3

MII/MIII 0.934-4-0.010 0.946 0.9874-0.011 0.978±0.032

L~/LxI

L~/Lm

L~JI-qH

0.09104-0.0015 0.0837 1.09 4-0.02

0.0871 +0.0011 0.0812 1.07 4-0.02

0.9594-0.005 0.971 0.988 4-0.006

a) Mean values of 11 measurements. The errors are twice the standard error of the mean. b) The errors given are twice the standard error of the mean. The intensities obtained were normalized to M m = 100 and are given in table 1. This table also includes normalized theoretical values from the works by Bhalla 9) and by Hager and Seltzer 7). In the latter case, the internal conversion coefficients were obtained by energy interpolations using both the computer program given in ref. 7), and the methods of graphical interpolation described in ref. 3). N o comparison is made with values f r o m the tabulation by Pauli s), since the inter- and extrapolation in Z that must be performed might introduce large errors. The experimental intensities given in table 1 are mean values of between 7 and I 1 measurements, and the errors are twice the standard error of the mean. The mean value of the errors in the individual measurements calculated with the use of formula (1) in ref. 3) are of the order of 10 ~ for the M l line, 2 ~o for the MII and Mia lines and 50 ~ for the Miv and Mv lines.

INTERNAL CONVERSION RATIOS (II)

575

The comparison between the experimental and theoretical relative M intensities shows deviations for the Mn/MIII ratios especially for the transitions studied in tT°Yb and 1s2W. The Mn/Mni ratios experimentally obtained are all lower than the theoretical values, and the deviations seem to increase with increasing energy and/or atomic number. A study of the relative M subsbell intensities for the 80.57 keV transition in 166Er, where the smallest experimental errors were obtained, shows another interesting deviation from theory. The MI/M n and Mt/M m ratios are about 6 ~o larger than predicted by theory, while the MH/M m ratio almost agree with theory. In the studies of L subshell ratios of pure E2 transitions 1-4), deviations were obtained for the L f f L i i and Lt/~a ratios, while the La/Ltn ratio agreed with theory. In table 2, the experimental M subshell ratios are compared with the theoretical ones from the calculation by Bhalla, and for comparison also the earlier obtained 3) L subshell ratios are compared with theory. The ratios obtained by Arnoux and Gizon 14) are also given in table 2 and support the deviation reported in the present work. In a note added in proof to ref. 15), Dragoun and Jahn report deviations of a few per cent for ratios involving the M~ shell also for E2 transitions in x92pt. It seems at the moment urgent to confirm the observed M anomalies through measurements by other groups. The cause of the earlier observed L anomaly is still uncertain, and a verification of discrepancies also for the M shells might be of importance for the explanation. This work has been financially supported by Statens R~d f6r Atomforskning.

References 1) P. Erman, G. T. Emery and M. L. Perlman, Phys. Rev. 147 (1966) 858 2) W. Gelletly, J. S. Geiger and R. L. Graham, Bull. Am. Phys. Soc. 11 (1966) 352 3) S.-E. Karlsson, I. Andersson, O. Nilsson, G. Malmsten, C. Nordling and K. Siegbahn, Nucl. Phys. 89 (1966) 513 4) S.-E. Karlsson, S. HOgbergand 0. Nilsson, Phys. Lett. 24B (1967) 148 5) M. E. Rose, Internal conversion coefficients (North-Holland Publ. Co., Amsterdam, 1958) 6) L. A. Sliv and I. M. Band, in Alpha-, beta- and gamma-ray spectroscopy, ed. by K. Sieghahn (North-Holland Publ. Co., Amsterdam, 1965) appendix 5 7) R. S. Hager and E. C. Seltzer, Nucl. Data A4 (1968) 1 8) H.-C. Pauli, COO-1420-136 (1967) 9) C. P. Bhalla, Phys. Rev. 157 (1967) 1136 10) 0. Nilsson, I. ThorOn, G. Malmsten and S. HOgberg, Nucl. Phys. A120 (1968) 561 11) Y. Y. Chu and M. L. Perlman, Phys. Rev. 135 (1964) B319 12) O. Nilsson, S.-E. Karlsson, I. Andersson, C. Nordling and K. Siegbahn, Nucl. Instr. 47 (1967) 13 13) K. Siegbahn, C. Nordling, S.-E. Karlsson, S. HagstrOm, A. Fahlman and I. Andersson, Nucl. Instr. 27 (1964) 173 14) M. Arnoux and A. Gizon, Compt. Rend. 264 (1967) 1518 15) O. Dragoun and P. Jahn, Nucl. Phys. A101 (1967) 305