Nuclear Instruments and Methods in Physics Research A312 (1992) 378-384 North-Holland
NUCLEAR INSTRUMENTS & METNODS
IN PNVSICS RESEARCH Suoton A
The re-evaluation of
153
Gd decay data
V.P. Chcchcv and A.G. Egorov
V.G. Khlopin Radium Institute, 28 Shvernir avenue, 194021 Leningrad, USSR For the last ten years, work on the more precise definition of decay data of applied radionuclides has been carried out at the V.G. Khlopin Radium Institute . The results of a `"Gd decay data evaluation are presented in this report . Account has been taken of recent measurements of the emission probabilities of y and K X rays in the decay of iszGd . The new experimental data result in considerably more precise values of the `S-'Gd decay data in comparison with earlier recommended data.
1. Introduction Since 1980 the decay data of 300 applied radionuclides have been evaluated at the Khlopin Radium Institute [1-4]. Many of these evaluations, especially refs. [1,2], require revision on account of the publication of new measurement results. A good example is the evaluation of 153 Gd [1] (see also ref . [5]) . Measurements of y and K X ray emission probabilities for 153Gd have been undertaken at the Khlopin Radium Institute [6,7]; the absence to date of such data makes a re-evaluation particularly desirable . 2. Measurements of the absolute and relative emission probabilities of Y and K X rays in the decay of 153 Gd Absolute intensities of the 69.7, 97.4 and 103 .2 keV y rays 1,,9.7 = (2 .44 ± 0.13), Iy97.a = (29.0 ± 1 .5), 1y103 .2 = (21 .3 ± 1 .0) photons per 100 decays (P = 0.95) have been measured using Ge(Li), Si(Li) detectors . The specific activity of 153 Gd in the initial solution was measured using the 4-rrß(e)-y(X)-coincidence method . In the efficiency calibration procedure for the Gc(Li), Si(Li) detectors, y rays from the decays of 57Co, 1"9 Cd, 133Ba, 24 'Am were used. The intensities of Eu characteristic K X ray components IKa2 = (33 .1 ± 1 .3), IKa1 = (59 .3 ± 2 .3), IKLA - 1 = (18 .9 ± 0.8), IKP'2 = (5 .08 ± 0.21) photons per 100 decays (P = 0.95) have been measured using a Si(Li) spectrometer . The asymmetric photopeak shape and the continuous distribution of pulses corresponding to the registration of Compton scattering photons [8] were taken into consideration . In the analysis of Ka and Kßi lines their fine structure has been taken into account ; the energies and relative intensities (Ka,/ K(x 1 ), (Kß 3 /Kß,/Kß 5) given in refs. [9] and [10] respectively have been used. Elsevier Science Publishers B.V.
The preliminary measurements of the y ray and K X rays emission probabilities obtained with 4TrNaI(TI)spectrometcr and 4Tr(PCC)X,c-y coincidence equipment at the Institute of Research, Production and Application of Radioisotopes (Prague, CzechoSlovakia) confirm our results [11]. The relative emission probabilities of the most intense y rays from the decay of 153Gd have been measured in r:any works [12-201 . The results of these are in good agreement with those reported here to within the reported experimental errors. Fewer measurements of the relative intensities of weak y rays have been carried out [18,19,221: the results of such measurements are in disagreement (table 1). An intrinsic germanium detector with high resolution was used for the measurement of the y and K X ray relative intensities by Singh et al. [18]. The measurements [19] were made with a Si(Li) detector for the 3-80 keV photons, and with a HPGe detector for the y rays of energy > 50 keV . The results of the measurements [19] have been confirmed in work by Rao et al. [20], who measured also the relative emission probabilities for K X rays from the decay of 153Gd (table 5). Grigorev et al. [22] used a planar Gc(Li) detector with FWHM 500 eV at 122 keV for their measurements of the weak y rays. 3. Evaluation technique Criteria for selecting published data and the methods of data processing used in this work correspond to those described elsewhere [1-4] . These rules assume, in ordinary cases, calculation of the weighted mean -sing as weights the inverses of the squares of the author's measurement uncertainties in the form of standard deviations 00.
!! P.
-
C l ec'hel -. A . G . hgurrrl ~ / Re -c"l udfeutirm
At the same time an analysis of data consistency is done using the X -' criterion at the significance level ().()5: X -= [(Il - 1)/ ( r~21]S-< 4 -)0r Here
it
I
is the number of measurements; (1a,)
(rin1 =
is the internal error of the weighted mean accounting for weight of measurement results, where a, ± Via, are the results of measurements with uncertainties expressed as standard deviations; S=
1
a
n - 1
,=e
w' a -
fi
2'
1/12
1: M, ci, i-i
is the external error of the weighted mean accounting for spread of results, where
is the weight of the ith measurement result ; and (X = )'y 1 ~~1 is the tabulated value. When the X` criterion is fulfilled the weighted mean n --- E,'- ^a, is taken as the result of the evaluation with the associated uncertainty. (7'int
if o, ? S. ;
Here t°is the "student's" value at confidence level (1.65 . Use of the "student's" coefficient ( t, = 1 .52_ t_, = 1 .31, t 4 = 1.19 and so on) provides the necessary increase in the evaluated uncertainty when the number of measurements is small. We also use the rule that an evaluated uncertainty should not be smaller than the minimum measurement error (crmi d possible at the modern experimental level. In the cases when it is difficult to estimate the (a7m;n ), the uncertainty of the mean value is taken to be not smaller than the minimum error (Aa,)min of the experimental results n, ± Ja, reported by authors . When the X = criterion is not fulfilled we use the following possibilities for proceeding further: (a) to change the weight, (h) to take the unweighted mean, (c) to reject some values on the basis of objective or subjective reasons, (d) to adopt one of the experimental values reported by authors with an increased uncertainty of that value . In general we choose the method of changing weights adopted by the IAEA-CRP participants [21]. Sometimes however the situation makes it necessary to apply rules (b), (c) or (d).
qr l` rC1r1 decay daia
379
The rule (h) is used when inconsistent data have relative uncertainties close to each cattier. The rule (c) is used only when doubtful data have been obtained using obsolete methods and instruments or when it is necessary to choose between two discrepant seats cat measurements. The rule (d) is used when there is no alternative car when only one of the experimental values is consistent with the fatality of data can a decay scheme . In the last case the uncertainty of the evaluated quantity may be calculated as r1
(a, -1
a A )1[n(n 2 - 1)]
where a A is the adopted value.
)
4. Evaluation of the decay data of c -r"Gd -1.1. Evahiation of radiation intensities The main radiations accompanying the decay of Gd arc gamma rays. X rays and conversion electrons . Using the rules described in section 3 it is not difficult to evaluate the relative intensities of gamma rays with energies more than 68 keV . The results are presented in table l . Corresponding to them the evaluated gamma-ray emission probabilities and total y + cc intensities (per 1(l0 decays) are presented in table 2. In table 2 all the values of the intensities are normalized using the result of the absolute measurement IYy, = 29.(x5}'-C of Geidelman et al. [6]. The experimental, theoretical and evaluated values of the internal conversion coefficients (ICC) a K and a,, are shown for gamma transitions in the decay of '"Gd in table 3. The scarcity and discrepant nature of the experimental data for low energy gamma rays in the '53 Gd decay make difficult the assessment of the relative intensities of gamma-rays with energies less than 6$ keV. However we have chosen one or another experimental or calculated value of the relative intensity of low energy gamma rays using the data on conversion electrons [141. the data on transition multipolarities [161, the theoretical conversion coefficients [23"24] and transition intensity balance correlations for each level of ""-"Eu . A special problem is bound up with the large value of the 19.5 keV Y ray intensity measured in refs. [18,19] . This value is in disagreement with evaluations from conversion electron data and violates the transition intensity balance on the basis of an assumption of E2 multipole order for the transition 3/2' (103.15 keV) - 7/2 + (53 .37 keV). We therefore retain the early evaluation of the 19.5 keV Y ray int--nsity [1] obtained from conversion electron data [141 and theoretical E? L-conversion coefficients [231. This results in V. NUCLEAR DATA
384)
-ahêation of
E P Clecha ; A .Ci .
Z:
2 :: i7. rn
®r
décay data
"t ri
e
s ei Z! x = z ~ M
12
r
- rj
e :;5
Ie
oc
Me N CD
ëz c
O
'E
-Z
0
=~
-Ir Il
rl:
= Ic
r!
.d
O G.
l
i
i
i
i r-
i
i
-
1 5; ~r'
a: oses
,A
i O
- -~ e! l" - r'! = = x' = = = = r'l = c
rq
1
C
c
c~
r= . 4-
z 'a 0 -, 1 ; « = ~r' 'C r-
, i; r`~ 01 zo, :OÎ
01
u CD 2 n~ ~:~ < - c , -J
V.P. Chechev, A.G. Egoroi * / Re-evaluation of 1s-;Gd decay data
381
Table 2 Evaluated values of y ray emission probabilities (ly;) and total (y +ce)-intensities of gamma transitions data y ray
ly; [% decays] 1161 ;'
y14 y20 y21 y54 y68 y70 y75 y83 y89 y97 y103 y152 yl73
1,j +c,, [% decays] [20] `'
0.0 17(6) ` 0.0015(3) < 0 .003 0.012(3) 2.4401) 0.075(23) 0.202) 0.067(20) 2908) °' 2007) n < 0.017 0.03(3)
and experimental
0.042(5) 0.021(3) 0.0206) 0.017(2) 0.021(3) 2.49(8) 0.081(9) 0.19503) 0.063(8) 2908) 21 .7(6) 0.017(4) 0.042(8)
evaluated value (this work)
[16] a
t201 ;'
0.017(9) 0.00013(2) < 0.003 0.017(5) 0.021(3) 2.44(9) 0.081(9) 0.20303) 0.069(8) 2908) 21 .4(6) 0.0035(6) 0.041(4)
0.18013) 0.40004) < 0.03 0.020(6) 15.9(8) 0.11029) 1 .07(4) 0.37(5) 38.5(13) 56.207) < 0.017 0.04(3)
evaluated
value
(this work) 0.52(5) 0.52(7) 0.102) 0.206) 0.038(3) 16 .05) 0.13102) 0.94(5) 01X2) 37.900) 59.217) 0.019(4) 0.058(7)
0.2101) 0.43(5) < 0.014 0.21(6) 0.038(5) 15.9(6) 0.13105) 0.98(7) 0.25(3) 37.901) 58.408) 0.0038(6) 0.057(6)
`' Authors' original values of relative emission probabilities (laya =100) have been multiplied by the value 0 Authors' value: ly7(, = 2.3(1)%, lyya = 27.3(12)%, ly =19.400rc . c Calculated from conversion electrons data.
a value for the total (y + ce) intensity of the 19.8 keV transition equal to 0.43(5)% in agreement with earlier evaluations [14,20]. If we adopt the results of the 19.8 keV y ray intensity measurements [18,19] we obtain an anoma+ lously low [CC for this 3/2 + - 7/2 E2 transition . It is possible that the previously observed intense 19.8
Table 3 Internal conversion coefficients "K, y ray
y14 y20 y21 y54 y68 y 70 y75 y83 y89 y97 y103 y152 y173
Multipolarity
E1 E2 (El) M1 E1 Mi + E2 El M1+E2 M1 + E2 E1 Mi+E2 E1 M1 +E2
aK 1161
8.80(8) 0.66(1) 4.50(3) 0.62(4) 2.42(2) 2.l2(2) 0.28(3) 1.44(2) 0.079(1) 0.300(4)
atota,
keV peak arose at least in part from summing, namely as the sum of the unobserved 5.75 kcV El transition 3/2 ¢ -> 5/2 - and the known 14.(6 keV El transition 5/2- -> 7/2 {. In this case the transition intensity balance for the levels 103.18 keV and 97.43 keV is correct to within 0.5% decays, with 1,6 = I;,4 a conclusion not inconsistent with the experimental errors. However the
for y ray transitions in the decay of
1s3Gd
obtained in different works
Qctot
theory
[201
9.04(18) a 0.650) a 4.74(10) 0.76(14) 2.5308) 2.42(5) a 0.274(6) 1.47(3) 0.082(2) 0.300(6)
a
Theoretical values from ref. [24]. b Obtained by us from data on ly+ce ,
ly, UK
9.32 0.664 4.48 0.510 2.36 2.17 0.258 1.44 0.0782 0.293
8).
evaluated value (this work)
9.1(2) 0.66(2) 4.50) 0.51(1) 2.40(5) 2.17(5) 0.258(5) 1.44(3) 0.078(1) 0.300(6)
[16] 1'
[20] 1'
theory [23]
evaluated value (this work)
10.8 0.75 5.52 0.54 4.27 4.52 0.33 1 .73 0.400
11 .2 24 .0 3.86 11 .1 0.83 5.42 0.62 3.81 2.62 0.307 1.73 0.100 0.389
11 .2 3.29 x 10 .3 3.7 11 .1 0.798 5.42 0.611 3.82 2.63 0.307 1 .73 0.093 0.38
11 .2(2) 3.29(7) x 10 3 3.70) 11 .1(2) 0.80(2) 5.50) 0.62(2) 3 .84(8) 2 .63(6) 0.307(7) 1 .73(3) 0.093(2) 0.390)
cited in refs . [16,20]. V. NUCLEAR DATA
V.P. Checher, A. G. Egorot , / Re-evahiation of ts-'Gd decay data
382
We have performed an evaluation of the intensities of the K X-radiation components for the 's-'Gd decay using previous experimental data [16,20] and the results of our own recent measurements [7] (see table 5). The evaluated conversion electron intensities have been obtained on the basis of the evaluated values of ICC and I,,' . They are presented in table 6. ;
Table 4 Evaluated values of absolute intensities I(EC) of the "'Gd electron capture branches and log ft values Level energy [keV]
1(EC) [% decays]
269,73 172M 151.62 . 97 .43 83 .37 il
0.M03(3) 16 .40) 0.16(7) 42.909 37.801) 0.0508) 2.7(21)
log ft z 8.9 7.88 10.0
4.2. Evaluation of other decay characteristics of
7 .73
312 +
ô O
Co CO
t
0.0003(3) >_ 8.9 O
5/2+
151.62
7/2- --
103.18
3/2+
97.43
5/2-
83 .37
7/2+-
0
5/2+
vM N
O Ô ttj O V
CO C)
N (- CM Cm
C
172.85
153Gd 64
E
O O
7/2+ -
O C O
n
(0
Co
CD ^ M t0 p
N Ô Ô O
N
10 __
W w N .-
16 .4(6)
e
usaov`~:~.- co ~n - *__O
_t-R .
vv CD N r- CO CM O C)
0.16(7)
7.88 10 .0
Ô
~ r-
N C)
-_
Gd
The evaluated half-life of 15;Gd has been obtained using measurement results published in 1950-1972 [25-27] as well as in ref. [1]. Two sets of experiments have been devoted to measuring the decay energy Q(EC) of 153Gd . One of them involved measuring intensities of K capture to 15;Eu levels. It resulted in Q(EC) = 240 keV. The other one involved using different nuclear reactions; it resulted in Q(EC) = 485 keV. Omitting the discussion of reasons for the large discrepancy (see for example [18]), we have adopted the evaluation of Wapstra et al. [28], Q(EC) = (483 .9 f 2.3) keV, derived from analysis of nuclear masses. Additional arguments for this choice arc the evaluations in refs. [22,29]. One of these [29]
9.0
reported experimental conditions of the measurements [18,191 (the detector-source distance was 10 cm) seem to exclude the possibility of significant summing. Our experimental gamma spectrum in the 20 keV energy region does not include the 19.8 keV gamma line though the 14.06 keV line is displayed distinctly: we deduce that ly.o < 0.21-j14. Analysis of the transition intensity balance for the levels of 'S. Eu (cads to the evaluated data presente('. in table 4; the associated log ft values are also given.
269.73
tS-;
v
C) O
--42.9(19)
7.66
-37.8(ii) ~)
77.73 .73
__ -
!t' T 153E u 63 Fig. 1 . The decay scheme of 1"Gd.
-_
0 .05(18)
2.7(21)
9.0
V. P. Checher, A . G. Egorm- / Re-et -ahiation of 1S- 'Gd decay data
383
Table 5 Experimental and evaluated values of relative and absolute K K ray emission probabilities (IKX, ) in the decay of "'Od KX j
Ka, Ka t Kß' Kß2
I Kx, / 1y97
1 KX, / 1y97
IKX, [%% decays]
[171
[20]
(171 1
[20] `'
[7,8] h
evaluated value (this work)
1 .150(34) 2.06(6) 0.638(17) 0.l44(5)
1 .203(18) 2 .202(33) 0.663(12) 0.186(4)
33 .4(13) 59.7(24) 18.5(7) 4.18(18)
34 .9(11) 63 .9(20) 19.2(6) 5 .39(19)
33.1(7) 59.3(12) 18.9(4) 5.08(ll)
33.6(7) 60.4(17) 18.9(4) 5.((3)
`' Calculated by us with using ly y7 h Absolute measurements .
=
29.0(8)% decays .
Table 6 Summary of ev«Iuated values of the decay data of ts 'Gd T, 12 [d] Q(EC) [keV] Eyt [keV] 14.0640(4) 19 .8131(4) 21 .2309(8) 54 .1916(4) 68.2556(5) 69.6734(2) 75.4226(3) 83.3676(3) 89 .4865(3) 97 .4316(3) 103 .1807(3) 151 .6232(6) 166.550) 172.8541(5) KX t Kot, Ku 1 Kß 1 Kß' ce t K (y54) L (yl4) L (-y20) MNO (yt4) MNO (y20) K (y70) K (y75) K (y83) K (y89) K (y97) K (y103) L (y70) L (y75) L (y83) L (y89) L (y97) L (y103) K (y173) L (y173)
241 .6(4) 483.9(23) I,, eel . units 0.06(3) 4.5(5)x 10 -4 < 0.01 0.058(16) 0.071(11) 8 .4(2) 0 .28(3) 0.70(4) 0.24(3) 100 73.7(6) 0 .012(2) 0 .0010(10) 0 .140(14) EKX, [keV]
40.902 41 .542 46.999 48 .280 Ett, [keV] 5 .673 6.01-7 .08 11 .76-12.83 12.26-14.06 18.01-19.81 21 .154 26 .904 34 .849 40.968 48.913 54.622 61 .62-62.59 67 .37-68.44 75 .32-76.39 81 .44-82 .51 89.38-90 .45 95 .13-96 .20 124.335 164.80-165 .87
Jy t [% decays) 0 .017(9) 1N2) x 10 4 < 0.003 0.017(5) 0.021(3) 2.44(9) 0 .081(9) 0 .203(13) 0.069(8) 2908) 21 .4(6) 0.0035(6) 3(3)x 10 -4 0 .041(4) IKx, [% decays]
33A7) 60.407) 18A4) 5 .00) I,,:r [% decays] 0.15(5) 0.15(8) 0.33(4) 0.042(21) 0 .100) 11 .0(5) 0 .041(4) 0.49(3) 0.15(2) 7.5(3) 30.801) 1 .78(9) 0 .0064(7) 0 .23205) 0 .0250) 1 .110) 4.6807) 0.0120) 0.0025(3)
384
V.P. Chechet}, A.G. Egorot, / Re-evaluation of 1s.;Gd decay data
involved a third, independent method depending upon the ratio of reduced probabilities of the electron capture to the 103.18 keV and 172.85 keV levels belonging s; to the same rotational band of ' Eu: Q(EC) = 500±")° keV . This result rejects the value 240 kcV at the confidence level P = 0 .99 . The observation of the weak 166.55 keV gamma transition from the 269 .73 keV level of t 53 Eu [22] leads to the same conclusion . Using our evaluated total intensity of K X rays, K conversion coefficients and y ray emission probabilities we have also evaluated the absolute intensities of K capture to 1 s; Eu levels and obtained Q(EC)=315±s0" keV . This result is consistent with our adopted value Q(EC), see above .
5. Results of evaluation The main results of our evaluation of the decay data of ' S; Gd are shown in table 6 . Most of the y ray energy values adopted here are from the measurements with a bent crystal spectrometer [31], while some have been calculated from the decay scheme (fig. 1). The K X ray energy values have been calculated from the data of Browne and Firestone [5]. The uncertainties of all the values in table 6 are presented at the confidence level P = 0 .68 (1Q), in brackets in units of the last significant digit . The decay scheme of ' S ; Gd corresponding to the evaluated data is shown in fig . 1 . The absolute intensity of the electron capture to the ground state of 153 Eu as obtained from our data (2.7 ± 2.1)% is less than that given by former evaluations (except for that of Grigorev et al . [22]) .
References [1]
Yu.V. Kholnov, V .P. Chechev, Sh .V . Kamynov et al., Characteristics of Radiation from Radioactive Nuclides Used in the National Economy: Evaluated Data (in Russian) (Atomizdat . Moscow, 1980). [2] Yu .V . Kholnov, V.P . Chechev, Sh.V. Kamynov et al ., Evaluated Values of Nuclear Characteristics of Radioactive Nuclides Used in the National Economy (in Russian) (Energoizdat, Moscow, 1982) . [3] Yu .V. Kholnov, V .P . Chechev, Sh.V. Kamynov and N .K . Kuzmenko, Evaluated Values of Nuclear Characteristics of Radioactive Nuclides Used in Technics and Medicine (in Russian) (Energoatomizdat, Moscow, 1984) . [4] V .P . Chechev, N .K. Kuzmenko, V.O. Sergeev and K .P. Artamonova, Evaluated Values of Nuclear Characteristics of Transuranium Nuclides (in Russian) (Energoatomizdat, Moscow, 1988).
[5] E. Browne and R.B . Firestone, Table of Radioactive Isotopes, ed . V .S. Shirley (Wiley, New York, 1986) . [6] A.M . Geidelman, A .G. Egorov, Yu .S . Egorov et al ., Proc . 40th Conf. on Nuclear Spectroscopy and Atomic Nucleus Structure, Leningrad, 1990 (in Russian) (LO Nauka, Leningrad, 1990) p . 485 . [7] V.P . Chechev, Proc. 41st Conf. Nuclear Spectroscopy and Atomic Nucleus Structure, Minsk, 1991 (in Russian) (LO Nauka, Leningrad, 1991) p. 505 . [8] A .G . Egorov, Yu .S. Egorov, V.G . Nedovesov, S .A . Sidorenko, Yu .L . Chereshkevich, G .E . Shchukin and K.P . Yakovlev (in Russian) Izmeritelnaya Technica 2 (1990) 47 . [9] C .M . Lederer and V.S. Shirley, Tables of Isotopes (Wiley, New York, 1978) . [10] S .I . Salem, S.L. Panossian and R.A. Krause, ADNDT 14 (1974) 91 . [11] P. Dryak, J . Plch, P . Kovar and R . Vasa, Measuring the yield of ' S 'Gd gamma photons, Appl . Radiat . Isot. (1991) to be published . [12] P . Alexander, Phys. Rev . 134B (1964) 449 . [13] D.T. Ewan and A.J. Tavendale, Canad . J . Phys . 42 (1964) 2286 . 1141 P. Boyer et al., Nucl . Phys. A99 (1967) 213 . [15] R.L. Heath, Gamma-ray spectrum catalogue, ANCR1000-2, vol . 2 (1974). [16] V .A. Sergienko and V.M. Lebedev (in Russian), Izv . Akad. Nauk SSSR, Ser . Fiz. 38 (1974) 802 . [17] Ts. Vylov, B .P . Osipenko and V .G . Chumin (in Russian), in : Elementary Particles and Fields . 6 (1978) 1350. [18] K. Singh, B .S . Grewal and H .S . Sahota, J . Phys. G11(3) (1985) 399 . [19] S .S . Rao, K .B . Rao, V.S. Rao and H .C. Padhi, Indian J . Phys. A62(5) (1988) 560 . [20] S .S . Rao, K.B. Rao, V .S . Rao and H .C . Padhi, J . Phys . G14 (1988) 1259 . [21] Decay Data of Transactinium Nuclides, Technical Reports Series No . 261 (IAEA, Vienna, 1986) ; Gamma-Ray Standards for Detector Calibration, INDC(NDS)-196/GE (1987) . [22] E.P . Grigorev, V .O . Sergeev, Ya. Beker and M. El-Khosht (in Russian), Izv . Akad. Nauk SSSR, Ser . Fiz. 45 (1981) 795 . [23] R .S . Hager and E.C . Seltzer, Nucl . Data Tables A4(1,2) (1968) 1 . [24] F. Rösel, H .M. Fries, K. Alder and H.C. Pauli, Atomic Data and Nucl . Data Tables 21 (1978) 292. [25] R .E . Hein and A .F . Voigt, Phys . Rev. 79 (1950) 783 . [26] D .C. Hoffman, JINC 25 (1963) 1196 . [27] J .F. Emery et al ., Nucl . Sci . Eng . 48 (1972) 319 . [281 A .H . Wapstra and G . Audi, Nucl . Phys. A432 (1985) 1 . [29] R .-D . von Dincklage, Australian J . Phys . . .8(1198511671 3 [30] W . Bambynek, in : X-84, X-ray and Inner Shell Processes in Atoms, Molecules and Solids, ed . A . Meisel (Leipzig . 1984) . [31] G .L . Borchert, Z. Naturforsch . 31A (1976) 387 .