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Internal conversion of E2 transitions in 152Sm and 154Gd
Nuclear Physics A96 (1967) 33--41; (~) North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher
INTERNAL CONVERSION OF E2 TRANSITIONS IN 152Sm AND 154Gd L. HOLMBERG, V. STEF/~NSSON and B.-G. PETTERSSON Institute of Physics, University of Stockholm, Stockholm, Sweden R e c e i v e d 19 December 1966 Abstract: In a recent investigation the K-conversion electron particle parameters for three E2 transi-
tions in the deformed nuclei 152Sm and 154Gd were found to be anomalous; for the 245 keV transition in 152Sm the reported deviation from the theoretical value was 394-9 %. A n e w measurement has been carried out in this work. For the transitions of 122 keV in x52Sm and of 123 keV in l~*Gd the values found, expressed in units of finite-size corrected theoretical values, are b~(122)/b2°(122) = 0.994-0.04, b2(123)/b~°(123) = 0.994-0.03. For the 245 keV transition, which is of low intensity, a fairly high accuracy in the value obtained for the particle parameter was made possible by use o f the b4 method. From the geometrical relation between b~ and b4, we obtain
b~(245)/b~O(245) : 1.02-4-0.04. It is shown that if only dynamic contributions to the tabulated values are assumed, this result corresponds to a value for the conversion coefficient of CtK(245)/CtK°(245) = 1.014-0.015.
E
RADIOACTIVITY 152Eu [from mEu(n, ~,)], l~4Eu [from 158Eu(n, y)]; measured 7,ce (0). l~Sm, 15'Gd deduced K-conversion electron particle parameters, co. Enriched targets.
1. Introduction In several investigations of the K-conversion process of E2 transitions in deformed nuclei, deviations from theoretical values have been reported. Compilations of experimental conversion coefficients indicated correlations between these deviations and the nuclear deformation 1) or the N/Z ratio z). However, these trends have not been confirmed by more recent experiments 3). Three E2 transitions in the deformed nuclei lS2Sm and lS4Gd have been investigated not only by means of conversion coefficient measurements but also by determinations of K-conversion electron particle parameters. Whereas no, or only moderate, discrepancies have been reported for the conversion coefficients 4), pronounced deviations in the values for the particle parameters were found 5). Dynamic effects due to the nuclear penetration of orbital electrons have been observed for retarded dipole transitions 6). The E2 transitions mentioned, however, connect rotational states and are considerably enhanced over single-particle values. According to the 33
34
L. HOLMBEROet al.
present point of view concerning the role of nuclear dynamics in internal conversion, penetration effects are not expected in these transitions 7). A contribution of static effects to the conversion process, which is not considered in existing tabulations, is due to the deviation from spherical symmetry of the nuclear Coulomb field caused by the electric quadrupole moment. Such an effect should, of course, be correlated to the degree of deformation of the nucleus. Thus far no calculation of the quadrupole effect has been performed. An estimate by Church and Weneser 8) indicates that the influence on the conversion coefficient should be, at most, of the order of 1 ~o. To clarify the nature of the E2 internal conversion process, precise measurements of deviations from present theoretical values are obviously needed. Knowledge of both the conversion coefficient and the particle parameter is preferable in order to determine the two effective conversion matrix dements. The nuclei lS2Sm and lS4Gd are deformed and suitable for an investigation of the static quadrupole effect. For the two transitions of energy 122 keV and 123 keV the particle parameter is normally close to its limiting value of 2 and, therefore, is not very sensitive to small contributions to the conversion process. For the 245 keV transition, however, the particle parameter is a sensitive tool. The value for b2(245), found by Hamilton et aL, deviates from the theoretical value by 39_ 9 ~o. In this experiment the electron particle parameters for the three transitions mentioned were obtained, to an accuracy of 3-4 ~o. The analysis has been carried out to give the static contributions to the most sensitive matrix element R+ 2, or, for the case of dynamic effects, to give the effective values of the two radial matrix elements. 2. Apparatus and source preparation
In the electron-gamma angular correlations the electrons were focussed in a magnetic lens spectrometer of the Gerholm type 9). This spectrometer is provided with an electron baffle system optimized for the determination of the second-order terms in the Legendre expansion of the angular correlation function. In the experiment to determine the fourth-order terms, this baffle system was replaced by a modified "A,-baffle" system 10). Necessary corrections to the measured angular correlations caused by the finite take-off angle of the spectrometer were determined in singlecounting runs with the P2 and/'4 baffles 9,1 o). Rotational asymmetries, which could cause deviations from the values f2 a n d f4 determined in this way, are negligible, as is shown elsewhere 11). The gamma radiation was detected by a 5.1 cm x 5.1 cm NaI(T1) scintillation crystal coupled to a Philips 56 AVP photomultiplier tube. The gamma detector was operated automatically between four different positions on the angular correlation table. The coincident gamma spectrum was registered in a multi-channel analyser with a split memory (Intertechnique SA 40). For each position, a 100-channel part of the memory was used. In the gamma-gamma angular correlation experiments, a second gamma detector was mounted on the angular correlation table. The gamma radiation, corresponding
E~ TRANSIIIONSIN 152SmAND 154Gd
35
to the same transition as the conversion electrons formerly focussed in the magnetic lens, was selected in a single-channel analyser. For the source preparation, 99.9 ~o pure europium oxide was isotope-separated at Chalmer's Technical University, Gothenburg. The ~51Eu and 153Eu isotopes were collected on aluminium backings of thickness 1.0 mg/cm2. The Eu ions were prevented from entering the backing material by the application of a decelerating voltage and reached the backing with a final energy of 0.2 keV. Active ~52Eu and X54Eu sources were obtained by a 14 d neutron irradiation of the isotope-separated samples in a flux of 1.2 x 101¢ n/cm 2 • sec.
3. Measurements of b2(122) and b2(123) To determine the electron particle parameter b 2 for the 122 keV transition in lS2Sm and for the 123 keV transition in 154Gd the (14097-122K, 7) and (1276y- 123K, ~) angular correlations were measured. The first component in the coincidence combination has not to be pure in these measurements. However, in the second component, contributions to the accepted parts of the electron or gamma spectra other than those belonging to the 122 keV or 123 keV transitions had to be eliminated. Further, the selected portions of the coincident gamma spectra should be of reasonably high intensity and have at least one large correlation coefficient, A2(7~ ) o r A4(77 ). Attenuations due to static and time-dependent interactions should cancel in our determinations of the particle parameters. Most of the statistics for the gamma-electron cascades was collected with thin sources. The attenuation due to scattering of TABLE 1 The experimental results for the 122 keV transition in lssSm and the 123 keV transition in 154Gd
Source
c2A2(yK)" 102 c~ A2(TK)" 102 A4()'K). 102 As(7~,)" 102 A,(77). 102 b2
&0,K)
b2(average) b2°
122 keV (mSm)
123 keV (154Gd)
1
2
1
21.8 4-0.3 0.76 4- 0.06 28.6 4-2.4 2.1 4- 2.0 14.4 +0.5 1.1 4-0.7
27.2 4-0.7 +2.0o 1.00_0.01 27.2 4-0.7 1.2 4-2.5
14.5 4-0.2 0.904-0.03 16.1 4-0.6 -- 1.5 -4-1.0 8.7 4-0.3 0.0 d_0.4
16.2 4-0.2 0.98±0.01 16.5 i 0 . 3 2.1 ±0.9
1.984-0.18
1.884-0.08
1.854-0.10
1.904-0.07
1.90 4- 0.07 1.91
2
1.88 4- 0.06 1.90
The theoretical values of the particle parameters are denoted by b2°. The correlation coe/ficients are corrected for the finite solid angle of the detectors. The factors c2 correcting for the attenuation caused by the source thickness were obtained from the nomogram by Gimmi 12). From the ratio ca(1)A20,K; 1)/A2(TK; 2) the thickness of the thick sources, labelled 1, may be determined, cf. table 2.
36
L. HOLMBERGet aL
the electrons in the source material should be restricted to a few per cent for these sources. Uncertainties in the theory for source scattering would then influence our results by values much smaller than the statistical errors. For all sources the thickness could be estimated from a measurement of the source area, as the amount of Eu deposit was known. The scattering correction factors were obtained from the nomogram by Gimmi 12), which is based on the theory by Frankel la). The correlation functions were evaluated from the coincidence rates measured at the three angles 95 ° (265°), 135 ° and 180 ° with respect to the spectrometer axis. The coincidence spectra were normalized on the single counting rates in the photopeaks of 1409 keV and 1276 keV, respectively. The accidental coincidences were measured by inserting a 100 nsec delay in one of the coincidence channels. The factors f2 and f4 correcting for the finite take-off angle of the spectrometer were determined as described in the foregoing. The correction factors for the gamma detectors were taken from Yates 1,). The experimental values of the coefficients in the Legendre expansion of the correlation functions are given in table 1. The particle parameter b2 is obtained from the ratio A2(vK)/A2(?7 ).
4. Measurement of b2(245) and b4(245) To determine the particle parameter b 2 for the 245 keV transition in 1528m, the method described in refs. lo, 15) was used. As the (8687-2457) correlation has a fairly large A 4 coefficient and the 868 keV gamma line is of high intensity in the coincidence spectrum, it was possible to determine the fourth-order electron particle parameter b,. As is seen from the geometrical relation given by Biedenharn and Rose 16) b2 = 1 . 4 - --,b* 2.5
(1)
the errors in the determination of b, are reduced in an evaluation of b 2. An accurate value of b2 may therefore be calculated from an experimental value of b,. The angular correlation functions for the (8687-245K, ~) cascades were evaluated according to the procedure described in sect. 3. Only for the determination of the scattering correction factors was a special technique used. To obtain a high coincidence rate, the thicker of the two sources of 152Eu (source 1) was used. For the correlation (14097-122K) source 1 and, the thin, source 2 were used. The correction factor c2(122K; 2) for source 2 was estimated as .1. na+o.oo . . . o.ol. From the ratio c2(1)A2(7-122K; 1)/A2(7-122K; 2), the correction factor c2(122K; 1) is obtained within narrow limits of error. The nomogram 12) then gives the correction factors c2(245K; 1) and c4(245K; 1) for the conversion electrons of the 245 keV transition.
E2 TRANSITIONSIN 152SinAND 154Gd
37
With the coincidence combination chosen, the conversion electrons appear as the second member of the cascade. No after effects, due to the formation of holes in the electron shells, could then influence the correlation function. In this case, neither could the difference in recoil energy at gamma and electron emission cause different attenuations. The experimental values of the coefficients A2 and A 4 are given in table 2. The particle parameter b4 is found from the ratio A4(TK)/A,~(??), the parameter b2 is determined directly from A2(~K)/A2(TT ) and calculated from b4 by use of eq. (1). TABLE 2 Experimental results for the 245 keV transition in 152Sm k=2 ckAk(7K). 10~ ck A~0,K). 102 A~(7,y)- 102 Ak(yK) b t - A~(~/)
bl(calc, from b4) bz °
k=4
21.7 4-0.7 0.944-0.01 23.1 4-0.8 13.6 4-1.3
11.3 4-2.0 0.8754-0.02 12.9 4-2.3 --14.3 4-1.5
1.704-0.17
--0.90 4-0.18
1.764-0.07 1.73
The factors e~ correcting for the source thickness are obtained from Gimmi's nomogram and the determination o f the thickness o f source 1 described at table 1.
5. Analysis of the conversion processes From the experimental results the difference between the effective and the tabulated radial conversion matrix elements may be determined. Rose's tabulation 17) gives the matrix elements in the point nucleus approximation. The values given by Band et aL is) are calculated with consideration to the finite size of the nucleus but are restricted to Z-values larger than 81. The finite-size correction for the Z-region of interest was estimated in the following way. The two tables were compared for 80 < Z < 90. The values for the matrix element R_ 3 were found to be the same within 0.5 ~o. For R_3, therefore, the Rose values are used. The difference in the R+2 matrix elements between the two tables was extrapolated from the high-Z region to Z = 62 and Z = 64. The matrix elements corrected for the finite size of the nucleus are in the following designated R °_3 and R ° 2. The formalism for the analysis of dynamic contributions to the conversion process has been worked out by Green and Rose 19). The dynamic increments were found to be imaginary, and a relation was given connecting the penetration parameters ~+ 2 and 27_a. From the particle parameters, unique values of the penetration parameters may thus be obtained provided that the static matrix elements are known.
.,oo Z-3
I +300
I *200
Fig. 1. The K-conversion coefficient and the particle parameter for the 122 keV transition and the 123 keV transition as functions of the penetration parameter 27-s deft_ned by Green and Rose xt). The lowenergy approximation 27s = 0.362~_a has been used.
070
/
\~/"
.2oo _1~//o
o.sob2~ ._~_
o.~o
\
_,oo,~
\
/
/ (~K
1.1o
\
// /
,.2o~,
/ \
\ \
-100
\
-200
\
I
\
I
\
b~
b2
I
,200
I
I I
,300
Z_3
Fig. 2. The K-conversion coefficient and particle parameter for the 245 keV transition as functions of the penetration parameter 27_3 defined by Green and Rose xD). The low-energy approximation 2~2 = 0.3827_s has been used.
0 70
080
0.90
1.10
~.20 -
\
O0
E2 TRANSITIONSIN z6~SmAND 154Gd
39
Figs. 1 and 2 show the conversion coefficient and the particle parameter versus ~_ 3. From the figures the consistency of pairs of experimental values for these two quantities may be tested. Table 3 gives experimentally determined conversion coefficients and the values deduced from measured particle parameters. The table shows that no TABLE 3 A comparison between the conversion coefficients deduced from experimental b= values under the assumption of dynamic contributions and experimental ctK values Hamilton et al. ~) =K(ded.)/CtK°
b=/bz °
122 keV ("=Sm) 245 keV ("=Sin) 123 keV ("4Gd)
0.874-0.09 0.614-0.09 0.744-0.04
0.92--0.96 ~1.27 0.97--1.06
Experimental conv.coeff. *)
Present work bz/b= °
~K(ded.)/CtK °
~K(exp.)/~K °
0.99t0.04 1.024-0.04 0.994-0.03
0.94-- 1.08 1.00--1.03 0.95--1.06
1.074-0.06 1.01±0.11 0.974-0.04
1.20 -
/ 1.10 -
/
/
/
1.00
-3
-2
2
3
4
~r~Inn R.z
0.90 -
b2
0.80-
0.70Fig. 3. The K-conversion coefficient and particle parameter for the 245 keV transition as functions o f the imaginary part of the matrix element R=, in fact of ~/~ Im R=. This matrix element should be most easily affected by short-range effects and the matrix element R_s is given its normal value R°_a.
40
L. HOLMBERGet aL
consistent interpretation of the anomalous b2 values obtained by Hamilton e t al. is possible in terms of dynamic effects. Static effects due to the quadrnpole distortion of the nuclear Coulomb field are not included in the tabulated matrix elements. An estimate by Church and Weneser s) indicates that the conversion coefficient should not be affected by more than 1 ~o. N o estimate of the influence on the different matrix elements by this effect has been published. However, due to the short range of the quadrupole field, we conclude that the finite-size sensitive element R+2 would be most affected. For E2 transitions of 200-500 keV in nuclei in the rare-earth region, the particle parameter is a valuable tool for the investigation of small effects in the internal conversion process. I f the influence on the conversion coefficient is restricted to 1 ~o, the normal value for R_ 3 may be used in the calculation of the particle parameter. The particle parameter is therefore a measure of the matrix element R+ 2. Fig. 3 shows b2 as a function of R+2 for the 245 keV transition. For the conversion process of the three E2 transitions investigated, no discrepancies between experimental and tabulated values have been found in this work. N o influence of dynamic effects is expected for these enhanced transitions and also the static quadrupole effects seem to be too small to be determined with the accuracy obtained so far. O f the transitions investigated the 245 keV transition in 1~2Sm is the most suitable for conversion process studies by measurement of the particle parameter. The fairly high accuracy obtained in the value for this particle parameter was made possible by use of the b 4 method lo, 15). This technique is applicable to many similar transitions and is adequate to discover rather small contributions to the conversion process, which are unaccounted for in the tabulated matrix elements. We wish to express our gratitude to Laborator T. R. Gerholm for the excellent research facilities he put at our disposal and for his stimulating interest in this work. Our thanks are due to Docent O. Alm6n for the isotope separation of the source material. One of us (V.S.) has received a grant from the Icelandic Science Foundation. This work has been sponsored by the Swedish Atomic Research Council.
References 1) 2) 3) 4)
B. N. Subba Rao, Nuovo Cim. 17 (1960) 189 E. M. Bernstein, Phys. Rev. Lett. 8 (1962) 100 Internal conversion processes, ed. by J. H. Hamilton (Academic Press, New York, 1966) I. F. W. Jansen et aL, R. J. Herickhoff et al., ibid; R. S. Dingus, W. L. Talbert Jr. andM. G. Stewart, Nuclear Physics 83 (1966) 545 5) J. H. Hamilton, E. F. Zganjar, T. M. George and W. H. Hibbits, Phys. Rex,. Lett. 14 (1965) 567 6) T. R. Gerholm and B.-G. Pettersson, in Alpha-, beta- and gamma-ray spectroscopy, ed. by K. Siegbahn (North-Holland Publ. Co., Amsterdam, 1965) 7) M. E. Rose, ibid.
E2 TRANSITIONS IN 152Sm AND 154Gd
8) 9) 10) 11) 12) 13) 14) 15)
41
E. L. Church and J, Weneser, Ann. Rev. Nucl. Sci. 10 (1960) 193 T. R. Gerholm, R. Othaz and M. S. E1-Nesr, Ark. Fys. 21 (1962) 253 B.-G. Pettersson, L. Holmberg and T. R. Gerholm, Nuclear Physics 65 (1965) 454 L. Holmberg, B.-G. Pettersson and T. R. Gerholm, to be published F. Gimmi, E. Heer and P. Scherrer, Helv. Phys. Acta 29 (1956) 147 S. Frankel, Phys. Rev. 83 (1951) 673 M. J. L. Yates, in Alpha-, beta- and gamma-ray spectroscopy, op. cit. B.-G. Pettersson and L. Holmberg, in Role of atomic electrons in nuclear transformations, Proc. Int. Conf., Warsaw, (1963) 16) L. C. Biedenharn and M. E. Rose, Revs. Mod. Phys. 2,5 (1953) 729 17) M. E. Rose, Internal conversion coefficients (North-Holland Publ. Co., Amsterdam, 1958) 18) I. M. Band, M. A. Listengarten and L. A. Sliv, in Alpha-, beta- and gamma-ray spectroscopy, op. cit.
19) T. A. Green and M. E. Rose, Phys. Rev. 110 (1958) 105
INTERNAL CONVERSION OF E2 TRANSITIONS IN 152Sm AND 154Gd L. HOLMBERG, V. STEF/~NSSON and B.-G. PETTERSSON Institute of Physics, University of Stockholm, Stockholm, Sweden R e c e i v e d 19 December 1966 Abstract: In a recent investigation the K-conversion electron particle parameters for three E2 transi-
tions in the deformed nuclei 152Sm and 154Gd were found to be anomalous; for the 245 keV transition in 152Sm the reported deviation from the theoretical value was 394-9 %. A n e w measurement has been carried out in this work. For the transitions of 122 keV in x52Sm and of 123 keV in l~*Gd the values found, expressed in units of finite-size corrected theoretical values, are b~(122)/b2°(122) = 0.994-0.04, b2(123)/b~°(123) = 0.994-0.03. For the 245 keV transition, which is of low intensity, a fairly high accuracy in the value obtained for the particle parameter was made possible by use o f the b4 method. From the geometrical relation between b~ and b4, we obtain
b~(245)/b~O(245) : 1.02-4-0.04. It is shown that if only dynamic contributions to the tabulated values are assumed, this result corresponds to a value for the conversion coefficient of CtK(245)/CtK°(245) = 1.014-0.015.
E
RADIOACTIVITY 152Eu [from mEu(n, ~,)], l~4Eu [from 158Eu(n, y)]; measured 7,ce (0). l~Sm, 15'Gd deduced K-conversion electron particle parameters, co. Enriched targets.
1. Introduction In several investigations of the K-conversion process of E2 transitions in deformed nuclei, deviations from theoretical values have been reported. Compilations of experimental conversion coefficients indicated correlations between these deviations and the nuclear deformation 1) or the N/Z ratio z). However, these trends have not been confirmed by more recent experiments 3). Three E2 transitions in the deformed nuclei lS2Sm and lS4Gd have been investigated not only by means of conversion coefficient measurements but also by determinations of K-conversion electron particle parameters. Whereas no, or only moderate, discrepancies have been reported for the conversion coefficients 4), pronounced deviations in the values for the particle parameters were found 5). Dynamic effects due to the nuclear penetration of orbital electrons have been observed for retarded dipole transitions 6). The E2 transitions mentioned, however, connect rotational states and are considerably enhanced over single-particle values. According to the 33
34
L. HOLMBEROet al.
present point of view concerning the role of nuclear dynamics in internal conversion, penetration effects are not expected in these transitions 7). A contribution of static effects to the conversion process, which is not considered in existing tabulations, is due to the deviation from spherical symmetry of the nuclear Coulomb field caused by the electric quadrupole moment. Such an effect should, of course, be correlated to the degree of deformation of the nucleus. Thus far no calculation of the quadrupole effect has been performed. An estimate by Church and Weneser 8) indicates that the influence on the conversion coefficient should be, at most, of the order of 1 ~o. To clarify the nature of the E2 internal conversion process, precise measurements of deviations from present theoretical values are obviously needed. Knowledge of both the conversion coefficient and the particle parameter is preferable in order to determine the two effective conversion matrix dements. The nuclei lS2Sm and lS4Gd are deformed and suitable for an investigation of the static quadrupole effect. For the two transitions of energy 122 keV and 123 keV the particle parameter is normally close to its limiting value of 2 and, therefore, is not very sensitive to small contributions to the conversion process. For the 245 keV transition, however, the particle parameter is a sensitive tool. The value for b2(245), found by Hamilton et aL, deviates from the theoretical value by 39_ 9 ~o. In this experiment the electron particle parameters for the three transitions mentioned were obtained, to an accuracy of 3-4 ~o. The analysis has been carried out to give the static contributions to the most sensitive matrix element R+ 2, or, for the case of dynamic effects, to give the effective values of the two radial matrix elements. 2. Apparatus and source preparation
In the electron-gamma angular correlations the electrons were focussed in a magnetic lens spectrometer of the Gerholm type 9). This spectrometer is provided with an electron baffle system optimized for the determination of the second-order terms in the Legendre expansion of the angular correlation function. In the experiment to determine the fourth-order terms, this baffle system was replaced by a modified "A,-baffle" system 10). Necessary corrections to the measured angular correlations caused by the finite take-off angle of the spectrometer were determined in singlecounting runs with the P2 and/'4 baffles 9,1 o). Rotational asymmetries, which could cause deviations from the values f2 a n d f4 determined in this way, are negligible, as is shown elsewhere 11). The gamma radiation was detected by a 5.1 cm x 5.1 cm NaI(T1) scintillation crystal coupled to a Philips 56 AVP photomultiplier tube. The gamma detector was operated automatically between four different positions on the angular correlation table. The coincident gamma spectrum was registered in a multi-channel analyser with a split memory (Intertechnique SA 40). For each position, a 100-channel part of the memory was used. In the gamma-gamma angular correlation experiments, a second gamma detector was mounted on the angular correlation table. The gamma radiation, corresponding
E~ TRANSIIIONSIN 152SmAND 154Gd
35
to the same transition as the conversion electrons formerly focussed in the magnetic lens, was selected in a single-channel analyser. For the source preparation, 99.9 ~o pure europium oxide was isotope-separated at Chalmer's Technical University, Gothenburg. The ~51Eu and 153Eu isotopes were collected on aluminium backings of thickness 1.0 mg/cm2. The Eu ions were prevented from entering the backing material by the application of a decelerating voltage and reached the backing with a final energy of 0.2 keV. Active ~52Eu and X54Eu sources were obtained by a 14 d neutron irradiation of the isotope-separated samples in a flux of 1.2 x 101¢ n/cm 2 • sec.
3. Measurements of b2(122) and b2(123) To determine the electron particle parameter b 2 for the 122 keV transition in lS2Sm and for the 123 keV transition in 154Gd the (14097-122K, 7) and (1276y- 123K, ~) angular correlations were measured. The first component in the coincidence combination has not to be pure in these measurements. However, in the second component, contributions to the accepted parts of the electron or gamma spectra other than those belonging to the 122 keV or 123 keV transitions had to be eliminated. Further, the selected portions of the coincident gamma spectra should be of reasonably high intensity and have at least one large correlation coefficient, A2(7~ ) o r A4(77 ). Attenuations due to static and time-dependent interactions should cancel in our determinations of the particle parameters. Most of the statistics for the gamma-electron cascades was collected with thin sources. The attenuation due to scattering of TABLE 1 The experimental results for the 122 keV transition in lssSm and the 123 keV transition in 154Gd
Source
c2A2(yK)" 102 c~ A2(TK)" 102 A4()'K). 102 As(7~,)" 102 A,(77). 102 b2
&0,K)
b2(average) b2°
122 keV (mSm)
123 keV (154Gd)
1
2
1
21.8 4-0.3 0.76 4- 0.06 28.6 4-2.4 2.1 4- 2.0 14.4 +0.5 1.1 4-0.7
27.2 4-0.7 +2.0o 1.00_0.01 27.2 4-0.7 1.2 4-2.5
14.5 4-0.2 0.904-0.03 16.1 4-0.6 -- 1.5 -4-1.0 8.7 4-0.3 0.0 d_0.4
16.2 4-0.2 0.98±0.01 16.5 i 0 . 3 2.1 ±0.9
1.984-0.18
1.884-0.08
1.854-0.10
1.904-0.07
1.90 4- 0.07 1.91
2
1.88 4- 0.06 1.90
The theoretical values of the particle parameters are denoted by b2°. The correlation coe/ficients are corrected for the finite solid angle of the detectors. The factors c2 correcting for the attenuation caused by the source thickness were obtained from the nomogram by Gimmi 12). From the ratio ca(1)A20,K; 1)/A2(TK; 2) the thickness of the thick sources, labelled 1, may be determined, cf. table 2.
36
L. HOLMBERGet aL
the electrons in the source material should be restricted to a few per cent for these sources. Uncertainties in the theory for source scattering would then influence our results by values much smaller than the statistical errors. For all sources the thickness could be estimated from a measurement of the source area, as the amount of Eu deposit was known. The scattering correction factors were obtained from the nomogram by Gimmi 12), which is based on the theory by Frankel la). The correlation functions were evaluated from the coincidence rates measured at the three angles 95 ° (265°), 135 ° and 180 ° with respect to the spectrometer axis. The coincidence spectra were normalized on the single counting rates in the photopeaks of 1409 keV and 1276 keV, respectively. The accidental coincidences were measured by inserting a 100 nsec delay in one of the coincidence channels. The factors f2 and f4 correcting for the finite take-off angle of the spectrometer were determined as described in the foregoing. The correction factors for the gamma detectors were taken from Yates 1,). The experimental values of the coefficients in the Legendre expansion of the correlation functions are given in table 1. The particle parameter b2 is obtained from the ratio A2(vK)/A2(?7 ).
4. Measurement of b2(245) and b4(245) To determine the particle parameter b 2 for the 245 keV transition in 1528m, the method described in refs. lo, 15) was used. As the (8687-2457) correlation has a fairly large A 4 coefficient and the 868 keV gamma line is of high intensity in the coincidence spectrum, it was possible to determine the fourth-order electron particle parameter b,. As is seen from the geometrical relation given by Biedenharn and Rose 16) b2 = 1 . 4 - --,b* 2.5
(1)
the errors in the determination of b, are reduced in an evaluation of b 2. An accurate value of b2 may therefore be calculated from an experimental value of b,. The angular correlation functions for the (8687-245K, ~) cascades were evaluated according to the procedure described in sect. 3. Only for the determination of the scattering correction factors was a special technique used. To obtain a high coincidence rate, the thicker of the two sources of 152Eu (source 1) was used. For the correlation (14097-122K) source 1 and, the thin, source 2 were used. The correction factor c2(122K; 2) for source 2 was estimated as .1. na+o.oo . . . o.ol. From the ratio c2(1)A2(7-122K; 1)/A2(7-122K; 2), the correction factor c2(122K; 1) is obtained within narrow limits of error. The nomogram 12) then gives the correction factors c2(245K; 1) and c4(245K; 1) for the conversion electrons of the 245 keV transition.
E2 TRANSITIONSIN 152SinAND 154Gd
37
With the coincidence combination chosen, the conversion electrons appear as the second member of the cascade. No after effects, due to the formation of holes in the electron shells, could then influence the correlation function. In this case, neither could the difference in recoil energy at gamma and electron emission cause different attenuations. The experimental values of the coefficients A2 and A 4 are given in table 2. The particle parameter b4 is found from the ratio A4(TK)/A,~(??), the parameter b2 is determined directly from A2(~K)/A2(TT ) and calculated from b4 by use of eq. (1). TABLE 2 Experimental results for the 245 keV transition in 152Sm k=2 ckAk(7K). 10~ ck A~0,K). 102 A~(7,y)- 102 Ak(yK) b t - A~(~/)
bl(calc, from b4) bz °
k=4
21.7 4-0.7 0.944-0.01 23.1 4-0.8 13.6 4-1.3
11.3 4-2.0 0.8754-0.02 12.9 4-2.3 --14.3 4-1.5
1.704-0.17
--0.90 4-0.18
1.764-0.07 1.73
The factors e~ correcting for the source thickness are obtained from Gimmi's nomogram and the determination o f the thickness o f source 1 described at table 1.
5. Analysis of the conversion processes From the experimental results the difference between the effective and the tabulated radial conversion matrix elements may be determined. Rose's tabulation 17) gives the matrix elements in the point nucleus approximation. The values given by Band et aL is) are calculated with consideration to the finite size of the nucleus but are restricted to Z-values larger than 81. The finite-size correction for the Z-region of interest was estimated in the following way. The two tables were compared for 80 < Z < 90. The values for the matrix element R_ 3 were found to be the same within 0.5 ~o. For R_3, therefore, the Rose values are used. The difference in the R+2 matrix elements between the two tables was extrapolated from the high-Z region to Z = 62 and Z = 64. The matrix elements corrected for the finite size of the nucleus are in the following designated R °_3 and R ° 2. The formalism for the analysis of dynamic contributions to the conversion process has been worked out by Green and Rose 19). The dynamic increments were found to be imaginary, and a relation was given connecting the penetration parameters ~+ 2 and 27_a. From the particle parameters, unique values of the penetration parameters may thus be obtained provided that the static matrix elements are known.
.,oo Z-3
I +300
I *200
Fig. 1. The K-conversion coefficient and the particle parameter for the 122 keV transition and the 123 keV transition as functions of the penetration parameter 27-s deft_ned by Green and Rose xt). The lowenergy approximation 27s = 0.362~_a has been used.
070
/
\~/"
.2oo _1~//o
o.sob2~ ._~_
o.~o
\
_,oo,~
\
/
/ (~K
1.1o
\
// /
,.2o~,
/ \
\ \
-100
\
-200
\
I
\
I
\
b~
b2
I
,200
I
I I
,300
Z_3
Fig. 2. The K-conversion coefficient and particle parameter for the 245 keV transition as functions of the penetration parameter 27_3 defined by Green and Rose xD). The low-energy approximation 2~2 = 0.3827_s has been used.
0 70
080
0.90
1.10
~.20 -
\
O0
E2 TRANSITIONSIN z6~SmAND 154Gd
39
Figs. 1 and 2 show the conversion coefficient and the particle parameter versus ~_ 3. From the figures the consistency of pairs of experimental values for these two quantities may be tested. Table 3 gives experimentally determined conversion coefficients and the values deduced from measured particle parameters. The table shows that no TABLE 3 A comparison between the conversion coefficients deduced from experimental b= values under the assumption of dynamic contributions and experimental ctK values Hamilton et al. ~) =K(ded.)/CtK°
b=/bz °
122 keV ("=Sm) 245 keV ("=Sin) 123 keV ("4Gd)
0.874-0.09 0.614-0.09 0.744-0.04
0.92--0.96 ~1.27 0.97--1.06
Experimental conv.coeff. *)
Present work bz/b= °
~K(ded.)/CtK °
~K(exp.)/~K °
0.99t0.04 1.024-0.04 0.994-0.03
0.94-- 1.08 1.00--1.03 0.95--1.06
1.074-0.06 1.01±0.11 0.974-0.04
1.20 -
/ 1.10 -
/
/
/
1.00
-3
-2
2
3
4
~r~Inn R.z
0.90 -
b2
0.80-
0.70Fig. 3. The K-conversion coefficient and particle parameter for the 245 keV transition as functions o f the imaginary part of the matrix element R=, in fact of ~/~ Im R=. This matrix element should be most easily affected by short-range effects and the matrix element R_s is given its normal value R°_a.
40
L. HOLMBERGet aL
consistent interpretation of the anomalous b2 values obtained by Hamilton e t al. is possible in terms of dynamic effects. Static effects due to the quadrnpole distortion of the nuclear Coulomb field are not included in the tabulated matrix elements. An estimate by Church and Weneser s) indicates that the conversion coefficient should not be affected by more than 1 ~o. N o estimate of the influence on the different matrix elements by this effect has been published. However, due to the short range of the quadrupole field, we conclude that the finite-size sensitive element R+2 would be most affected. For E2 transitions of 200-500 keV in nuclei in the rare-earth region, the particle parameter is a valuable tool for the investigation of small effects in the internal conversion process. I f the influence on the conversion coefficient is restricted to 1 ~o, the normal value for R_ 3 may be used in the calculation of the particle parameter. The particle parameter is therefore a measure of the matrix element R+ 2. Fig. 3 shows b2 as a function of R+2 for the 245 keV transition. For the conversion process of the three E2 transitions investigated, no discrepancies between experimental and tabulated values have been found in this work. N o influence of dynamic effects is expected for these enhanced transitions and also the static quadrupole effects seem to be too small to be determined with the accuracy obtained so far. O f the transitions investigated the 245 keV transition in 1~2Sm is the most suitable for conversion process studies by measurement of the particle parameter. The fairly high accuracy obtained in the value for this particle parameter was made possible by use of the b 4 method lo, 15). This technique is applicable to many similar transitions and is adequate to discover rather small contributions to the conversion process, which are unaccounted for in the tabulated matrix elements. We wish to express our gratitude to Laborator T. R. Gerholm for the excellent research facilities he put at our disposal and for his stimulating interest in this work. Our thanks are due to Docent O. Alm6n for the isotope separation of the source material. One of us (V.S.) has received a grant from the Icelandic Science Foundation. This work has been sponsored by the Swedish Atomic Research Council.
References 1) 2) 3) 4)
B. N. Subba Rao, Nuovo Cim. 17 (1960) 189 E. M. Bernstein, Phys. Rev. Lett. 8 (1962) 100 Internal conversion processes, ed. by J. H. Hamilton (Academic Press, New York, 1966) I. F. W. Jansen et aL, R. J. Herickhoff et al., ibid; R. S. Dingus, W. L. Talbert Jr. andM. G. Stewart, Nuclear Physics 83 (1966) 545 5) J. H. Hamilton, E. F. Zganjar, T. M. George and W. H. Hibbits, Phys. Rex,. Lett. 14 (1965) 567 6) T. R. Gerholm and B.-G. Pettersson, in Alpha-, beta- and gamma-ray spectroscopy, ed. by K. Siegbahn (North-Holland Publ. Co., Amsterdam, 1965) 7) M. E. Rose, ibid.
E2 TRANSITIONS IN 152Sm AND 154Gd
8) 9) 10) 11) 12) 13) 14) 15)
41
E. L. Church and J, Weneser, Ann. Rev. Nucl. Sci. 10 (1960) 193 T. R. Gerholm, R. Othaz and M. S. E1-Nesr, Ark. Fys. 21 (1962) 253 B.-G. Pettersson, L. Holmberg and T. R. Gerholm, Nuclear Physics 65 (1965) 454 L. Holmberg, B.-G. Pettersson and T. R. Gerholm, to be published F. Gimmi, E. Heer and P. Scherrer, Helv. Phys. Acta 29 (1956) 147 S. Frankel, Phys. Rev. 83 (1951) 673 M. J. L. Yates, in Alpha-, beta- and gamma-ray spectroscopy, op. cit. B.-G. Pettersson and L. Holmberg, in Role of atomic electrons in nuclear transformations, Proc. Int. Conf., Warsaw, (1963) 16) L. C. Biedenharn and M. E. Rose, Revs. Mod. Phys. 2,5 (1953) 729 17) M. E. Rose, Internal conversion coefficients (North-Holland Publ. Co., Amsterdam, 1958) 18) I. M. Band, M. A. Listengarten and L. A. Sliv, in Alpha-, beta- and gamma-ray spectroscopy, op. cit.
19) T. A. Green and M. E. Rose, Phys. Rev. 110 (1958) 105