Applied Radiation and Isotopes 87 (2014) 87–91
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Applied Radiation and Isotopes journal homepage: www.elsevier.com/locate/apradiso
Precise test of internal-conversion theory: Transitions measured in five nuclei spanning 50 r Zr78 J.C. Hardy a,n, N. Nica a, V.E. Iacob a, S. Miller a, M. Maguire a, M.B. Trzhaskovskaya b a b
Cyclotron Institute, Texas A&M University, College Station, TX 77845-3366, USA Petersburg Nuclear Physics Institute, Gatchina 188300, Russia
H I G H L I G H T S
Five internal conversion coefficients (ICCs) have been measured to better than 7 2%. Transitions were selected to be sensitive to the assumptions used in ICC calculations. Results establish that the atomic vacancy must be accounted for in ICC calculations.
art ic l e i nf o
a b s t r a c t
Available online 26 November 2013
In a research program aimed at testing calculated internal-conversion coefficients (ICCs), we have made precise measurements of αK values for transitions in five nuclei, 197Pt, 193Ir, 137Ba, 134Cs and 119Sn, which span a wide range of A and Z values. In all cases, the results strongly favor calculations in which the finalstate electron wave function has been computed using a potential that includes the atomic vacancy created by the internal-conversion process. & 2013 Elsevier Ltd. All rights reserved.
Keywords: Internal conversion measurements 119 Sn M4 transition Test theory
1. Introduction Internal conversion is a crucial component of most nuclear decay schemes. Yet its contribution is usually not measured but rather is obtained from tabulated internal conversion coefficients (ICCs), which are applied to the measured relative gamma-ray intensities. Most decay schemes are thus highly dependent on the reliability of tabulated ICCs. Unfortunately, though various tables of ICCs have become available over the last half-century, until recently their accuracy has never been well established. As short a time ago as 2002, only 20 directly measured ICCs had a claimed precision of 2% or better and, together with other less-precise values, they actually suggested that there was a systematic difference of up to 3% between experiment and the various available calculations (Raman et al., 2002). One aspect of ICC calculations was of particular concern. The final-state electron wave function must be calculated in a field that adequately represents the remaining atom. But should that representation include the atomic vacancy created by the conversion process? Some calculations included it and some did not. This ambiguity over the presence or absence of the atomic vacancy seems surprising in retrospect. It has long been known from X-ray data that the lifetimes for K-shell vacancies are of the order of
n
Corresponding author. Tel.: þ 1 979 845 1411; fax: þ 1 979 845 1899. E-mail address:
[email protected] (J.C. Hardy).
0969-8043/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.apradiso.2013.11.033
10 15 to 10 17 s, which, as illustrated in Fig. 1, is appreciably longer than the time it takes for even the lowest energy electron to leave the atom. Thus the vacancy must surely be incorporated into the potential perceived by the outgoing conversion electron. Even so, the 2002 survey showed better agreement between measurement and theory if the electronic hole was ignored and, as a result, the ICC tables published immediately afterwards (Band et al., 2002) were computed with the hole deliberately ignored. Stimulated by this paradox, in 2003 we began a program to measure precisely the K-shell conversion coefficients, αK, for a number of E3 and M4 transitions with energy close to the atomic K-shell binding energy; these are particularly sensitive to the treatment of the hole and, overall, provide a demanding test of ICC calculations. So far, we have measured and reported on three M4 transitions – in 197Pt (Nica et al., 2009), 193Ir (Nica et al., 2004) and 137Ba (Nica et al., 2008) – and on one E3 transition – in 134Cs (Nica et al., 2008). We have also just completed a measurement on the M4 transition from the 90-keV isomer in 119Sn, which we will describe briefly here. The precision of these results ranges from 0.5% to 1.9%. In all cases, over a wide range of atomic numbers (50 rZr78) our results disagree with ICC calculations that ignore the atomic hole, but are fully consistent with calculations in which the atomic hole is incorporated according to the “frozen orbital” approximation (see Section 4). By 2008, our early results from this program influenced a reevaluation of ICCs by Kibédi et al. (2008) and the development of BrIcc, a new data-base obtained using the code by Band and
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single transition that can convert in the atomic K shell; and (2) the relative efficiency of the photon detector must be well calibrated over an energy range that includes both the K X-rays and the transition γ ray. The first condition has been satisfied by all five transitions that we have measured to date. Fig. 2 shows the decay scheme of the 90-keV isomer in 119Sn, our most recent case. Since the K-shell binding energy for tin is 29.2 keV, only the 65.66-keV transition converts in that shell. To meet the second condition, our principal asset is an HPGe detector, which we have calibrated to 70.15% precision in relative efficiency ( 70.20% absolute) between 50 and 1400 keV at a source-to-detector distance of 151 mm. The procedures we used to achieve this calibration have been described in detail in previous publications (Hardy et al., 2002; Helmer et al., 2003, 2004). The advantage of using such a single detector for both X and γ rays is that we can use a common efficiency calibration to determine the ratio εγ/εK. This worked well for 197Pt and 193Ir, whose X rays are well above 50 keV, the lower limit of our original precise calibration. However, for the more recent cases, 137Ba, 134Cs and now 119Sn, we had to use supplementary methods to extend our calibration down to 25 keV.
Fig. 1. Comparison of the K-vacancy lifetime with the approximate time taken for an electron from the K shell to leave the atom. The K-vacancy lifetime is taken from Keski-Rahkonen and Krause (1974) and is plotted against Z (bottom horizontal scale). The electron escape time is plotted as a function of its energy (top horizontal scale) and was calculated assuming an atomic radius of 1.4 Å.
Trzhaskovskaya (1993), which is based on Dirac–Fock calculations. In conformity with our conclusions, a version of this code was used, which incorporates the “frozen orbital” approximation to account for the atomic hole. The BrIcc data-base has been adopted by the National Nuclear Data Center (NNDC) and is available online for the determination of ICCs.1 Our experimental results obtained since 2008 continue to support that decision and have extended our verification tests to higher and lower Z values. We have gone as high as Z ¼78 (platinum) and, with the result presented here, as low as Z ¼50 (tin).
2. Experimental method For an isolated electromagnetic transition that converts in the atomic K shell, the observation of a K X-ray is a signal that an electron conversion has taken place; whereas a γ ray indicates that no conversion has taken place. If both X rays and γ rays are recorded in a measurement, then the value of αK is given by α K ωK ¼
N K εγ ; N γ εK
ð1Þ
where ωK is the K-shell fluorescence yield; NK and Nγ are the respective peak areas of the K X-rays and the γ ray; and εK and εγ are the respective detector efficiencies. For the fluorescence yield, we use the evaluation of Schönfeld and Janssen (1996), which quotes ωK values typically to better than 0.5% precision. For our 193 Ir experiment we actually measured the ωK value for iridium (Nica et al., 2005) and found excellent agreement with the tabulated value; so for all subsequent αK measurements we have simply adopted Schönfeld and Janssen's tabulated ωK values. Apart from the need for adequate statistics, the success of the method represented by Eq. (1) depends upon two conditions being satisfied: (1) The entire decay scheme must be dominated by a 1
Available at bricc.anu.edu.au/.
3. The
119m
Sn measurement
We populated the 119Sn isomeric state via thermal neutron capture on a 98.8% enriched 118Sn metal foil, 6.8-μm thick. The foil, which was 1 cm2 in area, was activated for 120 h at a flux of 7.5 1012 neutrons/(cm2 s) in the Triga reactor at the Texas A&M Nuclear Science Center. Such a long activation time was needed because of the very low neutron cross section, sth ¼0.01 barn, for the production of 119mSn from 118Sn; but it brought with it a very negative consequence. Some of the small impurities in the foil, which would not normally have been a concern, had a significant impact on the HPGe spectrum because their neutron cross sections were considerably higher than the cross section to produce 119mSn. Furthermore, the total conversion coefficient, αT, for the 65.66-keV transition from 119mSn is 5000, so while the K X-rays from it were quite abundant, the γ ray produced a very small peak which, when the source was fresh, was located atop a relatively high Compton background produced by the various impurity activities. Not only that, but two of the impurities, 75Se and 182Ta, both produced γ rays that overlapped the 65.66-keV γ ray from the 119m Sn transition, creating a single broad group at 66 keV. In the end, we had no choice but to wait for time to solve our problem. Both 75Se (t1/2 ¼ 120 d) and 182Ta (t1/2 ¼115 d) have halflives more than a factor two shorter than 119mSn (t1/2 ¼293 d). We simply re-measured the source 19 months after it had first been activated, after which time the two contaminant activities had decreased by a factor of 7 or 8 compared to 119mSn. The relevant portions of the recorded spectrum are shown in Fig. 3. The summed contribution of 75Se and 182Ta to the 66-keV group was only 7.1%, an amount easily corrected for. The already small contribution to the K X-rays from other tin isotopes was also reduced, to about 1%. Finally, since almost all other impurities were also shorter lived than 119mSn, there were no intense γ rays left in the spectrum at energies above 65.7 keV, so the Compton background was reduced drastically at 66 keV, which consequently greatly improved the peak-to-background ratio for the peak whose intensity we needed to determine. With impurities successfully dealt with, there remained the problem of calibrating our detector at 25 keV, the energy of the tin K X-rays. There is a special difficulty encountered at these low energies, which we have addressed in a previous paper (Nica et al., 2007): Some of the photons from any radioactive source scatter off nearby materials – including air – in the vicinity of the HPGe
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Fig. 2. Decay scheme for the 293-day isomer in Symochko et al. (2009).
119
Sn. The data are taken from
more like a shelf that extends only 2–3 keV below the peak energy. At our energy resolution of 1 keV in this region, an important part of the continuum gets “hidden” in, and potentially counted together with, the peak itself. The number of counts in the “hidden” continuum is very dependent not only on the source-detector geometry, but also on the details of its neighborhood. For this reason it is impossible to define a universal efficiency calibration with useful precision below 50 keV. Rather, one must examine each geometry as a special case, which must be calibrated based on its specific properties. We followed two different approaches to this part of the analysis. In the first, described fully for another similar case by Nica et al. (2007), we employed Monte Carlo calculations with the CYLTRAN code – the same code used in our calibration procedures (Hardy et al., 2002; Helmer et al., 2003, 2004) – to simulate the scattering “shelf”; then we scaled up the result to match the small component of the shelf visible in the data; and finally used that scaled-up result to determine the component of the shelf contained within the peak. Our second approach was to make a separate measurement on a calibration source 109Cd, which decays by electron capture to 109 Ag followed by the emission of an 88-keV γ ray and silver X rays, with Kα and Kβ X-ray groups situated at 22.1 keV and 25.0 keV respectively, about 3 keV below the tin K X-rays. The 88keV transition can convert in the K shell so the silver K X-rays arise both from internal conversion of this transition ( 20%) and from the electron-capture process ( 80%). If we rewrite Eq. (1) to include the contribution from electron capture, and rearrange it so as to yield the detector efficiency for the K X-rays we obtain εK ¼
Fig. 3. Portions of the photon spectrum recorded 19 months after the tin source had been activated. Shown are the two energy regions of interest in the determination of the αK value for the 65.7-keV transition in 119Sn. The peaks at 23.9 keV and 65.7 keV correspond to the only two γ rays emitted in the decay of 119m Sn. The 67.8-keV γ ray comes from a 182Ta impurity, which had already decayed by nearly five half-lives before this spectrum was recorded.
detector setup, and subsequently enter the detector. The scattered photons from a particular transition then lead to a continuum in the energy spectrum extending to lower energy from the peak created by the unscattered photons. For photons above 50 keV this continuum is rather flat and extends to energies well below the corresponding peak so, by extrapolation, its contribution to the area of the peak can easily be determined and removed. However, for peaks with energies as low as 25.2 keV and 28.6 keV, the energies of the tin Kα and Kβ X-rays respectively, the continuum is
89
Pγ NK εγ ; ωK ðαK P γ þ P ec;K Þ Nγ
ð2Þ
where the new parameters Pγ and Pec,K are the probabilities per parent decay for γ-ray emission and electron capture respectively. We took Pγ ¼ 0.03626(20) from the precise evaluation by the IAEA (2008), and Pec,K ¼0.8125(11) from a calculation with the LOGFT code of the National Nuclear Data Center (NNDC).2 The 88-keV transition in 109Ag is an M4. Its calculated αK also depends on whether the atomic vacancy is included or not, but the two values only differ by about 3%. We used the mean value of the two calculations, and adopted an uncertainty of 7 1.5%, which encompasses both values. Because this uncertainty applies only to the 20% of the K X-rays coming from internal conversion, its contribution to the right hand side of Eq. (2) is about 0.3%, which is only a minor component of the overall uncertainty associated with our final result. The silver and tin X rays have very similar energies so by using the same experimental setup for the 119mSn and 109Cd measurements, we could be sure that the scattering shelves were the same for both our calibration and for the case we wished to determine. All that remained then was to adjust the efficiency measured at the silver K X-ray energies of 22–25 keV to the tin K X-ray energies of 25–29 keV. This we did using the slope of the calibration curve as calculated by the CYLTRAN code. The two methods used for dealing with the scattering contribution to the K X-ray peaks gave consistent results and yielded a value for εK that has a precision of 71.0% relative to the wellestablished efficiency curve for our detector above 50 keV. The details of the 119Sn measurement and its analysis will appear in a longer publication (Nica et al., 2013). Our preliminary result for the αK value of the 65.66-keV transition from this isomeric state is αK ¼ 1620 7(27). This result can be compared 2
Available at www.nndc.bnl.gov/logft/.
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Table 1 Measured αK values for the five precisely measured transitions considered in this work. The experimental results are compared with calculated values that were based on three different assumptions: (1) the atomic vacancy is ignored; (2) the vacancy is included but the other atomic orbitals of the initial-state atom are considered “frozen”; and (3) the vacancy is included but the other orbitals satisfy the self-consistent field (SCF) of the final-state ion. The uncertainties on the calculated values caused by uncertainties on the transition energies are omitted as being negligible by comparison to the experimental uncertainties. Parent state
Transition
Measured αK
Energy (keV) 197m
Pt Ir 137m Ba 134m Cs 119m Sn 193m
346.5(2) 80.22(2) 661.659(3) 127.502(3) 65.66(1)
χ2
Calculated αK values based on following assumptions No hole
4.23(7) 103.0(8) 0.0915(5) 2.742(15) 1610(27)
“Frozen orbitals”
4.191 4.276 92.0 103.3 0.09068 0.09148 2.677 2.741 1544 1618 217
0.67
SCF
4.265 99.7 0.09139 2.73 1603 18.0
with the two previous, less-precise measurements of the same quantity, 1860(150) (Drost et al., 1971) and 1610(82) (Abreu et al., 1975).
4. Current status of new precise ICC values The results of the five measurements so far completed in our program to test ICC calculations are listed in Table 1 and illustrated in Fig. 4, where they are compared with αK values calculated either with the vacancy ignored or with it included based on one of two alternative assumptions. The first of these is the “frozen orbital” assumption, in which the continuum electron wave function is calculated in the ion field constructed from the bound wave functions of the neutral atom; this assumes that the hole is unfilled and the atomic orbitals have no time to rearrange after the electron's removal. Under the second of these assumptions the continuum wave functions are calculated in the self-consistent field (SCF) of the ion, indicating full relaxation of the ion orbitals. The bottom row of the table gives the χ2 for each set of calculations when it is compared with the data. Clearly, the “no hole” calculation is in strong disagreement with measurement. There also appears to be a preference for the “frozen orbital” approximation over the SCF alternative, but it needs to be noted that almost all the discrimination between these two approximations comes from a single measurement: that of 193Irm. With that case removed, the remaining four only show a very slight preference for the “frozen orbital” approximation.
5. Conclusions We have measured precise αK values for four M4 transitions and one E3 transition, in nuclei ranging from Z¼ 50 up to Z¼78, and from A ¼119 to A¼ 197. They demonstrate conclusively that ICC calculations must derive the wave function of the outgoing electron in a field that takes account of the atomic vacancy. The measurements also show a preference for the calculations that take account of the vacancy by assuming that the remaining atomic orbitals are “frozen” in the configurations they had in the initial state of the neutral atom. If the “frozen orbital” approximation is used, our results suggest that calculated ICC values can be relied on to 7 1%, at least for E3 and M4 transitions.
Fig. 4. Percentage differences between the measured and calculated ICCs for two Dirac–Fock calculations: one (a) is without the atomic vacancy and the other (b) is with it included in the “frozen orbital” approximation. The points shown as solid diamonds in both plots correspond to the twenty cases listed by Raman et al. (2002) with better than 2% precision; as indicated at the bottom, five are for E2 transitions, three for E3, and the remainder are for M4 transitions. The points shown as open circles correspond to our five more-recently measured αK values. For the cases of 134mCs, 137mBa and 197mPt, the earlier Raman values are shown in grey; for 119mSn and 193mIr there were no earlier values with sub-2% precision.
Acknowledgements This work is supported by the U.S. Department of Energy under Grant No. DE-FG02-93ER40773 and by the Robert A. Welch Foundation under Grant No. A-1397.
References Abreu, M.C., Godinho, M.M., Gil, F.B., 1975. K internal-conversion coefficient of the M4 65-keV transition in 119Sn. Phys. Rev. C: Nucl. Phys. 11, 2103. Band, I.M., Trzhaskovskaya, M.B., 1993. Internal conversion coefficients for lowenergy nuclear transitions. At. Data Nucl. Data Tables 55, 43–61. Band, I.M., Trzhaskovskaya, M.B., Nestor Jr., C.W., Tikkanen, P., Raman, S., 2002. Dirac–Fock internal conversion coefficients. At. Data Nucl. Data Tables 81, 1–334. Drost, H., Weiss, W., Weyer, G., 1971. Lifetime of the 23.8 keV state in 119Sn. Z. Naturforsch. 26a, 1092. Hardy, J.C., Iacob, V.E., Sanchez-Vega, M., Effinger, R.T., Lipnik, P., Mayes, V.E., Willis, D.K., Helmer, R.G., 2002. Precise efficiency calibration of an HPGe detector: source measurements and Monte Carlo calculations with sub-percent precision. Appl. Radiat. Isot. 56, 65–69. Helmer, R.G., Hardy, J.C., Iacob, V.E., Sanchez-Vega, M., Neilson, R.G., Nelson, J., 2003. The use of Monte Carlo calculations in the determination of a Ge detector efficiency curve. Nucl. Instrum. Methods Phys. Res., Sect. A 511, 360–381. Helmer, R.G., Nica, N., Hardy, J.C., Iacob, V.E., 2004. Precise efficiency calibration of an HPGe detector up to 3.5 MeV, with measurements and Monte Carlo calculations. Appl. Radiat. Isot. 60, 173–177. IAEA, 2008. Update of X ray and Gamma ray Decay Data Standards for Detector Calibrations and Other Applications. International Atomic Energy Agency, Vienna, Austria, ISBN: 92-0-113606-4. Keski-Rahkonen, O., Krause, M.O., 1974. Total and partial atomic-level widths. At. Data Nucl. Data Tables 14, 139–146. Kibédi, T., Burrows, T.W., Trzhaskovskaya, M.B., Davidson, P.M., Nestor Jr., C.W., 2008. Evaluation of theoretical conversion coefficients using BrIcc. Nucl. Instrum. Methods Phys. Res., Sect. A 589, 202–229. Nica, N., Hardy, J.C., Iacob, V.E., Raman, S., Nestor Jr., C.W., Trzhaskovskaya, M.B., 2004. Precise measurement of αK for the M4 transition from 193Irm: a test of internal-conversion theory. Phys. Rev. C: Nucl. Phys. 70, 054305. Nica, N., Hardy, J.C., Iacob, V.E., Montague, W.E., Trzhaskovskaya, M.B., 2005. Precise measurement of K-shell fluorescence yield in iridium: An improved test of internal-conversion theory. Phys. Rev. C: Nucl. Phys. 71, 054320. Nica, N., Hardy, J.C., Iacob, V.E., Rockwell, W.E., Trzhaskovskaya, M.B., 2007. Test of internal-conversion theory with measurements in 134Cs and 137Ba. Phys. Rev. C: Nucl. Phys. 75, 024308.
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Nica, N., Hardy, J.C., Iacob, V.E., Balonek, C., Trzhaskovskaya, M.B., 2008. Internal conversion coefficients in 134Cs, 137Ba, and 139La: a precise test of theory. Phys. Rev. C: Nucl. Phys. 77, 034306. Nica, N., Hardy, J.C., Iacob, V.E., Goodwin, J., Balonek, C., Hernberg, M., Nolan, J., Trzhaskovskaya, M.B., 2009. Further test of internal-conversion theory with a measurement in 197Pt. Phys. Rev. C: Nucl. Phys. 80, 064314. Nica, N., Hardy, J.C., Iacob, Miller, S., Maguire, M., Trzhaskovskaya, M.B., 2013. Further test of internal-conversion theory with a measurement in 119Sn. To be published.
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Raman, S., Nestor Jr., C.W., Ichihara, A., Trzhaskovskaya, M.B., 2002. How good are the internal conversion coefficients now? Phys. Rev. C: Nucl. Phys. 66, 044312. Schönfeld, E., Janssen, H., 1996. Evaluation of atomic shell data. Nucl. Instrum. Methods Phys. Res., Sect. A 369, 527–533. Symochko, D.M., Browne, E., Tuli, J.K., 2009. Nuclear data sheets for A ¼ 119. Nucl. Data Sheets 110, 2945–3105.