- Email: [email protected]
FT values measured to ±0.1% for superallowed beta transitions: Metrology at sub-second time scales
Applied Radiation and Isotopes 87 (2014) 297–301
Contents lists available at ScienceDirect
Applied Radiation and Isotopes journal homepage: www.elsevier.com/locate/apradiso
FT values measured to 70.1% for superallowed beta transitions: Metrology at sub-second time scales J.C. Hardy n, V.E. Iacob, H.I. Park, L. Chen, N. Nica, V. Horvat, R.E. Tribble, I.S. Towner Cyclotron Institute, Texas A&M University, College Station, TX 77845-3366, USA
H I G H L I G H T S
Established metrology facility for accelerator-produced short-lived activities. Measured half-lives and beta branching ratios to high precision. Precision is 0.03% for half-lives and 0.1% for branching ratios. Results have important impact on electroweak Standard Model.
art ic l e i nf o
a b s t r a c t
Available online 18 November 2013
Because of angular-momentum conservation, superallowed β decay between 0 þ analog states involves only the vector part of the weak interaction, so its measured ft value can be used to determine the vector coupling constant, GV. If many such transitions are measured, then the constancy of GV can be established and several important tests made on fundamentals of the electroweak Standard Model. We have developed apparatus that allows us to measure half-lives to 7 0.03% and branching ratios to 70.1% or better, for cyclotron-produced activities with half-lives as short as 100 ms. We present an overview of the equipment and a summary of more than 10 years of results. & 2013 Elsevier Ltd. All rights reserved.
Keywords: Beta decay Half lives Branching ratios
1. Introduction Superallowed beta decay between nuclear analogue states1 with isospin, T¼1, and spin-parity, Jπ ¼ 0 þ , occurs only via the vector current of the weak interaction: angular momentum conservation completely rules out the axial-vector component, which must carry off a spin of one and cannot connect two states that both have spin zero. Furthermore, the strength of such a transition – its ft value – is affected only by the small difference between the analogue parent and daughter configurations resulting from isospin symmetry breaking, not by the dominant nuclear structure common to them both. As a result, the measured ft value can be related directly to the vector coupling constant, GV, with the intervention of only a few small ( 1%) calculated terms to account for radiative and isospinsymmetry-breaking effects. These corrections can be calculated with 10% relative precision or better; so, with sufficient experimental
precision, GV can be determined from a single superallowed transition to 70.1%. If many such transitions can be measured with similar precision, the constancy of GV can be demonstrated and an average value extracted with still better precision. Once a reliable value for GV has been determined, it is only a short step to obtain from it the value of Vud, the largest element in the quark-mixing matrix known as the Cabibbo–Kobayashi–Maskawa (CKM) matrix; and only another short step to the most demanding available test of the unitarity of that matrix (Hardy and Towner, 2009). Since the unitary CKM matrix is a central pillar of the three-generation Standard Model of particle physics, any experimentally determined deviation from CKM unitarity would be a signature of new physics beyond the Model; and even uncertainty limits on a result that agrees with unitarity can serve as a constraint on possible candidates for new physics. These are important goals that probe fundamental physics, but they can only be met if the transition ft values have been measured to better than 70.1%.
n
Corresponding author. Tel.: þ 1 979 845 1411; fax: þ 1 979 845 1899. E-mail address: [email protected] (J.C. Hardy). 1 Analogue states are states in neighboring isobars whose structure is the same except that a proton in one has been replaced by a neutron in the other. Their wave functions would be identical if the small Coulomb interaction among the protons and the charge-dependent terms in the nuclear force could be turned off. Both states are said to have the same isospin quantum number; and the small differences between them are described as being caused by isospin symmetrybreaking effects. 0969-8043/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.apradiso.2013.11.018
2. The experimental challenge The ft value that characterizes any β transition depends on three measured quantities: the total transition energy, QEC; the half-life, t1/2, of the parent state; and the branching ratio, R, for the particular transition of interest. The QEC value is required as a
298
J.C. Hardy et al. / Applied Radiation and Isotopes 87 (2014) 297–301
measure of the available phase space in the computation of the statistical rate function, f, while the half-life and branching ratio combine to yield the partial half-life, t. Since our goal is to achieve 70.1% uncertainty on the ft value itself, we must do significantly better than that on each of the three contributing experimental quantities. The most severe requirement is on QEC. Since f is approximately proportional to QEC5, the transition energy must actually be measured an order-of-magnitude more precisely, to 70.01%: i.e. to 7500 eV in 5 MeV, which is a median value for QEC. This sort of precision is now possible, even for short-lived nuclides (t1/2 4 100 ms), with Penning traps specially adapted to operate on-line with an accelerator that produces the activity to be studied. Our measurements have been made with the “Jyfltrap” at the University of Jyväskylä cyclotron, where we collaborate with the inhouse group there. This is a particularly powerful facility since it can produce both the parent and the daughter nucleus of a superallowed transition and alternate automatically between the two, thus making it possible to interleave mass measurements of them both. This way, most systematic uncertainties disappear in the result for QEC, which is the difference between the two masses. This work on superallowed β decays has recently been reviewed (Eronen and Hardy, 2013) and will not be described in further detail here. Our half-life and branching-ratio measurements are being performed at the Texas A&M University Cyclotron Institute. To illustrate the issues involved, we present in Fig. 1 the partial decay scheme of 38Ca (β) 38Km (β) 38Ar. It encompasses two superallowed 0 þ -0 þ transitions: the first from 38Ca to the isomeric first excited state in 38K, and the second from that isomeric state to the ground state of 38Ar, which is stable. In any measurement that detects positrons from a 38Ca source, one must therefore deal not only with the parent decay but also with the growth and decay of the daughter. For cases of this type, we are currently able to measure the parent half-life to better than 7 0.05%. However, for a source like 38Km, with a single decay component, we have achieved 70.02%. So far, we have measured half-lives that ranged from 400 ms to 71 s. With the precision of both the QEC value and the half-life now well below the 0.1% level, the demands on the branching-ratio measurements can be somewhat relaxed, although obviously their uncertainties must be no worse than 70.1%, which is already
38 20
3341
1+,0
0.5%
1698
1+,0
20.0%
458 130
1+,0 2.81% 0+,1 76.5% 924 ms
0 38 19
K 19
0+,1 444 ms
Ca 18
Q EC = 6612
3+,0
Q EC = 6044
0+,1 38 18
99.97%
Ar 20
Fig. 1. Decay schemes of 38Ca and 38Km showing only those features relevant to their superallowed β decays. All energies are in keV; the QEC values shown are for the superallowed branches. Three weak branches to higher excited states have been omitted: their branching ratios total o 0.2%. The data are taken from Cameron and Singh (2008) and Park et al. (2011). Note that the γ decay from the 130-keV isomer to the 38K ground state is a very weak 0.03% branch.
a level of precision quite unprecedented in direct beta-decay branching-ratio measurements. In some cases like that of 38Km decay, the superallowed branching ratio is 100% – guaranteed by the unfavored spin/parities of all energetically available excited states in the daughter – so no high-precision measurement is required. But for complicated cases like that of 38Ca, such measurements cannot be avoided. Now, after a decade of preparation and tests, we have at last reached this precision for the superallowed branch in the decay of 38Ca, and we anticipate being able to add several more favorable cases in the very near future. Our method is to detect the β-delayed γ rays emitted from levels in 38K in an HPGe detector, whose absolute efficiency has been determined to high precision.
3. The experimental arrangement Our experimental arrangement combines: (1) a production facility that can provide a pure (typically 499.8%) source of a selected short-lived activity; (2) a rapid tape-transport system that can periodically move the collected source to a shielded counting location in under 200 ms; and (3) two possible counting configurations at that location depending on whether a branching ratio or a half-life is being measured. For the former we use a combination of a thin scintillator and an HPGe detector for β–γ coincidence measurements; for the latter, we use a 4π gas proportional counter of “pill-box” style split into two halves, with the tape passing between the halves and the collected sample being stopped exactly at the center for each measurement period. Taking 38Ca as an example, we achieve the goal of source purity by using a production reaction with inverse kinematics, 1H (39K,2n)38Ca, and selecting the desired reaction product with a recoil spectrometer (see Fig. 2). A primary beam of 30-AMeV 39K from the Texas A&M superconducting cyclotron impinges on a liquid-nitrogen-cooled hydrogen gas target, with the fully stripped 38 Ca ejectiles being subsequently separated by their charge-tomass ratio, q/m. A position-sensitive silicon detector, which can be inserted temporarily at the focal plane of the spectrometer, allows us to identify any impurities in the beam. With that detector removed, the 38Ca beam from the spectrometer's acceptance slits then exits the vacuum system through a 51-μm-thick Kapton window, passes through a 0.3-mm-thick BC404 scintillator, used to count the ions, and then through a stack of aluminum degraders, finally stopping inside the 76-μm-thick aluminized Mylar tape of a fast tape-transport system. The combination of q/m selectivity in the spectrometer and range separation in the degraders provides implanted samples that we have determined to be better than 99.7% pure 38Ca, with the main surviving trace contaminants being 35Ar and 36K. Up to 20,000 atoms of 38Ca can be implanted in the tape in one second. Each 38Ca sample is accumulated in the tape for typically 1.6 s; then the beam is turned off and the tape moves the sample in 200 ms to the shielded counting location, where data are collected for 1.6 s, after which the cycle is repeated. This computercontrolled sequence is repeated continuously, for up to a week, until sufficient statistics have been accumulated. Fig. 2 also shows the arrangement we use to measure branching ratios. The sample is positioned precisely between a 1-mmthick BC404 scintillator to detect β þ particles, and our 70% HPGe detector for γ rays. We save β–γ coincidences event-by-event, recording the energies of each beta and gamma, the time difference between them, and the time that the event itself occurred after the beginning of the counting period. For each cycle we also record the number of 38Ca atoms deposited in the tape as a function of time, the total number of beta and gamma singles, and the output from a laser ranging device that records the distance of
J.C. Hardy et al. / Applied Radiation and Isotopes 87 (2014) 297–301
Momentum Achromat Recoil Spectrometer (MARS)
299
39
K beam (1170 MeV) H2 gas target
Shielding HPGe detector
Tape Deck
* Sample
Tape Deck
Thin plastic detector
Fig. 2. Experimental arrangement used for the 38Ca branching-ratio measurement. For the half-life measurements, the HPGe detector and thin plastic β detector are replaced by a 4π gas proportional counter; the tape passes between the halves of that counter and stops when the collected source is centered between them.
the stopped tape from the HPGe detector. From cycle to cycle the latter distance can change by a few tenths of a millimeter, enough to require a small adjustment to the HPGe detector efficiency.
4. Measurement methods We determine β-decay branching ratios from the corresponding intensities of the β-delayed γ-ray peaks, which predominantly correspond to γ-transitions to the isomeric 0 þ state at 130 keV in 38 K (see Fig. 1). If the γ ray de-exciting state i in the daughter is denoted by γi, then the β-branching ratio, Ri, for the β-transition populating that state can be written: Ri ¼
N βγi k; Nβ εγi
ð1Þ
where Nβγi is the total number of β–γ coincidences measured in the γi peak, Nβ is the total number of β singles, εγi is the detector efficiency for γ ray, γi, and k is a small correction factor (i.e. k 1) that accounts for dead-time and pile-up (together, a 1.3% effect), coincident summing (γ's with 511-keV annihilation radiation, a 2.8% effect), and the differences in the β-detector efficiency for the different energy transitions participating in the 38Ca decay (a 0.1% effect). We eliminate random coincidences separately by using the β–γ relative-time spectrum, in which the prompt coincidence peak stood prominently above the flat random distribution. Eq. (1) highlights the importance of having a pure sample – so that Nβ can be relied upon – as well as having a precise absolute efficiency calibration for the γ-ray detector, and a reasonable knowledge of relative efficiencies in the beta detector. Our HPGe detector's absolute efficiency has been accurately determined (to 70.2% for 50–1400 keV γ rays and to 70.4% up to 3500 keV) from source measurements and Monte Carlo calculations (Helmer et al., 2003, 2004). The relative efficiency of the plastic scintillator has been determined as a function of β energy by Monte Carlo calculations, which have been checked by comparison with measurements on conversion-electron sources (Golovko et al., 2008). As can be seen from Fig. 1, by measuring the β-delayed γ rays – i.e. γ rays in 38K that are emitted following the β decay of 38Ca – we can obtain branching ratios for all the 38Ca β-decay branches
except the superallowed one. Of course, we can obtain the ratio for the latter by summing all the measured branches and subtracting the total from 100%. This has a very salutary effect on the relative precision. Since the total branching ratio for all the nonsuperallowed transitions is about 23%, a relative precision of 0.3% on that total becomes a relative precision of 0.09% on the 77% value for the superallowed branch. For half-life measurements, preamplified signals from our 4π gas proportional counter are passed to a high-gain ( 500) fast filter amplifier, with saturating pulses being clipped. The amplified and clipped pulses are then passed to a discriminator with very low threshold (150–250 mV). The discriminator output is split and sent to two fixed-width, nonretriggering and nonextending gate generators, which establish different dominant dead times in the two separate streams, both of which are multiscaled. Having two channels with different dead times allows us to confirm that our corrections for dead-time losses are accurate. See Iacob et al. (2010) for a more complete description of this system. Recently we have also been developing a digital-pulse system, which allows us to store each pulse and its time of arrival digitally for later analysis. For single component decays the analysis is straightforward. However, in cases like that of 38Ca (see Fig. 1), the detected positron-decay spectrum combines the 444-ms decay of 38Ca with the growth and decay of its 924-ms daughter 38Km. To achieve the ultimate precision, it is important for us to know, rather than to fit, the number of daughter nuclei relative to the number of parent nuclei when the counting period begins. Although we implant a pure beam of 38Ca, some of these nuclei will have decayed in our collected sample before it is moved to the counting position, and the daughterto-parent ratio can only be reliably calculated if we know of any changes in the rate of deposition of 38Ca that might have occurred during the production period of each cycle. Signals from the thin plastic detector between the exit of the spectrometer and the tape give us the exact deposition rate, which we record as a function of time for each cycle and use subsequently to determine the daughterto-parent ratio at the start of each counting period. The main contributors to the final uncertainty on the 38Ca half-life are the uncertainties in (1) the 38Km daughter's half-life, and (2) the small amount of 35Ar impurity present in the collected samples (see Table I in Park et al., 2011).
300
J.C. Hardy et al. / Applied Radiation and Isotopes 87 (2014) 297–301
5. Current status of results Measurements of the ft values for superallowed 0 þ -0 þ β transitions have been going on for more than half a century with ever increasing precision. The most recent survey of world data was published by Hardy and Towner in 2009. It lists the ft values for 13 transitions, which were precisely determined from more than 150 independent measurements – including many of ours – which have contributed to the three input quantities, QEC, t1/2 and R, for each superallowed transition. On average, each quantity has been independently determined four times, making this a very robust data set. An overview of the results is shown as the solid circles in Fig. 3, where the three measured properties for each transition appear in the top three panels, and the corresponding ft values appear in the fourth panel. In order to expose the fundamental physics underlying these ft values, it is conventional to combine the small theoretical corrections with each ft value and define a “corrected” t value, which is written (Hardy and Towner, 2009) t f tð1 þ δ′R Þð1 þ δNS δC Þ ¼
K 2G2V ð1 þ ΔVR Þ
;
ð2Þ
where K¼ 8120.2787(11) 10 10 GeV 4 s, δC is the isospinsymmetry-breaking correction and ΔVR , δ′R and δNS are radiative corrections. The transition-dependent corrections are applied to ft, while the transition-independent correction, ΔVR , is lumped together with the vector coupling constant, GV. The lowest panel in Fig. 3
10
Q EC (MeV)
5 0 2 0
log t1/2 (s) -2 0
-1 -2 3090
log R
shows these corrected t values. It is striking to see in the figure that the three experimental quantities change over orders of magnitude in the span from Z¼5 to Z¼36, yet the ft values change by less than 3%, and the final corrected t values are all consistent with a single constant value with 70.03% precision: 3071.81(83) s. This convincingly proves the constancy of GV2 to the same precision. Although it is beyond the scope of this paper to go into the details of how the resultant value for GV can be used to test the unitarity of the CKM matrix, the final result itself is too impressive to ignore. The sum of squares of the experimental values for the three elements in the top row of the matrix currently gives the result 1.0001(6) (Hardy and Towner, 2013), in stunning agreement with the unitarity expectation of the Standard Model. The value of Vud, which is derived from the superallowed result for GV, is by far the dominant contributor to this sum. A complete description of this aspect of the subject appears in a review article by Towner and Hardy (2010). One might well ask why it is interesting to add still more points to the plots in Fig. 3. The answer comes from the fact that the uncertainty on Vud is now dominated not by experiment but by the theoretical correction terms that appear in Eq. (2). In particular, δC and δNS both depend on nuclear-structure calculations and can differ significantly from transition to transition. It is they which are almost entirely responsible for replacing the variations in the plotted ft values with the consistency seen in the t values. The calculations of δC and δNS are completely independent of the ft-value measurements, so their effectiveness in removing the variations goes a long way to supporting their validity. However their uncertainties remain significant and any improvement would improve the Vud uncertainty as well. This can best be done through measurements made of new transitions with very large calculated δC and δNS corrections. The argument is that if the t values for transitions that have large correction terms are consistent with the others, then we can be assured of the calculations' reliability for the transitions whose corrections are much smaller. The theoretical uncertainty could thus be reduced. The superallowed transition from 38Ca, which we have used in this report to illustrate our techniques, is just such a case: its ft value has never before been measured precisely and it has relatively large correction terms. Its results appear as open circles in Fig. 3, published results for its QEC value (Eronen et al., 2011) and its half-life (Park et al., 2011) in the top two panels and a preliminary value for its branching ratio, 77.4(1) %, in the third panel. Clearly, in spite of its having unusually large corrections, its t value agrees well with the other transitions. 6. Conclusions
ft (s) We have established a metrology facility for short-lived activities that are produced with an accelerator. With it, we have measured half-lives and β branching ratios to high precision (0.03% for half-lives and 0.1% for branching ratios). Our methods have been described briefly and their capabilities illustrated with measurements on the superallowed β decay of 38Ca.
3060 3030 3080 3070
Acknowledgements
3060 0
10
20
30
40
Z of daughter nucleus Fig. 3. Results from the most recent survey of 13 precisely measured superallowed 0 þ -0 þ β transitions appear as solid black circles. The parents of these transitions, from left to right, are 10C, 14O, 22Mg, 26Alm, 34Cl, 34Ar, 38Km, 42Sc, 46V, 50Mn, 54Co, 62 Ga and 74Rb. The top three panels present the average of measured QEC, log t1/2 and log R values for each transition. The bottom two panels give the corresponding ft and t values. The shaded horizontal line in the bottom panel represents the overall average t value for all transitions. All uncertainties are shown: in the cases where none are visible, they are smaller than the data point. Recent results for 38Ca are shown as open circles.
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 Cameron, J.A., Singh, B., 2008. Nuclear data sheets for A ¼ 38. Nucl. Data Sheets 109, 1–170. Eronen, T., Gorelov, D., Hakala, J., Hardy, J.C., Jokinen, A., Kankainen, A., Kolhinen, V.S., Moore, I.D., Penttila, H., Reponen, M., Rissanen, J., Saastamoinen, A., Aysto, J.,
J.C. Hardy et al. / Applied Radiation and Isotopes 87 (2014) 297–301 2011. QEC values of the superallowed β emitters 10C, 34Ar, 38Ca, and 46V. Phys. Rev. C: Nucl. Phys. 83, 055501. Eronen, T., Hardy, J.C., 2013. High-precision QEC-value measurements for superallowed decays. Eur. Phys. J. A 48, 48. Golovko, V.V., Iacob, V.E., Hardy, J.C., 2008. The use of Geant4 for simulations of a plastic β-detector and its application to efficiency calibration. Nucl. Instrum. Methods Phys. Res., Sect. A 594, 266–272. Hardy, J.C., Towner, I.S., 2009. Superallowed 0 þ -0 þ nuclear β decays: a new survey with precision tests of the conserved vector current hypothesis and the standard model. Phys. Rev. C: Nucl. Phys. 79, 055502. Hardy, J.C., Towner, I.S., 2013. CKM Unitarity normalization tests, present and future. Ann. Phys. 525, 443. Helmer, R.G., Hardy, J.C., Iacob, V.E., Sanchez-Vega, M., Nelson, 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.
301
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. Rad. Isot 60, 173–177. Iacob, V.E., Hardy, J.C., Banu, A., Chen, L., Golovko, V.V., Goodwin, J., Haovat, V., Nica, N., Park, H.I., Trache, L., Tribble, R.E., 2010. Precise half-life measurement of the superallowed β þ emitter 26Si. Phys. Rev. C: Nucl. Phys. 82, 035502. Park, H.I., Hardy, J.C., Iacob, V.E., Banu, A., Chen, L., Golovko, V.V., Goodwin, J., Horvat, V., Nica, N., Simmons, E., Trache, L., Tribble, R.E., 2011. Precise half-life measurement of the superallowed β þ emitter 38Ca. Phys. Rev. C: Nucl. Phys. 84, 065502. Towner, I.S., Hardy, J.C., 2010. The evaluation of Vud and its impact on the unitarity of the Cabibbo–Kobayashi–Maskawa quark-mixing matrix. Rep. Prog. Phys 73, 046301.
Contents lists available at ScienceDirect
Applied Radiation and Isotopes journal homepage: www.elsevier.com/locate/apradiso
FT values measured to 70.1% for superallowed beta transitions: Metrology at sub-second time scales J.C. Hardy n, V.E. Iacob, H.I. Park, L. Chen, N. Nica, V. Horvat, R.E. Tribble, I.S. Towner Cyclotron Institute, Texas A&M University, College Station, TX 77845-3366, USA
H I G H L I G H T S
Established metrology facility for accelerator-produced short-lived activities. Measured half-lives and beta branching ratios to high precision. Precision is 0.03% for half-lives and 0.1% for branching ratios. Results have important impact on electroweak Standard Model.
art ic l e i nf o
a b s t r a c t
Available online 18 November 2013
Because of angular-momentum conservation, superallowed β decay between 0 þ analog states involves only the vector part of the weak interaction, so its measured ft value can be used to determine the vector coupling constant, GV. If many such transitions are measured, then the constancy of GV can be established and several important tests made on fundamentals of the electroweak Standard Model. We have developed apparatus that allows us to measure half-lives to 7 0.03% and branching ratios to 70.1% or better, for cyclotron-produced activities with half-lives as short as 100 ms. We present an overview of the equipment and a summary of more than 10 years of results. & 2013 Elsevier Ltd. All rights reserved.
Keywords: Beta decay Half lives Branching ratios
1. Introduction Superallowed beta decay between nuclear analogue states1 with isospin, T¼1, and spin-parity, Jπ ¼ 0 þ , occurs only via the vector current of the weak interaction: angular momentum conservation completely rules out the axial-vector component, which must carry off a spin of one and cannot connect two states that both have spin zero. Furthermore, the strength of such a transition – its ft value – is affected only by the small difference between the analogue parent and daughter configurations resulting from isospin symmetry breaking, not by the dominant nuclear structure common to them both. As a result, the measured ft value can be related directly to the vector coupling constant, GV, with the intervention of only a few small ( 1%) calculated terms to account for radiative and isospinsymmetry-breaking effects. These corrections can be calculated with 10% relative precision or better; so, with sufficient experimental
precision, GV can be determined from a single superallowed transition to 70.1%. If many such transitions can be measured with similar precision, the constancy of GV can be demonstrated and an average value extracted with still better precision. Once a reliable value for GV has been determined, it is only a short step to obtain from it the value of Vud, the largest element in the quark-mixing matrix known as the Cabibbo–Kobayashi–Maskawa (CKM) matrix; and only another short step to the most demanding available test of the unitarity of that matrix (Hardy and Towner, 2009). Since the unitary CKM matrix is a central pillar of the three-generation Standard Model of particle physics, any experimentally determined deviation from CKM unitarity would be a signature of new physics beyond the Model; and even uncertainty limits on a result that agrees with unitarity can serve as a constraint on possible candidates for new physics. These are important goals that probe fundamental physics, but they can only be met if the transition ft values have been measured to better than 70.1%.
n
Corresponding author. Tel.: þ 1 979 845 1411; fax: þ 1 979 845 1899. E-mail address: [email protected] (J.C. Hardy). 1 Analogue states are states in neighboring isobars whose structure is the same except that a proton in one has been replaced by a neutron in the other. Their wave functions would be identical if the small Coulomb interaction among the protons and the charge-dependent terms in the nuclear force could be turned off. Both states are said to have the same isospin quantum number; and the small differences between them are described as being caused by isospin symmetrybreaking effects. 0969-8043/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.apradiso.2013.11.018
2. The experimental challenge The ft value that characterizes any β transition depends on three measured quantities: the total transition energy, QEC; the half-life, t1/2, of the parent state; and the branching ratio, R, for the particular transition of interest. The QEC value is required as a
298
J.C. Hardy et al. / Applied Radiation and Isotopes 87 (2014) 297–301
measure of the available phase space in the computation of the statistical rate function, f, while the half-life and branching ratio combine to yield the partial half-life, t. Since our goal is to achieve 70.1% uncertainty on the ft value itself, we must do significantly better than that on each of the three contributing experimental quantities. The most severe requirement is on QEC. Since f is approximately proportional to QEC5, the transition energy must actually be measured an order-of-magnitude more precisely, to 70.01%: i.e. to 7500 eV in 5 MeV, which is a median value for QEC. This sort of precision is now possible, even for short-lived nuclides (t1/2 4 100 ms), with Penning traps specially adapted to operate on-line with an accelerator that produces the activity to be studied. Our measurements have been made with the “Jyfltrap” at the University of Jyväskylä cyclotron, where we collaborate with the inhouse group there. This is a particularly powerful facility since it can produce both the parent and the daughter nucleus of a superallowed transition and alternate automatically between the two, thus making it possible to interleave mass measurements of them both. This way, most systematic uncertainties disappear in the result for QEC, which is the difference between the two masses. This work on superallowed β decays has recently been reviewed (Eronen and Hardy, 2013) and will not be described in further detail here. Our half-life and branching-ratio measurements are being performed at the Texas A&M University Cyclotron Institute. To illustrate the issues involved, we present in Fig. 1 the partial decay scheme of 38Ca (β) 38Km (β) 38Ar. It encompasses two superallowed 0 þ -0 þ transitions: the first from 38Ca to the isomeric first excited state in 38K, and the second from that isomeric state to the ground state of 38Ar, which is stable. In any measurement that detects positrons from a 38Ca source, one must therefore deal not only with the parent decay but also with the growth and decay of the daughter. For cases of this type, we are currently able to measure the parent half-life to better than 7 0.05%. However, for a source like 38Km, with a single decay component, we have achieved 70.02%. So far, we have measured half-lives that ranged from 400 ms to 71 s. With the precision of both the QEC value and the half-life now well below the 0.1% level, the demands on the branching-ratio measurements can be somewhat relaxed, although obviously their uncertainties must be no worse than 70.1%, which is already
38 20
3341
1+,0
0.5%
1698
1+,0
20.0%
458 130
1+,0 2.81% 0+,1 76.5% 924 ms
0 38 19
K 19
0+,1 444 ms
Ca 18
Q EC = 6612
3+,0
Q EC = 6044
0+,1 38 18
99.97%
Ar 20
Fig. 1. Decay schemes of 38Ca and 38Km showing only those features relevant to their superallowed β decays. All energies are in keV; the QEC values shown are for the superallowed branches. Three weak branches to higher excited states have been omitted: their branching ratios total o 0.2%. The data are taken from Cameron and Singh (2008) and Park et al. (2011). Note that the γ decay from the 130-keV isomer to the 38K ground state is a very weak 0.03% branch.
a level of precision quite unprecedented in direct beta-decay branching-ratio measurements. In some cases like that of 38Km decay, the superallowed branching ratio is 100% – guaranteed by the unfavored spin/parities of all energetically available excited states in the daughter – so no high-precision measurement is required. But for complicated cases like that of 38Ca, such measurements cannot be avoided. Now, after a decade of preparation and tests, we have at last reached this precision for the superallowed branch in the decay of 38Ca, and we anticipate being able to add several more favorable cases in the very near future. Our method is to detect the β-delayed γ rays emitted from levels in 38K in an HPGe detector, whose absolute efficiency has been determined to high precision.
3. The experimental arrangement Our experimental arrangement combines: (1) a production facility that can provide a pure (typically 499.8%) source of a selected short-lived activity; (2) a rapid tape-transport system that can periodically move the collected source to a shielded counting location in under 200 ms; and (3) two possible counting configurations at that location depending on whether a branching ratio or a half-life is being measured. For the former we use a combination of a thin scintillator and an HPGe detector for β–γ coincidence measurements; for the latter, we use a 4π gas proportional counter of “pill-box” style split into two halves, with the tape passing between the halves and the collected sample being stopped exactly at the center for each measurement period. Taking 38Ca as an example, we achieve the goal of source purity by using a production reaction with inverse kinematics, 1H (39K,2n)38Ca, and selecting the desired reaction product with a recoil spectrometer (see Fig. 2). A primary beam of 30-AMeV 39K from the Texas A&M superconducting cyclotron impinges on a liquid-nitrogen-cooled hydrogen gas target, with the fully stripped 38 Ca ejectiles being subsequently separated by their charge-tomass ratio, q/m. A position-sensitive silicon detector, which can be inserted temporarily at the focal plane of the spectrometer, allows us to identify any impurities in the beam. With that detector removed, the 38Ca beam from the spectrometer's acceptance slits then exits the vacuum system through a 51-μm-thick Kapton window, passes through a 0.3-mm-thick BC404 scintillator, used to count the ions, and then through a stack of aluminum degraders, finally stopping inside the 76-μm-thick aluminized Mylar tape of a fast tape-transport system. The combination of q/m selectivity in the spectrometer and range separation in the degraders provides implanted samples that we have determined to be better than 99.7% pure 38Ca, with the main surviving trace contaminants being 35Ar and 36K. Up to 20,000 atoms of 38Ca can be implanted in the tape in one second. Each 38Ca sample is accumulated in the tape for typically 1.6 s; then the beam is turned off and the tape moves the sample in 200 ms to the shielded counting location, where data are collected for 1.6 s, after which the cycle is repeated. This computercontrolled sequence is repeated continuously, for up to a week, until sufficient statistics have been accumulated. Fig. 2 also shows the arrangement we use to measure branching ratios. The sample is positioned precisely between a 1-mmthick BC404 scintillator to detect β þ particles, and our 70% HPGe detector for γ rays. We save β–γ coincidences event-by-event, recording the energies of each beta and gamma, the time difference between them, and the time that the event itself occurred after the beginning of the counting period. For each cycle we also record the number of 38Ca atoms deposited in the tape as a function of time, the total number of beta and gamma singles, and the output from a laser ranging device that records the distance of
J.C. Hardy et al. / Applied Radiation and Isotopes 87 (2014) 297–301
Momentum Achromat Recoil Spectrometer (MARS)
299
39
K beam (1170 MeV) H2 gas target
Shielding HPGe detector
Tape Deck
* Sample
Tape Deck
Thin plastic detector
Fig. 2. Experimental arrangement used for the 38Ca branching-ratio measurement. For the half-life measurements, the HPGe detector and thin plastic β detector are replaced by a 4π gas proportional counter; the tape passes between the halves of that counter and stops when the collected source is centered between them.
the stopped tape from the HPGe detector. From cycle to cycle the latter distance can change by a few tenths of a millimeter, enough to require a small adjustment to the HPGe detector efficiency.
4. Measurement methods We determine β-decay branching ratios from the corresponding intensities of the β-delayed γ-ray peaks, which predominantly correspond to γ-transitions to the isomeric 0 þ state at 130 keV in 38 K (see Fig. 1). If the γ ray de-exciting state i in the daughter is denoted by γi, then the β-branching ratio, Ri, for the β-transition populating that state can be written: Ri ¼
N βγi k; Nβ εγi
ð1Þ
where Nβγi is the total number of β–γ coincidences measured in the γi peak, Nβ is the total number of β singles, εγi is the detector efficiency for γ ray, γi, and k is a small correction factor (i.e. k 1) that accounts for dead-time and pile-up (together, a 1.3% effect), coincident summing (γ's with 511-keV annihilation radiation, a 2.8% effect), and the differences in the β-detector efficiency for the different energy transitions participating in the 38Ca decay (a 0.1% effect). We eliminate random coincidences separately by using the β–γ relative-time spectrum, in which the prompt coincidence peak stood prominently above the flat random distribution. Eq. (1) highlights the importance of having a pure sample – so that Nβ can be relied upon – as well as having a precise absolute efficiency calibration for the γ-ray detector, and a reasonable knowledge of relative efficiencies in the beta detector. Our HPGe detector's absolute efficiency has been accurately determined (to 70.2% for 50–1400 keV γ rays and to 70.4% up to 3500 keV) from source measurements and Monte Carlo calculations (Helmer et al., 2003, 2004). The relative efficiency of the plastic scintillator has been determined as a function of β energy by Monte Carlo calculations, which have been checked by comparison with measurements on conversion-electron sources (Golovko et al., 2008). As can be seen from Fig. 1, by measuring the β-delayed γ rays – i.e. γ rays in 38K that are emitted following the β decay of 38Ca – we can obtain branching ratios for all the 38Ca β-decay branches
except the superallowed one. Of course, we can obtain the ratio for the latter by summing all the measured branches and subtracting the total from 100%. This has a very salutary effect on the relative precision. Since the total branching ratio for all the nonsuperallowed transitions is about 23%, a relative precision of 0.3% on that total becomes a relative precision of 0.09% on the 77% value for the superallowed branch. For half-life measurements, preamplified signals from our 4π gas proportional counter are passed to a high-gain ( 500) fast filter amplifier, with saturating pulses being clipped. The amplified and clipped pulses are then passed to a discriminator with very low threshold (150–250 mV). The discriminator output is split and sent to two fixed-width, nonretriggering and nonextending gate generators, which establish different dominant dead times in the two separate streams, both of which are multiscaled. Having two channels with different dead times allows us to confirm that our corrections for dead-time losses are accurate. See Iacob et al. (2010) for a more complete description of this system. Recently we have also been developing a digital-pulse system, which allows us to store each pulse and its time of arrival digitally for later analysis. For single component decays the analysis is straightforward. However, in cases like that of 38Ca (see Fig. 1), the detected positron-decay spectrum combines the 444-ms decay of 38Ca with the growth and decay of its 924-ms daughter 38Km. To achieve the ultimate precision, it is important for us to know, rather than to fit, the number of daughter nuclei relative to the number of parent nuclei when the counting period begins. Although we implant a pure beam of 38Ca, some of these nuclei will have decayed in our collected sample before it is moved to the counting position, and the daughterto-parent ratio can only be reliably calculated if we know of any changes in the rate of deposition of 38Ca that might have occurred during the production period of each cycle. Signals from the thin plastic detector between the exit of the spectrometer and the tape give us the exact deposition rate, which we record as a function of time for each cycle and use subsequently to determine the daughterto-parent ratio at the start of each counting period. The main contributors to the final uncertainty on the 38Ca half-life are the uncertainties in (1) the 38Km daughter's half-life, and (2) the small amount of 35Ar impurity present in the collected samples (see Table I in Park et al., 2011).
300
J.C. Hardy et al. / Applied Radiation and Isotopes 87 (2014) 297–301
5. Current status of results Measurements of the ft values for superallowed 0 þ -0 þ β transitions have been going on for more than half a century with ever increasing precision. The most recent survey of world data was published by Hardy and Towner in 2009. It lists the ft values for 13 transitions, which were precisely determined from more than 150 independent measurements – including many of ours – which have contributed to the three input quantities, QEC, t1/2 and R, for each superallowed transition. On average, each quantity has been independently determined four times, making this a very robust data set. An overview of the results is shown as the solid circles in Fig. 3, where the three measured properties for each transition appear in the top three panels, and the corresponding ft values appear in the fourth panel. In order to expose the fundamental physics underlying these ft values, it is conventional to combine the small theoretical corrections with each ft value and define a “corrected” t value, which is written (Hardy and Towner, 2009) t f tð1 þ δ′R Þð1 þ δNS δC Þ ¼
K 2G2V ð1 þ ΔVR Þ
;
ð2Þ
where K¼ 8120.2787(11) 10 10 GeV 4 s, δC is the isospinsymmetry-breaking correction and ΔVR , δ′R and δNS are radiative corrections. The transition-dependent corrections are applied to ft, while the transition-independent correction, ΔVR , is lumped together with the vector coupling constant, GV. The lowest panel in Fig. 3
10
Q EC (MeV)
5 0 2 0
log t1/2 (s) -2 0
-1 -2 3090
log R
shows these corrected t values. It is striking to see in the figure that the three experimental quantities change over orders of magnitude in the span from Z¼5 to Z¼36, yet the ft values change by less than 3%, and the final corrected t values are all consistent with a single constant value with 70.03% precision: 3071.81(83) s. This convincingly proves the constancy of GV2 to the same precision. Although it is beyond the scope of this paper to go into the details of how the resultant value for GV can be used to test the unitarity of the CKM matrix, the final result itself is too impressive to ignore. The sum of squares of the experimental values for the three elements in the top row of the matrix currently gives the result 1.0001(6) (Hardy and Towner, 2013), in stunning agreement with the unitarity expectation of the Standard Model. The value of Vud, which is derived from the superallowed result for GV, is by far the dominant contributor to this sum. A complete description of this aspect of the subject appears in a review article by Towner and Hardy (2010). One might well ask why it is interesting to add still more points to the plots in Fig. 3. The answer comes from the fact that the uncertainty on Vud is now dominated not by experiment but by the theoretical correction terms that appear in Eq. (2). In particular, δC and δNS both depend on nuclear-structure calculations and can differ significantly from transition to transition. It is they which are almost entirely responsible for replacing the variations in the plotted ft values with the consistency seen in the t values. The calculations of δC and δNS are completely independent of the ft-value measurements, so their effectiveness in removing the variations goes a long way to supporting their validity. However their uncertainties remain significant and any improvement would improve the Vud uncertainty as well. This can best be done through measurements made of new transitions with very large calculated δC and δNS corrections. The argument is that if the t values for transitions that have large correction terms are consistent with the others, then we can be assured of the calculations' reliability for the transitions whose corrections are much smaller. The theoretical uncertainty could thus be reduced. The superallowed transition from 38Ca, which we have used in this report to illustrate our techniques, is just such a case: its ft value has never before been measured precisely and it has relatively large correction terms. Its results appear as open circles in Fig. 3, published results for its QEC value (Eronen et al., 2011) and its half-life (Park et al., 2011) in the top two panels and a preliminary value for its branching ratio, 77.4(1) %, in the third panel. Clearly, in spite of its having unusually large corrections, its t value agrees well with the other transitions. 6. Conclusions
ft (s) We have established a metrology facility for short-lived activities that are produced with an accelerator. With it, we have measured half-lives and β branching ratios to high precision (0.03% for half-lives and 0.1% for branching ratios). Our methods have been described briefly and their capabilities illustrated with measurements on the superallowed β decay of 38Ca.
3060 3030 3080 3070
Acknowledgements
3060 0
10
20
30
40
Z of daughter nucleus Fig. 3. Results from the most recent survey of 13 precisely measured superallowed 0 þ -0 þ β transitions appear as solid black circles. The parents of these transitions, from left to right, are 10C, 14O, 22Mg, 26Alm, 34Cl, 34Ar, 38Km, 42Sc, 46V, 50Mn, 54Co, 62 Ga and 74Rb. The top three panels present the average of measured QEC, log t1/2 and log R values for each transition. The bottom two panels give the corresponding ft and t values. The shaded horizontal line in the bottom panel represents the overall average t value for all transitions. All uncertainties are shown: in the cases where none are visible, they are smaller than the data point. Recent results for 38Ca are shown as open circles.
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 Cameron, J.A., Singh, B., 2008. Nuclear data sheets for A ¼ 38. Nucl. Data Sheets 109, 1–170. Eronen, T., Gorelov, D., Hakala, J., Hardy, J.C., Jokinen, A., Kankainen, A., Kolhinen, V.S., Moore, I.D., Penttila, H., Reponen, M., Rissanen, J., Saastamoinen, A., Aysto, J.,
J.C. Hardy et al. / Applied Radiation and Isotopes 87 (2014) 297–301 2011. QEC values of the superallowed β emitters 10C, 34Ar, 38Ca, and 46V. Phys. Rev. C: Nucl. Phys. 83, 055501. Eronen, T., Hardy, J.C., 2013. High-precision QEC-value measurements for superallowed decays. Eur. Phys. J. A 48, 48. Golovko, V.V., Iacob, V.E., Hardy, J.C., 2008. The use of Geant4 for simulations of a plastic β-detector and its application to efficiency calibration. Nucl. Instrum. Methods Phys. Res., Sect. A 594, 266–272. Hardy, J.C., Towner, I.S., 2009. Superallowed 0 þ -0 þ nuclear β decays: a new survey with precision tests of the conserved vector current hypothesis and the standard model. Phys. Rev. C: Nucl. Phys. 79, 055502. Hardy, J.C., Towner, I.S., 2013. CKM Unitarity normalization tests, present and future. Ann. Phys. 525, 443. Helmer, R.G., Hardy, J.C., Iacob, V.E., Sanchez-Vega, M., Nelson, 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.
301
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. Rad. Isot 60, 173–177. Iacob, V.E., Hardy, J.C., Banu, A., Chen, L., Golovko, V.V., Goodwin, J., Haovat, V., Nica, N., Park, H.I., Trache, L., Tribble, R.E., 2010. Precise half-life measurement of the superallowed β þ emitter 26Si. Phys. Rev. C: Nucl. Phys. 82, 035502. Park, H.I., Hardy, J.C., Iacob, V.E., Banu, A., Chen, L., Golovko, V.V., Goodwin, J., Horvat, V., Nica, N., Simmons, E., Trache, L., Tribble, R.E., 2011. Precise half-life measurement of the superallowed β þ emitter 38Ca. Phys. Rev. C: Nucl. Phys. 84, 065502. Towner, I.S., Hardy, J.C., 2010. The evaluation of Vud and its impact on the unitarity of the Cabibbo–Kobayashi–Maskawa quark-mixing matrix. Rep. Prog. Phys 73, 046301.