Branching ratio of the super-allowed beta decay of 10C
B. Blank, M. Aouadi, P. Ascher, M. Gerbaux, J. Giovinazzo, S. Grevy, T. Kurtukian Nieto, M.R. Dunlop, R. Dunlop, A.T. Laffoley, G.F. Grinyer, P. Finlay
aa r X i v : . [ nu c l - e x ] A p r EPJ manuscript No. (will be inserted by the editor)
Branching ratio of the super-allowed β decay of C B. Blank , M. Aouadi , P. Ascher , M. Gerbaux , J. Giovinazzo , S. Gr´evy , T. Kurtukian Nieto , M.R. Dunlop ,R. Dunlop , A.T. Laffoley , G.F. Grinyer , and P. Finlay Centre d’Etudes Nucl´eaires de Bordeaux Gradignan, UMR 5797 CNRS/IN2P3 - Universit´e de Bordeaux, 19 Chemin duSolarium, CS 10120, F-33175 Gradignan Cedex, France Department of Physics, University of Guelph, Guelph, Ontario N1G 2W1, Canada Department of Physics, Univeristy of Regina, Regina, SK S4S 0A2, Canada Department of Physics and Astronomy, KU Leuven, Celestijnenlaan 200 D, B-3001 Leuven, Belgiumthe date of receipt and acceptance should be inserted later
Abstract
In an experiment performed at the ISOLDE facility of CERN, the super-allowed β -decay branch-ing ratio of C was determined with a high-precision single-crystal germanium detector. In order to eval-uate the contribution of the pile-up of two 511 keV γ quanta to one of the γ -ray peaks of interest at1021.7 keV, data were not only taken with C, but also with a Ne beam. The final result for thesuper-allowed decay branch is 1.4638(50)%, in agreement with the average from literature.
PACS.
XX.XX.XX No PACS code given
Super-allowed 0 + → + β decay is a powerful tool to ex-plore properties of the fundamental weak interaction. The-se transitions have been used to test the conserved vectorcurrent (CVC) hypothesis as well as to determine the vec-tor coupling constant G v and the V ud Cabbibo-Kobayashi-Maskawa quark mixing matrix element [1]. To achievethese goals, the f t value of 0 + → + β decays has tobe measured precisely, which requires precise knowledge ofthe β -decay Q value, half-life and super-allowed branchingratio for as many nuclei as possible. Once this is achieved,the corrected F t values can be determined: F t = f t (1 + δ ′ R )(1 + δ NS − δ C ) = k G v (1 + ∆ vR )where δ ′ R , δ NS , and ∆ vR are radiative corrections and δ C is an isospin breaking corrections. With these corrected F t values, physics beyond the standard model (SM) ofparticle physics can be explored.These extensions of the SM can be of different nature,one of them being the addition of scalar or tensor cur-rents to the well-known vector and axial-vector currents.The possible addition of a small scalar contribution to theFermi transitions can be tested with 0 + → + β decay.With only the vector current contributing, the corrected F t values should be constant, whereas the addition of ascalar term yields F t values which, due to an additionalterm in the Fermi function, are dependent on the Q value a) Present address: Xanadu, 777 Bay Street, Toronto, On-tario, M5G 2C8, Canada of the decay. This can be observed in particular for nu-clei with small Q values, i.e., in the series of well-known0 + → + β decays, for the lightest super-allowed emitters C and O (see Figure 7 in [1]). un c e r t a i n t y ( x - ) C fT
B.R. d ’ R d C - d NS Figure 1.
Error budget for the F t value of C. By far thehighest contribution comes from the super-allowed branchingratio of C. B. Blank et al. : Branching ratio of the super-allowed β decay of C Table 1.
Literature values for the super-allowed branching ratio of C prior to the present experiment.Sherr Freeman Robinson Kroupa Nagai Fujikawa Savard averageet al. [2] et al. [3] et al. [4] et al. [5] et al. [6] et al. [7] et al. [8] [1]1.65(20) % 1.523(30) % 1.465(14) % 1.465(9) % 1.473(7) % 1.4625(25) % 1.4665(38) % 1.4646(19) %
Before the present work, the world data for C decaywere as follows [1]: – the Q value is Q EC = 1907.994(67) MeV yielding astatistical rate function of f = 2.30169(70) – the half-life is T / = 19301.5(25) ms [9] – the super-allowed branching ratio is BR = 1.4646(19) %.This value stems effectively from two experiments per-formed with large germanium detector arrays. Valuesof 1.4665(38)% [7] and 1.4625(25)% [8] were obtained.Table 1 gives all literature values. – the theoretical corrections are δ ′ R = 1.679(4)% and δ C − δ NS = 0.520(39)%.The value of ∆ vR is presently discussed in several the-oretical papers [10,11,12,13,14] and has a considerableuncertainty. However, as it is not affecting the determi-nation of the corrected F t value for C, we refrain fromcommenting on its value.
Figure 2.
Partial decay scheme of C. The quantities mea-sured in the present experiment are given in red.
In Figure 1, we plot the uncertainties of these differentinputs for the determination of the F t value of C. Thebranching ratio is by far the most important contributorto the error bar of the F t value for this nucleus. The aimof the present work is to contribute to the improvementof the super-allowed branching ratio of C. Although thedecay scheme of this nucleus is quite simple (see Figure 2), the difficulty in the present endeavour arises from the factthat the γ ray at 1021.7 keV has to be measured in thepresence of possible pile-up of two 511 keV photons in the γ -ray detector. Therefore, in addition to the measurementof the C decay itself, additional measurements with Nehave been performed, a nucleus which is also a β + emitterwith a half-life (17.22 s) and a Q value (3238.4 keV) similarto those of C but no γ ray close to the pile-up energy. The experiment was conducted at the ISOLDE facility ofCERN. A 1.4 GeV proton beam from the PS-Booster im-pinged on a CaO target with an maximum intensity ofabout 2 µ A for the production of C and about a factorof 5 less for the production of Ne. C and Ne wereionised with a VD7 plasma ion source [15]. After mass se-lection with the ISOLDE high-resolution separator HRS,the beam was sent to the LA1 experimental station, wherethe detector set-up was mounted. The ISOLDE beam gatewas constantly open to accept the full intensity extractedfrom the ISOLDE target. However, the number of pro-ton pulses in a CERN ”supercycle” was varied over thewhole experiment ranging from 3 out of about 30 cyclesper supercycle to half of the cycles in a supercycle. Forruns where we took half of the cycles in a supercycle (infact one out of two cycles), the detection rate was constantover the course of the run. For runs with only a few cyclesper supercyle, they were spread roughly regularly over thesupercycle (e.g. cycles 1, 11, and 21 for 30 cycles per su-percycle) to have a detection rate as constant as possiblein our detectors.There was no detectable contamination for the Nebeam, whereas the situation was worse for the C runs.At the beginning of the experiment, tests were made bythe target team to check whether the production of atomic C is more favourable than the production of C Omolecules. It turned out that CO molecules are producedwith an intensity about a factor 2 larger than atomic C.In addition, the HRS could not be set on masses as smallas A=10. However, at mass 26, not only C O arrivedat the detection station, but also C O and N . Theproduction of C O was negligibly small (2.8 × − com-pared to C O). N was produced as much as C Oand gave thus twice as much 511 keV γ rays.The detection set-up (Figure 3) consisted of a vacuumchamber with an aluminium catcher foil (200 µ m thick-ness) and a double-sided silicon strip detector (DSSSD,500 µ m thickness) with 16 X and 16 Y strips and a pitch of3mm, installed about 1 mm behind the catcher foil. TheDSSSD served to optimise and control the implantation . Blank et al. : Branching ratio of the super-allowed β decay of C 3
Figure 3.
The experimental set-up of the present experiment.In the vacuum chamber, a catcher foil intercepted the C Oand Ne beams. The implantation distribution was followedon-line by detecting the β particles in a double-sided siliconstrip detector installed about 1 mm behind the catcher foil.The precisely calibrated germanium detector was installed ata distance of 15.00(1) cm or 20.00(1) cm from the catcher foil. profile of the beam on the catcher foil. Gamma rays weredetected outside the vacuum chamber (1.9 mm window ofaluminium) by a precisely efficiency calibrated germaniumdetector [16] at a distance of 15 or 20 cm. The full-energydetection efficiency for the γ rays of interest at 718.3 keVand 1021.7 keV were 0.28279(17)% and 0.22348(15)% at adistance of 15 cm as well as 0.17671(66)% and 0.14157(83)%at 20 cm.The germanium detector was precisely calibrated in ef-ficiency at a distance of 15 cm [16]. If the detector modelwe use in the simulations were perfect, the efficiencies cal-culated at a distance of 20 cm should be correct, too.However, an inspection of the measurements at 15 cm andat 20 cm (see below) evidenced a systematically higherbranching ratio at 20 cm. We therefore embarked in anew series of calibration measurements of the germaniumdetector efficiency at 20 cm. For this purpose, we per-formed measurements at 15 cm and 20 cm with sourcesof Co,
Cs, and
Bi. The measurements with thetwo Co lines and the 1063 keV line of
Bi allowed usto determine the efficiency ratio between the 15 cm and20 cm positions for an energy close to the 1022 keV lineof C, whereas we used the Cs γ ray at 662 keV andthe Bi line at 570 keV to determine the experimentalefficiency ratio for the 718 keV γ ray for C. We assumedthat the variation of the ratios with energy is sufficientlysmall so that the slightly lower calibration energies for the718 keV line and the slightly higher calibration lines forthe 1022 keV line yield acceptable ratios for the energiesof C.The finding was that the calculated efficiencies of the718 keV and 1022 keV lines at 20 cm were factors of0.8(29) × − and 4.8(15) × − too small, respectively.We therefore corrected the calculated efficiencies at 20 cmwith these factors. For the uncertainties, we added in quadra- ture the error bar of the correction factor and the correc-tion factor itself to the uncertainty of the calculated ef-ficiency, which yields in the end the larger error bars forthe efficiencies at 20 cm.Two data acquisitions (DAQ) were run in parallel. Thefirst DAQ had a single parameter which was the germa-nium energy. In addition, a scaler module was read foreach event. This scaler counted the number of proton pulsesent to ISOLDE since the beginning of the run, the num-ber of γ -ray triggers from the germanium detector and thetime of each event with a precision of 1 millisecond. Thisdata acquisition was triggered only by the germanium de-tector.The second data acquisition was only used on-line. Itregistered the germanium energy signal and the energysignals from the 32 strips of the DSSSD. Similar to the firstDAQ, a scaler registered the proton pulses, the germaniumtriggers and the time. This DAQ allowed us to optimisethe beam implantation profile by detecting the β -decayposition profile with the DSSSD and to supervise it duringthe experiment. It was triggered by the detection of a β particle in the DSSSD. After optimisation, the beam spotwas centred on the catcher foil and had a size of about8 mm (FWHM) in X and Y, negligible compared to thedistance of the source from the detector. As mentioned in the introduction, the main difficulty inthe present experiment is to correctly evaluate the 511 keV -511 keV pile-up which adds to the 1021.7 keV peak fromthe decay of C. For this purpose, the C activity trans-ported to the detection set-up was largely varied by takingmore or less proton pulses per supercycle which modifiesthe pile-up probability as a function of the 511 keV de-tection rate per second squared. In addition, we modifiedonce during the experiment the distance between the ra-dioactive sample and the germanium detector entrancewindow from 15 cm to 20 cm therefore varying both thetotal rate and the pile-up probability. This pile-up prob-ability is also directly proportional to the shaping timeof the germanium signal. We therefore used two shapingtimes for the germanium signal of 2 µ s and 1 µ s. Table 2gives details about the settings used in the different runsof the experiment.The idea of these changes in decay rate in the set-up, indistance and in shaping time is that in the end we have toget the same branching ratio, independent of the settings.This procedure is meant to search for systematic errors inour measurements and will be tested below.However, these changes were not enough to quantita-tively evaluate the pile-up probability. For this purpose,we spent an important part of the beam time on mea-surements with Ne (about 18 h as compared to 78 hfor C). Ne has decay characteristics similar to C,however, without having a γ ray at 1022 keV. Therefore,counts above background in this region can only comefrom pile-up of two 511 keV γ rays. By measuring the B. Blank et al. : Branching ratio of the super-allowed β decay of C Table 2.
Settings used throughout the experiment. Germa-nium signal shaping times and germanium distance were mod-ified several times during the experiment.isotope run number shaping time distance C 42 - 55 2 µ s 15 cm C 56 - 97 1 µ s 15 cm C 98 - 116 2 µ s 15 cm Ne 118 - 127 2 µ s 15 cm Ne 128 - 133 1 µ s 15 cm Ne 134 - 144 2 µ s 20 cm C 145 - 173 2 µ s 20 cm
511 keV and the 1022 keV rate, we are able to determinethe pile-up probability on an absolute scale.
Figure 4.
Gamma-ray spectrum in the region of the 1022 keVpeak. The upper part shows a spectrum from a Ne run, wherethe pile-up contribution from two 511 keV γ quanta and thebackground is visible. The lower spectrum contains in addition γ rays at 1021.7 keV from the decay of the second excited stateof C. The different curves give the different contributions tothe spectrum. The pile-up contribution in the lower figure iscalculated and subtracted before determining the integral ofthe peak.
Figure 4 shows the region around E γ = 1022 keV for arun with a Ne beam and with a C beam. In the Necase, the spectrum can be described by a background- contribution step function and a Gaussian with a low-energy tail. In the case of C, the additional peak at1021.7 keV is seen on top of these two contributions.The pile-up correction as introduced below dependssensitively on the counting rate of the 511 keV γ rays.Therefore, a run selection was performed where only runswith a constant 511 keV γ -ray rate were kept. Changesin this rate were caused by modifications of the CERNsupercycle or other problems with the PS-Booster or theISOLDE front-end during a run. These problems forcedus to remove 33 runs out of 99 for the C measurementsand 1 run (out of 26) for the Ne measurements totallingabout 34% and 3.5% of the running time for each isotope,respectively.
Figure 5.
Simulated γ -ray spectrum for a single-energy γ rayof 511 keV. The time distribution of the events was takenfrom a Ne run (run 118, see figure 7 for the time structureof this run). Depending on the time difference between twoevents, a total signal energy between 1022 keV (no or negli-gible time difference between two events) and 511 keV (timedifference longer than the signal width) is found. Events above1022 keV come from triple and quadruple coincidences. Theedge at about 600 keV is due to the fact that we use a DAQtime window of 10 µ s. For a signal shaping time of 2 µ s, thesecond event starts to be cut by this time constraint. In order to correctly determine the number of countsunder the 1021.7 keV peak, we have to subtract this pile-up contribution. As mentioned earlier, the pile-up of two511 keV γ ray depends quadratically on the rate of these γ rays and on the time difference between the two events.If the time difference is close to zero, an energy signal at1022 keV results. The more the two γ rays are separatedin time, the lower is the signal energy with the lower limitbeing a 511 keV signal. This limit corresponds in fact tothe case where there is no pile-up of the signals in thedetector. The exact shape of the pile-up peak in the spec-trum depends on the signal shape from the electronics (inparticular the shaping amplifier).Figure 5 shows a simulation where only 511 keV γ rays were considered. The events between 511 keV and1022 keV come from two events which overlap more and . Blank et al. : Branching ratio of the super-allowed β decay of C 5 more in time. At 1022 keV, a perfect overlap is reached.Above 1022 keV, triple coincidences and above 1533 keVquadruple coincidences come into play. The pile-up proba-bility for each run can be determined by these simulationsas the number of counts above the 511 keV peak. It variedas a function of the total counting rate of the germaniumdetector between 0.2% and 2% for the different runs. De-tails of the MC simulations will be given below. Ne runs
We used the Ne runs to determine the pile-up probabil-ity. For this purpose, the pile-up peak at 1022 keV andthe 511 keV peak were fit to determine their functionalform and their intensity. It was found that the shape ofthe 1022 keV peak is always the same, independent of thesignal shaping time or the pile-up rate. Only the pile-upprobability, i.e. the number of counts in the pile-up peak,depends on these two parameters. Therefore, the 511 keVrate and the 1022 keV pile-up rate can be linked by thefollowing formula: N = N ∗ τ (1)where N x are the rates of the 511 keV and 1022 keV peaksand τ is a pile-up time. We found in addition that τ is con-stant for a fixed experimental shaping time of the experi-ment electronics. To go from a shaping time of 2 µ s (mostof the runs) to 1 µ s, the pile-up time has simply to be di-vided by two. Figure 6 shows the pile-up times for all Neruns as determined with the formula above. Although the χ of all the average values is about 2, we consider thatwe can use a constant pile-up time for all runs. Figure 6.
Pile-up times as determined from formula 1 for each Ne run. The average values for the different settings agreewith each other satisfactorily, although the χ is only about2 for the different averages. The values for the 1 µ s runs weremultiplied by a factor 2. Now that we have determined the exact functionalform and the pile-up time with the Ne runs, we can use this information for the pile-up subtraction of the C runs (see Figure 4). However, this procedure is onlycorrect, if the time distribution is the same for both nu-clei. An inspection of this time distribution (see Figure 7)shows that this is not at all the case. The noble gas char-acter of Ne allows this isotope to diffuse and effuse inthe ISOLDE target - ion-source (TIS) ensemble extremelyrapidly. Therefore, a well-pronounced time structure dueto the proton impact on the ISOLDE target and the Nehalf-life is seen in the case of Ne (lower figure), whichis completely absent in the case of the C O moleculesand its contaminants, which are extracted from the TISensemble much slower that the proton beam time struc-ture and the C half-life.As in the case of Ne this time distribution is notconstant, a correction factor has to be applied when com-paring Ne and C. This factor will be determined inthe following via Monte-Carlo (MC) simulations. C run time (s) G e t r i gg e r ( / s ) Run = 94 Ne run time (s) G e t r i gg e r ( / s ) Run = 1181000120014001600180020002200 0 20 40 60 80 100 120 140 160 180 20035004000450050005500 0 20 40 60 80 100 120 140 160 180 200
Figure 7.
The two figures show the different event time struc-tures as seen by the germanium detector. The upper part showsthe germanium triggers as a function of time for a run with the C activity, whereas the lower spectrum shows the same in-formation for a Ne run. Although both nuclei have approxi-mately the same half-life, the time structure at the experimentis largely different due to the different release properties forCO molecules and the associated contaminants and Ne. Inthe latter spectrum, the impinging of the PS Booster protonbeam on the ISOLDE target (every 12s and 13.2s, multiples ofthe PS Booster time structure of 1.2 s) is clearly visible. Forthe C runs, the contaminants O and N with their longerhalf-lives also contribute to wash out the time structure.
If the time structure of the Ne and the C runs werethe same, the pile-up probability determined with Necould be used directly for the C runs. However, this isnot the case. Therefore, we developed a MC procedureto determine a correction factor to correlate the pile-upprobabilities of Ne and C. B. Blank et al. : Branching ratio of the super-allowed β decay of C Figure 8.
Experimental spectra and a spectrum generated bya Monte-Carlo procedure. a) Experimental spectrum from a Ne run over basically the full energy range. b) Same spec-trum, however, with the 1022 keV pile-up peak removed andthe 511 keV peak increased to compensate for the removal ofcounts from this peak by pile-up (see text for details). c) Sim-ulated spectrum from a Monte-Carlo simulation which uses asinputs the energy distribution from the spectrum in b) and theevent time structure as displayed in fig. 7. The dashed verti-cal lines indicate the region where the effect of pile-up of two511 keV γ rays was removed. This MC procedure uses the energy spectrum of eachindividual run and the associated time structure we mea-sured with the scaler module with a precision of 1 ms.Within one millisecond, we distributed the events ran-domly. In order to simulate the pile-up, we first removedfrom the experimental spectrum (see Figure 8a) all counts above background in the region of the 1022 keV peak. Forthis purpose, we first set all channels between 900 keV and1050 keV to zero and added then a smooth backgroundwith statistical fluctuations. In addition, we increased thenumber of counts in the 511 keV peak by the pile-up prob-ability (0.2% - 2% for the different runs, see figure 5, whichallowed us to determine the percentage of 511 keV eventsremoved from the 511 keV peak due to pile-up) to producea 511 keV peak ”without the effect of pile-up losses in thispeak”. The result is shown in Figure 8b. This is then theenergy input for the MC simulations. When used togetherwith the event time distribution we can generate a simu-lated spectrum with its pile-up contribution (Figure 8c).The only free parameter in these simulations is the”simulation shaping time”, a parameter in the functionalform of the germanium detector signal used in the simula-tions which is equivalent to the experimental shaping timeand varies the time width of the signal. It was adjustedsuch that it matched the time structure of the experimen-tal signal.This procedure can be applied to the Ne runs butalso to the C runs, where in addition to the pile-upcounts also the 1021.7 keV counts are removed. As wecan not remove all pile-up events from the input energyspectrum (we correct only the 511 keV and the 1022 keVregions), the simulated spectrum differs from the experi-mental one by several aspects. For example, the simulatedspectrum is generally shifted towards higher energies, be-cause the experimental input spectrum contains γ raysthat are already piled-up. The simulation further piles-up these same events and shifts events to higher energies.This is particularly visible below 511 keV where counts inthe spectrum are lost. However, as we are only interestedin the regions around the 511 keV and the 1022 keV peaks,we believe that this procedure is sufficiently correct.Once these simulations were completed, the 511 keVand the 1022 keV peaks were fit as for the experimen-tal spectra. The integrals of these peaks are plotted inFigure 9. In order to determine the matching factor be-tween the Ne and the C data, we fit these data witha second-order polynomial with a free scaling factor forthe Ne data to account for the different time structure.The result is a scale factor of 1.04(3). The error bar wasdetermined by varying the simulation shaping factor by ±
200 ns which is roughly the parameter range where theexperimental and the simulation signal shape are in goodagreement. γ ray of C A direct test of the pile-up correction during the C runsis not possible with the 511 keV - 511 keV pile-up, becauseon top of the pile-up peak, the γ rays of energy 1021.7 keVadd. However, the pile-up can at least be checked to someextent with the pile-up of two γ rays of 718 keV. For these γ rays, the statistics is about a factor of 10 lower than for511 keV γ rays, but it allows us nonetheless to test thecorrection. . Blank et al. : Branching ratio of the super-allowed β decay of C 7
Figure 9.
Results from the MC simulations of all runs (seetext for details). The number of counts in the 1022 keV pile-up peak is plotted versus the number of counts in the 511 keVpeak squared. This plot allows us to readjust the data from the Ne runs by a small factor to take into account the differentevent time structures of the C and the Ne runs. The Nedata have to be increased by a factor of 1.04(3). The line isthe fit of the data after correction with its uncertainty (dashedlines). The open blue symbols are equivalent to the full bluesymbols before multiplying them with the scale factor.
The same analysis as for the 511 keV pile-up has there-fore been done also for this γ ray. By means of equation 1we determined the pile-up time τ run by run. The result isshown in Figure 10. The pile-up time is in perfect agree-ment with the value obtained with the 511 keV pile-upduring the Ne runs and of the order of 1 µ s (to be com-pared to Figure 6). Figure 10.
Pile-up times as determined for all C runs fromthe pile-up of two 718 keV γ rays from the decay of the firstexcited state of C. The runs from 78 to 98 are very lowstatistics runs and thus have large fluctuations. The values forthe 1 µ s runs were multiplied by a factor of 2. The results for the super-allowed branching ratio of Care obtained run by run as follows. For each C run, threepeaks are fitted: (i) the 511 keV annihilation peak, (ii) the718 keV peak from the γ decay of the first excited state of B to its ground state, and (iii) the 1021.7 keV peak fromthe decay of the second excited state of B to its first ex-cited state after subtraction of the pile-up contribution.The pile-up contribution is obtained from the countingrate of the 511 keV γ rays by means of equation 1 and anadditional small correction factor to take into account thedifference in time structure between a Ne and a C run(see section 3.2). The number of pile-up counts thus de-termined is subtracted from the γ -ray spectrum with thecorrect pile-up peak shape after which the 1021.7 keV peakcan be fitted with a Gaussian and a background function.As there is no β -decay feeding of the ground stateof B within the limits of the precision of our experi-ment, the super-allowed branching ratio of interest is ob-tained from the efficiency-corrected counting-rate ratio of1021.7 keV to 718 keV γ rays. Figure 11 shows this branch-ing ratio for the different C runs. Averaging these run-by-run results yields a branching ratio of BR = 1.4638(39)%with a normalised χ ν = 1.18. This result contains alreadythe increase of the uncertainty by the square root of the χ ν . Figure 11.
Super-allowed branching ratio as determined runby run. The average of all data is BR = 1.4638(39)% with χ ν =1.18 (already included in the error bar given). The individualaverages are 1.4660(48)% (2 µ s, 15 cm), 1.4591(65)% (1 µ s, 15cm), and 1.4717(111)% (2 µ s, 20 cm). The χ ν values are 0.99,1.39, and 1.11 and were used to inflate the uncertainties quoted. The measurements with different electronics shaping timesand with different distances between the activity and thegermanium detector agree with one another. The aver-aging of all individual runs yields a reduced χ ν of 1.18, B. Blank et al. : Branching ratio of the super-allowed β decay of C which is a sign of good agreement of the branching ra-tios determined for the different runs. In addition, thebranching ratios determined as the averages for the differ-ent settings (two different shaping times, one additionalposition) agree with each other (1.4660(48)% (2 µ s, 15cm), 1.4591(65)% (1 µ s, 15 cm), and 1.4717(111)% (2 µ s,20 cm)). Therefore, there is no reason to add a systematicuncertainty from the different experimental settings.A first systematic uncertainty comes from the factorapplied between the Ne and C pile-up correction. Asstated above, this factor is 1.04(3). By refitting the 1022 keVpeak with factors of 1.01 and 1.07, we obtain branchingratios of BR = 1.4664(40)% and 1.4607(41)%. This en-ables us to determine a systematic deviation with respectto the central value of ± Ne data. It is determined by five parameters: (i) the po-sition of the peak kept fixed once optimised, (ii) the sigmaof the Gaussian kept also fixed because strongly correlatedwith the parameters of the tail function (see next param-eters), (iii) the step function for the background definedas a certain percentage of the peak height, (iv) the posi-tion of the tail on the low-energy side of the peak, and(v) the pile-up time ( τ = 1.012(12) µ s, see equation 1),which determines the number of pile-up counts from thenumber of counts from the 511 keV counting rate. How-ever, we do not consider the systematic error due to thislast parameter, because this parameter being determinedin the fit of the Ne data the error is largely includedin the variation of the Ne/ C correction factor. Thesystematic errors obtained by varying these parameterswithin their error bars are shown in table 3. With thesesystematic errors included, we obtain our final experimen-tal result for the super-allowed branching ratio of C ofBR = 1.4638(50)%.
Table 3.
Error budget for the present experiment. The sta-tistical uncertainty is summed quadratically with the differ-ent systematic uncertainties to yield a total uncertainty of0.0050%. error type uncertainty (%)experimental statistics 0.0038efficiency simulation 0.0009pile-up correction: Ne/ C pile-up factor 0.0029background step function 0.0001tail position 0.0010total uncertainty 0.0050
Our new value of the super-allowed branching ratio of Cis in agreement with the literature average of 1.4646(19) %. The error bar is a factor 1.5 to 2 larger than the most pre-cise literature values [7,8]. If we average our value withliterature values with an uncertainty less than a factorof 10 larger than the smallest error bar, as prescribed inRef. [1], we obtain a new average branching ratio of BR =1.4644(18)%.Our result slightly modifies the previous world average.As our result is mainly statistics limited, a new experimentwith an improved beam production and increased puritycould allow to yield a competitive result. As an improve-ment of the production rate of C seems to be difficultto achieve, a higher statistics experiment will thereforerequire a longer beam time. However, as the present ex-periment already lasted 5.5 days, a factor of 2 more beamtime is certainly a limit. The measurement at 20 cm con-tributed little to the final result and should certainly beomitted for a future experiment. It would be probablymost reasonable to perform a future measurement onlywith a shaping time of 1 µ s which allows the highest ratewith the smallest pile-up contribution.The production rate of N was as strong as the rateof C- O. This yields twice as much 511 keV γ raysfrom N than from C- O. The contamination from N could be removed by the use of e.g. a Multi-reflectionTime-of-flight Spectrometer (MR-ToF-MS) or a Penningtrap with a resolving power in excess of 10 . If the 511 keVrate can thus be divided by a factor of 3, the pile-up woulddecrease by a factor of 10 and become much less of a prob-lem. We have performed a measurement of the super-allowed β -decay branching ratio of C. After production and sep-aration by the ISOLDE facility, the C- O activity wasconstantly implanted in a catcher foil in front of our pre-cisely efficiency calibrated germanium detector to measurethe γ rays emitted in the decay of C.Our result of BR = 1.4638(50)% is a factor of 1.5 to 2less precise than the most precise literature values. Never-theless the present result demonstrates that the problemswith the pile-up of two 511 keV γ rays can be overcome.In a future experiment, a higher precision can be reachedwith a longer beam time and a better beam purificationscheme. However, it will be very challenging to reach thesame precision for the branching ratio as for the half-lifeand the Q value of C. Acknowledgment
We would like to thank the ISOLDE staff for their ef-forts during the present experiment. The research leadingto these results has received funding from the EuropeanUnion’s Horizon 2020 research and innovation programmeunder grant agreement no. 654002. . Blank et al. : Branching ratio of the super-allowed β decay of C 9
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