We report on a new measurement of the strength of the superallowed 0+-&gt;0+
transition in the beta-decay of 10C: 10C(0+,g.s.)-&gt;10B(0+,1.74MeV)+e+nu. The
experiment was done at the LBNL 88-inch cyclotron using forty seven GAMMASPHERE
germanium detectors. Precise knowledge of this branching ratio is necessary to
compute the superallowed Fermi ft, which gives the weak vector coupling
constant and the u to d element of the Cabibbo-Kobayashi- Maskawa quark mixing
matrix

Asztalos, SJ

Clark, RM

Deleplanque-Stephens, M-A

Fallon, P

Freedman, SJ

Fujikawa, BK

Greene, JP

Lee, I-Y

Lising, LJ

Macchiavelli, AO

MacLeod, RW

Reich, JC

Rowe, MA

Shang, S-Q

Stephens, FS

Wasserman, EG

eScholarship - University of California

Lawrence Berkeley National LaboratoryLBL PublicationsTitleA New Measurement of the Partial 0+-&gt;0+ Half Life of 10C with GAMMASPHEREPermalinkhttps://escholarship.org/uc/item/5681774pAuthorsFujikawa, BKAsztalos, SJClark, RMet al.Publication Date1998-05-29 Peer reviewedeScholarship.org Powered by the California Digital LibraryUniversity of CaliforniaarXiv:nucl-ex/9806001v1  30 May 1998A New Measurement of the Partial 0+ → 0+ Half Life of 10C with GAMMASPHERE.B.K. Fujikawa, S.J. Asztalos, R.M. Clark, M.-A. Deleplanque-Stephens, P. Fallon, S.J. Freedman, I-Y. Lee, L.J.Lising, A.O. Macchiavelli, R.W. MacLeod, J.C. Reich, M.A. Rowe, S.-Q. Shang, F.S. Stephens, and E.G. WassermanUniversity of California and the Lawrence Berkeley National Laboratory, Berkeley, CA 94720J.P. GreeneArgonne National Laboratory, Argonne, IL 60439(July 24, 2013)We report on a new measurement of the strength ofthe superallowed 0+ → 0+ transition in the β-decay of 10C:10C(0+, g.s.) →10 B(0+, 1.74MeV) + e+ + ν. The experimentwas done at the LBNL 88-inch cyclotron using forty sevenGAMMASPHERE germanium detectors. Precise knowledgeof this branching ratio is necessary to compute the superal-lowed Fermi f t, which gives the weak vector coupling constantand the u to d element of the Cabibbo-Kobayashi-Maskawaquark mixing matrix.23.40.-sThe most precise value of the u to d element ofthe Cabibbo-Kobayashi-Maskawa (CKM) quark mix-ing matrix is obtained from measurements of su-perallowed 0+ → 0+ Fermi β-decays in nuclear sys-tems. Specifically, these decay rates determine the nu-cleon weak vector coupling constant GV giving Vud:G2V = G2F |Vud|2(1 + ∆R) where GF is the Fermi cou-pling constant obtained from the muon lifetime and ∆Ris a nucleus independent (“inner”) radiative correction.The conserved vector current (CVC) hypothesis impliesthat superallowed f t-values within isospin-1 multipletsare related to GV by:f (1 + δR)(1 − δC)t ≡ Ft =KG2V |MV|2 (0.1)where |MV|2= 2 is the vector matrix element, f is thefamiliar Fermi statistical rate function, δR is the nu-cleus dependent (“outer”) radiative correction, δC is thecharge dependent correction to |MV|2 = 2 due to isospinsymmetry breaking, and K is the usual β-decay con-stant. The corrected Ft include nuclear and radiativeeffects. Precise determination of GV requires precisionmeasurements of the partial 0+ → 0+ half-life, the β end-point energy, and reliable theoretical calculations of δRand δC. Reference [1] summarized the status of mea-surements and calculations for 10C, 14O, 26Alm, 34Cl,38Km, 42Sc, 46V, 50Mn, and 54Co. The constancy ofFt for these nine precisely measured superallowed de-cays supports the CVC hypothesis. This review suggests|Vud| = 0.9740± 0.0005. Together with the two other el-ements in the first row of the CKM matrix taken fromref. [2], this tests the unitary of the CKM matrix. The re-sult, |Vud|2+ |Vus|2+ |Vub|2≡ |V|2= 0.9972± 0.0013,is more than two standard deviations from the unitaryconstraint.A violation of CKM unitary requires the StandardModel to be extended. A more mundane explanationis unaccounted systematic uncertainties in the difficulttheoretical calculations needed to extract Vud. The cal-culation of the isospin symmetry breaking correction δCis regarded as the most problematic. Figure 1 showsthe most precisely measured Ft as a function of daugh-ter nucleus charge Z. Possible unaccounted Z-dependentcorrections motivated extrapolations to zero charge usingsecond and third order polynomials fits to δC-corrected[3] or uncorrected [4] f t values. The agreement of the ex-trapolated values with unitary suggests that incompleteisospin corrections might explain the discrepancy. The f tfor the superallowed Fermi β decay of 10C is of particularinterest: 10C has the lowest nuclear charge of a superal-lowed Fermi decay. Moreover, all existing calculationsagree that δC for10C is small enough to be neglected.The necessary experimental input are the totalhalf-life, the branching fraction for 10C(0+, g.s.) →10B(0+, 1.74MeV) + e+ + ν, and the superallowed end-point energy. The half-life (19.290 ± 0.012 seconds [5])and the recently revised endpoint energy (885.86 ± 0.12keV [6,7]) are known to high precision; the limiting exper-imental input is the 0+ → 0+ branching ratio. Figure 2shows the 10B and 10C levels important for this measure-ment. The β decay of 10C goes to the 10B(0+, 1.740MeV)or the 10B(1+, 0.718MeV) state. The allowed decay tothe 10B(1+, 2.154MeV) level is known to be small ex-perimentally (< 8 × 10−6) as expected from the mea-ger available energy. The forbidden β decay to the 10Bground state is suppressed by about 10−10. The decayto the 10B(0+, 1.740MeV) state is followed with γ-raysat 1022 keV and 718 keV. The direct ground state de-cay of the 10B(0+, 1.740MeV) level is magnetic octupole,with an estimated branch below 10−12 [8]. The decay tothe 10B(1+, 0.718MeV) state is followed by a single 718keV γ-ray. Therefore the 0+ → 0+ branching ratio is thesame as the γ-ray intensity ratio:b =Iγ(1022keV)Iγ(718keV)=Y(1022keV)Y(718keV)ǫ(718keV)ǫ(1022keV)(0.2)where Y(γ) is the γ-ray yields from 10C β-decay and ǫ(γ)1full energy γ-ray detection efficiencies.This experiment was performed with the GAMMAS-PHERE [9] detector at the Lawrence Berkeley NationalLaboratory 88-Inch Cyclotron. Three measurements arerequired: a measurement of the γ-ray yield ratio follow-ing β-decay, the full energy γ-ray detection efficiencyratio, and the 2 × 511 keV pileup background to the1022 keV γ-ray peak. For the β-decay measurement,the 10C source is produced with the 10B(p, n)10C reac-tion using a 325µg/cm2 thick target of 99.5% enriched10B on a 600µg/cm2 thick carbon backing and a 250 nA8 MeV proton beam. The β delayed γ-rays from 10Cdecay were detected by forty-seven GAMMASPHEREgermanium detectors. The usual BGO Compton sup-pressors were turned off in order to avoid possible sys-tematic effects from “false vetoes” by an unrelated γ-ray. A 35 second beam-on/beam-off cycle with a 1 sec-ond delay was used. We use a technique employed bya previous experiment [3] for measuring the γ-ray ef-ficiency ratio. The efficiency is measured in situ withthe γ-rays of interest by tagging γ cascades preparedby exciting the 10B(1+, 2.154MeV) state. A reducedintensity 10 nA proton beam is used to populate thisstate with 10B(p, p′)10B∗. The 10B(1+, 2.154MeV) →10B(0+, 1.740MeV) transition is tagged with the 414 keVγ-ray. The 10B(0+, 1.740MeV) state then decays to the10B ground state by emitting exactly one 1022 keV γ-rayand one 718 keV γ-ray. The distribution of these γ-ray isisotropic because the cascade begins with the 0+ state.Figure 3a shows the β-delayed γ-ray energy spectrum.We use the following procedure to determine the γ-rayyields. The region around the γ-ray peak is fit to afunction imitating the peak and a smooth underlyingbackground. The peak is modeled by a Gaussian hav-ing small exponential tails and the background is takenas a quadratic polynomial with a resolution smoothedstep function. The step function accounts for the discon-tinuity in the background caused by scattering of γ-raysin inactive material in front of the detector. Peaks forbackground radiation are included. The fit is performedby minimizing a Ξ-square function [10] using MINUIT[11]. The fitting procedure is used only for determiningthe background; the yields are computed by subtractingthe fitted background from the data.Figure 3b shows the γ-ray spectrum from the10B(p, p′)10B∗ reaction. The gating process is as follows.A fit to the 414 keV peak is performed using the methoddescribed. The result is used to determine the energywindow, defined to be ±1σ centered about the peak. The414 keV peak is on a smooth background which includesCompton scattering of higher energy γ-rays. The effect ofthis Compton background is estimated by taking elevenadditional energy gates below and twelve above the 414keV peak. The Compton background is determined foreach gate and a quadratic polynomial interpolation isused to estimate the Compton background under the 414keV γ-ray peak. The background under the 414 keV peakalso includes a small double escape peak from the 1436keV γ-ray which is emitted in the 10B(1+, 2.154MeV) →10B(1+, 0.718MeV) transition. Since the 1436 keV γ-rayis always emitted with a 718 keV γ-ray and never witha 1022 keV γ-ray, a small correction is applied to theefficiency ratio. This correction is determined from thenumber of counts in the single escape peak and the ra-tio of double to single escapes from an EGS4 [12] MonteCarlo simulation. The accidental γ414 − γ coincidenceswere corrected for by subtracting counts obtained in non-coincident time gates. The accidental gates were normal-ized to the coincidence gate by taking advantage of thefact that it is impossible for two 718 keV γ-rays to bein true coincidence. The normalization factor is chosensuch that the γ718 − γ718 coincidences disappears in thesubtracted spectrum.Since the 1022 keV γ-ray is emitted during the slowdown of the recoiling 10B, a small correction is made toaccount for the kinematical change in solid angle and theDoppler energy shift. The overall correction is reducedbecause of the symmetry of GAMMASPHERE. The sizeof the correction was calculated with Monte Carlo inte-gration using the differential 10B(p, p′)10B∗ cross sectionsfrom ref. [13], the lifetimes and cascade branching ratiosfrom ref. [14], and the stopping powers from ref. [15].The number of background 2 × 511 keV pileup countsin the 1022 keV γ-ray peak is measured using 19Ne asa source of positrons. The 19Ne source is prepared insitu with the 19F(p, n)19Ne reaction by bombarding a325µg/cm2 thick PbF target on a 600µg/cm2 thick car-bon foil backing with a 100 nA 8 MeV proton beam. Likethe 10C decay measurement, a 35 second bombardmentand counting cycle was used. The 19Ne decay is similarto 10C with a 17.239 ± 0.014 sec. half-life and a simi-lar β endpoint energy (1705.38 ± 0.80 keV). The 19Neis a source of 511 keV annihilation γ-rays with no true1022 keV γ-ray, and the entire peak at 1022 keV is dueto pileup. In order to normalize the 19Ne data to the10C data, we use the following technique. The GAM-MASPHERE data stream contains a 1 MHz clock andthe absolute time of each trigger is known to 1 µs. Usingthis information, we determine the number N (2 × 511) of511 keV γ-rays within a 1 µs time bin that follow a 511keV γ-ray with an arbitrary delay for each detector. Likethe summing of two annihilation γ-rays this is a purelyrandom process. Neglecting, for the moment, smalldead time corrections (which are later corrected for),N (2 × 511) = (R511 · T) (R511 · τbin) where R511 is therate of 511 keV γ-rays in a single detector, T is the count-ing time, and τbin = 1 µs is the bin width. Similarly, thenumber of 2 × 511 keV pileup counts in the energy spec-trum is given by: Y (2 × 511) = (R511 · T) (R511 · τpu)where τpu is the pileup rejection time in the GAMMAS-PHERE amplifiers. The rate independent ratio2Y (2 × 511)N (2 × 511)=τpuτbin(0.3)is used to compute the summing correction.With the exception of the 2 × 511 keV pileup, randompileup does not effect the ratio in eqn. 0.2. However, thecorrelated pileup of γ-rays from a single cascade is a pos-sible systematic effect. Specifically, both the 718 keV and1022 keV γ-rays can deposit energy into the same detec-tor, in effect removing counts from the full energy peaks.The effect cancels to first order in the efficiency ratio andan EGS4 [12] Monte Carlo simulation indicates that thiseffect is −0.032(3)%. However, due to the smallness ofthe 10C 0+ → 0+ branch, this effect is significant in thedecay measurement. Only about 1.5% of the 718 keVγ-rays are emitted with a 1022 keV γ-ray, but all 1022keV γ-rays come with a 718 keV γ-ray. Systematically,more 1022 keV γ-rays will be removed from the full en-ergy peak. The pileup correction for a single detectoris estimated by measuring coincidences between differentdetectors in the GAMMASPHERE array. Neglecting,forthe moment, threshold corrections, small variations indetector sizes, and the small γ − γ angular correlation,the pileup correction is equal tofPU =1 + Y(1022·x)Y(1022)1 + Y(718·x)Y(718)(0.4)where Y(γ) is the total γ-ray yield and Y(γ · x) is theγ-ray yield when there is a coincident event in a sec-ond detector. The correction for detector size and γ − γangular correlation are straight forward. The detectorsize is simply scaled by Y(718keV). Since the transition10B(0+, 1.740MeV) → 10B(1+, 0.718MeV) is pure M1and the transition 10B(1+, 0.718MeV) → 10B(3+, g.s.) isprimarily E2, the γ − γ angular correlation is equal to:P (cos θ) = 1 − 0.0714 · P2 (cos θ) [16]. The correction forthreshold is more problematic. GAMMASPHERE usesconstant fraction discriminators (CFD) whose thresholdsare not easily described. To avoid this problem, we en-force a software threshold at 417 keV, well above theCFD threshold. An EGS4 [12] Monte Carlo simulationof GAMMASPHERE is used to correct for the fractionof events below 417 keV.The room background was measured for 17.5 hours af-ter the run. No γ-rays were found in the region of 718keV. However, a background γ-ray, with an energy of1022.6± 0.4 keV, was observed. Based upon constraintson half-life, intensity, and associated γ-rays, the only pos-sible source is the β decay of 120Sb. This was probablyproduced through proton activation, 120Sn(p, n)120Sb, ofthe aluminum alloy foil lining the inside of the GAMMA-SPHERE scattering chamber. In addition to a 1023 keVγ-ray, the β decay of 120Sb emits a 197.3 keV γ-ray withnearly equal intensity. We use this 197.3 keV γ-ray toscale the background spectrum to the 10C decay data inorder to subtract the 120Sb contamination.The summary of all corrections are shown in table I.The strength of the 10C superallowed 0+ → 0+ branch isdetermined to beb = [1.4665± 0.0038(stat)± 0.0006(syst)]× 10−2 (0.5)where the systematic error dominated by the uncer-tainty in the EGS4 threshold correction in the cor-related pileup correction. A comparison with previ-ous experiments is shown in table II. This result isabout one standard deviation from the results of ref. [3].Our result for b along with previous measurements ofthe β endpoint energy and the total lifetime gives 10CFt = 3068.9± 8.5 sec. and |Vud| = 0.9745 ± 0.0014, us-ing the usual radiative corrections and the isospin break-ing corrections δC = 0.16(3)% from ref. [1]. The uni-tary test is satisfied with data from this experiment,|V|2 = 0.9983± 0.0029, but the error is large. Thepresent experiment seems to favor a Z dependence correc-tion of ref. [4] but is statistics limited and a more preciseexperiment is necessary to help resolve the issue.ACKNOWLEDGMENTSThis work was supported in part by the US DOE undercontract numbers DE-AC03-76SF00098 and W-31-109-ENG-38.[1] E. Hagberg, et al., in Non-Nucleonic Degrees of FreedomDetected in Nucleus, ed. T. Minamisono, et al., (WorldScientific, 1996).[2] Particle Data Group, Phys. Rev. D54, 1 (1996).[3] G. Savard, et al., Phys. Rev. Lett. 74, 1521 (1995).[4] D.H. Wilkinson, Nucl. Inst. Meth. A335, 201 (1993).[5] P.H. Barker, et al., Phys. Rev. C41, 246 (1990).[6] S.C. Barker, et al., Phys. Rev. C40, 940 (1989).[7] P.H. Barker, private communication.[8] M.A. Kroupa, et al., Nucl. Inst. Meth. A310, 649 (1991).[9] I-Y. Lee, Nucl. Phys. A520, 641c (1990).[10] S. Baker, et al., Nucl. Inst. Meth. 221, 437 (1984).[11] F. James, et al., Comp. Phys. Comm. 10, 343 (1975).[12] W.R. Nelson, et al., SLAC Report-265 (1985).[13] B.A. Watson, et al., Phys. Rev. 187, 1351 (1969).[14] F. Ajzenberg-Selove, Nucl. Phys. A490, 1, (1988).[15] J.F. Ziegler, et al., The Stopping and Range of Ions inSolids, (Pergamon Press, 1985).[16] H. Frauenfelder and R.M. Steffen, in: α-, β-, and γ-RaySpectroscopy, ed. K. Siegbahn, (North-Holland, 1968).[17] D.C. Robinson, et al., Nucl. Phys. A181, 645 (1972).[18] Y. Nagai, et al., Phys. Rev. C43, R9 (1991).3307530703065Ft(0+→0+) (Seconds)2520151050Daughter Nucleus Charge ZFt=3072.1±0.9 sec.Ft=3068.3±2.5 sec.This Expt.FIG. 1. The Ft (solid circles) of the nine precisely mea-sured superallowed decays (10C, 14O, 26Alm, 34Cl, 38Km, 42Sc,46V, 50Mn, and 54Co) plotted as a function of the daughternucleus charge Z. The solid line is the weighted average. Thedashed line is the result of a linear fit and the open square isthe extrapolation of this fit to zero charge. The open circle isthe 10C Ft using the superallowed branching ratio from thismeasurement.19.290±0.012 sec. 0+, 3.648 MeV2mec21+, 2.154 MeV0+, 1.740 MeV1+, 0.718 MeV3+, g.s.1.46%98.53%10C10B414 keV1022 keV718 keV<8×10-6FIG. 2. The relevant energy levels of 10B and 10C.107106105104Counts(a)105106107Counts(b)103104105Counts1.2MeV1.00.80.60.40.2Energy(c)FIG. 3. (a) The β-delayed γ-ray energy spectrum. (b) Theprompt γ-ray energy spectrum. (c) The prompt γ-ray energyspectrum gated by the 414 keV γ-ray. The peaks at 718 keVand 1022 keV in the delayed spectrum are from the β-decayof 10C. The remaining peaks are due to positron annihilation,room background, neutron activation, and background protonreactions, primarily: 10B(p, α)7Be. The peaks at 718 keVand 1022 keV in the gated spectrum are used to measurethe relative efficiency. The residual 414 keV γ-ray peak in(c) disappears after corrections are made for accidentals andCompton background.TABLE I. Summary of the experimental corrections madein the measurement of the superallowed branching ratio.Correction Size AffectsAccidental Coincidences −(1.94 ± 0.02)% EfficiencyCompton Background −(0.049 ± 0.008)% EfficiencyDouble Escape Peak −(0.020 ± 0.004)% EfficiencyKinematic Shift −(0.019 ± 0.051)% Efficiency2 × 511 keV Pileup −(1.25 ± 0.19)% β-decayCorrelated Pileup −(0.032 ± 0.003)% Efficiency+(0.44 ± 0.05)% β-decay120Sb Background −(0.23 ± 0.11)% β-decay4TABLE II. Comparison of 10C superallowed 0+ → 0+branching ratios.Branching Ratio Reference(1.465 ± 0.014) × 10−2 [17](1.473 ± 0.007) × 10−2 [18](1.465 ± 0.009) × 10−2 [8](1.4625 ± 0.0025) × 10−2 [3](1.4665 ± 0.0038) × 10−2 This work(1.4645 ± 0.0019) × 10−2 World Average5

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A New Measurement of the Partial 0+-&gt;0+ Half Life of 10C with GAMMASPHERE

https://escholarship.org/uc/item/5681774p

A New Measurement of the Partial 0+->0+ Half Life of 10C with GAMMASPHERE

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A New Measurement of the Partial 0+-&gt;0+ Half Life of 10C with GAMMASPHERE

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A New Measurement of the Partial 0+->0+ Half Life of 10C with GAMMASPHERE