Q-value of the superallowed β decay of 62 Ga

Transcription

1 Physics Letters B 636 (2006) Q-value of the superallowed β decay of 62 Ga T. Eronen a,,v.elomaa a, U. Hager a, J. Hakala a, A. Jokinen a, A. Kankainen a,i.moore a, H. Penttilä a, S. Rahaman a, S. Rinta-Antila a, A. Saastamoinen a, T. Sonoda a,j.äystö a, A. Bey b,b.blank b, G. Canchel b, C. Dossat b, J. Giovinazzo b, I. Matea b, N. Adimi c a Department of Physics, P.O. Box 35 (YFL), FIN University of Jyväskylä, Finland b Centre d Études Nucléaires de Bordeaux-Gradignan, Le Haut-Vigneau, F Gradignan cedex, France c Faculté de Physique, USTHB, BP32, El Alia, Bab Ezzouar, Alger, Algeria Received 8 December 2005; received in revised form 1 March 2006; accepted 26 March 2006 Editor: V. Metag Abstract Masses of the radioactive isotopes 62 Ga, 62 Zn and 62 Cu have been measured at the JYFLTRAP facility with a relative precision of better than AQ EC value of ( ± 0.54) kev for the superallowed decay of 62 Ga is obtained from the measured cyclotron frequency ratios of 62 Ga 62 Zn, 62 Ga 62 Ni and 62 Zn 62 Ni ions. The resulting Ft-value supports the validity of the conserved vector current hypothesis (CVC). The mass excess values measured were ( ± 1.0) kev for 62 Ga, ( ± 0.9) kev for 62 Zn and ( ± 0.9) kev for 62 Cu Elsevier B.V. All rights reserved. PACS: e; s; g; Dr Keywords: Penning trap; Atomic mass; Q-value; Ft-value 1. Introduction According to the conserved vector current hypothesis (CVC), the matrix elements of the superallowed Fermi transitions between the 0 + isobaric analog states (IAS) should all be equal, independent of nuclear structure apart from small terms for radiative and isospin-symmetry breaking corrections. Provided this is true, the experimental values of the comparative half-life (ft) corrected for isospin mixing and radiative corrections Ft, allow for an accurate determination of the weak vector coupling constant G V. This value combined with the muon decay constant G μ allows the extraction of V ud, the weak coupling matrix element between up and down quarks in the Cabibbo Kobayashi Maskawa (CKM) quark mixing matrix. Combining this value with other data on the matrix elements of the first row of the CKM matrix, V us and V ub, it becomes possible to test the unitarity of the CKM matrix and the validity of the electroweak * Corresponding author. address: tommi.eronen@phys.jyu.fi (T. Eronen). standard model. Depending on which value for V us is taken from the recent literature, the current world data as reviewed by Hardy and Towner implies a slight failure for the unitarity test by a maximum of 2.4 standard deviations [1]. More recently, a new measurement of the Q EC -value of the superallowed β decay of 46 V is indicating a need for the re-evaluation of the Q EC -values of all the nine best-known cases employed in the unitarity analysis [2]. Therefore, it is now becoming of utmost importance to improve the Q EC -value data for these cases as well as to provide accurate data on new cases, as represented by 62 Ga studied in this Letter. Following the notations of Hardy and Towner [1], the true Ft-value for the (T = 1) decays is obtained using the equation Ft ft(1 + δ R )(1 + δ NS δ C ) K = 2G 2 V (1 + ΔV R ) = constant, where f is the β decay phase-space factor, t is the partial half-life, K is a constant, δ R, δ NS and Δ V R are radiative cor- (1) /$ see front matter 2006 Elsevier B.V. All rights reserved. doi: /j.physletb

2 192 T. Eronen et al. / Physics Letters B 636 (2006) rections and δ C accounts for the isospin-symmetry breaking correction, see Refs. [1,3] for a detailed discussion on these correction terms. A critical survey of 20 superallowed nuclear β decays [1] shows that the corrected Ft-values are constant to three parts in In the case of the nine best known transitions, the experimental ft-values are known to better than 0.15%. In most of the cases [1], the correction terms (δ NS δ C ), δ R and Δ V R, obtained from theory, are the limiting factors for improving the accuracy of the determination of the value of the vector coupling constant G V.UsingEq.(1) together with the radiative corrections as determined by the theory and assuming the validity of the conserved vector current, the isospin correction δ C can be experimentally determined providing thus important means to improve the theoretical model calculations. Currently, the dominant source of uncertainty in δ C arises from the disagreement between the results from different theoretical calculations. To extend the well-known cases, it is important to measure new cases where nuclear structure dependent corrections are large or particularly challenging for model calculations. Typically, these are nuclei with T z = 1 as well as heavy T z = 0 nuclei with Z>30. Recently, three such cases 22 Mg [4 6], 34 Ar [7] and 74 Rb [8 10] have been studied with high precision for their Q EC -value but with only a modest accuracy for the half-life or the superallowed decay branch resulting in more moderate accuracies for their Ft-values ranging between 0.24 and 0.40% [1]. The next heaviest nucleus in the series of T z = 0, T = 1, I π = 0 + superallowed β emitters beyond 54 Co is 62 Ga, which is a particularly interesting T z = 0 nucleus because its β decay half-life has already been determined with high precision in several experiments yielding an average value of ( ± 0.038) ms [11 13]. The current value and precision of the experimental branching ratio is ( )%. However, possible additional unobserved Gamow Teller transitions could increase the branching ratio to the excited 1 + states in 62 Zn, calling for more precise measurements of these transitions [14]. Priorto the present work, the Q EC -value of 62 Ga has been determined in only one experiment where a β end-point measurement resulted in a value of (9171 ± 26) kev [15]. In this Letter we present the first precise measurement of the Q EC -value and the mass of 62 Ga employing a double Penning trap setup connected to the on-line isotope separator IGISOL at the University of Jyväskylä [16]. In the same experiment, the masses of 62 Zn and 62 Cu were determined using 62 Ni as the reference ion whose mass excess is given with 0.6 kev uncertainty in the most recent atomic mass evaluation tables [17]. 2. Experimental method All nuclei of interest were produced in reactions induced by 48MeVprotonsimpingingona3mg/cm 2 thick enriched 64 Zn target. The recoil ions were slowed down and thermalized in the gas cell of an ion guide using 150 mbar helium pressure [18]. The ions were then transported by gas flow and electric fields through a differentially pumped electrode system into high vacuum and accelerated to 30 kev. After mass separation in a 55 dipole magnet the ions were injected into a buffer-gas filled RF-quadrupole for cooling and bunching before injection into a double Penning trap system for isobaric purification and mass measurements. The production rates with a 25 µa proton beam at the focal plane of IGISOL were measured at maximum to be 600 ions/s for 62 Ga, /sfor 62 Zn, 10 6 /sfor 62 Cu and 10 5 /sfor 62 Ni. In a Penning trap ions are confined by a strong homogeneous magnetic field and by a weak electric quadrupole field. The ions in the trap have three eigenmotions: one axial motion with a frequency of ν z and two radial motions consisting of magnetron and reduced cyclotron motions with frequencies ν and ν +,respectively. The sum of these two frequencies equals to the true cyclotron frequency ν + ν + = ν c = 1 qb (2) 2π m, where q and m are the charge and the mass of the ion and B is the magnetic flux density [19]. The trap setup at JYFL, termed JYFLTRAP, consists of a gas-filled radio frequency quadrupole cooler (RFQ) [20] and a double cylindrical Penning trap system which contains two traps: one for isobaric purification and the other for high precision mass measurements [21]. The whole setup is placed on a high-voltage platform about 100 V below the level of the acceleration voltage of IGISOL. The two Penning traps are placed in the warm bore of a 7 Tesla superconducting magnet that has two homogeneous regions of 1 cm 3 in volume separated by 20 cm at the centre of the magnet. The purification trap has a field homogeneity B/B of better than 10 6 and the precision trap better than A mass resolving power m/ m of about 10 5 is typically obtained for the purification trap allowing for a clean separation of the studied A = 62 isobars [21,22] before injection to the precision trap. A mass measurement is performed by determining the true cyclotron frequency of the ion in the precision trap. The mass of the ion of interest is obtained by comparing its cyclotron frequency with a well-known reference mass. In a measurement cycle the ions are first captured and cooled in the buffer-gas filled RFQ which at a set time injects a lowenergy ion bunch into the purification trap. In this trap the ions are captured by a time-varying electric potential, thermalized and cooled axially to the center of the potential by collisions with helium buffer gas atoms. Then, the ions are excited by successive dipole and mass-selective quadrupole RF fields, centering only the ions of interest corresponding to their true cyclotron frequency given by Eq. (2). A typical cycle in the purification trap consisted of 25 ms axial cooling, 5 ms dipole (magnetron) and 40 ms quadrupole (cyclotron) excitation and finally 10 ms radial cooling before ejection into the precision trap which operates in vacuum. In the precision trap, the magnetron radius of the ions is first increased with a dipole electric field for 5.5 ms using a phase-locking technique [23] leading to a magnetron radius of about 0.6 mm. Then the quadrupole cyclotron excitation is switched on to mass-selectively convert the magnetron motion to reduced cyclotron motion. The duration of the quadrupole

3 T. Eronen et al. / Physics Letters B 636 (2006) excitation was chosen to be between 100 and 400 ms and a corresponding amplitude to give rise to one full conversion in the resonance frequency of Eq. (2). The detection of the resonance frequency is based on the time-of-flight technique [24]. Dueto large energy ratio (about 10 6 ) between the two radial motions, a significant decrease in the time-of-flight (TOF) from the trap to the ion detector is observed when the ions have even a modest component of reduced cyclotron motion. This is due to conversion of the radial energy into axial kinetic energy in the fringe field of the magnet. The absolute minimum of the time-of-flight occurs when the ions have been excited at their true cyclotron frequency. 3. Results The experimental setup was first tuned by using 40 Ar + ions produced in collisions between the primary proton beam and argon atoms mixed in helium. Next, the Q EC -value of 62 Ga was determined by measuring the cyclotron frequencies of 62 Ga and 62 Zn in repeated successive measurements. The masses of 62 Ga, 62 Zn and 62 Cu were determined using 62 Ni as the reference ion. In the relative Q EC -value measurements most of the systematic effects cancel out. The only contribution to the uncertainty arises from the measured frequency uncertainties, even without a contribution from the reference mass uncertainty. The total error consists of statistical fitting uncertainty of a resonance curve as well as of systematic errors due to count rate variations and magnetic field fluctuations. In the absolute mass determination the uncertainty of the mass of the reference ion and possible mass-dependent errors have to be also included in the total error. Over the entire measurement period a total of nearly 50 resonances were recorded for both 62 Ga and 62 Zn. In addition, the Q EC -value of 62 Ga was determined from several measurements of the 62 Ga 62 Ni and 62 Zn 62 Ni ion pairs. Fig. 1 shows two samples of time of flight resonance curves measured for 62 Ga and 62 Zn. Fig. 2 shows the Q EC -values determined from 12 individual measurements with a 150 ms excitation time for both 62 Ga and 62 Zn. Tables 1 and 2 summarize all the data obtained in all different experiments in February, March and September The number of detected ions in each measurement cycle was kept below 2 ions/bunch in average. This was done to minimize the systematic uncertainty caused by a high number of ions in the trap. At the time when the measurements were done, no individual recording of the ion bunches was possible. Later on, individual bunch recording was made possible and a count rate class [25] analysis could be performed to characterise possible shifts in frequency due to a varying number of ions. Due to a low yield, it was not possible to use 62 Ga to characterise the effect. However, measurements of 62 Cu were done with 400 ms and 200 ms excitation times and varying the number of incoming ions. It was found that the true cyclotron frequency of 62 Cu usually shifted to higher frequencies when the number of ions was increased. The behaviour was found to be linear and the observed shift was determined to be 8 mhz/(1 ion/bunch). To account for this effect, the difference between the detected num- Fig. 1. Examples of time-of-flight resonance curves for 62 Ga and 62 Zn. For each frequency, 120 bunches were recorded to get the time-of-flight. An excitation time of 150 ms was used. The scanning time for one spectrum was 20 minutes and the total number of ions detected for the resonances was about 5000 and for 62 Ga and 62 Zn, respectively. In these cases, the obtained resonance frequency, ν c,for 62 Ga is (57) Hz and for 62 Zn, (37). The time-of-flight resonance curve for 62 Ga is offset by 60 µs for clarity. Fig. 2. A series of individual measurements of the Q EC -value of 62 Ga measured in February ber of ions in a bunch (typically 1.5) and the ideal ( 0.6 when 60% detection efficiency is assumed), is used as a systematic uncertainty. Since the shift is present in both the reference and the ion of interest, a total shift of Hz (corresponding to 0.38 kev) was taken as a systematic uncertainty. This compensates effects due to possible impurity ions in the trap originating, for instance, from radioactive decay of ions in the trap. The production rates of the measured ions slowly decreased while running the experiment. Even though the detection rate slowly decayed, no noticeable change in the obtained frequency ratios was observed. A small, slow fluctuation in the magnetic field strength was observed during the experiment. To take this into account, reference frequency measurements were always done before and after the frequency measurement

4 194 T. Eronen et al. / Physics Letters B 636 (2006) Table 1 Summary of the data from the Q EC -value measurements. The symbol # denotes the number of measurements done. The uncertainties given are statistical and due to the fitting of the TOF-frequency curves and reference frequency interpolation. The final value is given also with systematic errors included Date Measurement/reference T RF (ms) # Frequency ratio Q EC (kev) February Ga/ 62 Zn (92) (53) March Ga/ 62 Zn (135) (78) March Ga/ 62 Zn (274) (158) Ga Zn/Ni a 62 Ni as ref 150/ (86) Weighted average (38) Final (including statistical and systematic errors) (54) a Q EC -value determined by using the frequency ratios of 62 Ga 62 Ni and 62 Zn 62 Ni from Table 2. Table 2 Summary of the mass excess values obtained by using 62 Ni as the reference ion. The symbol # denotes the number of measurements done. The uncertainties given are statistical and due to the fitting of the TOF-frequency curves and reference frequency interpolation. The error of the final mass excess value in addition to the statistical uncertainty consists of a systematic error and an uncertainty in the 62 Ni reference ion mass Date Measurement/reference T RF (ms) # Frequency ratio Mass excess (kev) February Ga/ 62 Ni (157) March (217) March (271) Average (115) Final (10) February Zn/ 62 Ni (123) September (145) Average (94) Final (9) February Cu/ 62 Ni (235) September (87) Average (82) Final (9) of the ion of interest. The frequency value obtained by interpolating the two reference frequencies is then used in the calculations. The Q EC value for the 62 Ga decay obtained as a weighted mean of the relative measurements given in Table 1 is kev with a statistical uncertainty of 0.38 kev. The final value of ( ± 0.54) kev is obtained by adding the statistical (0.38 kev) and systematic (0.38 kev) errors quadratically. The masses of 62 Ga and 62 Zn were determined using 62 Ni as a reference ion. These measurements resulted in the mass excess values of ( ±1.0) kev and ( ±0.9) kev for 62 Ga and 62 Zn, respectively, when using the mass excess value of ( ± 0.6) kev for the reference ion 62 Ni [17]. Note that in addition to the statistical and systematic errors, the mass excess values have an error contribution also from the reference mass uncertainty. The new mass excess value of 62 Zn is in agreement with but more precise than the previously adopted value of ( ± 10) kev. The mass excess of 62 Cu was also measured. The obtained value of ( ± 0.9) kev deviates from the previously adopted value of ( ± 4) kev given in [17]. However, the previous experimental values obtained via β end-point and the (p,n) reaction threshold measurements scatter by as much as 24 kev with individual uncertainties of 10 kev. 4. Discussion The new experimental value of ( ± 0.54) kev for the decay energy of 62 Ga yields a value of ( ± 8.3) for the statistical rate function f [1,26]. The half-life of ( ± )% yield the final ft-value of ( )sfor 62 Ga. This value, when corrected for radiative and isospin mixing effects according to 0.038) ms and the branching ratio of ( Table IX of Ref. [1], results in an Ft-value of ( ) which is in good agreement with the current world average of (3073.5±1.2) given in the review by Hardy and Towner [1],see also Fig. 3. The experimental contribution to the uncertainty is now dominated by the branching ratio measurement, as can be seen from Table 3. The overall uncertainty, however, is strongly influenced by the uncertainties of the theoretical corrections, in particular (δ NS δ C ) whose fractional uncertainty is as large as In order to gain a deeper understanding of the calculation of δ C it is of interest to solve the experimental value of δ C employing the CVC in the framework of Eq. (1). Using a value of δ NS from [3], δ C =( ) is obtained which is somewhat higher but still in agreement with the adopted theoretical value of (1.38±0.16)given in [3] as well as with the value of 1.42 obtained by Sagawa et al. [27]. In the paper of Ormand and Brown

5 T. Eronen et al. / Physics Letters B 636 (2006) Régional d Aquitaine. A.J. and H.P. are indebted to financial support from the Academy of Finland (Project Nos and ). References Fig. 3. Ft-values for the most precisely known superallowed β emitters. The five most recently measured cases are labelled by the parent nucleus. The horizontal lines denote one standard deviation around the world average Ft-value of ( ± 1.2) given in Ref.[1]. The newest values marked by filled circles for 46 Vand 62 Ga are not included in this average. Table 3 Fractional uncertainties contributing to the 62 Ga Ft-value/parts in 10 4 Quantity f Half-life Branching ratio δ NS δ C δ R Uncertainty the value of δ C varies between 1.30 and 1.69, respectively, when Hartree Fock or Woods Saxon (WS) wave functions are used [28]. Therefore, our result does not favor either of these two calculations. In conclusion, the Q EC -value for the superallowed decay of 62 Ga has been measured with a precision comparable to the nine best known cases. The corresponding ft-value is more precise than the other recently measured new cases, 22 Mg, 34 Ar and 74 Rb. Therefore, it has become of great importance to measure the branching ratio more precisely in order that the decay of 62 Ga becomes relevant as a contribution to the unitarity test of the CKM matrix. As pointed out earlier, a new measurement of the Q EC -value of the superallowed decay of 46 V is indicating a need for the re-evaluation of the Q EC -values of all of the nine best-known cases [2]. Currently, the Ft-value for 46 V is the only one outside of one standard deviation of the current world average value. This necessitates new measurements for the Q EC -values of the well-known cases such as 26m Al, 42 Sc, 46 V, 50 Mn and 54 Co which all are available as ion beams at the JYFLTRAP facility. 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