application/xmlDouble-beta decay Q values of 116Cd and 130TeS. RahamanV.-V. ElomaaT. EronenJ. HakalaA. JokinenA. KankainenJ. RissanenJ. SuhonenC. WeberJ. ÄystöPenning trapMass SpectrometerDouble-beta decayQ valueNeutrino massPhysics Letters B 703 (2011) 412-416. doi:10.1016/j.physletb.2011.07.078journalPhysics Letters BCopyright © 2011 Elsevier B.V. All rights reserved.Elsevier B.V.0370-2693703420 September 20112011-09-20412-41641241610.1016/j.physletb.2011.07.078http://dx.doi.org/10.1016/j.physletb.2011.07.078doi:10.1016/j.physletb.2011.07.078http://vtw.elsevier.com/data/voc/oa/OpenAccessStatus#Full2014-01-01T00:14:32ZSCOAP3 - Sponsoring Consortium for Open Access Publishing in Particle Physicshttp://vtw.elsevier.com/data/voc/oa/SponsorType#FundingBodyhttp://creativecommons.org/licenses/by/3.0/

Journals

S300.3

PLB27836S0370-2693(11)00897-510.1016/j.physletb.2011.07.078Elsevier B.V.Experiments

Fig. 1

A schematic drawing of the JYFLTRAP Penning trap mass spectrometer together with IGISOL facility.

Fig. 2

Ramsey time-of-flight (TOF) resonances of 116Sn+ (top) and 116Cd+ (bottom) from the precision trap. The shadowed boxes represent the density of the number of detected ions.

Fig. 3

Atomic mass difference of 116Cd and 116Sn obtained from individual measurements. The error bars comprise the statistical plus the count-rate uncertainties and the uncertainty due to the magnetic field fluctuations.

Fig. 4

Atomic mass difference of 130Te and 130Xe obtained from individual measurements. The error bars comprise the statistical and the count-rate uncertainties and the uncertainty due to the magnetic field fluctuations.

Table 1

Weighted average frequency ratios (r¯) and Q values of 116Cd and 130Te measured at JYFLTRAP. The final uncertainty normalized with the χ2 is given in the parenthesis. “#” and Tex represent the number of doublet measurements and the employed excitation scheme, respectively. The χ2 values are 0.85 and 0.90 for 116Cd and 130Te, respectively.

MotherDaughter#Tex (ms)Frequency ratio, r¯=νdνmQ value (keV)116Cd116Sn3825-450-251.000 026 0603(12)2813.50(13)130Te130Xe5125-450-251.000 020 8834(19)2526.97(23)Table 2

Phase-space integrals G2ν in units of yr−1 for 116Cd and 130Te. The axial-vector coupling constants gA=1.0 and 1.254 and the electron rest mass me=510.998903(4) keV[17] were used in the calculations. The uncertainty for G is estimated solely from the Q-value uncertainty.

NucleusQ value (keV)G2ν×10−18 forG0ν×10−14 forgA=1.0gA=1.254gA=1.0gA=1.254116Cd2813.50(13)3.3141(13)8.1951(32)2.0655(3)5.1076(9)2809(4) [17]3.268(40)8.08(10)2.053(10)5.078(25)130Te2526.97(23)1.8850(14)4.6613(36)1.8078(5)4.4703(14)2530.3(20) [17]1.906(13)4.714(31)1.816(5)4.490(12)Table 3

Experimental (Ex) nuclear matrix elements M2ν for 116Cd and 130Te and comparison with the theoretically computed values. For detailed notation see Ref. [10].

NucleusEx forSRPAQRPARQRPAgA=1.0gA=1.254WSAWSWSAWS

[36,37]

[38]

[39]

116Cd0.105(4)0.066(2)0.0360.051––130Te0.028(4)0.018(3)0.0160.0280.0090.009Table 4

C0ν factors for 116Cd and 130Te nuclei for the 0νββ-decay process.

NucleusC0ν

[40]

C0ν

[41]

116Cd3.30–9.334.08–15.3130Te3.28–8.763.22–11.3Double-beta decay Q values of 116Cd and 130Te

Rahaman

⁎

mrahaman@lanl.gov

V.-V.

Elomaa

Eronen

Hakala

Jokinen

Kankainen

Rissanen

Suhonen

Weber

ÄystöDepartment of Physics, P.O. Box 35 (YFL), FIN-40014 University of Jyväskylä, Finland⁎Corresponding author.1

Present address: LANL, Physics Division, P-23, MS H803, Los Alamos, USA.

Present address: Turku PET Center, Abo Akademi University, 20500 Turku, Finland.

Present address: Fakultät für Physik, LMU München, 85748 Garching, Germany.

Editor: V. Metag

Abstract

The Q values of the 116Cd and 130Te double-beta decaying nuclei were determined by using a Penning trap mass spectrometer. The new atomic mass difference between 116Cd and 116Sn of 2813.50(13) keV differs by 4.5 keV and is 30 times more precise than the previous value of 2809(4) keV. The new value for 130Te, 2526.97(23) keV is close to the Canadian Penning trap value of 2527.01±0.32 keV (Scielzo et al., 2009) [1], but differs from the Florida State University trap value of 2527.518±0.013 keV (Redshaw et al., 2009) [2] by 0.55 keV (2σ). These values are sufficiently precise for ongoing neutrinoless double-beta decay searches in 116Cd and 130Te. Hence, our Q values were used to compute accurate phase-space integrals for these double-beta decay nuclei. In addition, experimental two-neutrino double-beta decay nuclear matrix elements were determined and compared with the theoretical values. The neutrinoless double-beta decay half-lives for these nuclei were estimated using our precise phase-space integrals and considering the range of the best available matrix elements values.

Keywords

Penning trapMass SpectrometerDouble-beta decayQ valueNeutrino mass

Introduction

Neutrinoless double-beta decay (0νββ) is a rare, second-order weak-interaction process in which two identical neutrons within the nucleus decay into two protons and two electrons. A virtual neutrino is exchanged in this process if neutrinos were massive Majorana particles; i.e. particle is identical to its anti-particle. The 0νββ-decay process also violates the lepton-number conservation. Thus, this process is not allowed in the Standard Model. The observation of this process would unfold the physics beyond the Standard Model and will open a new physics era in the study of the fundamental properties of neutrinos. For example, the absolute scale of the neutrino mass eigenstates and their hierarchy would be resolved. Also if the neutrino is its own anti-particle, then a natural explanation for the matter/anti-matter asymmetry arises (leptogenesis). A comprehensive review on double-beta decay is provided in Refs. [3,4].At present, 116Cd and 130Te with high Q values are gaining interest as promising candidates for searching the signal of the neutrinoless double-beta decay. At the Laboratori Nazionali del Gran Sasso (LNGS), the CUORICINO experiment [5] has tested a prototype cryogenic bolometer detector and is constructing the high-resolution CUORE [6] experiment to contain approximately 750 kg of TeO2 or ∼200 kg of 130Te. The COBRA experiment [7,8] has tested a prototype of four high-resolution semiconductor detectors made of cadmium zinc telluride (CdZnTe) each with a volume 1 cm3 and an active mass of 6.53 g. A future COBRA experiment under construction contains several hundred of such detectors with a total volume of 64,000 cm3 and several hundred kilograms of sample [9]. Both experiments plan to use modern high-resolution detectors for detecting a possible 0νββ signal, where the precise Q values of 116Cd and 130Te are essential information.A mono-energetic peak might appear as a signature for the neutrinoless double-beta decay at the position of the Q value of the involved transition. This peak will reside within a continuum of background events within any detector. The signal-to-background ratio depends therefore upon the narrowness of the peak and the background rate. In practice, the best experimental resolution is about 1–4 keV. As a result one needs to know the peak location or the Q value to a precision better than 1 keV. For the COBRA experiment a semiconductor detector itself is also a source with an energy resolution of 1% at 2805 keV. The CUORE bolometer detector will have an absolute resolution of about 0.4 keV. In the present work we have measured the corresponding Q values with a precision of better than 300 eV which is sufficient for this purpose. Moreover, we have made the first direct Q-value measurement of 116Cd using a Penning trap spectrometer. The Q value for 130Te has been measured previously by two groups using the Canadian Penning trap [1] at the Argonne National Laboratory and the former MIT trap at Florida State University [2]. These two values differ by nearly two sigma from each other. Additional motivation for the precise Q-value measurements stems from the calculation of the precise phase-space integrals G and experimental nuclear matrix elements M for two-neutrino double-beta decaying nuclei [10].In this Letter, we present new and more accurate measurements for the atomic mass differences between 116Cd and 116Sn, and between 130Te and 130Xe. The experiments have been performed using the Penning trap setup JYFLTRAP at the Accelerator Laboratory of the University of Jyväskylä, Finland. The power of this setup for such type of measurements was recently demonstrated by the accurate determination of the double-beta decay Q values of 76Ge, 100Mo [11], 112Sn [12], and 74Se [13].2

Experimental method

At JYFLTRAP [14] (shown in Fig. 1

) the Q-value determination is conducted by measuring the cyclotron frequency of an ion stored in a Penning trap [15]. The cyclotron frequency νc is given by(1)νc=12πqmB, where B is the magnetic field, m is the mass, and q the charge of the ion. Using an off-line spark ion source, a mixed beam of 116Cd (mother) and 116Sn (daughter) were produced at the Ion Guide Isotope Separator On-line (IGISOL) facility [16,11]. This allowed the measurement of the cyclotron frequencies of the 116Cd and 116Sn isotopes in a consecutive manner. For producing the 130Te and 130Xe pair, the electrode of the off-line ion source was replaced by the natural tellurium and xenon was added in small amounts to the helium carrier gas. Hence, the Q value which equals the atomic mass difference for double-beta decay can be obtained by using the following formula:(2)Q=mm−md=(νdνm−1)(md−me), where mm and md are the masses of the mother and daughter atoms and νdνm is their cyclotron frequency ratio. The daughter nucleus was used as a reference atom and its mass excess value was obtained from Ref. [17]. me is the mass the electron. The electron binding energy differences between mother and daughter atoms are on the order of few eV and can be neglected at the level of precision in our experiment.

Ions were extracted from the off-line source by a combination of an electric field and a helium flow and were subsequently guided by a sextupole ion guide (SPIG) into a differential pumping stage where they were accelerated to 30 keV and mass-separated with a 55° dipole magnet with a mass resolving power M/ΔM of ∼500. The ions were then transported to a radiofrequency quadrupole (RFQ) structure where they were cooled and accumulated [18]. Finally, the ions were extracted in short bunches and were injected into the double Penning trap system for isobaric purification and precision mass measurement.JYFLTRAP consists of two Penning traps placed inside the warm bore of a 7-T superconducting magnet, separated by a narrow channel having a length of 5 cm and diameter of 2 mm for differential pumping. The first trap is the purification Penning trap, where the mass-selective buffer-gas cooling technique is applied for further axial cooling and isobaric cleaning [19]. The mass resolving power of the purification trap was on the order of 105 in these measurements.In addition, a time-separated dipolar excitation was applied in the precision trap (Ramsey method) [20] to ensure a single ion species is selected [21]. This was performed in the following way: first, the mass-selective reduced cyclotron frequency ν+ (removal frequency) was applied for one ion species as two time-separated fringes of 5 ms with a waiting time of 20 ms (5–20–5 ms). This increases the reduced cyclotron radius of the unwanted ions. At the end of the excitation the ions were sent back to the purification trap. Thus the excited ions (i.e. the unwanted ions) could not pass the 2-mm channel between the traps. In the purification trap, the buffer-gas cooling technique was re-applied and finally a pure ion sample was transported to the precision trap for the cyclotron frequency (νc) measurement. A detailed description of the Ramsey dipolar cleaning and the resulting precision improvement in the cyclotron frequency measurement can be found in Refs. [21,22].At first, the cyclotron frequency was determined by employing the time-of-flight (TOF) technique [23] with an excitation time of 100 ms in a single-fringe quadrupolar excitation scheme (conventional excitation scheme). Once the cyclotron frequency was determined, a quadrupolar Ramsey excitation was applied in order to determine the cyclotron frequency with higher precision [24,25].A typical Ramsey TOF resonance is shown in Fig. 2

for 116Sn (top) and 116Cd (bottom). A Ramsey excitation with two time-separated fringes of 25 ms and a waiting time of 450 ms was applied for these particular cases.

Analysis and results

For 116Cd a total of 38 cyclotron frequency measurements were performed with 116Sn as a reference. For 130Te a total of 51 measurement were collected with 130Xe as a reference. A Ramsey excitation sequence of 25–450–25 ms was used for both measurements. For 116Cd the weighted average value of the frequency ratio results in r¯=1.0000260603(12). The inner and outer statistical uncertainties (δr¯) [26] of the weighted average frequency ratio are 1.24×10−9 and 8.98×10−10, respectively. The ratio of these values (Birge ratio) is below 1 which confirms that the scattering of the data is statistical. For 130Te the weighted average value of the frequency ratio results in r¯=1.0000208834(19). In this case the Birge ratio is below 1 as well which confirms that the scattering of the data is statistical.In the determination of the cyclotron frequency ratio the following systematic uncertainties were taken into account: The number of ions present in the trap can cause a shift in the cyclotron frequency. This was taken into account by plotting the center value of the fitted cyclotron resonance as a function of the detected number of ions [27]. The cyclotron frequency equivalent to one ion in the trap was determined from a linear extrapolation to a value of 0.6 observed ions (detector efficiency = 60%) and used for the Q-value determination along with the uncertainty of the extrapolation. Hence, the uncertainty due to the count-rate class is added to the statistical uncertainty. A detailed description of the count-rate class analysis is presented in Ref. [27].The drift of the magnetic field was considered by an interpolation of the reference frequencies measured before and after the cyclotron frequency measurement of the ion of interest. This linear interpolation does not consider the short-term fluctuations of the magnetic field. This was accounted for by adding σB(ν)/ν⋅ΔT=5.7(8)×10−11/min⋅ΔT[28,29], multiplied by the time difference (ΔT) between the two consecutive reference measurements, quadratically to the uncertainty of the frequency ratio. As the Q value is determined by the cyclotron frequency ratio between the mother and daughter ions having the same Aq, possible mass-dependent and other systematic uncertainties cancel.The Q value can be derived from the weighted average frequency ratio using Eq. (3). Due to the same mass number of the parent and daughter the term inside the parenthesis in Eq. (3) is very small (∼2–3×10−5). Thus the uncertainty contribution due to the absolute uncertainty of the daughter mass md to the Q value is negligible. Figs. 3 and 4

show the weighted average Q values of 116Cd and 130Te with the uncertainties. The weighted average cyclotron frequency ratio r¯ and Q values for 116Cd and 130Te are given in Table 1

Discussion

By employing a Penning trap measurement we provide a new and significantly improved Q value of 2813.50(13) keV for the neutrinoless double-beta decay of 116Cd. In the case of 130Te our Q value, 2526.97(23) keV, is in an excellent agreement with the Canadian Penning Trap value of 2527.01(32) keV [1] but differs by 0.55(23) keV from the considerably more accurately reported Florida State University value of 2527.518(13) keV [2]. Without further more detailed studies of both approaches it is difficult to explain the origin of this deviation to be other than statistical fluctuation. The FSU experiment measured cyclotron frequency ratios of pairs of triply charged ions simultaneously trapped in a Penning trap and derived the true cyclotron frequency by using the Brown–Gabrielse invariance theorem [30], whereas the CPT and JYFLTRAP experiments determine the sideband frequency (w++w−). According to a recent study by Gabrielse presented in Ref. [31] the use of the sideband frequency method can be possible for precision measurements on the relative precision level of 10−9, especially when the ions of the same mass number are compared. This has been confirmed in our previous measurements of the Q values of several super-allowed beta decays and double-beta decays [11–13,22,32–34].The phase-space integral G depends sensitively on the Q value which is more accurately calculable with our improved results. In this Letter, we are presenting more accurate and precise phase-space integrals. These were evaluated using numerical methods of the phase-space integral by using computer algorithms. The Mathematica was used as a platform. The results of the numerical integrals of Eqs. A.1 and A.27 in Ref. [10] are summarized in Table 2

. The phase-space integrals are presented here for the two extreme values of the axial-vector coupling constant gA=1.00 (strong quenching) and 1.254 (bare nucleon) of the weak nucleonic current.

The uncertainty in G is estimated solely from our Q value uncertainty. The other uncertainty (in addition to the uncertainty from the Q value) in G comes from the Fermi-function approximation for the exact solution of the Dirac equation for a homogeneously charged sphere. The relativistic Fermi approximation limits the accuracy of G to three digits.Using the recommended experimental half-lives T1/22ν[35] of the double-beta decay and our precise phase-space integrals G2ν, the experimental nuclear matrix element M2ν=1/(T1/22ν×G2ν) is derived and given in Table 3

for 116Cd and 130Te. In addition, a comparison between the theoretically computed nuclear matrix elements and the experimental values is summarized. In case of 116Cd the nuclear matrix element M2ν is computed in two different approaches and the results are 0.036 to 0.051. It is remarkable to notice that the experimental value of M2ν=0.064 for gA=1.254 is close to the computed value via the QRPA (AWS) basis (see Table 3). In case of 130Te the computed nuclear matrix element M2ν varies between 0.009 to 0.028. The range of the experimental M2ν values reside within the computed spectrum.

The half-life T1/20ν of the neutrinoless double-beta decay process can be expressed as(3)T1/20ν=C0ν〈mν〉2×1023 years, where the effective neutrino mass 〈mν〉 is given in eV. The factor C0ν is the product of the nuclear matrix element M0ν squared and the phase-space integral G0ν of the 0νββ-decay process. The calculated range of the C0ν factor by using our phase-space values from Table 2 and the set of nuclear matrix elements from Refs. [40,41] are given in Table 4

. These sets of nuclear matrix elements M0ν were calculated by employing the pnQRPA [40,41] and the RQRPA models [41]. In these models, the nucleon–nucleon short-range correlations have been accounted. The range of computed matrix elements stems from the uncertainty in the value of the axial-vector coupling coefficient, gA=1.0–1.254, and from the variation in the value of the proton–neutron particle–particle interaction strength gpp, used to fit the experimental range of the 2νββ half-life.

In the case of 116Cd, the experimental nuclear matrix element M2ν for gA=1.254 is very close to the computed value. The range of the experimental M2ν values for 130Te reside within the theoretical values calculated by employing various models. The range of the C0ν factors for the neutrinoless double-beta decay for 116Cd and 130Te are computed using our new phase-space integrals and recently published nuclear matrix elements. Using the values from Table 4 and Eq. (3) one finds the 0νββ-decay half-life range within T1/20ν=(0.83–3.83)×1027 years for 116Cd by taking mν=20 meV, a value covering the inverted mass hierarchy [4].5

Conclusions

By employing Penning trap measurements the accurate double-beta decay Q values have been derived for two cases of current interest, 116Cd and 130Te. The new values provide important improvement for sensitivity for the neutrinoless double-beta decay search experiments. The half-life estimates based on the new Q values coupled with the matrix element calculations based on the pnQRPA and the RQRPA models suggest that the neutrinoless double-beta decay mode could be within reach of the next-generation of experiments [4].

Acknowledgements

This work has been supported by the TRAPSPEC Joint Research Activity project under the EU 6th Framework program “Integrating Infrastructure Initiative – Transnational Access”, Contract Number: 506065 (EURONS) and by the Academy of Finland under the Finnish Center of Excellence Program 2006–2011 (Nuclear and Accelerator Based Physics Program at JYFL).

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