PHYSICAL REVIEW C 88, 035502 (2013)

Examination of the possible enhancement of neutrinoless double-electron capture in 78Kr

S. Bustabad,1,2,* G. Bollen,1,2 M. Brodeur,1 D. L. Lincoln,1,2 S. J. Novario,1,2 M. Redshaw,1,3 R. Ringle,1 and S. Schwarz1

1National Superconducting Cyclotron Laboratory, East Lansing, Michigan 48824, USA2Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA

3Department of Physics, Central Michigan University, Mount Pleasant, Michigan 48859, USA(Received 29 January 2013; revised manuscript received 24 April 2013; published 13 September 2013)

Penning-trap mass spectrometry was used at the Low-Energy Beam and Ion Trap (LEBIT) facility at theNational Superconducting Cyclotron Laboratory (NSCL) to investigate 78Kr, a candidate for resonantly enhancedneutrinoless double-electron capture (0νECEC). The newly determined Q value of 2847.75 (27) keV is 1.4 keVgreater than the value from the most recent atomic mass evaluation [Chin. Phys. C 36, 1603 (2012)], a change oftwo sigma, and the uncertainty has been reduced by a factor of three. The change in the Q value shifts allowed0νECEC in 78Kr further from resonant enhancement. With the improved determination of the Q value, all knownexcited states can now be confidently excluded from possible 78Se candidates that could lead to resonantlyenhanced 0νECEC.

DOI: 10.1103/PhysRevC.88.035502 PACS number(s): 21.10.Dr, 23.40.−s, 07.75.+h, 14.60.Pq

I. INTRODUCTION

Although long regarded as a hopelessly feeble process,some hope in the experimental feasibility of observing neu-trinoless double-electron capture (0νECEC) has revived inthe last decade. If 0νECEC were observed, it would indicatethe Majorana nature of neutrinos, and a measurement of thehalf-life could be used to determine the absolute mass scaleof neutrinos. If neutrinos are Majorana particles, detection of0νECEC may be possible through a resonant enhancementof the process when either the ground or excited state ofthe daughter is nearly degenerate with the parent. Resonantenhancement, originally proposed by Winter [1], has beenanalyzed by Sujkowski and Wycech [2] who estimate thatsuch a degeneracy could increase the decay rate of a specifictransition by a factor of ∼106. This increase could makethe half-life of a 0νECEC process comparable to those ofneutrinoless double-beta decay (0νββ). In order to evaluatethe degree of possible enhancement for a 0νECEC reaction,the Q value Qεε of the reaction must be well known.

The decay rate for neutrinoless double-electron capture,λεε , is given by

λεε = M2

�2 + �2/4� ≡ M2F, (1)

where � is the so-called degeneracy parameter, � is the sum ofthe widths of the excited state and the two-electron-hole state,and M is the product of the leptonic phase-space factor, thenuclear matrix element, and the effective neutrino mass [3].It is convenient to define the quantity �/(�2 + �2/4) as theso-called resonance parameter F . Qεε enters into the decayrate through the degeneracy parameter: � = Qεε − B2h − Eγ ,where B2h is the binding energy of the two-electron hole andEγ is the excitation energy of the daughter. In general � is largeand greatly suppresses the decay rate; � is typically hundredsof keV whereas � is typically a few tens of eV or less. If,

*bustabad@nscl.msu.edu

however, the Q value of a neutrinoless double-electron-capturecandidate were equal to the sum of Eγ and B2h to within a fewtens of eV, then � would be on the order of �, and the decayrate would be greatly enhanced.

In recent years, various Penning-trap groups have begunto measure Qεε for neutrinoless double-electron-capture can-didates with sufficient precision to confirm or reject thepossibility for resonant enhancement [4–12]. 78Kr is one of theremaining possible candidates that still has a large uncertaintyassociated with its Q value, over 700 eV [13]. Despitethe ambiguous Q value, double-electron capture in 78Kr isbeing probed. Recent results of a search at Baksan NeutrinoObservatory for two-neutrino double-K-shell-electron capturein 78Kr have been published [14]. For the neutrinoless mode,the 2+ excited state in 78Se at 2838.49 (7) keV [15] has beenidentified as a possible candidate that could lead to resonantenhancement [16]. The capture to an excited state is appealingbecause the 0νECEC process would be accompanied by acascade of gamma rays that could be used as a signatureto identify the 0νECEC. A better evaluation of the possibleenhancement for neutrinoless double-electron capture in 78Krrequires a more precise knowledge of the Q value. In this work,a new determination of the Q value is reported, and the impacton the potential of 78Kr as a 0νECEC candidate is discussed.

II. METHOD AND RESULTS

The Q value for double-electron capture in 78Kr wasmeasured by Penning-trap mass spectrometry with the Low-Energy Beam and Ion Trap (LEBIT) facility at the NationalSuperconducting Cyclotron Laboratory (NSCL). The layout ofthe facility is illustrated in Fig. 1, and for a detailed descriptionof LEBIT, see Ref. [18]. Singly charged ions of 78Kr and78Se were produced simultaneously with a plasma ion sourcewith a selenium charge and krypton-doped helium supportgas. A rough balance of the ratio of the number of 78Kr and78Se ions was maintained within approximately a factor offive by adjusting parameters of the ion source, including the

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S. BUSTABAD et al. PHYSICAL REVIEW C 88, 035502 (2013)

plasma ionsource

beam coolerand buncher

9.4 T Penningtrap system

90o bender

MCP detector

FIG. 1. Schematic of Low-Energy Beam and Ion Trap (LEBIT)facility.

position of the selenium charge, the degree of filament heating,the proportion of krypton in the support gas, and the overallpressure of the support gas. After the source, helium ionswere removed in preliminary mass filtering by exploiting themass-dependent stability of the ion motion in a compact radiofrequency quadrupole (RFQ) ion-guide system. Ions were thenguided electrostatically to the LEBIT RFQ cooler and buncher[19] that converted the continuous beam of ions to cooledion bunches that were subsequently released for transport tothe Penning trap. Additional mass filtering was performed inthe transport line to the trap by time-of-flight mass separationwith a pulsed electric steerer acting as a fast beam gate. Thegate effectively removed ions with mass numbers other thanA = 78. Both 78Kr+ and 78Se+ were then captured in the9.4 T Penning trap of LEBIT [18]. For the preparation ofpure samples of 78Kr ions in the Penning trap, 78Se ions wereremoved by applying a 100 millisecond azimuthal dipole rfelectric field at their reduced cyclotron frequency [20,21]. Viceversa, for preparing pure 78Se samples, the dipole rf field wasset to drive 78Kr ions out of the trap.

The ratio of cyclotron frequencies of 78Se and 78Kr,νc(78Se

+)/νc(78Kr

+), was measured using the time-of-flight

ion cyclotron resonance (TOF-ICR) technique [17,22]. In thismethod, the cyclotron frequency of an ion is determined bya series of time-of-flight measurements. A purified sample oftrapped ions is exposed to an applied quadrupole rf electricfield and then ejected from the trap. The time between trapejection and detection on a downstream microchannel plate(MCP) is recorded. The rf frequency νrf is varied, and themeasurement is repeated for a new ion bunch resulting in acyclotron resonance as shown in Fig. 2. The minimum in timeof flight corresponds to when ions have been resonantly excitedin the trap with νrf equal to the cyclotron frequency of the ion.

Over a period of two weeks, a total of 209 cyclotron-frequency measurements of 78Se

+and 78Kr+ were taken

with an excitation time of 750 ms; each lasted roughly30 minutes and approximately 400 to 2000 ions weredetected for each measurement. To account for magnetic-field drifts, cyclotron resonances of 78Kr+ were taken bothbefore and after each 78Se+ resonance. Bracketing pairsof 78Kr+ cyclotron-frequency measurements were linearlyinterpolated to determine the cyclotron frequency of 78Kr+at the time of the 78Se+ cyclotron-frequency measurement. Inthis manner, νc(78Se

+)/νc(78Kr

+) was determined; from the

entire collection of data, presented in Fig. 3, an average valueof νc(78Se

+)/νc(78Kr

+) = 1.000 039 236 5 (37) was obtained.

FIG. 2. (Color online) One of 209 cyclotron resonances used inthe measurement of νc(78Se+)/νc(78Kr+). The solid line is a theo-retical fit [17] of the data employed to determine the correspondingcyclotron frequency.

In this measurement, any systematic error is considerablysmaller than the overall statistical error of 3.7 × 10−9. Mostsystematic errors are proportional to the mass differencebetween measured ions. A recent unpublished study foundthat LEBIT mass-dependent systematic effects lead to an errorof less than ×10−9 × mdiff, where mdiff is the mass differencebetween measured ions in atomic mass units. Considering themass difference between 78Kr and 78Se, ∼10−3 u, it is clearthat any error due to mass-dependent systematic effects is wellbelow the statistical error. Systematic errors due to nonlinearmagnetic-field fluctuations have also been determined to bewell below 1 × 10−9 for measurements with a similar timeperiod, ∼1 hour for an individual cyclotron-frequency ratiomeasurement [23]. The primary systematic effect that required

FIG. 3. Collection of measured cyclotron-frequency ratios of78Se+ and 78Kr+ ions about the mean value. The error bars representthe statistical error associated with each measurement. The shaded barrepresents the overall uncertainty in the measurement, 3.7 × 10−9.

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EXAMINATION OF THE POSSIBLE ENHANCEMENT OF . . . PHYSICAL REVIEW C 88, 035502 (2013)

evaluation was the effect of Coulomb interactions betweenmultiple ions in the trap. If any residual contaminant ionswere still present in the trap, frequency shifts that increasewith the total number of trapped ions would occur [21].Accordingly, only events with five or fewer detected ionswere considered in the measurement of νc(78Se

+)/νc(78Kr

+).

Taking into account the detector efficiency of roughly 80%,the limit corresponds to a maximum of six simultaneouslytrapped ions. This limit eliminated occasional events with alarge number of ions, but it did not significantly affect thestatistics of the measurement since the vast majority of eventshad six or fewer trapped ions. In addition, an analysis [24]was performed in which cyclotron-frequency measurementswere sorted by the number of detected ions. No evidenceof a correlation between frequency measurements and countrate was observed, which indicates that contamination wasnegligible. The successful removal of contaminant ions wasconfirmed by verifying that no ions were detected on the MCPwhen dipole rf electric fields were set to drive both 78Se+ and78Kr+ out of the trap. Finally, the average of all data has aBirge ratio [25] of 1.05 (5), which is a strong indication thatfluctuations in the data are purely statistical and that systematicerror is negligible.

The Q value for double-electron capture Qεε can beexpressed by

Qεε = [M(Af ) − me]c2

[νc(A+

f )

νc(A+i )

− 1

], (2)

where M(Af ) is the atomic mass of the daughter, me is the massof the electron, and νc(A+

f )/νc(A+i ) is the ratio of cyclotron

frequencies of daughter and mother ions. The measuredratio of νc(78Se

+)/νc(78Kr

+) together with the atomic mass

value of 78Se reported in the 2012 atomic mass evaluation(AME) [13] yields a new determination of the Q value:Qεε = 2847.75 (27) keV. This new value differs by 1.4 keVfrom the 2012 AME value, a shift of two sigma, and theuncertainty has been reduced by a factor of three.

The measured value of νc(78Se+

)/νc(78Kr+

) indicates adiscrepancy in the currently accepted atomic mass values of78Kr and 78Se. Although the Q value depends sensitivelyon νc(78Se

+)/νc(78Kr

+), within the obtained precision it is

insensitive to the atomic-mass value of 78Se used in Eq. (2).

III. ANALYSIS AND CONCLUSIONS

Using the new determination of Qεε , the possibility ofresonance enhancement of 0νECEC to known excited statesin 78Se was investigated. For the identified 2+ excited stateat 2838.49 (7) keV, two possible neutrinoless double-electroncaptures are presented in Table I. In this case, captures fromouter electron orbitals must be considered because K capture isenergetically forbidden. The presented electron orbitals for thecaptures reflect that the spin must change by two units and thatthe parity should not change to avoid suppression. The width

TABLE I. Parameters governing the possible neutrinoless double-electron capture in 78Kr to the 2+ excited state at 2838.49 (7) keV in78Se. Presented in the columns are the atomic levels of the capturedelectrons, the radiative width, the binding energy of the two-electronhole, the degeneracy parameter, the resonance parameter, and theenhancement factor.

Orbitals �/eV B2h/keV �/keV F/(keV−1) EF

L1M4 3.9 1.71 7.55 (28) 6.8 × 10−5 1.2 × 105

L3M2 3.2 1.60 7.66 (28) 5.5 × 10−5 9.6 × 104

� was calculated for each transition by summing the widthsof the electron levels given in Ref. [26]. Since the width of thetwo-electron-hole state dominates �, the width of the nuclearexcited state can be neglected to a very good approximation.The binding energy of the two-electron hole was approximatedby summing the two individual electron binding energiesgiven in Ref. [27]. The approximation introduces an errormuch less than 500 eV [28] and is thus reasonable sinceIt does not change the final conclusion of this work. Thedegeneracy parameter, presented in Table I, was calculated foreach transition using the newly determined Q value. For bothtransitions the degeneracy parameter is greater than 7 keV,quite far from the tens-of-eV degeneracy that would leadto strong enhancement. The listed error in � considers theuncertainty in the newly measured Q value and the uncertaintyof the energy of the nuclear excited state; it does not includeuncertainty related to the above-mentioned approximationregarding B2h. With the multiple-keV size of �, it can alreadybe concluded that the 2+ state in 78Se is a poor candidate forresonant enhancement.

The resonance parameter and the enhancement factor (EF)have been calculated for both transitions and are given inTable I. The enhancement factor is the ratio of the resonanceparameter F of the considered transition to that of the nonreso-nant KK capture to the nuclear ground state. Not surprisingly,the mismatch in energy reflected in the large degeneracyparameters gives rise to small resonance parameters and weakenhancement factors, ∼105. These enhancement factors areminuscule compared to maximum enhancement factors of∼1012 for � = 0.

The decay rate, given by Eq. (1), will be further hamperedby a small value of M. The necessity to consider outerelectron captures will lead to suppression in the leptonicphase-space factor, and the need for the 0+ → 2+ transitionto proceed through hadronic recoil will suppress the nuclearmatrix element by approximately 5.44 × 10−4 [5]. Thiscombination causes the 2+ state in 78Se to be a quite unfa-vorable candidate for neutrinoless double-electron capture.The next closest known states in 78Se are at 2754.46 (17)and 2864.12 (7) [15] and are too far away for any hope ofenhancement.

In conclusion, with the newly determined Q value fordouble-electron capture in 78Kr, we can now confidentlyrule out all known excited states in 78Se as possible can-didates for resonantly enhanced neutrinoless double-electroncapture.

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