Observation of Non-Exponential Orbital Electron Capture Decays of Hydrogen-Like 140 Pr and 142 Pm Ions
Yu.A. Litvinov, F. Bosch, N. Winckler, D. Boutin, H.G. Essel, T. Faestermann, H. Geissel, S. Hess, P. Kienle, R. Knöbel, C. Kozhuharov, J. Kurcewicz, L. Maier, K. Beckert, P. Beller, C. Brandau, L. Chen, C. Dimopoulou, B. Fabian, A. Fragner, E. Haettner, M. Hausmann, S.A. Litvinov, M. Mazzocco, F. Montes, A. Musumarra, C. Nociforo, F. Nolden, W. Plaß, A. Prochazka, R. Reda, R. Reuschl, C. Scheidenberger, M. Steck, T. Stöhlker, S. Torilov, M. Trassinelli, B. Sun, H. Weick, M. Winkler
OObservation of Non-Exponential Orbital Electron Capture Decays ofHydrogen-Like
Pr and
Pm Ions
Yu.A. Litvinov ab ∗ , F. Bosch a , N. Winckler ab , D. Boutin b , H.G. Essel a , T. Faestermann c , H. Geissel ab ,S. Hess a , P. Kienle cd , R. Kn¨obel ab , C. Kozhuharov a , J. Kurcewicz a , L. Maier c , K. Beckert a , P. Beller † ,C. Brandau a , L. Chen b , C. Dimopoulou a , B. Fabian b , A. Fragner d , E. Haettner b , M. Hausmann e ,S.A. Litvinov ab , M. Mazzocco af , F. Montes e , A. Musumarra gh , C. Nociforo a , F. Nolden a , W. Plaß b ,A. Prochazka a , R. Reda d , R. Reuschl a , C. Scheidenberger ab , M. Steck a , T. St¨ohlker ai , S. Torilov j ,M. Trassinelli a , B. Sun ak , H. Weick a , M. Winkler aa Gesellschaft f¨ur Schwerionenforschung GSI, 64291 Darmstadt, Germany b Justus-Liebig Universit¨at, 35392 Gießen, Germany c Technische Universit¨at M¨unchen, 85748 Garching, Germany d Stefan Meyer Institut f¨ur subatomare Physik, 1090 Vienna, Austria e Michigan State University, East Lansing, Mi 48824, U.S.A. f Dipartimento di Fisica, INFN, I35131, Padova, Italy g INFN-Laboratori Nazionali del Sud, I95123 Catania, Italy h Universit´a di Catania, I95123 Catania, Italy i Ruprecht-Karls Universit¨at Heidelberg, 69120 Heidelberg, Germany j St. Petersburg State University, 198504 St. Petersburg, Russia k Peking University, Beijing 100871, China
We report on time-modulated two-body weak decays observed in the orbital electron capture of hydrogen-like Pr and Pm ions coasting in an ion storage ring. Using non-destructive single ion, time-resolvedSchottky mass spectrometry we found that the expected exponential decay is modulated in time with a modulationperiod of about 7 seconds for both systems. Tentatively this observation is attributed to the coherent superpositionof finite mass eigenstates of the electron neutrinos from the weak decay into a two-body final state.
1. Introduction
The accelerator facility of GSI Darmstadt withthe heavy ion synchrotron SIS coupled via theprojectile fragment separator FRS to the cooler-storage ring ESR offers a unique opportunity fordecay studies of highly ionized atoms. It is possi-ble to produce, separate, and store for extended ∗ Corresponding author. E-mail: [email protected] † periods of time exotic nuclei with a well-definednumber of bound electrons [1]. Basic nuclearproperties such as masses and lifetimes are mea-sured by applying the mass- and time-resolvedSchottky Mass Spectrometry (SMS) [2,3].The dependance of β -lifetimes on the atomiccharge state q of the parent ion has an obvious im-pact on our understanding of the processes ongo-ing in stellar nucleosynthesis [4]. Several success-ful experiments studying weak decay of highly-1 a r X i v : . [ nu c l - e x ] J a n Yu.A. Litvinov, F. Bosch, N. Winckler, et al. charged atoms have been performed in the past,e.g., the experimental discovery of bound-statebeta decay ( β b ) at the example of fully-ionized Dy [5]. Due to β b decay, fully ionized Renuclei decay by 9 orders of magnitude faster thanneutral atoms [6]. The first direct measurementof the ratio of bound and continuum β -decay offully-ionized Tl was achieved by a direct ob-servation of the decay and growth of the numberof parent and daughter ions using SMS [7]. In thecourse of the present study the first measurementsof orbital electron capture (EC) in hydrogen-like(H-like) and helium-like (He-like) Pr ions havebeen performed [8,9]. It was found that the ECdecay rate in H-like
Pr ions is about 50%higher than in He-like ions. This result includ-ing the measured EC/ β + branching ratios can beexplained by standard weak decay theory [10,11].The change of the mass manifests a radioactivedecay and is evidenced by a corresponding cor-related change of the revolution frequency. Thearea of the Schottky frequency peak is propor-tional to the number of stored ions and to thesquare of the atomic charge state, q . The SMS issensitive to single stored ions with atomic chargestates q ≥
30 [3]. However, due to a large vari-ance in determination of the peak areas, it be-came apparent that only by restricting to three in-jected parent ions at maximum one could excludeany uncertainty in the determination of the exact number of circulating ions. With this constraintthe time of the decay of each stored ion can beprecisely determined. On this basis single parti-cle decay-spectroscopy has been developed whichallows for an unambiguous and background-freeidentification of a certain decay branch [8,12].This leads, however, to a very laborious collec-tion of data which requires at least some thou-sand measurements to get a statistically reason-able number of decays.Here we report on the first experiments whichused time-resolved single-particle decay spec-troscopy for studying the time evolution of two-body weak decays, i.e. EC and β b -decays of ra-dioactive ions in the ESR. The physics motiva-tion was the question whether or not the electronneutrinos generated in such decays as coherent su-perposition of mass eigenstates would affect the Figure 1. Decay schemes of neutral Pr (upperpanel) and
Pm (lower panel) atoms [14].exponential decay [13]. H-like
Pr and
Pmions have been selected for these studies. Bothnuclei decay to stable daughter nuclei via eitherthe three-body positron emission or the two-bodyEC-decay. Well-known decay schemes of neutral
Pr and
Pm atoms [14] are illustrated in Fig-ure 1. Both systems decay mainly by a single al-lowed Gamow-Teller (1 + → + ) transition. Theweak transitions to excited states can be safelyneglected in our context. These nuclides havequite different decay energies ( Q EC values) andlifetimes, thus allowing a detailed comparison ofthe time evolution of the decays with different Q EC and lifetimes. Both Q EC -values are suffi-ciently large to be easily resolved by SMS. Fur-thermore, their half-lives are much larger than thetime needed for the preparation of the ions. bservation of Non-Exponential Orbital Electron Capture Decays of Hydrogen-Like Ions
2. Experiment
H-like Pr and Pm ions were pro-duced by fragmentation of primary beams of Sm fast extracted from the SIS with energiesin the range between 500-600 MeV per nucleon.The duration of the extraction pulse was less than1 µ sec which is essential since we require a well-defined time of the creation of the ions. Berylliumproduction targets placed at the entrance of theFRS with thicknesses of 1 and 2 g/cm have beenapplied. The important parameters used for theexperiment are summarized in Table 1. Three in-dependent experiments were performed with Prions (runs 1,2 and 3) and one with Pm ions (run4) for comparison.The fragments of interest were separated in-flight with the FRS using the B ρ -∆E-B ρ method[15]. For this purpose, a 731 mg/cm aluminumdegrader was inserted at the middle focal planeof the FRS. In runs 3 and 4 a 256 µ m niobiumfoil after the degrader has been used in addition.In this way we separated Pr and Pm fragments without isobaric contaminations at theexit of the FRS. More details on the separationof pure Pr ions in these experiments can befound in Ref. [12].Single bunches (less than 1 µ s long) of sep-arated ions containing on the average only twoparent ions were injected into the ESR at the in-jection energy of 400 MeV per nucleon and thenstored in the ultrahigh vacuum ( ∼ − mbar).Their velocity spread caused by the productionreaction was reduced within 6-10 sec first bystochastic pre-cooling [16] and then by electroncooling [17] to a value of ∆ v/v ≈ · − . Theions coasted in the ring with a velocity of 71% ofthe speed of light, corresponding to a relativisticLorentz factor of 1.43.The 30 th harmonics of the revolution frequency f of about 2 MHz (circumference of the ring is108.3 m) was measured by the Fourier frequencyanalysis of the signals induced by the coastingions at each revolution in pick-up plates. Forcooled ions f is uniquely related to the mass-over-charge ratio M/q of the stored ions, which is thebasis for the Schottky mass measurements [18].Thus the ions of interest and their decay prod- ucts could be unambiguously identified.The data were acquired with the commercialrealtime spectrum analyzer Sony-Tektronix 3066.It was triggered with the logic signal correspond-ing to the start event of the injection kicker of theESR. After each trigger event, the analyzer wasrecording a given number of Fourier transformednoise power spectra - FFT (Fast Fourier Trans-form) frames. Each FFT frame had a bandwidthof 5 kHz and was collected for 128 msec. Eachsubsequent frame was started after a defined de-lay of 64 msec (runs 1, 3 and 4) or 50 msec (run2). The recorded data were automatically storedon disk for off-line analysis.In the ESR, the transition from the parent tothe daughter ion in a nuclear decay is evidencedby a well-defined change ∆ f of the revolution fre-quency. Thus, by keeping the number of coast-ing ions small we could continuously monitor the”mass” of each ion in time and determine pre-cisely its decay time. In our case the parent ionscould have three possible fates, namely EC or β + -decay or a loss due to atomic charge exchangereactions.Since the atomic charge state q does not changein the EC-decay, ∆ f is determined by the massdifference ( Q EC -value) between the parent anddaughter nuclei. The corresponding change inthe revolution frequency is a few hundred Hzonly (about 270 Hz for the case of Pr andabout 310 Hz for the case of
Pm) (30 th har-monics). The decay is characterized by the cor-related disappearance of the parent ion and ap-pearance of the daughter ion. The appearancein the frequency spectrum is delayed by about900 ±
300 msec needed to cool the recoiling daugh-ter ions. Their kinetic energies are 44 eV and90 eV (c.m.) for the cases of
Ce and
Nddaughter nuclei, respectively. The ESR latticeand the applied ion-optical setting guarantee that all recoil ions still remain in the acceptance irre-spective on the direction of their emission.In β + -decay the atomic charge changes byone unit and the frequency of the correspondingdaughter ion is shifted by about -150 kHz (30 th harmonics). This frequency shift is by far largerthan our small observation band, and the decayis only seen by a decrease of the number of the Yu.A. Litvinov, F. Bosch, N. Winckler, et al. parent ions. Such a disappearance, however, can-not be distinguished from the loss of the ion dueto atomic capture or loss of an electron by reac-tions with the atoms of the residual gas or theelectrons of the cooler. However, from the lossesobserved for the stable daughter ions a loss con-stant λ loss ≤ · − sec − (the loss constantsfor H-like parent ions and fully-ionized daughterions are almost the same [7]) could be extractedwhich is at least one order of magnitude smallerthan the EC and β + decay constants λ EC and λ β + , respectively. We also note that mechanicalscrapers of the ESR were positioned to removethe decay products of the atomic charge-exchangereactions and the β + -decay daughter ions.Two out of many thousand runs are illustratedin Figure 2 as a water-flow diagram starting at thetime of the injection into the ring. These exam-ples show one (upper panel) and two (lower panel)injected parent ions. Each horizontal line rep-resents a frequency spectrum with 8 Hz/channelaveraged over five consecutive FFT frames. Thefirst several seconds are needed for the com-bined stochastic and electron cooling. The de-cay times are clearly seen. We emphasize thatsuch a continuous observation of both the par-ent and daughter ions excludes any possible time-dependent alteration of the detection efficiency.
3. Data analysis and results
The aim of the analysis was to study preciselythe decay characteristics of each EC-decaying ion.For this purpose, at least two independent visualand one automatic analysis have been applied tothe data of each experimental runs.For achieving a better signal-to-noise ratio onemay average several subsequent Schottky spectraas it is done in Figure 2. In this way, however,one reduces the time resolution. In the visualanalysis we analyzed the un-averaged FFT framesor the average over two subsequent frames. Forthe automatic analysis we had to average 5 FFTframes in order to achieve a sufficient signal-to-noise ratio. The details of the automatic dataevaluation are described in Refs. [19,20].The analysis was done by inspection of eachFFT spectrum taken as a function of time. Then the time of appearance of a daughter nucleus fol-lowing the decay of its mother was determined. Itwas demanded that the decay times determinedin independent analysis agree within less than onesecond. Only the times of the appearance of thedaughter nuclei were considered, which are de-layed compared to the decay of the mother ionby about 900 ±
300 msec.The decay times from the three runs with H-like
Pr were combined. These results and theresults for
Pm ions are illustrated in Figure 3and in Figures 4 and 5, respectively. The time ofthe injection into the ESR is within 1 µ s the timeof the creation of the ions. The data were fittedwith the exponential decay function: dN EC ( t ) dt = N (0) · λ EC · e − λt , (1)where N (0) is the number of parent ions at thetime t = 0, the time of injection and λ = λ EC + λ β + + λ loss . The ratio of λ EC /λ β + is 0.95(8) forthe H-like Pr and is expected to be about 0.32for the H-like
Pm [9].It is clear to see that the expected exponentialdecrease of the EC-decays as a function of timeshows a superimposed periodic time modulation.To account for this modulation we fitted the datawith the function: dN EC ( t ) dt = N (0) · e − λt · (cid:103) λ EC ( t ) , (2)where (cid:103) λ EC ( t ) = λ EC · [1 + a · cos ( ωt + φ )] with anamplitude a , an angular frequency ω , and a phase φ of the modulation. For the case of Pm ionsonly the first 33 seconds after the injection werefitted with Eq. 2 due to the short half-life of themother nuclei and, thus, the fast damping of themodulation amplitude.The fits were done with the MINUIT package[21] using the χ minimization and the maximumlikelyhood methods which yielded consistent re-sults. The fit parameters are given in Table 2.From the angular frequency ω of Table 2 wecan extract the periods of the modulation of7.06(8) sec and 7.10(22) sec (laboratory frame)for Pr and
Pm ions, respectively. The pres-ence of the modulation frequencies was also con-firmed by Fast Fourier Transforms (see insets in bservation of Non-Exponential Orbital Electron Capture Decays of Hydrogen-Like Ions a agreewithin the error bars. The average value of bothsystems is (cid:104) a (cid:105) = 0 .
4. Discussion
The observed periodic modulations of the ex-pected exponential decrease of the number of EC-decays per time unit still suffer from restrictedstatistics. However, the ”zero hypothesis” of apure exponential decay can be already rejectedaccording to the χ /DoF -values from Table 2 onthe 99% confidence level (one-sided probabilities p = 0 . the complete and uninterrupted infor-mation upon the status of each stored ion . Fur-thermore, the parent and daughter ions from bothsystems coast on different orbits in the ESR andhave different circulation times. We can also ex-clude binning effects or the variance of the de-lay between the decay of the mother and the ”re-appearance” of the daughter ion, since these ef-fects lead to an uncertainty of the decay time thatis much smaller than the observed period.It is very probable that the H-like Pr aswell as the
Pm ions with nuclear spin I = 1 + are produced in a coherent superposition of thetwo 1 s hyperfine states with total angular mo-menta F = 1 / F = 3 /
2. This could leadto well-known quantum beats with a beat period T = h/ ∆ E , where ∆ E is the hyperfine splitting.However, those beat periods should be more thantwelve orders of magnitude shorter than the ob-served ones.The weak decay conserves the F quantum num-ber, and since the final state (fully ionized daugh-ter nuclei with I = 0 + and emitted electron neu-trino ν e ) has F = 1 /
2, the EC-decay from the F = 3 / not allowed [8,9]. Only a hypo-thetical, yet unknown, mechanism which trans-fers the parent ions periodically within 7 seconds from the F = 1 / F = 3 / (cid:126)q ν or neither of them[25,26,27,28,29]. In our case, this question can beaddressed properly only in the context of wave-packets since we observe the decaying system ina restricted region of space and time. This neces-sarily generates an uncertainty of both momen-tum and energy. An attempt to interpret themodulation times in this framework has beenmade in Ref. [30].Disregarding momentum and energy spread ina simplified picture and restricting to two neu-trino mass eigenstates, one gets from momentumand energy conservation for an initial state withenergy E and momentum P = 0 in the c.m. sys-tem : E + M + p M = E (3) E + M + p M = E, (4)where E i = (cid:112) p i + m i denotes the energy of thetwo neutrino mass eigenstates with masses m and m , respectively, p i / M the correspondingkinetic energies of the recoiling daughter nuclei,and where M is the mass of the daughter nucleus. In the following we set c =1. Yu.A. Litvinov, F. Bosch, N. Winckler, et al.
By combining these two equations and neglectinga term given by the ratio of the recoil energy andthe mass of the daughter nucleus we arrive at (seee.g. Ref. [31,32]):∆ E = E − E ≈ ∆ m M , (5)where ∆ m = m − m .The modulations could be caused by the en-ergy splitting ∆ E which is indicated by almostthe same observed modulation periods for bothdecaying nuclei Pr and
Pm with almost thesame nuclear masses M but with quite differ-ent neutrino energies and, thus, momenta. Oneexpects for a mass of 140 mass units and for∆ m ≈ − eV [33] a period in the c.m. systemof roughly T=10 sec. Besides the fact that thisestimate is based on several assumptions manyquestions remain. How could the coherence ofthe entangled quantum states be preserved overtime spans of some ten seconds? What is theeffect of the continuous monitoring of the stateof the ion? Is the ”phase” between the entangledneutrino mass eigenstates set back to zero at eachobservation?It is obvious that our findings must be corrobo-rated by the study of other two-body beta decays(EC and β b ). Furthermore, it has to be investi-gated how the oscillation period–if persisting atall–depends on the nuclear mass M . Mandatoryare also investigations of three-body β -decays,where oscillations should be washed out due tothe broad distribution of neutrino (sc. recoil) en-ergies. Finally, an interesting case arises whenthe decaying nucleus is not free, but couples tothe full phonon spectrum in the lattice of a solid. Acknowledgements
We would like to express our deep grati-tude to W. Henning for his continuous sup-port and invaluable advice. It is a pleasureto acknowledge many fruitful and engaged dis-cussions with L. Batist, K. Blaum, P. Braun-Munzinger, H. Emling, A. F¨aßler, B. Franzke,S.J. Freedman, L. Grigorenko, A. Ivanov, H.-J. Kluge, E. Kolomeitsev, R. Kr¨ucken, K. Lind- ner, M. Lindroth, G. M¨unzenberg, Z. Patyk,K. Riisager, A. Sch¨afer, J. Schiffer, D. Schwalm,R. Schuch, N. Severijns, H. St¨ocker, P.M. Walker,J. Wambach, and H. Wilschut. We would liketo thank in particular H. Feldmeier, M. Kleber,K.H. Langanke, H. Lipkin, P. Vogel, Ch. Wein-heimer, and K. Yazaki for intensive theoreticaldiscussions. We are grateful to Th. M¨uller andA. Le F`evre for the help in the data evaluation.We are indebted to the HADES and IKAR collab-orations for their help and flexibility concerningthe beam time schedule. The excellent support bythe accelerator team of GSI decisively contributedto the successful achievement of our experiments.One of us (M.T.) acknowledges the support bythe A. von Humboldt Foundation.
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Table 1Primary beam, target and degrader parameters, number of measurements. Each line represents a differentexperimental run labelled in the first column. The ion of interest is given in the second column. Energyof the
Sm primary beam E ( Sm) and the thickness of the beryllium production target L ( Be) aregiven in the third and fourth columns, respectively. The number of measurements performed in each run inj is given in the last column.run ion E ( Sm) L ( Be) inj [MeV/u] [mg/cm ]1 Pr Pr Pr Pm Pr (upper part) and
Pm (lower part) EC-decay data illustrated inFigures 3, 4 and 5. The fits are done according to Eq. 1 and Eq. 2 which is indicated in the first column.The corresponding χ /DoF ( DoF = degrees of freedom) are given in the last column.Fit parameters of
Pr dataEq. N λ EC λ a ω χ /DoF Pm dataEq. N λ EC λ a ω χ /DoF bservation of Non-Exponential Orbital Electron Capture Decays of Hydrogen-Like Ions Upper panel: a series of consecutive frequency spectra of a single parent Pr ion decaying tothe daughter Ce ion 49.92 sec after the injection into the ESR. Lower panel: two injected Pm ionsdecay 18.64 sec and 67.84 sec after the injection. The first ion decays by electron capture to a Nd ion. Thesecond ion decays by β + -decay or is lost due to atomic charge exchange reactions. The times of the correlateddisappearance of the parent ions and the appearances of EC-daughter ions are clearly seen. The first few secondsare needed for cooling. The frequency differences between parent and daughter ions correspond to Q EC values of3.35 MeV and 4.83 MeV for Pr and Pm ions, respectively. Yu.A. Litvinov, F. Bosch, N. Winckler, et al.
Figure 3. Number of EC-decays of H-like
Pr ions per second as a function of the time after the injectioninto the ring. The solid and dashed lines represent the fits according to Eq. 1 (without modulation) andEq. 2 (with modulation), respectively. The inset shows the Fast Fourier Transform of these data. A clearfrequency signal is observed at 0.14 Hz (laboratory frame). bservation of Non-Exponential Orbital Electron Capture Decays of Hydrogen-Like Ions
Pm ions per 0.64 seconds as a function of the time after theinjection into the ring. The solid line represents the exponential decay fit according to Eq. 1 until 33 secafter injection (continued as a dotted line). The inset shows the FFT spectrum obtained from the datauntil 33 sec. The reduced resolution compared to Figure 3 is explained by a smaller number of pointsused for the FFT. A clear FFT peak is observed at about 0.14 Hz (laboratory frame).2