A new technique for elucidating β -decay schemes which involve daughter nuclei with very low energy excited states
M. Venhart, J. L. Wood, A. J. Boston, T. E. Cocolios, L. J. Harkness-Brennan, R.-D. Herzberg, D. T. Joss, D. S. Judson, J. Kliman, V. Matousek, S. Motycak, R. D. Page, A. Patel, K. Petrik, M. Sedlak, M. Veselsky
aa r X i v : . [ phy s i c s . i n s - d e t ] J un A new technique for elucidating β -decay schemes which involve daughter nucleiwith very low energy excited states M. Venhart a, ∗ , J. L. Wood b , A. J. Boston a , T. E. Cocolios c,d , L. J. Harkness-Brennan e , R.-D. Herzberg e , D. T. Joss e ,D. S. Judson e , J. Kliman a , V. Matouˇsek a , ˇS. Motyˇc´ak f , R. D. Page e , A. Patel e , K. Petr´ık a , M. Sedl´ak a , M. Veselsk´y a a Institute of Physics, Slovak Academy of Sciences, SK-84511 Bratislava, Slovakia b Department of Physics, Georgia Institute of Technology, Atlanta, GA 30332, USA c School of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, United Kingdom d KU Leuven, Instituut voor Kern- en Stralingsfysica, B-3001 Leuven, Belgium e Oliver Lodge Laboratory, University of Liverpool, Liverpool, L69 7ZE, UK f Faculty of Electrical Engineering and Information Technology, Slovak University of Technology, SK-812 19 Bratislava, Slovakia
Abstract
A new technique of elucidating β -decay schemes of isotopes with large density of states at low excitation energieshas been developed, in which a Broad Energy Germanium (BEGe) detector is used in conjunction with coaxial hyper-pure germanium detectors. The power of this technique has been demonstrated on the example of Hg decay.Mass-separated samples of
Hg were produced by a deposition of the low-energy radioactive-ion beam delivered bythe ISOLDE facility at CERN. The excellent energy resolution of the BEGe detector allowed γ rays energies to bedetermined with a precision of a few tens of electronvolts, which was su ffi cient for the analysis of the Rydberg-Ritzcombinations in the level scheme. The timestamped structure of the data was used for unambiguous separation of γ rays arising from the decay of Hg from those due to the daughter decays.
Keywords:
Broad Energy Germanium detector, γ -ray spectroscopy, level scheme
1. Introduction
The β decay process plays a fundamental role in stud-ies of nuclear structure. The process is defined by aninitial state, a ground state or an isomer of the parentisotope, which ideally has an accurately known energy(mass), spin and parity. To study this process, modernexperimental methods are used to produce very puresources using isotope separation techniques. Atoms(ions) can be separated by mass either electromagnet-ically or by using a laser induced ionisation step [1],with the latter also able to separate isomers from groundstates. The decay process results in the population ofstates in the daughter nucleus with spins close to that ofthe parent nucleus. Elucidation of the excited states ofthe daughter nucleus proceeds via γ -ray and conversion-electron spectroscopy [2, 3]. Energies of excited statesare deduced via energy sums and di ff erences of the ob-served radiations. Spins and parities of excited states ∗ Corresponding author
Email address: [email protected] (M. Venhart) are deduced via multipolarities of the observed radia-tions, in reference to the (known) ground-state spin andparity of the daughter nucleus. Angular correlation orangular distribution data for γ rays can also be used todetermine spins and multipolarities.Radioactive decay plays a leading role in the modernstudy of nuclear structure, through the experimental in-vestigation of the thousands of nuclei that lie far fromstability. The challenge is in the complexity of thesestudies, especially when the nuclei involved possess oddmass or, even more challenging, when the daughter is anodd-odd nucleus, due to the high level density. Hereinwe address the further challenge where a high level den-sity occurs at very low excitation energy.The occurrence of a high level density at low excita-tion energy results in major challenges for observing thede-exciting transitions [2]. Generally, low-energy tran-sitions proceed preferentially by internal conversion.High-resolution conversion electron spectroscopy [4] istechnically very demanding and only a few researchgroups have pursued this technique. Further, the useof coincidence spectroscopy to reliably sequence de- Preprint submitted to Nuclear Instruments and Methods in Physics Research Section A October 10, 2018 ay paths can be di ffi cult or impossible because of iso-merism (coincidence delay) occurring for some of thelow-lying excited states. In the face of such challenges,only the Rydberg-Ritz combination principle [5] pro-vides a means for elucidating a decay scheme, thus pro-viding reliable excited state information for the daugh-ter nucleus. Generally, the complexity of odd-massdecay schemes (many hundreds of γ rays) renders theRydberg-Ritz technique too ambiguous to be useful, un-less γ -ray energies are measured to a precision betterthan 50 eV. We have therefore developed and applied anew experimental technique for these studies.In this work, a Broad Energy Germanium detector(BEGe) [6] has been used in combination with stan-dard coaxial germanium detectors in the study of the Hg → Au decay scheme using mass separatedsources from the ISOLDE facility at CERN. This de-cay possesses a feature that occurs commonly when the Q value of the β decay is large, namely the concen-tration of the β decay process to a few highly excitedstates in the daughter nucleus. These states can decayto many low-lying states, primarily by γ -ray emission.Using a combination of the high resolution of the BEGedetector and γ - γ coincidence spectroscopy, energy dif-ferences of decay sequences reveal low-lying excitedstates even where the transitions between the low-lyingexcited states are not observed. Further, we operatedthe BEGe detector at a gain of 27 eV / ch so that energiesaccurate to ±
10 eV could be obtained for most of theobserved γ rays.
2. Experimental details
The experiment was performed at the ISOLDE facil-ity located at CERN. It uses a pulsed beam of protonswith an energy of 1.4 GeV and an average intensity of1.5 µ A for production of radioactive ion beams. The
Hg species were produced by spallation reactions in amolten lead target. The reaction products were di ff usedout of the target using high temperature, ionised witha plasma ion source and extracted with a 30 kV electricpotential. After extraction from the ion source, the beamwas separated employing the General Purpose Separatorof the ISOLDE facility, which has one analysing mag-net [7].The mass-separated radioactive-ion beam of Hgwith an energy of 30 keV was then delivered to theTATRA tape transportation system [8]. The sampleswere created by a deposition of the beam on a tapemade of amorphous metal. The activity was collectedfor a period of 1 s, after which the sample was trans-ported into the measurement position where γ rays fol- χ = 1.00 red. F i t r e s i dua l c oun t s / e V σ Figure 1: (Colour online) a) Part of the γ -ray singles spectrum de-tected with the BEGe detector. Indicated is a fit with multiple gaus-sians with linear background. b) fit residuals with indicated 2 σ confi-dence interval (red dashed lines). lowing the radioactive decay were detected by an ar-ray of three di ff erent High Purity Germanium (HPGe)detectors. A BE2020 type BEGe [6] detector, whichhas a non-bulletized disc shape with an active diame-ter of 51 mm and a thickness of 20 mm was used to de-tect γ rays within the 40 - 980 keV range. This detectorhas excellent energy resolution and a low-energy detec-tion limit, relative to coaxial detectors, due to the elec-trode configuration employed in BEGe detectors and afabrication process that optimises the charge collectiontimes across a wide energy range. Two additional p-typecoaxial detectors with relative e ffi ciency of 70 % wereused to detect γ rays up to 2.5 MeV. Both coaxial detec-tors were mounted perpendicularly to the BEGe detec-tor. A source-to-detector distance of 5 cm was used forall three detectors. After 30 s of data collection, a newsample was made and the process was repeated.The signals from the HPGe detector preamplifierswere analysed using a commercial Pixie-16, 14-bit,250 MHz digitiser [9], designed by the XIA, Inc. Priorto digitising, the signals were amplified and their dc o ff -sets were adjusted using fast operational amplifiers. Again of 8 was used for the BEGe detector, which opti-mised use of the dynamic range such that signals aris-ing from γ -rays up to 980 keV could be digitised. Inthis mode, each ADC channel was equivalent to approx-imately 27 eV. When combined with the almost idealgaussian shape [10] of peaks in the BEGe energy spec-trum, this allowed doublets at the level of 0.3 keV sep-aration to be distinguished by a deconvolution of γ -raysingles spectra. The data acquisition system was oper-ated in a triggerless mode, i.e., all channels were read2 = 1.02 red. F i t r e s i dua l -150-100-5050100150150 796 800 804 808 812 816 820 824200250300350 c oun t s / e V Energy [keV] 2 σ Figure 2: (Colour online) a) Part of the γ -ray singles spectrum de-tected with the BEGe detector. Indicated is a fit with multiple gaus-sians with linear background. b) fit residuals with indicated 2 σ confi-dence interval (red dashed lines). out and timestamped individually. For each particularsample of Hg, the internal clock of the digitiser wasreset to zero prior to the start of the measurement. Thestream of timestamped data was recorded on disk andcoincidence information was reconstructed o ffl ine.
3. Level scheme construction
The level scheme construction procedure used in thepresent analysis is based on three steps: (i) the determi-nation of γ ray energies as precisely as possible usingthe γ -ray singles spectrum detected with the BEGe de-tector, (ii) separation of γ rays due to the decay of Hgfrom its daughter decays and / or room background and(iii) analysis of γ - γ coincidence relationships. Through-out data acquisition, no instablities in the γ -ray energyspectra such as peak drift or peak shape degradiationwere observed, such that a single set of energy calibra-tion data could be used. The calibration data were ac-quired immediately after the end of the Hg samplescollection using a
Eu source. A quadratic polyno-mial function was used for the energy calibration of theBEGe detector. In this part of the analysis, the coaxialdetectors were not employed.Due to the excellent charge collection in the BEGedetector and good statistics from the experiment, thepeaks in the acquired energy spectra were almost iden-tifical in gaussian shape with a very smooth background[10]. Therefore, a gaussian fit with linear backgroundwas used to determine the energies of transitions in the γ -ray singles spectrum. Fits were performed in sev-eral short intervals, which covered the full energy rangeof the γ -ray singles spectrum. For each particular fit,its goodness was investigated by using the reduced chi squared ( χ red . ) test and in addition, fit residuals wereplotted. An illustrative example of the fit of two γ linesis given in Fig. 1a. For the fit given in Fig. 1a the χ red . = σ confi-dence interval. The χ red . of 1.00 and fit residuals wellwithin the 2 σ confidence suggest that fitting function,i.e., two separate gaussians with linear background verywell describes the data.The ability to detect γ rays above 0.5 MeV with verygood resolution and almost ideal gaussian shape is a keyfactor in our analysis, since it allows the precise deter-mination of high-energy γ rays and their exact place-ment in the level scheme. Due to the amplification ofthe BEGe detector preamplifier signals, the highest ob-served γ -ray energy was 980 keV, as discussed previ-ously. We therefore define our high-energy range as500 keV to 980 keV in this experiment. An illustrativeexample of the high-energy γ -ray singles spectrum isgiven in Fig. 2a together with the fit used, which was 11gaussian distributions with linear background. The χ red . of 1.02 indicates a very good fit, which is corroboratedwith fit residuals well within 2 σ confidence interval, asshown in Fig. 2b.A typical complication related to odd-mass studiesin a region where intruder configurations are present atlow excitation energies is a great level density (typically15-30 excited states below 500 keV) and thus complex-ity of measured spectra. This complexity is enhancedby the presence of γ rays from other decay branchesof the studied isotope, the decay of daughter isotopes,radioactive-ion beam contaminants, interaction of neu-trons that are present in the experimental hall and theroom background. The BEGe detector allows the elu-cidation of a complex decay scheme in the presence ofthese complicating factors. The data were sorted into a γ -ray energy vs. timestamp matrix. Subsequently, γ -rayspectra using 0 - 5 s and 0 - 30 s time windows were pro-jected. The background, which was slightly di ff erentin these projections, was subtracted using the TSpec-trum class [11] of the ROOT package. Both spectrawere normalised using known γ rays due to Hg and
Au decays, subsequently subtracted from each otherin a way that a spectrum containing only γ rays due tothe decay of Hg was produced. A separate spectrumdominated by γ rays due to the daughter activities, roombackground, etc., was also produced. This allows forunambiguous isolation of γ rays due to the decay of theinvestigated isotope.The power of this technique is demonstrated in theexample shown in Fig. 3a, which gives the total γ -raysingles spectrum detected with the BEGe within the 50 -3 c oun t s / k e V AuPtIrOs . ( ) H g
160 eV A u K α P t K α K α x rays K β x rays
67 68 69666564012345 a) Singles a) Deconvoluted:
Hgdaughters
Figure 3: (Colour online) a) Spectrum of γ -ray singles of mass-separated Hg samples. K α characteristic X rays are evident. Notethat, Au K α (66.991 keV) and Pt K α (66.831 keV) lines are not re-solved and same applies for Pt, Ir, Os, etc. b) Deconvoluted spectra of γ -ray singles of Hg isotope (blue spectrum) and its daughter decays(red spectrum), see the text for details. The insert gives the expansionof both spectra, the Au K α and Pt K α lines are clearly resolved.
90 keV energy range. The monotonic sequence of Au,Pt, Ir, and Os K α characteristic x-rays is distorted onlywith the presence of the 60.37 keV peak that is known tooccur in the Hg decay [12]. Fig. 3b) shows the sep-arated spectra of events due to the
Hg decay (blue)and due to daughter decays (red). In the
Hg decayspectrum (blue) only Au K α and K α are present, whilecharacteristic x-rays of lighter elements, i.e., due todaughter decays, are subtracted. The known 60.37 keVtransition is properly identified to be due to the Hgdecay. In the γ ray singles spectrum shown in Fig. 3a,the Au K α (66.991 keV) and Pt K α (66.831 keV) linesare not resolved. After the deconvolution, both compo-nents are clearly resolved, as shown in the Fig. 3b insert.Similar analysis was performed throughout the full en-ergy range of the BEGe detector γ ray spectrum.To construct the level scheme, γ - γ coincidences ofthree types were analysed separately: (i) gating on theBEGe and projecting spectrum of coaxial detectors, (ii)gating on coaxial detectors and projecting the spectrumof the BEGe detector and (iii) coincidences betweenboth coaxial detectors. To enhance the statistical qual-ity of the coincidence spectra, all available data wereused, corresponding to the 32 hours of measurement.Relevant coincidence spectra are given in Fig. 4 and theconstructed level scheme in Fig. 5.Transitions were localised in the level scheme usingthe coincidence relationships and Rydberg-Ritz combi-nation principle, facilitated through the precise deter-mination of energies from the BEGe spectrum, see adiscussion above). In the case that several combina- tions, i.e., various sums or di ff erences were available,the excitation energies of levels were determined usingthe weighted average. A typical example is the firstexcited state, in which the excitation energy was de-termined using energy di ff erences between transitionsfeeding the ground state and first excited state, arisingfrom deexcitation of the 178.25, 289.37, 317.78, and779.80 keV states, shown in Fig. 6. Energy di ff erencesof transitions feeding the ground state and first excitedstate, respectively of 12.74(1), 12.71(3), 12.73(2), and12.72(5) keV were also obtained, as shown in Fig. 6.Within experimental uncertainties all values are con-sistent. Weighted averaging of these values gives theenergy of 12.73(1) keV for the first excited state of the Au. This approach has been used for all energy levelsindicated in the level scheme given in Fig. 5.The excitation energy of the initial and final states to-gether with the γ ray energy for identified transitionsdue to Hg decay are tabulated in Tab. 1. For eachtransition, the γ -ray energies obtained using the gaus-sian fit of the BEGe γ -ray singles spectrum were com-pared with expected value, i.e., the di ff erence of excita-tion energies of initial and final states. The experimentaluncertainties were calculated propagating the peak cen-troid uncertainties and also uncertainties of the coe ffi -cients of the calibration polynomial. The di ff erence be-tween the expected and measured values is denoted as ∆ in Tab. 1. A histogram of ∆ values is given in Fig 7. Thedistribution is centred around 0 eV. Since only two dec-imal digits are given for the γ ray energies, this meansthat most of events agree up to 10 eV. The worst casesare ±
30 eV, see Tab. 1 and Fig. 7.The physics impact of the constructed level schemederived from this experiment in understanding the nu-clear structure of odd-Au isotopes will be discussed in aforthcoming paper [13].
4. Conclusion
A BE2020 BEGe detector operated at ultra-high gainwas successfully used to construct the level scheme of
Au, which is a nucleus with a large density of excitedstates at low energy. The advantage of the BEGe detec-tor is not only excellent resolution but also the ability todetect high energy γ rays. Using this detector, γ -ray en-ergies with a precision below 50 eV (in most cases evendown to 10 eV) could be determined. To reach suchprecision, it is critical to operate the detector at ultra-high gains and also to ensure the stability of the elec-tronics. With precisely determined γ -ray energies, theRydberg-Ritz combination principle on the 30 eV preci-4 i E f E γ ∆ = E i - E f - E γ [keV] [keV] [keV] [eV] Table 1: Excitation energy of initial ( E i ) and final ( E f ) states in the Au isotope. Corresponding γ -ray energy, determined from the γ -ray singles spectrum detected with the BEGe detector are also given( E γ ). The ∆ is a di ff erence between expected transition energy, i.e., E i - E f and γ -ray energy ( E γ ). Note that transitions denoted with anasterisk are very weak and on the the present level of the statistics,more precise energy could not be obtained. However, their placementin the level scheme is based on the γ - γ coincidence analysis. E xc i t a t i on E ne r g y [ k e V ] . ( ) . ( ) . ( ) . ( ) . ( ) . ( ) . ( ) . ( ) Figure 6: (Colour online) Rydberg-Ritz combination principle usedto determine the excitation energy of the first excited state. Four dif-ferences of γ -ray feeding the ground state and first excited state wereused to determine the precise energy. The di ff erence are given in agraph above the partial level scheme. sion could be used, which makes the process of complexlevel scheme construction much more simple.Properties of the BEGe detector, particularly thesmooth background continuum, allowed the peaks of in-terest to be distinguished from other processes such asfrom the decay of daughter activities. This is very im-portant since it simplifies the analysis and reduces therisk of misinterpreting observed transitions. It also pro-vides additional information on the daughter isotopes,which can be analysed separately.Even with the precision of the BEGe detector, the γ - γ coincidence analysis cannot be omitted. Thereforeit appears an optimum solution to combine the BEGedetectors with either larger volume BEGe detectors or5
10 20 30 40 50-50 -40 -30 -20 -1002468101214161820 Δ [eV] E v en t s Figure 7: (Colour online) Distribution of the ∆ , which is a di ff erencebetween expected transition energy (calculated as a energy di ff erenceof initial and final state) and γ ray energy detected with the BEGedetector for all relevant events, see Tab. 1. conventional coaxial detectors or clovers, which o ff erhigher e ffi ciency for γ rays above 1 MeV. Such sys-tems will play a major role in the future β decay studiesof isotopes that have many excited states at low ener-gies. Other promising detectors are novel Small AnodeGermanium detectors (SAGe) [14], which combine thegood energy resolution the BEGe with better e ffi ciencyfor γ rays above 1 MeV. Acknowledgement
Authors express their gratitude to the ISOLDE col-laboration, ISOLDE machine operators, and CERN ra-dioprotection team for excellent support. Very specialthanks goes to the ISOLDE physics coordinator Mag-dalena Kowalska. This work was supported by theSlovak Research and Development Agency under con-tract No. APVV-0177-11, by the Slovak Grant AgencyVEGA under contract No. 2 / /
14, by STFC UK,by STFC Consolidated Grant No. ST / F012071 /
1, bySTFC Consolidated Grant No. ST / L005670 /
1, by STFCContinuation Grant No. ST / J000159 /
1, by EU SeventhFramework through ENSAR No. 506065, by IWAP -Belgian Science Policy (BRix network P7 / /
010 from KU Leuven, and by FWO Flanders. T.E. Cocolios was supported by STFC Ernest RutherfordFellowship No. ST / J004189 / ReferencesReferences [1] Y. Blumenfeld, T. Nilsson, P. Van Duppen, Phys, Scr. T152(2013) 014023. [2] D. Rupnik, et al., Phys. Rev. C 58 (1998) 771.[3] C. D. Papanicolopulos, et al., Z. Phys. A 330 (1988) 371.[4] E. F. Zganjar, J. Phys. G: Nucl. Phys. (43) (2016) 024013.[5] W. Ritz, Astrophysical J. 28 (1908) 237.[6] L. J. Harkness-Brennan, et al., Nucl. Instrum. Methods Phys.Res., Sect. A 760 (2014) 28.[7] E. Kugler, et al., Hyperfine Int. 129 (2000) 23.[8] V. Matouˇsek, et al., Nucl. Instrum. Methods Phys. Res., Sect. A812 (2016) 118.[9] H. Tan, et al., in: Nuclear Science Symposium ConferenceRecord, NSS ’08, IEEE, 2008, p. 3196.[10] ˇS. Motyˇc´ak, et al., in preparation. (2016).[11] M. Morh´aˇc, Nucl. Instrum. Methods Phys. Res., Sect. A 401(1997) 113.[12] M. I. Macias-Marques, et al., Nucl. Phys. A 427 (1984) 205.[13] M. Venhart, et al., to be submitted to Phys. Lett. B (2016).[14] A. S. Adekola, et al., Nucl. Instrum. Methods Phys. Res., Sect.A 784 (2015) 124.
50 350200 250 300 a) Gate on 1509 keV1682.30 172.85 b) Gate on 1428 keV1682.30 254.45 c) Gate on 1393 keV1682.30 289.37 d) Gate on 1364 keV1682.30 317.78 e) Gate on 1242 keV1682.30 440.751008060402007006005004003002001008060407050200301060405020030106040502003010 Energy [keV] C oun t s / e V .
46 181 . * .
11 172 .
85 289 . . .
12 305 .
05 317 . .
29 252 .
400 Energy [keV]500 600 700 800 900 1000 i) Gate on 902.42 keV1682.30 779.80 j) Gate on 871.05 keV1682.30 811.25 k) Gate on 864.21 keV1682.30 818.061002003004001002003001401201008060402025015050035025015050 C oun t s / k e V e + ann i h . .
11 779 . . .
06 e + ann i h .
607 688 .
52 798 .
52 811 . . + ann i h . .
21 805 .
100 300150 200 250 350Energy [keV] l) Gate on 90.85 keV263.69 172.85 m) Gate on 462.04 keV779.80 317.78 n) Gate on 188.29 keV440.75 252.46 o) Gate on 516.11 keV779.80 263.69150200501001502505010020035025015050200150100500 C oun t s / k e V .
11 172 .
85 305 .
05 317 . C o m p t on sc a tt e r i nga r t e f a c t . . . .
85 252 . C oun t s / k e V h) Gate on 704.33 keV977.96 247.06 g) Gate on 173.96 keV247.06 88.06 f) Gate on 226.58 keV314.65 88.06 . .
33 730 . . . Figure 4: (Colour online) Spectra of γ rays detected in a prompt coincidence with a) b) c) d) e) f) g) h) i)
902 keV, j)
871 keV, k) l) m) n) o) γ rays in Au. The line marked by a star in the 1509 keV gate, see panel a) , is the 166.46 keV γ ray and is due to a 1505 keV γ ray in Au (notdiscussed here). The peak denoted as ’Compton scattering artefact’ in panel o) is due to scattering of 511 keV positron annihilation quanta betweenthe BEGe and coaxial detectors. Note that indicated energies were determined using the γ -ray singles spectrum measured with the BEGe detector,see the text for details. E xc i t a t i on E ne r g y [ M e V ] . ( ) . ( ) . ( ) . ( ) . ( ) . ( ) . ( ) . ( ) . ( )
161 250 . ( ) . ( ) . ( ) . ( ) . ( ) . ( ) . ( ) . ( ) . ( ) . ( ) . ( ) . ( )
607 516 . ( ) . ( ) . ( ) . ( ) . ( ) . ( ) . ( ) . ( ) . ( ) . ( ) . ( ) . ( ) . ( ) . ( ) Figure 5: Level scheme of
Au deduced in present work. Transition energies were determined using the γ -ray singles spectrum detected withthe BEGe detector, see the text for details. Note that γ rays above 1 MeV were detected with coaxial detectors only and their energies could notbe determined precisely due to high density of lines, therefore are given only only as integer. Also note that the 161 and 607 keV transitions weredominated with strong lines arising from daughter activities and therefore could not be determined precisely. However, their placement in the levelscheme is evident from γ - γ coincidence analysis.coincidence analysis.