Journal of Nuclear and Radiochemical Sciences, Vol. 23, pp. 1-4, 2023

ArticlesAccurate event assignment from the decay-correlated mass measurement of the superheavy
nuclide 257Db
Toshitaka Niwasea,*, Peter Schurya, Michiharu Wadaa and SHE-Mass collaboratorsa

KEK Wako Nuclear Science Center, Wako, Saitama 351-0198, Japan

Received November 3, 2022; Accepted January 12, 2023; Published online January 30, 2023
Decay-correlated mass spectroscopy using an α-TOF detector is a new technique for doing decay spectroscopy of
nuclides. Even for a small number of statistical events, with a yield of less than a few per day, the decay correlation
can discriminate true events from background events, allowing accurate high-precision mass measurements to be
made. In this paper, we discuss decay-correlated mass spectroscopy with a small number of statistics and theconfidence level of the observed values based on their decay energies and decay times. We determined the massof the superheavy element 257Db from 11 decay-correlated TOF detections with a precision of 1 ppm. This technique will be a major milestone in the path toward the comprehensive mass measurement of superheavy elements.

1. Introduction
Atomic mass is one of the most important static propertiesof nuclides. From Einstein’s equation E=mc2, scientists knowthat the binding energy of a nuclide corresponding to therequirement to stabilize the nucleus as a quantum many-bodysystem can be observed as the nuclide’s mass defect. As thebinding energies reflect the nuclear structure and interactionof nucleons, high-precision mass measurements provide
important information.
The multi-ref lection time-of-f light mass spectrograph(MRTOF-MS) is one device for high-precision mass spectroscopy. Prior to 2015, the development and use of an MRTOFMS for mass measurement of radioactive isotopes had only
been reported by ISOLDE1, RIKEN2 and GSI3. Since then, theconstruction and utilization of MRTOF-MS systems has
spread to laboratories world-wide, including Argonne National
Laboratory4 and GANIL5. Several MRTOF-MSs are deployedat the RIKEN RIBF for comprehensive mass measurement
covering all regions of the chart of the nuclides: fusion reaction products are measured in the SHE-Mass facility 6 combined with the gas-filled recoil ion separator GARIS-II 7,
multi-nucleon transfer products are measured in the system
coupled with the KEK Isotope Separation System KISS8, andin-flight fission products are measured in the system9 locatedbehind the ZeroDegree (ZD) spectrometer10 at BigRIPS.
Researchers of the SHE-Mass facility have recently succeeded in direct mass measurements of a superheavy nuclide
257
Db11. The key technology enabling this measurement was a
newly developed α-TOF detector12. We embedded a silicon
semiconductor detector (SSD) in a commercial time-of-flight(TOF) detector MagneTOF to produce the α-TOF detector thatenables correlated measurements of an ion’s TOF and its subsequent radioactive decay signal. The α-decay and spontaneous fission events are used as fingerprints to identify a nuclide– including its nuclear state – while significantly reducing thebackground. The development of decay-correlated mass measurements has opened a new frontier in nuclear spectroscopy
research by enabling discrimination of isomers that could not
be separated using the MRTOF-MS alone13. This α-TOF
detector allows for highly accurate identification of nuclides*Corresponding author. E-mail: tniwase@post.kek.jp

with extremely small fusion reaction cross sections, such as
superheavy elements, by distinguishing these rare events frombackground signals such as dark counts and contaminant ions.
In this paper, we detail event identification of the decaycorrelated analysis of the mass measurement of 257Db which
represents an investigation to assess the reliability of the
α-TOF detector used in combination with MRTOF-MS.
2. Experiment and results
Decay-correlated mass measurement of 257 Db was performed at the SHE-Mass-II facility, jointly operated under the
auspices of RIKEN Nishina Center and KEK Wako Nuclear
Science Center, within the RIKEN RI Beam Factory. Detailsof the experimental setup are described elsewhere11. Atoms of
the isotope 257Db were produced by the 208Pb(51V, 2n) reaction.
The evaporation residues were efficiently transported while
the unreacted primary beam and other background products
were suppressed by GARIS-II and were stopped and thermalized in a cryogenic helium gas cell at the focal plane. The
thermalized ions were extracted from the gas cell using a traveling wave radio frequency (RF) carpet14, transported by amultiple RF ion trap and injected into the MRTOF-MS. The
α-TOF detector was used as the ion detector for the
MRTOF-MS to obtain the ion arrival signal and subsequentα-decay. The α-TOF was energy calibrated by the α-decays of185
Hg produced by the 51V+139La reaction.
The TOF spectrum in the vicinity of 257 Db3+ is shown in
Figure 1(a). The upper part of the figure shows the time ofarrival of the events, in chronological order of observation.
The TOF values are plotted in terms of the TOF ratio ρ
between 257Db3+ and the 85Rb+ reference ion, to normalize thevalues across different lap numbers. The correlation of the
α-decay signals detected within an arbitrary correlation time
width from the TOF signals was taken. Details of the analysis
are described in sect. 3.
In total, we observed 14 TOF decay-correlated event candidates during 105 hours of measurement. Figure 1(b) plots eachdecay-correlated event in terms of detected α-decay energy
and time between implantation and subsequent α-decay;© 2023 The Japan Society of Nuclear and Radiochemical Sciences
Published on Web 01/30/2023

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NiwaseJ. Nucl. Radiochem. Sci., Vol. 23, 2023

(a)

(b)
accidental-TOF event

laps

E1
E2

E4E5

E7

325

E6

4

E10

E8

E9

324
327

E11
E12

6

E13

331

E14

2
1
0

1.004640

Es 249Md 253Lr 257Db

245

300

E3

2

Po

211

1.004645

1.0046450

1.0046455

E2

E4

102

E7

101

E10

E8

Es

245

E11

Md

249

E3
E12

E1

Lr

253

E14 E6
E5
E9

0

10

Db

257

E13

10-1

7

8
9
E [MeV]

10

Expected decay time distribution

Time [days]

0

Expected alpha energy distribution

Uncorrelated-TOF event

Decay time [s]Db correlated-TOF event

Figure 1. (a) The TOF spectrum and the time evolution of events near 257Db3+. To normalize the flight time for different lap numbers, TOF ratio
is plotted against the reference ion 85Rb+. The absolute TOF is about 10 ms and the domain of the plot, ±10 ppm, is about 200 ns. The red stars
indicate the decay-correlated events of the 257Db decay chain and the purple circles indicate the accidentally-correlated events of the transfer
products. (b) Two-dimensional distribution of TOF-correlated α-decay events in a plot of decay energy vs. decay time. The probability distributions in terms of decay time are shown in the right panel, and the detector response function for α-decay is shown in the top panel, superposedwith the α-singles spectrum with correlated event candidates denoted by colored marks.

events are named based on chronological order of observation.
The right panel of Figure 1(b) shows the anticipated decay
time probability distribution15 for each nuclide; multiple curves
are shown for 257Db and 253Lr to represent known isomers. The
upper panel shows the expected energy distribution for eachα-decay which could be observed in the 257 Db decay chain,with the α-decay singles spectrum superimposed. The correlated events appear to fall into two clusters corresponding to257
Db or 253Lr (E1, E5, E6, E9, E12, E13, E14) and 249Md or 245Es(E2, E3, E4, E7, E8, E10, E11). Table 1 tabulates the decayenergies and decay times of the 14 TOF decay-correlated
events.
3. Discussion
The decay-correlation analysis begins with identifying candidate events by selecting α-decay energy signals in the energy
range consistent with α-decays for the candidate nuclide. In
the present experimental case, the energy gate range is 7.0 to
9.5 MeV, which corresponds to the energy range of the α-decay
chain from 257 Db to 245 Es. A TOF spectrum is then constructed from TOF events in the vicinity (±100 ns) of the
expected location of 257Db occurring in a coincidence time (Tc)prior to the α-decay signal. The coincidence time is chosen
according to the half-life of the analyte nuclides.
3.1 Probability of a spurious correlation. In this experiment, the coincidence time Tc for TOF-α decay correlations
was chosen to be 120 s, which is sufficiently long enough toencompass decays of the granddaughter 245Es.
Using this Tc, the total number of α-decay singles events inthe analyte energy region (Nalpha) and the total measurement
time (Ttotal), we estimated the random correlation probability
Prandom, defined by eq 1.
Prandom =Nalpha×Tc
× 100 [%]
Ttotal(1)

The random correlation probability in the energy region of211
Po was estimated to be 7.3%. This estimation was based on
the 120 s coincidence time and 235 observed α-decay counts inthe 211Po energy region. There were 27 TOF singles events

observed in the TOF spectra in a 60 ns wide region centeredon the expected TOF for 257Db3+ – the range corresponded to
the full width at tenth maximum (FWTM) of the spectral peakbased on the peak shape of the 85Rb+ reference ion. Therefore,
we expected to observe ~2 accidental correlations with 211Po.
Similarly, the accidental correlation probabilities for islands inthe 257 Db-253Lr energy region and islands in the 249Md-245Es
energy region were calculated to be 1.6% and 1.3%, respectively.
3.2 Accuracy of each event. Each of the experimentallyobtained decay-correlated events was accurately determinedby comparing the measured values to the known decay properties – decay energies and decay times – of the nuclide. The
confidence level was evaluated as P(0,1) = 1 – g(z) using the2
area expressed as g(z) = ∫ z–z 12π exp –x2 dx by integration of
the probability density function of the standard normal distribution N(0,1). For example, when the measured data point (z)is 1σ away from the central value, its confidence level P(0,1) isP = 1 – 0.683 = 0.317.
When there are n systems in parallel, each of which has aconfidence level of Xi, the confidence level of the system as awhole, Φ, can be written as Φ = 1 – Пni=1 (1 –Xi). This evaluation is often used to evaluate the reliability of an entire system,
such as a parallel circuit consisting of multiple systems16. The
α-decay energy and decay time of each event were compared
to an arbitrary state of the nucleus of interest to evaluate theaccuracy of the event. When the confidence level of the decayenergy was set to Pene and the confidence level of the decay
time was set to Pdt, the accuracy of the acquired single event
was evaluated as Xstate = 1 – (1 – Pene)(1 – Pdt) from the convolution by these parallel systems.
The nucleus to be compared is in one of several excitedstates, but in a system like Db, where the states are unknown
and complex, it is difficult to distinguish individual states evenwith our mass resolving power and energy resolution. Thus,
we assumed that each state existed in parallel, and the certainty of the acquired event Φx could be expressed as a convolution of the accuracy of each state Xstate,Φx = 1 – Пnstate=1 (1 – Xstate).

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J. Nucl. Radiochem. Sci., Vol. 23, 2023

Accurate event assignment from the decay-correlated mass measurement

In the case of 257Db, three decay modes were intermingled,
but this calculation allowed us to evaluate Db like the event
itself, taking all states into account. Likewise, for 253Lr cases
we could estimate the certainty from the convolution of thetwo states. Table 1 summarizes the certainty Φx of each of the
14 decay-correlated events. The certainty Φ x was derived
from the confidence level of the energy and decay time compared to the decay chain of 257Db and the multinucleon transfer
product 211Po. Based on the reported decay properties, thestates of 257Db corresponding to decay energies of 9.155 MeV,
9.066 MeV, and 8.965 MeV were tentatively assigned to257
Db(1), 257Db(2), and 257Db(3), respectively, and the states of253
Lr corresponding to decay energies of 8.719 MeV and 8.786
MeV were tentatively assigned to 253Lr(1) and 253Lr(2), respectively. In the calculation, events with energy or decay time
confidence less than 2.5σ, i.e., less than P=0.01, were excluded
from the calculation. The 211Po is due to accidental coincidence, so only the reliability of the energy was considered.
3.3 Event assignments. Based on the certainty Φx shownin Table 1, the nuclide identification was performed for each of
the decay-correlated events. For the energy uncertainties, theenergy resolution of the α-TOF detector, σ E =140 keV, wasused.
3.3.1 Events 1, 5, 6, 9, 13, 14. For events 1, 5, 6, 9, 13, and 14
we measured α-energies and decay times that were consistent
with 257 Db. Event 1 had the same degree of confidence forboth 257Db(1) and 257Db(2) states. Events 5 and 14 had equal
degrees of confidence for all states. Events 6, 9, and 13 wereconsistent only with 257 Db(1), tentatively assigned as theJ π=1/2- isomeric state, from confidence calculations. The relative intensity of 257 Db(1) is reported to be 19%17, and the
expected number of events to reach this intensity is 1.14 out of
6 events. Given a Poisson distribution with an expected valueof 1.14 events, the probability that the number of observed
events is more than 3 is 11%. Based on the above reasoning,
we determined that these 6 events were correlated with the
decay of 257Db.
3.3.2 Event 12. Event 12 agreed with the decay propertiesof 257Db(3) and 253Lr(1) and 253Lr(2) with similar levels of confidence. The confidence level was slightly higher for 253Lr
than for 257Db, thus event 12 was identified as 253Lr. Only one

3

Lr decay-correlation event was observed. Considering thebranching ratio of α-decay and the detection efficiency of the
α-TOF detector, the expected number of events was 2.9 ± 1.7
counts. Our observed events were consistent with statisticalfluctuations in the 1.2σ range.
3.3.3 Events 2, 3, 11. The decay properties of events 2, 3,
and 11 were in good agreement with those of 249Md, and theconfidence levels of other nuclides were all below 0.01. Thus,
we concluded that these three events were correlated with249
Md decay.
3.3.4 Event 8. The decay property of event 8 was consistent with the decay properties of 245Es, and it was far from thedecay energy of 211Po, a multinucleon transfer reaction product. On the other hand, the detection probability for 245Es was
only 1.4%, as described below, and the expected number to beobserved from a total of 14 events was 0.3. When the expectedvalue was 0.3, the probability of observing one event was 22%,
which was not a small enough probability to reject. Also, if
we assumed that this was the decay of 249Md, the decay time
was consistent, but the decay energy was 2.6σ away from theliterature value17. Regardless of the nuclide identification, it
was still an event correlated with the decay chain of 257Db, but
we decided to trust the confidence level and to assume it wasan event correlated with 245Es decay.
3.3.5 Events 4, 7, 10. The decay energies of events 4, 7, and10 were in good agreement with the transfer product 211Po. The
decay times for all events were close to those of 245Es, but theenergies were more than 2.5σ away. As discussed in sect. 3.1,
the number of accidental coincidences in this energy region
was estimated to be about 2, which was consistent with theobserved number. Based on these evaluations, we determinedthat these three events were accidental coincidences with 211Po
and we excluded them from the mass analysis.
Based on the above event assignments, we determined that
11 of the 14 events were attributable to 257Db and daughters,
excluding the 3 events inferred to have been contributed by
211
Po. The 257Db nuclide exhibits at least one long-lived isomeric state18. Neither the state order nor the isomeric excitation have been confirmed as yet. The NUBASE19 recommends
an isomeric excitation of 140 keV based on systematics. The
present mass resolving power of the MRTOF-MS and
α-energy resolution of the α-TOF detector cannot separate the

TABLE 1: Summary of the certainty Φx of each decay-correlated event compared to the nuclides in the 257Db chain
Eα [MeV]dt [s]

Φ (257Db)

Φ (253Lr)Φ (249Md)

Φ (245Es)

Φ (211Po)

E1

9.19

3.54

0.96

<0.01

<0.01

<0.01

<0.01

E2

8.14

105

<0.01

<0.01

0.56

<0.01

<0.01

E3

8.02

18.5

<0.01

<0.01

0.94

<0.01

<0.01

E4

7.52

100.2

<0.01

<0.01

<0.01

<0.01

0.38

E5

9.00

0.7

0.92

<0.01

<0.01

<0.01

<0.01

E6

9.35

1.3

0.92

<0.01

<0.01

<0.01

<0.01

E7

7.48

93.9

<0.01

<0.01

<0.01

<0.01

0.71

E8

7.81

44

<0.01

<0.01

<0.01

0.39

<0.01

E9

9.35

0.36

0.15

<0.01

<0.01

<0.01

<0.01

E10

7.52

21.1

<0.01

<0.01

<0.01

<0.01

0.38

E11

8.08

43.4

<0.01

<0.01

0.96

<0.01

<0.01

E12

8.77

4.3

0.92

0.99

<0.01

<0.01

<0.01

E13

9.06

0.15

0.82

<0.01

<0.01

<0.01

<0.01

E14

9.16

1.2

0.99

<0.01

<0.01

<0.01

<0.01

4

J. Nucl. Radiochem. Sci., Vol. 23, 2023

ground and isomeric states in Db. Therefore, we assumed
that the measured events were split almost evenly between thetwo states, and we accounted for this by adding a systematic
uncertainty of 70 keV/c2.
From these 11 highly accurate events, we determined theatomic mass of 257Db to be m(257Db)=257.10742(25) u and themass excess to be ME(257Db)= 100 063(231) keV. This corresponded to a mass uncertainty of 9.7 × 10 -7, which was equivalent to a mass determination with a precision of 1 ppm.
257

4. Conclusion
In this paper, we discussed in detail the event identificationof the superheavy nuclide 257 Db measured using a newly
devised α-decay-correlated mass measurement method. Westrongly anticipate that such an identification method will
accelerate further direct mass measurements of superheavy
nuclides. Recently, we have also developed a β-TOF detector
with two layers of SSDs forming a telescope designed toextend the technique to β-decaying nuclides. This techniquewill be expected to provide comprehensive mass measurements covering not only superheavy nuclides but also a wide
range of nuclides in chart of the nuclides.
Acknowledgements
We express our gratitude to the RIKEN Nishina Center for
Accelerator-based Science and the Center for Nuclear Scienceat University of Tokyo for their support of online measurements. This work was financially supported by the Japan
Society for the Promotion of Science KAKENHI (Grant Nos.
17H06090 and No. 21J00670).
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