Search for Electron-Capture Delayed Fission in the New Isotope 244 Md

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Atomic nuclei with extreme numbers of protons and neutrons far away from the beta-stability line are one of the main objects to study the interplay of two fundamental interactions of nature, namely the repulsive electromagnetic and the attractive nuclear forces [1,2].However, such nuclei do not exist in nature, thus they have to be artificially produced in nuclear reactions [1,3].Of special interest are the heavy nuclei.According to theoretical models that describe an atomic nucleus as a charged liquid drop, they are unstable against fission due to the dominance of the "disruptive" Coulomb force over the attractive nuclear force (see recent review articles [2-4] and references therein).However, thanks to nuclear shell structure, fission in the heaviest nuclei is retarded [2][3][4].Once the fission probability is reduced, the stability of nuclei is determined by other radioactive decay modes such as α-particle emission and β decay (β AE and electron capture, EC).
The heaviest known nuclei with proton numbers Z > 105, thus, have been identified mostly by their α-decay chains, while their instability against β decay was so far investigated only scarcely [3,[5][6][7].Despite some speculation [8], such a decay path has not been identified conclusively yet in nuclei with Z > 105.Recently, it has been predicted that β decay of odd-odd superheavy nuclei (SHN) may be followed by fission of an excited even-even daughter SHN with a much larger probability than in the known cases for heavy nuclei up to Md (Z ¼ 101).This socalled β=EC-delayed fission (βDF=ECDF) was suggested to become one of the main decay modes of β-decaying SHN with probabilities that strongly depend on both height and shape of the fission barrier [9].Accordingly, the presence of βDF in SHN can be considered as a benchmark for examining the structure of the fission-barrier in SHN.
The known ECDF cases for nuclei with largest Z are 246m Md [10] and 250 Md [11].Their relatively high ECDF probability has been explained in Ref. [9] as being due to a negligible outer barrier influence.In this context, one of the next steps for examining the predictions given in Ref. [9] is the study of hitherto unknown 244 Md, for which an ECDF probability of about 20% has been predicted, if EC decay takes place.
In the present work, we report results from the 50 Ti þ 197 Au fusion-evaporation reaction in which the new isotope

244
Md was identified and decay properties of 245 Md, 241 Es, and 240 Es were confirmed.
The experiment was performed at the gas-filled transactinide separator and chemistry apparatus (TASCA) at GSI, Darmstadt [12].A pulsed (4-5 ms long pulses, 5 or 50/s repetition rate) 50 Ti 12þ beam with an average pulse intensity of ≈10 11 ions per pulse was accelerated by the universal linear accelerator UNILAC and bombarded a rotating 197 Au target [13] with an average thickness of about 0.63 mg=cm 2 .Two different beam energies resulting in center-of-target energies of 239.8 and 231.5 MeV were used [14], leading to compound nucleus excitation energies of E Ã ¼ 32.7 and 26.2 MeV at which the productions of vertical (X) and 48 horizontal (Y) strips on the front and back sides, respectively, was used to detect implanting ERs and their subsequent decays.The efficiency for implanting ERs into the DSSD was estimated to be 60% [16,18].Energy calibrations were performed using α decays of nuclei produced in the 48 Ca þ 176 Yb reaction and energy resolutions (FWHM) of both X and Y strips of the DSSD were about 40 keV for 5.8 MeV-α particles.
In the present experiment, all signals from the preamplifiers were processed with fast digital electronics, which replaced the previous combined analog and digital electronics [19][20][21][22][23][24].Signals from the X and Y strips were amplified with different gains to provide two energy branches up to about 20 and 200 MeV.The signals were digitized by 100 MHz-sampling FEBEX4 14-bit ADCs developed by the GSI experiment electronics department [19,25].The shape of each signal was stored in a 30 μslong trace.A multiwire proportional counter (MWPC) was mounted in front of the implantation detector.Any event with an energy in the range of E ¼ 6-20 MeV having a coincident MWPC signal was considered as implantation signal of an ER.
Spatial-(in the same X=Y strips) and time-(<30 s) correlated ER-like and α-like events were searched and the results are shown in Fig. 1(a).Three and ten events with E ¼ 8.6-8.9MeV were found at E Ã ¼ 26.2 and 32.7 MeV, respectively.
The energies of the three events observed at E Ã ¼ 26.2 MeV, at which the 2n channel cross section of the 50 Ti þ 197 Au reaction is expected to be larger than at E Ã ¼ 32.7 MeV, are in agreement with the known energies of 8.64(2) and 8.68(2) MeV for 245 Md [26].In the event-byevent analysis, we found a total of seven α-decay chains ending with α decays of 241 Es with E ¼ 8.12ð2Þ MeV [27].One such chain is shown in Fig. 2. Detailed data on all decay chains detected in the present work are given in Ref. [27].
The energies of the ten events observed at E Ã ¼ 32.7 MeV are shown in Fig. 1(c).They reveal three events within the energy range of 245 Md and the appearance of seven α events with higher energies.
Time distributions of all events assigned to 245 Md [27] and to its daughter 241 Es are shown in Figs.3(a) and 3(b), respectively.The half-lives of T 1=2 ¼ 0.33 þ0. 15  −0.08 s and 4.3 þ2. 4  −1.2 s, which are extracted according to Ref. [31], confirm the values of 0.35 Md produced in the 3n channel of the fusion-evaporation reaction of 50 Ti þ 197 Au.From the time distribution of these events T 1=2 ¼ 0.30 þ0. 19 −0.09 s was deduced as shown in Fig. 3(c).To confirm the identification, α-decay chains stemming from 244 Md, which includes the known 240 Es with an α-decay branch of 70%, were searched (see Ref. [27]).One of these chains is shown in Fig. 2  Md [28][29][30].Three more ER-α chains were followed by α events with E ¼ 7.06, 7.76, and 0.67 MeV after 2.99, 27.4, and 5.6 s, respectively [27].The latter one was assigned to an α particle escaping the DSSD in backward direction, thus only leaving a partial energy signal.The secondary events are attributed to 240 Es, which emits α particles within the wide energy range of 7.97-8.19MeV [27,28].
We note that energies of 7.06 and 7.76 MeV are significantly lower than the known energy range of 7.97-8.19 MeV for the α particles from 240 Es [27,28], for which we cannot give a definite answer based on the present data.It may happen that their energies were not fully detected, or they could originate from so far unknown α transitions in 240 Es or 240 Cf [27].Their assignment to 240 Es is further supported by the observation of one additional 6.89 MeV beam-off α-like event detected 106 s after the 7.76 MeV-α, which can be interpreted to originate from the decay of 236 Cm (see Fig. 2 and [27]).In fact, in one of the α-decay chains assigned to 245 Md, the energy of the α member belonging to 241 Es was 7.45 MeV, which could be a similar case as for the above events.
Another α event of 8.74 MeV assigned to 244 Md was followed by a fission (FI) event detected 83 ms later [27].This event is shown in Fig. 2 and is attributed to originate from ECDF of 240 Es, for which a branching of ≈5% is known [27,28].Finally, from the Δt of the four α events and one FI event following the α decay of 244 Md, T 1=2 ¼ 8 þ6 −2 s (see Fig. 3) was deduced, which is similar to the T 1=2 ¼ 6ð2Þ s of 240 Es and thus agrees with and confirms the findings in Ref. [28].These results confirm the assignment of 244 Md.
In addition, 6 and 11 FI events correlated with ER-like signals with energies of 8-14 MeV within a short time were observed at E Ã ¼ 26.2 and 32.7 MeV, respectively [27].The time distribution of the six events at E Ã ¼ 26.2 MeV shown in Fig. 3(e) results in T 1=2 ¼ 0.9 þ0.6 −0.3 ms, which is again in agreement with the findings in Ref. [26].Based on the known decay properties of 245 Md [4] and 247 Md [4,10], these events were attributed to originate from an isomeric 1=2 − ½521 state in 245 Md.Two of six ER-FI events are shown in Fig. 2.These six fission events result in σ ¼ 41 þ24 −17 pb.The time distribution of the eleven events at E Ã ¼ 32.7 MeV indicates the presence of an activity with longer T 1=2 than 245m Md.However, correlation times of these events are too short to be compatible with T 1=2 of the α-decaying state of 244 Md with T 1=2 ≈ 0.30 s.The nonobservation of fission events with a half-life similar to 244 Md reveals that we did not observe the EC decay, which would be source for the ECDF process in 244 Md.An upper limit of 0.14 can be deduced for the EC-decay branching in 244 Md based on the observed seven α-decay chains.Among the 11 FI events, we expect to detect up to three FI events with 0.9 ms half-life based on the present and known data [26] for 245;245m Md.Accordingly, the three FI events with shortest Δt corresponding to T 1=2 ¼ 0.7 þ1.0 −0.3 ms and produced with σ ¼ 22 þ20 −13 pb are attributed to originate from 245m Md [see Fig. 3(f)].The remaining eight FI events with T 1=2 ¼ 5 þ3 −2 ms, as shown in Fig. 3(f), have a different origin.We exclude an origin in actinide fission isomers because their production is negligibly low in transfer channels of 50 Ti þ 197 Au.The used Au target material was of high chemical purity, which excludes fusion or transfer reactions with impurities in the target as source.
Let us consider their potential association with 244 Fm (i) or 244 Md (ii).
(i) The isotope 244 Fm, which decays by spontaneous fission with T 1=2 ¼ 3.12 ms [30], is in fact, the only isotope, which would well explain the origin of the eight FI events [27].Hence, one could potentially attribute them to the decay of 244 Fm produced in the p2n channel.They result in σ ¼ 59 þ29 −21 pb, which is comparable with the 65 þ34 −25 pb deduced from the α events assigned to 244 Md.Correlation sequences, energy ranges of the α events, extracted half-lives are given in each plot.Correlation times of fission events observed at E Ã ¼ 26.2 and 32.7 MeV are shown in (e) and in (f), respectively.Curves correspond to the deduced half-lives according to Ref. [31].See text for details.
However, in this region of heavy nuclei, pxn channels are evidently populated alongside the xn ones, but with cross sections often a factor of 10 or more smaller than those of the xn ones [30,[32][33][34].Such a σ value for the p2n channel comparable to the xn ones is presently unknown for syntheses of heavy nuclei with Z ≳ 96 [30,33,34] while it is known to occur with high probabilities in the region of neutron-deficient nuclei with Z < 96 [21,35,36].
Nevertheless, if such an unexpectedly high p2n cross section occurs in the present study, this would indeed be an intriguing observation, which would substantially strengthen the motivation for syntheses of SHN in pxn channels, as suggested in Ref. [32].
(ii) These eight ER-FI events could also originate from 244 Md.In this case, fission would occur from a different state than the α-decaying one with T 1=2 ≈ 0.30 s.However, such a short-lived fission from an odd-odd nucleus, in which fission is known to be strongly retarded compared to even-even cases, has never been observed previously [5,6].Compared to even-odd and odd-even nuclei, where the hindrance factor for fission (the ratio between experimental and calculated unhindered half-lives [4]) is mainly determined by the property of a single unpaired nucleon [4], in the odd-odd cases, most low-lying states are characterized by a coupled single-proton and single-neutron configuration.However, the magnitude of fission hindrance in nuclei with odd numbers of both nucleon types is still unknown, as well as its dependence on the total spin and Nilsson orbital quantum numbers.Various semiempirical estimates exist and mostly predict that the hindrance is at least similar to, or higher than for neighboring isotopes or isotones [4].In this regard, a hindrance factor of about 10 4 has been attributed to 243 Fm (N ¼ 143 isotone of 244 Md) due to its unpaired single neutron.On the other hand, hindrance factors of >10 4 have been evaluated for the fissions of 247 Md and 247m Md (Z ¼ 101 isotope).Thus, for low-lying states in 244 Md one can assume that the spontaneous fission partial T 1=2 should have a gain relative to its unhindered T 1=2 by a factor of >10 4 .Unhindered T 1=2 is typically estimated as the geometric mean of the half-lives of neighboring even-even nuclei, i.e., 244;246 No and 242;244 Fm by which the effect of the fission barrier can be isolated.However, experimental data are only known for the latter isotopes, thus the partial fission T 1=2 of 244 Md can only be compared with the Fm isotopes.By taking 244 Fm, which is the even-even isobar of 244 Md, one can argue that fission from 244 Md has to have a partial T 1=2 much (>10 4 times) longer than 3.12(8) ms [30].However, this will be revised once also the T 1=2 < 4 μs of 242 Fm is considered.In this case, 5 þ3 −2 ms fission from 244 Md will be >10 3 times longer than the fission in 242 Fm, which would point to a large hindrance.Accordingly, these comparisons lead to a still incomplete picture of fission from the odd-odd 244 Md.Still, fission from 244 Md is not excluded to occur with a half-life of ≈5 ms.If this was the case, then such a short T 1=2 should be a result of effects from the neutron-proton configuration and fission barrier.
To conclude, the origin of the eight ER-FI events with 5 þ3 −2 ms cannot unambiguously be attributed to one particular of the above scenarios (i) and (ii).More interestingly, for neither scenario experimental evidence has been observed to date.Thus, each scenario would lead to an intriguing physics case.At the same time, both scenarios might contribute partially to the observed ER-FI events, leading to a third hypothetical scenario (iii).It could be that 244 Md was produced as a product of the 2n channel, but in a state that partially decays into 244 Fm via EC=β þ (hereafter: EC) decay with a short T 1=2 (<5 þ3 −2 ms).However, such a short T 1=2 has never been observed for EC decay [6], which is a process governed by the weak interaction.Keeping in mind that the scenario (iii) is hypothetical, nevertheless, additional analyses searching for the presence of an isomeric state in 244 Md were carried out.
An isomeric state is retarded to decay via electromagnetic transitions, thus, it deexcites predominantly through emission of a conversion electron (CE).Recently, it has been shown that CEs from the decay of short-lived isomeric states can be efficiently detected in the digital trace of the preceding signal [23,24,37].Since in the present experiment the shape of each signal was stored, we inspected the 30 μs-long traces of the seven ER signals followed by α decays of 244 Md, checking for the presence of a low-energy signal associated with the decay of an isomeric state.In one case, we found a low-energy signal, which can be attributed to the detection of a conversion electron [see Fig. 4(a)].This signal was detected 20 μs after the ER, which gives an estimate for the T 1=2 of a potential isomeric state.Despite that one event is insufficient to make a definite conclusion on its assignment, this observation indicated the existence of a short-lived isomeric state in 244 Md.Upon decay of this isomeric state in 244 Md by EC, a delayed fission resulting in ECDF with a probability of ≈20% could also take place as predicted in Ref. [9].
If such a short-lived EC decay occurred in 244 Md, then we might observe its ECDF branch by detecting ER-FI events with a similarly short correlation time, i.e., <30 μs.Two ER-like events with an additional FI-like signal in their traces were found and are shown in Figs.4(b) and 4(c).The energies of the implantation signals agree well with the average energy of ERs of 244 Md and 245 Md [27].These FI events occur 1.5 and 15.6 μs after the ER signals.
Overall, these two events and the one ER with a conversion electron lead to T 1=2 ≈ 9 μs for the decay of an isomeric state in 244 Md.The EC branching of this isomeric state calculated from the numbers of observed α-decay events of 244 Md and fissions from 244 Fm would be ≈44%.In the EC decay of this isomeric state, ECDF would occur with a probability of ≈20% based on the observed numbers of two short-and eight long-correlated ER-FI events assigned to 244 Fm.This result would be in fine agreement with the prediction from Ref. [9].However, despite these surprising outcomes of additional analyses, the short T 1=2 for an EC decay of only about 9 μs, which is more than about 10 6 orders of magnitude shorter than the typical partial EC-decay half-lives of known neutron-deficient nuclei, scenario (iii) remains a hypothesis.
In conclusion, we synthesized the new isotope 244 Md in the 50 Ti þ 197 Au reaction and observed its α decay with α-particle energies in the range of 8.73-8.86MeV and with a half-life of 0.30 þ0. 19 −0.09 s.We did not observe EC decay of 244 Md for which an upper limit of 0.14 was given.In addition, we detected eight short-lived fission events.Their origin has been discussed by involving three different possible scenarios, where each one leads to a previously unseen physics case.
We are grateful to GSI's ion-source and UNILAC staff, and the Experimental Electronics department for their support of the experiment.The results presented here are based on the experiment U308, which was performed at the beam line X8/TASCA at the GSI Helmholtzzentrum für Schwerionenforschung, Darmstadt (Germany) in the frame of FAIR Phase-0.

FIG. 4 .
FIG.4.The X-strip trace of the ER correlated with an α event with an energy of 8.81 MeV (assigned to 244 Md), in which the low-energetic signal (a close look is given in the inset) was observed (a).X-strip traces of ER-like events, in which the FIevent signal (energies are given) were detected are shown in (b) and (c).In the insets, the Y-strip traces, in which the FI-event signals are stored with full shapes are shown.Time differences between two signals are given.See text for details.
þ0.23 −0.16 s and 8 þ6 −4 s for 245 Md and 241 Es, respectively, as reported from an experiment using the 40 Ar þ 209 Bi reaction [26].Cross sections of σ ¼ 59 þ31 −23 pb and 28 þ26 −17 pb for 245 Md were deduced for the present 50 Ti þ 197 Au reaction at E Ã ¼ 26.2 and 32.7 MeV, respectively.Seven further α events with similar Δt but with E ¼ 8.73-8.86MeV were attributed to originate from and Examples of observed decay chains assigned to 245 Md and 244 Md at E Ã ¼ 26.2 and 32.7 MeV, respectively, are shown.Energies of ER, α and fission events are given in MeV and correlation times in s.
[28][29][30]Correlation times (Δt) of the α events to the preceding implantation (ER) signals shown as function of their energy (a).The events assigned to decays of 244 Md and 245 Md are marked by triangles and dots, respectively.The events observed at E Ã ¼ 26.2 and 32.7 MeV are marked by full and open symbols and their energies are shown in (b) and in (c), respectively.Gaussian peaks correspond to expected α-decay energies of the known 245 Md[26].See text for details.FIG.2.The known properties (α-decay energies are given inMeV) of the nuclei that could potentially be produced in the radioactive decay (α and electron capture) of 245 Md (Lit.[26]) and 244 Md (Lit.[28][29][30]) are shown on the left side.