Observation of New Neutron-rich Isotopes among Fission Fragments from In-flight Fission of 345 MeV/nucleon ²³⁸U: Search for New Isotopes Conducted Concurrently with Decay Measurement Campaigns

The experiment was performed with a ²³⁸U⁸⁶⁺ beam that was accelerated to 345 MeV/nucleon by the RIBF accelerator complex.²⁾ The production target used was a 2.92-mm-thick piece of beryllium. Fission fragments produced via in-flight fission of the ²³⁸U beam were separated and identified in flight using the BigRIPS separator and then transported to the EURICA setup,¹²⁾ where decay measurements were made, through the ZeroDegree spectrometer.⁴⁾ Figure 1 shows the experimental setup. The labels F0–F11 and D1–D8 in the figure indicate the focus locations and dipole magnets, respectively. The primary beam intensity was monitored by detecting light charged particles recoiling out of the target, in which we employed a monitor counter consisting of three layers of plastic scintillators. The ²³⁸U beam passing through the target was stopped at a beam dump installed at the exit of the first dipole magnet D1.¹³⁾ The beam intensity on target was typically ∼8 pnA. We made two-step isotope separation using wedge-shaped energy degraders placed at both the first and second stages of the BigRIPS separator: The degraders were inserted to the momentum dispersive foci F1 and F5.

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Figure 1. Schematic layout of the BigRIPS separator and succeeding ZeroDegree spectrometer. The labels Fn and Dn indicate the locations of foci and dipole magnets, respectively. Fission fragments emitted from the production target (F0) were separated and identified by the BigRIPS in-flight separator (F0–F7) and transported to the EURICA setup through the ZeroDegree spectrometer (F8–F11). The energy degraders used for isotope separation and the detectors used for particle identification are shown at the focus locations. See text for more details.

The experimental method was essentially the same as that used in our previous experiment.⁷⁾ The PID was performed by the TOF–\(B\rho\)–\(\Delta E\) method, in which the mass-to-charge ratio \(A/Q\) and the atomic number Z of fragments were derived by measuring the time of flight (TOF), magnetic rigidity (\(B\rho\)), and energy loss (\(\Delta E\)). Here, A and Q represent the mass value in atomic mass unit and charge number, respectively. The TOF was measured using thin plastic scintillators placed at the achromatic foci F3 and F7 in the second stage of the BigRIPS separator. The plastic scintillators were 0.2 mm thick and 120 mm\(^{\text{H}}\) \(\times\) 100 mm\(^{\text{V}}\) in area. The mean flight length between these plastic scintillators was 46.97 m. Two parallel plate avalanche counters (PPACs)¹⁴⁾ were installed at the F3, F5, and F7 foci to measure the position and angle of fragments at each focus. The measured position and angle were used to determine the fragment \(B\rho\) value by trajectory reconstruction. The \(\Delta E\) of fragments was measured using multisampling ionization chambers (MUSICs)¹⁵⁾ installed at the F7 and F11 achromatic foci. Six energy-loss signals were obtained from the MUSIC detector and averaged for the \(\Delta E\) measurement. Two clover-type high-purity germanium (Ge) detectors were installed at the F7 focus to perform isomer tagging, in which we verified and calibrated the PID by detecting delayed γ-rays emitted from known microsecond isomers among fission fragments.⁶⁾ During the isomer tagging, the fragments were implanted into an aluminum stopper inserted into the beam line at the F7 focus, so that delayed γ-rays could be measured. We first established the PID using the F7 MUSIC detector, and then used it to calibrate the F11 MUSIC detector. Once the PID using the F11 MUSIC detector was established, we extracted the F7 MUSIC detector from the beam line and ran the measurements to search for new isotopes concurrently with the EURICA decay measurements.

Note that fission fragments are not necessarily fully stripped at the present energy. Although fully stripped ions (\(Q=Z\)) are major components, in some cases, partially stripped ions, such as hydrogen-like ions (\(Q=Z-1\)), also appear in PID plots. The high \(A/Q\) resolution in the BigRIPS separator enables the identification of these charge states, as demonstrated in Refs. 6, 7, and 16.

Table I shows a summary of the experimental conditions. We ran five different separator settings shown in the table, which we refer to as the Sn, Pd, Rh, Nb, and Te settings, respectively (see Table I), according to the subject of each EURICA experiment. The central particles, for which we tuned the BigRIPS separator and ZeroDegree spectrometer, were chosen to be the fully stripped ¹³⁶Sn⁵⁰⁺, ¹³⁰Cd⁴⁸⁺, ¹²⁵Ag⁴⁷⁺, ¹¹⁸Ru⁴⁴⁺, and ¹⁴³I⁵³⁺ ions for the Sn, Pd, Rh, Nb, and Te settings, respectively. These settings were determined on the basis of detailed simulations with the code LISE⁺⁺,¹⁷⁾ in which the requirements of the EURICA decay measurement were taken into account, including the total beam-rate limits of less than 100 Hz (the limit of implantation rate). In the actual measurements, we adjusted the slit opening at the F1 focus and the slit openings at the F2 and F7 foci, according to the actual beam rate in the EURICA setup. The slits at the F1 focus and those at the F2 and F7 foci adjust the momentum acceptance and the selection of transmitted fragments, respectively. The measurement time and total primary-beam dose depended on the duration of the EURICA measurement. The live time of the data acquisition system was ∼98% for all the settings.

»View table Table I. Summary of the experimental conditions.

The analysis method for particle identification is essentially the same as described in our previous paper,¹⁶⁾ including the background removal. We determined the fragment \(B\rho\) values not only in the first half (F3–F5) of the second stage of the BigRIPS separator but also in the second half (F5–F7), which were denoted as \(B\rho_{35}\) and \(B\rho_{57}\), respectively, following the notation in Ref. 16. The fragment velocities (relative to the velocity of light) before and after the F5 degrader, denoted as \(\beta_{35}\) and \(\beta_{57}\), respectively, were derived from the measured TOF in combination with these \(B\rho_{35}\) and \(B\rho_{57}\) values. We calculated the \(A/Q\) value of fragments from the \(B\rho\) and velocity values thus obtained. The Z value was determined with the Bethe-Bloch formula using the measured \(\Delta E\) and the derived fragment velocity \(\beta_{57}\).

In the trajectory reconstruction to determine the fragment \(B\rho\) values, we used the first-order ion-optical transfer matrices that were derived experimentally. For each of the five settings, the first-order transfer matrix elements were derived from the position–position, angle–angle, position-angle, and angle-position correlations measured between the beginning and end of the sections, and from the position- and angle-TOF correlations at the F5 dispersive focus. We deduced the fractional \(B\rho\) deviation, denoted as \(\delta_{35}\) and \(\delta_{57}\) for the F3–F5 and F5–F7 sections, respectively, by using the transfer matrices, and calculated the \(B\rho_{35}\) and \(B\rho_{57}\) values as \(B\rho=B\rho_{0}(1+\delta)\), where \(B\rho_{0}\) represents that for the central trajectory. The absolute \(B\rho_{0}\) value was determined from the magnetic field of the dipole magnet measured with an NMR probe and the central trajectory radius of the dipole magnet determined from the magnetic field map. To improve the \(B\rho\) resolution and, accordingly, the \(A/Q\) resolution, the second-order matrices were also included in the trajectory reconstruction. We empirically determined the second-order matrix elements to minimize the dependences of \(\delta_{35}\) (\(\delta_{57}\)) on the horizontal position and angle at the F3 (F7) focus and also on the deduced \(A/Q\) value. Furthermore, we performed slewing correction for the TOF measurement to improve the \(A/Q\) resolution. The slewing correction was also empirically performed in which the dependence of the TOF on the signal pulse height of the plastic scintillators was minimized. In the isomer tagging, we observed delayed γ-rays from the following isomers: \(^{109m}\)Nb and \(^{117m,119m}\)Ru in the Nb setting, \(^{132m}\)Sn in the Rh setting, and \(^{132m}\)Sn and \(^{136m}\)Sb in the Pd, Sn, and Te settings.

Background events, such as those caused by scatterings and reactions in the detectors and degraders, signal pileups, and improper detector responses, were removed by investigating various correlation plots made using pulse-height and timing signals in the detectors as well as profiles of the beam spot and phase space at the foci. Consistency with the ion optics was also checked by comparing the trajectories between the foci to exclude ion-optically inconsistent events. Furthermore, we excluded events in which fragments changed their charge state or nuclear reactions, such as a neutron removal reaction, happened at the F5 degrader. In these cases, our PID method cannot properly derive the \(A/Q\) value, because the TOF was measured between the F3 and F7 foci and the velocity and \(A/Q\) value change at the F5 focus. Such events appear as backgrounds in the PID plot. See Ref. 16 for more details of our PID method and background removal.

In this data analysis, to remove the charge-changing and reaction events at the F5 focus, we investigated the correlation plot between the Z value derived from the \(\Delta E\) measurement using the MUSIC detector and that calculated from the energy loss in the F5 degrader. We refer to the latter Z value as \(Z_{\text{F5}}\). According to the Bethe-Bloch formula, the energy loss at the F5 degrader \(\Delta E_{\text{F5}}\) can be derived as \begin{equation} \Delta E_{\text{F5}}\propto d(Z^{2}/\beta_{35}^{2}), \end{equation} (1) where d represents the mean thickness of the energy degrader. From the difference in the total kinetic energy before and after passing through the F5 degrader, \(\Delta E_{\text{F5}}\) can also be derived as \begin{equation} \Delta E_{\text{F5}}=cQ(B\rho_{35}/\beta_{35}-B\rho_{57}/\beta_{57}). \end{equation} (2) These two equations are valid under the conditions that fragments are fully stripped and their \(A/Q\) values do not change before and after at the F5 degrader. From these equations, \(Z_{\text{F5}}\) can be approximately expressed as \begin{equation} Z_{\text{F5}}=a_{0}+a_{1}(\beta_{35}^{2}/d)(B\rho_{35}/\beta_{35}-B\rho_{57}/\beta_{57}), \end{equation} (3) where \(a_{0}\) and \(a_{1}\) are calibration coefficients, which are empirically determined so as to reproduce atomic numbers. The deviation from the above formula is small for hydrogen-like ions, provided that the charge state does not change at the F5 degrader. However, the deviation becomes quite significant if the charge-state changes at the F5 degrader or the neutron removal reaction occurs there. In the former case (i.e., the charge-state changes from hydrogen-like to fully stripped), \(\Delta E_{\text{F5}}\) can be derived as \begin{equation} \Delta E_{\text{F5}}=cQ(B\rho_{35}/\beta_{35}-B\rho_{57}/\beta_{57})-cB\rho_{35}/\beta_{35}, \end{equation} (4) and, in the latter case (i.e., a neutron escapes via the neutron removal reaction), \(\Delta E_{\text{F5}}\) can be derived as \begin{equation} \Delta E_{\text{F5}}=cQ(B\rho_{35}/\beta_{35}-B\rho_{57}/\beta_{57})-\gamma_{n}m_{n}+S_{n}, \end{equation} (5) where \(\gamma_{n}\) is the Lorentz factor of the escaped neutron, \(m_{n}\) is the neutron mass, and \(S_{n}\) is the neutron separation energy. In both cases, the energy loss \(\Delta E_{\text{F5}}\) becomes smaller than that given by Eq. (2) owing to the additional term. Thus, the determined \(Z_{\text{F5}}\) provides a greater value than the actual atomic number Z.

Figure 2 shows an example of the Z versus \(Z_{\text{F5}}\) correlation plot, which was obtained with the Te setting. The regions labeled A, B, and C in the figure represent events in which \(A/Q\) did not change, those in which a neutron escaped via the neutron removal reaction, and those in which the charge state changed from hydrogen-like to fully stripped ions, respectively. The tails extending down from region A can be attributed to reaction events that occurred in a detector after the F7 plastic scintillator or a vacuum partition window foil installed at the exit of the F11 chamber, because in such cases, the Z value changes before entering the F11 MUSIC detector. As can be seen in Fig. 2, the Z versus \(Z_{\text{F5}}\) correlation plot allows us to clearly identify and remove the charge-state changing events as well as the reaction events. Note that this analysis has markedly improved the performance of the PID, especially the background removal, in comparison with the previous analysis presented in Ref. 10. (Compare the PID plots.) Such performance is essential for identifying new isotopes produced with very low counts.

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Figure 2. (Color) Z versus \(Z_{\text{F5}}\) correlation plot for the fission fragments produced in the ²³⁸U+Be reaction at 345 MeV/nucleon. The experimental conditions are given as Te setting in Table I. Here, Z and \(Z_{\text{F5}}\) respectively represent the atomic numbers derived from the \(\Delta E\) measurement using the MUSIC detector and calculated from the energy loss in the F5 degrader. See text for the explanation of the regions labeled A, B, and C.

Unfortunately, in the case of the Te setting, the plastic scintillator installed at F7 was partially damaged during the measurement, so that we could not obtain normal signals for fragments passing through the damaged area, which was located ∼5 mm below the center of the scintillator. This significantly affected the TOF measurement and hence deteriorated the \(A/Q\) resolution in the PID. The detection efficiency was also affected. Therefore, in this analysis, we excluded such events by using the beam positions measured with the PPAC detectors.

We have conducted a search for new isotopes at the RIKEN RIBF using the in-flight fission of a 345 MeV/nucleon ²³⁸U beam in parallel with the EURICA decay spectroscopy measurements. The production, separation, and identification of fission fragments were carried out using the BigRIPS separator. Owing to high-resolution particle identification, excellent background removal, and thorough and various consistency checks achieved by an elaborate data analysis, we have identified a total of 36 new isotopes with \(Z=37{\text{--}}57\) in the very neutron-rich region. The production yields and production cross sections have also been measured for observed isotopes, including the new isotopes identified.

The nuclear chart in Fig. 7 shows the new isotopes observed in this work, along with those for which production yields were measured. As seen in the figure, we have significantly expanded the limits of known isotopes in this region of the nuclear chart. For instance, for Pd isotopes, we have reached as far as ¹³¹Pd, which is more neutron-rich by three neutrons than ¹²⁸Pd, a nucleus at the r-process waiting point at the \(N=82\) neutron magic number. We discovered ¹²⁸Pd in our previous experiment.⁷⁾ For Rh isotopes, we observed \(^{127,128}\)Rh and reached the \(N=82\) r-process waiting point for this element for the first time.

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Figure 7. (Color) Nuclear chart showing the new isotopes observed in this work (purple circles). The blue squares indicate the isotopes for which production yields were measured. The black and yellow squares are stable isotopes and known isotopes, respectively. The red solid lines show those with the magic numbers \(N=82\) and \(Z=50\).