Fission fragments mass distributions of nuclei populated by the multinucleon transfer channels of the 18O+232Th reaction

Abstract It is shown that the multinucleon transfer reactions is a powerful tool to study fission of exotic neutron-rich actinide nuclei, which cannot be accessed by particle-capture or heavy-ion fusion reactions. In this work, multinucleon transfer channels of the 18O + 232Th reaction are used to study fission of fourteen nuclei 231,232,233,234Th, 232,233,234,235,236Pa, and 234,235,236,237,238U. Identification of fissioning nuclei and of their excitation energy is performed on an event-by-event basis, through the measurement of outgoing ejectile particle in coincidence with fission fragments. Fission fragment mass distributions are measured for each transfer channel, in selected bins of excitation energy. In particular, the mass distributions of 231,234Th and 234,235,236Pa are measured for the first time. Predominantly asymmetric fission is observed at low excitation energies for all studied cases, with a gradual increase of the symmetric mode towards higher excitation energy. The experimental distributions are found to be in general agreement with predictions of the fluctuation–dissipation model.


Introduction
Induced nuclear fission is a unique decay process which may be described by the interplay of macroscopic (collective) and microscopic (single particle) degrees of freedom in a nucleus [1]. Such a description of the fission process allows for studies of nuclear shell structures, nuclear viscosity and their excitation energy dependence at extreme values of deformation. In particular, fission fragment (FF) mass distributions and their sensitivity to the excitation energy and isospin provide a deep insight into the mechanism of the process of fission (see e.g. [2,3]).
Since the discovery of fission more than 75 years ago [4], fission process was intensively studied in capture reactions with light particles (e.g. neutrons, protons, electrons) and gamma rays, as well as with spontaneously fissioning nuclei [5]. With the development of more versatile accelerators, complete-fusion reactions with heavy ions and also few-nucleon direct transfer reactions of e.g. (d,pf), ( 3 He,pf) or ( 6 Li,df) and similar types started to be exploited. Often, such studies concentrated mostly on the measurements of fission probabilities and their excitation energy dependence, see e.g. [6][7][8][9][10][11][12][13] and a review of experiments on the so-called 'surrogate' fission given in [14]. One of the first examples of fission fragments mass distribution (FFMD) measurements via the direct fewnucleon transfer was reported in [15] for the isotopes 227,228 Ac, studied with the 226 Ra( 3 He,df) and 226  β vibrational resonance was studied [16]. As a general rule, such studies mostly rely on the use of stable or long-lived primordial nuclides as a target, such as isotopes of Th, U and some of the long-lived heavier transactinides, some of the latter could also be obtained via the neutron activation in high-flux reactors. An extreme case of the latter approach is the spontaneous fission study of 259 Fm [17], produced in the 257 Fm(t,p) 259 Fm → (SF) reaction.
Overall, the region of nuclei accessible for early fission studies was limited to nuclei lying close to the beta-stability line or to very neutron-deficient isotopes produced in complete-fusion reactions.
Recently, several different approaches to perform FFMD measurements in the very neutron-deficient mercury-to-thorium nuclei were demonstrated in the reactions with radioactive beams. In particular, at ISOLDE, by using beta-delayed fission, fission properties of the very neutron-deficient 178,180 Hg (N/Z ∼ 1.25), 194,196 Po and of 202 Rn were investigated [18][19][20]. At FRS@GSI, by using lowenergy Coulex-induced fission of relativistic RIBs in inverse kinematics, comprehensive fission studies were performed for several tens of nuclei in the neutron-deficient Ac-U region [21]. The recent SOFIA experiment at GSI also followed the same approach but with a much improved technique [22]. Despite a wealth of new information produced by these methods, presently they can be applied to nuclei only up to 238 Np.
The scope of the present work is to explore the potential of the multinucleon transfer (MNT) reactions to measure FFMDs and their excitation energy dependence for the neutron-rich nuclei, which cannot be accessed by particle-capture and/or heavy-ion fusion reactions. The MNT channels of the 238 U + 12 C reaction in inverse kinematics were recently used to study fission of excited transactinide nuclei with the help of the large-acceptance magnetic spectrometer VAMOS@GANIL [23][24][25]. In these experiments, sufficiently-high A and Z resolution for FFs was achieved due to their kinematic boost, allowing the simultaneous measurement of the complete mass-and atomic-number distributions of fission fragments (at least for the light FF groups) using the magnetic spectrometer. For completeness, we also mention a recent nucleardecay spectroscopy study of fission fragments at the large-aperture magnetic spectrometer PRISMA (LNL, Legnaro, Italy) coupled to the high-resolution Advanced Gamma Tracking Array (AGATA) [26]. In that work, the initial fissioning nuclei in the vicinity of 238 U were produced in the near-barrier transfer channels of the 136 Xe + 238 U reaction. More generally, the use of the MNT reactions has recently attracted considerable attention to produce neutron-rich nuclei in the vicinity of the N = 126 shell closure [27] and also neutron-rich super-heavy elements [28,29].
In this Letter, we studied the MNT channels of the reaction 18 O + 232 Th in direct kinematics to obtain FFMDs and their excitation-energy dependence for fourteen excited isotopes of Th, Pa and U. An obvious advantage of this method is a relatively easy possibility to change the projectile and/or the target nuclei. In particular by using targets of the rarest highly-radioactive neutronrich isotopes heavier than 238 U (e.g. Cm and Cf), nuclei to be studied can be extended to isotopes far heavier than uranium, which cannot be used at the accelerator facilities for the inverse kinematics experiments similar to VAMOS or SOFIA.  The energy calibration of the E-detectors was performed by removing two E-detectors so that the elastically-scattered 18 O beam could hit the E-detector directly. The well-defined initial beam energy from the tandem and the measured scattering energy E elastic (θ) (as a function of the scattering angle) were then used to calibrate the strips of the E-detector. Elastic scattering was further used to calibrate the E-detectors, by determining the energy deposition in the E-detector as E elastic -E res , where E res is the energy measured in the E-detector after passing through the E-detector. From the peak of elastic scattering in the sum spec- trum E tot = E + E res , the energy resolution was obtained to be 1.0 MeV (FWHM), which also determines the precision for the excitation energies deduced in our study (see also in the follow-up text). Fig. 1(b) shows the E-E tot spectrum for ejectiles, where the parabolic lines correspond to different transfer channels, including a clear separation of specific isotopes. Isotopic assignment was done in respect of the elastically-scattered peak of 18 O and the missing line of 8 Be. It was further confirmed with the energy-loss calculation using the program SRIM [30]. The identification of the 12 C line was also checked by accelerating a 12 C beam and measuring the elastic peak. The data from E-E spectra were also used to deduce the excitation energy of the respective fissioning nuclei, which were determined from reaction Q-value [31] and the measured (angle-dependent) ejectile energies E and E tot . In this procedure we assumed that no excitation energy is given to the ejectile, thus the excitation energies quoted in the paper should be considered as upper limits only. Furthermore, though the precision of the deduced excitation energies is ∼ 1 MeV (see above), we bin the events into the ranges of excitation energy ∼ 10 MeV wide, as a compromise between the observed statistics within each bin and reasonably maintaining narrow bin sizes.

Experimental methods
The coincident FFs resulting from the fission of excited nuclei (after the MNT) are detected by four 200 × 200 mm 2 positionsensitive MWPC, see in Fig. 1(a). Operation conditions are described in [32]. The distance between the target and the center of the cathode was 224 mm, and each MWPC covers a solid angle of 0.67 sr. The positions of FFs's incidence on the MWPC were determined with a position resolution of 4.0 mm. FF time differences, T , between two coincident MWPCs were measure to determine the masses of both fragments.

Results
FFs masses were determined event-by-event from the kinematic analysis, whereby the measured T values and incident positions of both FFs were used. The momentum of the target-like fissioning recoil nucleus is determined by the measured momentum of ejectile under the assumption of a binary reaction process. To validate the calibration procedure, Fig. 3 compares a selection of deduced FFMD's (full black circles with the error bars) with the literature data (red open triangles) [33][34][35][36] for 233 Pa * , 233 Th * and 236 U * , obtained at comparable excitation energies. We note that the present FFMDs are typically broader than the literature data, which is due to limited mass resolution, mainly originating from a relatively thick target used in our study. The experimental mass resolution of σ m = 6.5 u was determined by comparing the measured FFMD for 233 Pa * at average excitation energy of E * ∼ 15 MeV with the literature data taken at comparable excitation energies in the p + 232 Th to 233 Pa * reaction [33,34]. For the sake of comparison with our data, the literature data were artificially broadened by the experimental resolution and are shown as red dashed curves, which are in a reasonable agreement with our data, thereby confirming the validity of the whole method. Fig. 3 also shows the benchmarking of the fitting procedure used to extract the most probable masses of the light and heavy peaks of the FFMDs. Following the procedure of [33] (in particular their Figs. 9-11), the fitting was performed by a combination of two main fission modes, mass-symmetric Standard (S) and asymmetric Standard-2 (S2) in [33], the respective Gaussian functions are shown by the thin blue lines with the final total fit given by a thick blue line. The fits demonstrate that quite a fair description of our data is obtained for all five cases in the figure. In particular, we stress a reasonable description of the FFMDs of 233 Pa * at three excitation energies, which shows a gradual increase of the symmetric component in the fitting function, in agreement with more precise data shown in e.g. [33]. We note that fitting in [33] also included two extra modes, Standard-1 (S1) of moderate massasymmetry and Standard-3 (S3) of super mass-asymmetry. However, these modes contribute less than ∼ 10% and ∼ 0.5%, respectively, to the total yield (see Figs. 9, 10 of [33]) and their weight is smaller than the uncertainty of our measurement. Therefore, their omission from our fits will not change the main conclusions of the present work. Fig. 4 summarizes the FFMDs obtained in this experiment for nuclei of 231−234 Th * , 232-236 Pa * and 234-238 U * , for excitation energy bins of 10 MeV. FFMDs of the 231,234 Th * , 234,235,236 Pa * nuclei were obtained for the first time. For the other nuclei, the known FFMD data were systematically extended to excitation energies as high as 60 MeV. It follows from Fig. 4 that mass-asymmetric fission dominates at low excitation energies for all measured nuclei. The yield in the mass-symmetric fission region increases with excitation energy (see also Fig. 3 for a zoom-in view for 233 Pa * ) and the double-humped shapes tend to become structureless due to weakening of shells responsible for asymmetric fission. It is also interesting to note that the measured spectra seem to reveal larger peak-to-valley ratio in the FFMDs for nuclei with larger isospin values, as seen for the most neutron-rich isotopes of the same element, considered at the same excitation energy (see, for instance, FFMDs for E * = 20-40 MeV). This might be explained by the growing influence of the magic 132 Sn nucleus on the mass di-vision, which is expected for lower mismatches in the N/Z -ratios between 132 Sn and the fissioning compound nucleus.
Concerning the results presented in Fig. 4 it should be stressed that initial excitation energy of a fissioning system, E * , can be reduced by evaporation of neutrons prior to fission, especially when the excitation energy is high. As shown in [37], the pre-scission neutron multiplicities M pre are expected to linearly increase with E * from a threshold for neutron-emission. Based on the parameters best fitted for isotopes of Pa and U elements, the M pre is estimated to evolve as 0.6, 1.  at A H = 140 ∼ 142, while the light-fragment peak gradually increases from A L ∼ 90 to ∼ 97 when the system transit from the lightest to the heaviest nuclei. An interesting finding in our work is that the location of the light-and heavy peaks are nearly con- stant through the measured excitation energy range, similar to the benchmark data of 233 Pa * [33]. Due to lower statistics, we prefer not to rely on the data fits for energies higher than E * = 40 MeV.

Discussion
The measured FFMDs are compared with calculations based on the fluctuation-dissipation model developed in [40], where description of fission in Langevin equations from the low-excited state were attempted, and a good reproduction of the measured FFMDs for 234,236 U * and 240 Pu * from E * = 20 MeV was obtained.
As described in [40], the nuclear shape and the corresponding energy is calculated by a two-center shell model [41]. The nuclear shape is defined by three parameters (distance between two potential centers, deformation of fragments, and mass-asymmetry), and the corresponding energy is given by a sum of the liquid-drop energy V LD and the shell correction energy V shell . The latter term is represented as V shell (0) exp(−E * /E d ) using the shell correction energy at the zero temperature V shell (0) and shell damping parameter E d , where E d = 20 MeV was chosen as in [40]. For simplicity, it was assumed that the total excitation energy of the system after multinucleon transfer reactions is given to the excitation energy (E * ) of the fissioning nucleus.
It was noticed that the calculated FFMDs have typically a rather narrow distribution in the region of E * < 20 MeV, see a few examples of the original calculations shown in blue in Fig. 4. Therefore the original theoretical curves were broadened with the experimental resolution (cf. a similar procedure in respect of Fig. 3) The resulting broadened theoretical FFMDs are shown by the red solid curves in Fig. 4. One can see that the calculated FFMDs reproduce reasonably well both the global shape of the experimental distributions and also the positions of the light and heavy-fragment peaks for most of studied nuclides, at the excitation energies below ∼ 30 MeV. This demonstrates the reasonable treatment of the shell correction energy at these excitation energies, and confirms the validity of the shell-damping energy of E d = 20 MeV originally introduced in [42], in contrast to a recently suggested value of E d = 60 MeV [43]. However, some local deviations are recognized, especially at higher excitation energies. For example, calculated spectra at E * = 30-40 MeV and higher energies show a tendency to favor the symmetric fission mode for most of the studied nuclei, whereas experimentally several nuclei still exhibit a clear mass asymmetry especially for the most neutron-rich isotopes (for example 234 Th * , 236 Pa * , 238 U * ). This observation might point out at too rapid shell dumping with growing excitation energy, especially for neutron rich isotopes. In summary, multinucleon transfer reactions were used to study the FFMDs and their excition energy dependence in fourteen compound nuclei excited up to E * = 60 MeV; the FFMDs of 231,234 Th * , 234,235,236 Pa * were measured for the first time.
For all studied cases, the shape of the mass distributions was found to be predominantly asymmetric at low excitation energies, with a gradual increase of the symmetric mode towards higher excitations. For a given isotope chain, the asymmetric mode tends to increase with neutron number, which can be interpreted in terms of the growing influence of doubly magic 132 Sn, under the hypothesis that the neutron-to-proton ratio of the compound nucleus is preserved in fission fragments. The measured FFMDs were compared with the three-dimensional Langevin calculations, which are found able to describe in most cases both the shape and the excitation energy dependence, at least up to E * ∼ 30 MeV.
The present experiment demonstrates that multinucleon transfer reaction is a useful tool to study fission properties of a number of short-lived neutron-rich actinide and transactinide nuclei. Several instrumental developments are however needed to increase the quality of the data, such as the use of thinner targets (50 ∼ 100 μg/cm 2 ), to improve on the mass resolutions, and of an array of γ -ray detectors, to measure possible excitation of the ejectile, which in turn will allow for a better determination of the excitation energy of the fissioning nucleus.