Zeptosecond contact times for element Z=120 synthesis

The synthesis of new superheavy elements beyond oganesson (Z=118) requires fusion reactions with projectile nuclei with proton numbers larger than that of 48 Ca (Z=20), which has been successfully employed for the synthesis of elements with Z=112-118. In such reactions, fusion is drastically hindered by fast non-equilibrated dynamical processes. Attempts to produce nuclei with Z=120 using the 64 Ni+ 238 U, 58 Fe+ 244 Pu, 54 Cr+ 248 Cm, and 50 Ti+ 249 Cf reactions have been made, which all result in larger Coulomb forces than for 48 Ca-induced reactions, but no discovery has been conﬁrmed to date. In this work, mass and angle distributions of ﬁssion fragments from these reactions have been measured with large angular coverage to aid in selection of the most promising projectile-target combination that would favor fusion. The results yield information on reaction contact times, with the longest exhibited by 50 Ti+ 249 Cf. © 2020 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP 3 .


Introduction
The search for new elements represents one of the main focus points of physics research. To date, all of the elements with atomic number Z≤118 have been discovered, accessing the locality of the so-called island of stability -a region of superheavy nuclei (SHN) with enhanced stability due to shell closures, predicted more than half a century ago [1,2]. Expectations of the locations of these shell closures vary, with early calculations predicting 'new' magic shells to appear at Z=114 and N=184 [3]. Most modern calculations predict closed proton shells at Z=114, 120, 124 or 126 and a neutron shell closure at N=172 and/or 184 (e.g., [4][5][6][7][8]). No clear indications of such a shell closure at Z=114 have yet been observed, giving a strong motivation to push to ever-heavier elements.
New beam and target combinations must be explored to reach beyond Z=118 as doubly-magic 48 Ca projectile ions, successfully used in fusion-evaporation reactions for the production of elements with Z=112-118 [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24], cannot presently be used due to insufficient amounts of target material with Z>98 [25]. Campaigns totaling about one year of accelerator beamtime searching for the element with Z=120 have been carried out using the 64 Ni+ 238 U [26], 58 Fe+ 244 Pu [27], 54 Cr+ 248 Cm [28,29] and 50 Ti+ 249 Cf [30,31] fusion-evaporation reactions. Despite this, element Z=120 remains undiscovered, suggesting that production cross sections are lower than those for 48 Ca-induced reactions. However, the important question of how much lower the production cross sections are remains unanswered, which is a critical issue for the planning of successful future SHN experiments.  Table 1 Summary of reaction properties. E beam is the beam energy and E c.m. /V B is the ratio of the reaction energy in the center-of-mass system (taking into account energy losses) to the calculated capture barrier V B [42]. 64  In order to synthesize SHN, projectile and target nuclei must have sufficient energy to overcome the Coulomb barrier and form a composite system (capture), which must then evolve into a compact compound nucleus (CN) that survives fission. The resulting evaporation residue (ER) cross section of the compound nucleus at an excitation energy E * can be described by the three-term expression where σ cap is the capture cross section, P C N is the probability for CN formation, and W C N is the survival probability of the CN against fission through particle evaporation. E * and L are the excitation energy and angular momentum of the CN, respectively.
The quasifission (QF) process, wherein the composite system fails to evolve into a CN after capture and reseparates into two fragments, occurs with probability P Q F = 1 − P C N [32,33]. In SHNformation reactions, QF takes place within a few zeptoseconds (1 zeptosecond (zs) = 10 −21 s) [32][33][34][35], faster than that of fission of the CN (fusion-fission, FF) and is the dominant process, thus severely hampering experimental efforts to produce SHN. P Q F depends sensitively on the reactant characteristics and can vary widely even for reactions that form the same CN (e.g., [36][37][38]). In-depth knowledge regarding the competition between FF and QF in SHN-formation reactions is therefore critical in order to validate and improve theoretical frameworks and thus provide reliable predictive power.
Angular distributions are a crucial characteristic of the QF process as they provide the most direct information regarding the contact time of the composite system. However, information regarding QF angular distributions for SHN-formation reactions is scarce: in the case of Z=120, only one data point has been previously measured for the 238 U+ 64 Ni reaction in inverse kinematics [32]. Mass and total-kinetic-energy (TKE) distributions of fission fragments have been measured for reactions using 64 Ni, 58 Fe and 50 Ti projectiles and actinide targets up to Cm (Z=96) at scattering angles of ≈ 90 • [39][40][41] thus providing no direct information regarding rotation times. In this letter, we present QF mass and angular distributions for four Z=120-formation reactions measured with large angular coverage, where significant differences in reaction dynamics are observed through the QF outcomes.

Beam characteristics
Two experimental campaigns were performed at the Heavy Ion Accelerator Facility operated by the Australian National University in Canberra, Australia. Pulsed beams of 64 Ni, 58 Fe, 54 Cr and 50 Ti were delivered by the 14UD electrostatic accelerator coupled with the superconducting linear post-accelerator providing energies close to the interaction barriers [42]. A summary of reaction parameters is shown in Table 1.

Target fabrication
A 160-μg/cm 2 target of 238 UF 4 on a 125-μg/cm 2 Al backing was used for the 64 Ni+ 238 U reactions. Targets of typically 0.1 mg/cm 2 (up to 0.6 mg/cm 2 ) of 244 Pu, 248 Cm and 249 Cf, isotopically enriched to levels > 97%, were produced at the Johannes Gutenberg University Mainz via molecular plating [43]. Actinide material was deposited on the Ti side of backing foils fabricated at GSI Darmstadt that consisted of 230-250 μg/cm 2 Al with a 23-39 μg/cm 2 Ti layer on top. The targets were oriented such that the actinide material faced the incoming beam ions with their normal at 60 • with respect to the beam direction to minimize the effects of the target thicknesses on the reconstruction of reaction kinematics. A carbon foil of thickness ∼40 μg/cm 2 was placed upstream of the targets to reduce contamination in the chamber from target material sputtered at backwards angles.

Event selection
An analysis using two-body kinematics was carried out for events measured in coincidence between the forward-angle MWPC and one of the two backward-angle MWPCs, allowing fission fragment mass ratios, defined as M R = m 1 /(m 1 + m 2 ) (where m 1 and m 2 are the fragment masses at scission), and scattering angles to be determined. Event-by-event corrections for energy losses were applied iteratively, and three-body events (e.g., fissioning targetlike nuclei following transfer reactions) were rejected by requiring that fragments were detected back-to-back in the center-of-mass frame. Further details of the experimental setup and analysis procedure are provided in references [44] and [45].

Mass-angle distributions (MADs)
Mass-angle distributions (MADs), defined as the center-of-mass scattering angle θ c.m. versus the mass ratio M R (see section 3.1), have been extensively used to probe QF and FF (e.g., [32,[45][46][47]). Examples of MADs measured in this work can be found in Fig. 1(a)-(e). The color mappings represent the double-differential cross section d 2 σ /(dθ c.m. dM R ). Key features of experimental MADs include elastic and quasielastic scattering of target-and projectilelike fragments, which appear at mass ratios M R = m T /(m T + m P ) and M R = m P /(m T + m P ) (where m T and m P are the target and projectile masses, respectively), and fission fragments, which are expected to appear in the central region between the elastic components. The extent of the correlation between mass and angle reflects the system rotation, with significant correlations visible for rotations ∼ 180 • or less. A lack of mass-angle correlation (i.e. a symmetric distribution centered at M R = 0.5) indicates rotation angles of > 360 • .

Angular distributions and mean scattering angles
In addition to MADs, changes in reaction dynamics can be studied in detail through 1-dimensional angular distributions of fission fragments, defined as the differential cross section dσ /dθ c.m. as a function of center-of-mass angle θ c.m. . An example region of light fragments with M R < 0.5 is marked by a black polygon in Fig. 1(e).
Contributions from elastically-scattered target-and projectilelike fragments are minimized through a two-dimensional cut on E K ,exp /E K ,calc versus M R , where E K ,exp are the measured total kinetic energies of the fragment pairs and E K ,calc are the expected values for fission calculated following references [48] and [49]. Resultant angular distributions, found in Figs. 1(h) and (i), are normalized by the total integrated fission cross sections and quantified by their weighted means (2) where N is the number of bins.

Extraction of contact times
Larger rotation angles of the intermediate system are associated with longer times before fragment separation and are, in general, indicative of more mass transfer and higher fusion probabilities.
The angle of rotation θ in the center-of-mass frame between capture and reseparation is related to the contact time t contact through the simple relationship where ω = L/J and L and J are the angular momentum and average moment of inertia (MoI), respectively. We convert mean scattering angles to contact times using the classical Monte Carlo model described in [35,45,50,51], which comprises the following components: angular momentum distributions for capture, the average MoIs during rotation, and classical Coulomb deflection angles on the incoming and outgoing trajectories. Angular momentum distributions were calculated using the coupled-channels code ccfull [52], taking into account the appropriate static deformations and vibrational states [53][54][55].
Classical rigid-body moments of inertia, calculated assuming a spherical projectile touching the tip of a deformed target nucleus and normalized to the moment of inertia of a rigid sphere J 0 =

Experimental MADs
MADs measured for the 64 Ni+ 238 U and 50 Ti+ 249 Cf reactions are shown in Fig. 1(a)-(c) and (d)-(e), respectively. A very high intensity of events originating mostly from scattered target and projectilelike fragments appear as expected at M R ≈ 0.2 and 0.8.
The MADs obtained for 58 Fe+ 244 Pu and 54 Cr+ 248 Cm are qualitatively similar and are shown in the Supplemental Material [58].
The region M R ≈ 0.25 − 0.75, where fission fragments are expected, is dominated by mass-asymmetric events that peak at M R ≈ 0.3 and 0.7 in all experimental MADs. Such double-humped mass distributions with maxima close to doubly-magic 208 Pb fragments have been widely observed in studies involving heavy projectiles and actinide targets and are a typical signature of QF (e.g., [32,33,50,[59][60][61]). No strong fission components with a symmetric mass split (M R = 0.5) are visible.

MADs simulated using time-dependent Hartree-Fock (TDHF) calculations
To aid the interpretation of the observed shifts in θ c.m. , which could be associated with the contributing angular momenta and the contact time of the composite system, we examine recent work carried out within the fully-microscopic TDHF framework. This describes the dynamical evolution of the reactants, and has been used to investigate mass-angle correlations for heavy-and superheavy-element formation reactions (e.g., [62][63][64][65]). As a deterministic theory, TDHF calculations provide a single outcome for a given set of initial conditions. Values of M R and θ c.m. for specified impact parameters b (corresponding to different orbital angular momentum L) were calculated in reference [66] for the 48 Ca+ 249 Bk reaction. This system leads to the formation of 297 Ts and is more asymmetric than those measured here (Z P Z T =1940). Collisions occurring both at tip (axial) and side (equatorial) configurations were considered, since nuclear orientation effects are known to play an important role in QF dynamics involving deformed targets [44,67,68]. It has been suggested that P Q F is larger for collisions occurring at the tip of well-deformed targets and inhibited for collisions at the side [44,69,70], and that P C N may even be enhanced in the more compact side orientations [68]. By taking the TDHF (M R , θ c.m. ) values calculated at center-of-mass energies of 211 and 218 MeV [66], we simulate MADs using an approach similar to that adopted in [63], wherein Gaussian distributions centered at each (M R , θ c.m. ) point were summed. Each Gaussian was weighted by 2L+1 with a standard deviation in angle of 20 • and a standard deviation in M R that varies linearly from 0.025 at an initial mass split (corresponding to elastically-scattered projectilelike fragments) to 0.07 at M R = 0.5 [45,63]. The simulated MADs, which underlay the TDHF outcomes in Fig. 1(f) and (g), are qualitatively similar to those obtained experimentally. More importantly, the TDHF predictions reproduce the trend of the angular shifts with energy apparent in the measured data, as can be seen explicitly in the θ c.m. distributions (see Fig. 1(j)).

Evolution of mean scattering angles with energy and reactant characteristics
The experimental θ c.m. values shown in Fig. 2(a) exhibit a clear systematic picture of mean scattering angles that reduce with increasing E c.m. /V B . Moreover, we observe a well-pronounced systematic shift of mean angles dependent on the entrance channel; i.e., reactions with lower Z P Z T (see Table 1) have lower values of θ c.m. than more symmetric reactions for any given value of E c.m. /V B . Mean scattering angles extracted from the MADs simulated using TDHF predictions for 48 Ca+ 249 Bk, also shown in Fig. 2(a), lie below those for 50 Ti+ 249 Cf as expected due to the increased asymmetry of the reactants, and follow the same trend with increasing energy. An equal weighting of tip and side collisions has been assumed; adjusting the tip:side ratio to 1:2 or 2:1 produces the same qualitative results.

Reaction contact times
In order to compare the reactions, differing entrance-channel properties (e.g., moments of inertia and angular momenta) must be taken into account. We therefore use the procedure detailed in section 3.4 to convert the mean scattering angles to contact times, defined as the time elapsed during the QF process between capture and the reseparation of fragments. In general, longer contact times should be associated with larger P C N as the likelihood of reaching full dynamical equilibrium in all degrees of freedom increases with time. Indeed, events assumed to lead to fusion in the TDHF calculations for 48 Ca+ 249 Bk exhibit contact times of at least 25 zs, much longer than those resulting in QF [66].
Average contact times extracted from experimental θ c.m. values for data measured for energies above the interaction barriers (where orientation effects are averaged) are shown in Fig. 2(b). Although the angular distributions show that QF dominates the negligible FF components, the extracted timescales are associated with the sum of QF and FF as the mass region included in the angular distributions extends to symmetry (M R =0.5). The times remain relatively constant with increasing E c.m. /V B despite the significant changes of mean scattering angles due to increasing angular momenta. Reactions with increasing entrance-channel asymmetry exhibit lengthening contact times, varying from ∼3 zs for 64 Ni+ 238 U to ∼5 zs for 50 Ti+ 249 Cf, and are in good agreement with the 3.1 zs estimated for the asymmetric mass component of the 238 U+ 64 Ni reaction by Tōke et al. [32]. Note that the relative trend is independent of the choice of model for J , which affects absolute values. Contact times associated with the simulated 48 Ca+ 249 Bk angular distributions, which were also extracted using the classical Monte Carlo model, are represented by black stars in Fig. 2(b) and match well to the times predicted directly by the TDHF framework in reference [66] (black squares). Previous contact-time estimates for 64 Ni+ 238 U and 58 Fe+ 244 Pu made using mass and TKE measurements measured at ∼ 90 • [40,60], employing the mass-drift formalism of reference [33], are ∼ 3 times shorter [71] than those extracted here.

Conclusions
To summarize, we have measured mass and angular distributions of fission fragments for four candidate reactions to be used for the synthesis of a new element with Z=120 at energies extending from below to ∼10% above the capture barriers.
Well-pronounced mass-angle correlations, which evolve with the bombarding energies, were observed for all four reactions and are attributed to originate from changing reaction contact times, in agreement with predictions from TDHF calculations. Our results have revealed a systematic picture of contact times that increase with decreasing Z P Z T , with the longest exhibited for 50 Ti+ 249 Cf. The lengthening of contact times for increasingly asymmetric reactions suggest that the probability of fusion, wherein equilibration of all internal degrees of freedom must be reached, will also be increased. These results support the conclusion that, of the reactions studied here, 50 Ti+ 249 Cf has the highest fusion probability and is the most promising reaction for Z=120 formation.

Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.