Observation of the competing fission modes in 178 Pt

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Introduction
Understanding of the nuclear fission process is important for many areas of fundamental science, technology, and medicine. In particular, fission is crucial for the existence of many transuranium nuclei, including the predicted long-lived superheavy isotopes [1,2], as well as for the heavy element formation in the astrophysical r-process [3][4][5][6]. Better knowledge of fission properties is also essential for our understanding of the antineutrino flux from nuclear reactors [7,8]. Regardless of the area, one needs detailed information on fission rates and fission fragment (FF) mass distributions (FFMDs).
At present, our experimental knowledge of fission is primarily limited to nuclei close to the stability line [9,10] and within a to the r-process is highly model dependent [3,5,6]. While there has been exciting progress in global modeling of nuclear properties, facilitated by advanced computing, a comprehensive, microscopic explanation of nuclear fission is still difficult to achieve, due to complexity of the process [11,12]. To advance theoretical modeling of fission, experimental FFMDs data are needed in broader range of N/Z -values, to test the isospin dependence of model predictions.
Due to its experimental accessibility, the neutron-deficient sublead region (N/Z ∼ 1.3) provides excellent testing ground for studies of the isospin dependence of fission observables. Due to its exotic N/Z ratio, new facets of the fission process can be expected. Indeed, the observation of asymmetric fission of 178,180 Hg [13,14] attributed to shell effects in pre-scission configurations [15][16][17][18] has generated an appreciable interest in this region, both experimentally and theoretically. Inspired by the 180   a Derived from the coupled-channel calculation of the CN production probabilities [34]. b Initial values from [35] corrected for rotation [36]. c Calculated in accordance with procedure described in [19].
have been experimentally studied for several neutron-deficient sub-lead nuclei [14,[19][20][21]. As shown by theory [15][16][17][22][23][24][25], the topology of potential energy surfaces (PES) in sub-lead nuclei is significantly different (flat, broad and rather structureless) from those in the actinides, which explains fairly low dependence of the corresponding experimental FFMDs on the compound nucleus (CN) excitation energy (cf. [19]). According to the global survey of calculated FFMDs [26], a new extended region of asymmetric fission is expected in neutron-deficient Re-Pb isotopes with 98 N 116. It is separated from predominantly asymmetricallyfissioning actinides by a zone of symmetric fission around Ir-At in the vicinity of N ∼ 120-126 [9], whose properties were extensively investigated in the past (cf., e.g., Refs. [27,28]). The experimentally studied neutron-deficient 178,180,182,190,195 Hg and 179,189 Au isotopes [13,14,[19][20][21] lie on the northern border of this region. As concluded in Ref. [26], new high-quality FFMDs data for selected sub-lead isotopes are needed to test and guide theoretical developments.
In the transitional regions between asymmetrically and symmetrically fissoning sub-lead nuclei, an interplay between different fission modes might exist, by analogy to light [29,30] and heavy [31,32] actinides. In view of PES properties in the sub-lead region [13,[15][16][17], an observation of a competition between fission modes will shed light on the nature of near-scission configurations of nuclei, which are some 60 nucleons lighter and greatly deficient in neutrons, as compared to actinides and transactinides. This Letter provides the first experimental demonstration of the existence of competing fission modes in sub-lead nuclei, by revealing the presence of asymmetric and symmetric fission modes through measurements of FFMDs from fission of 178 Pt.

Experiment
178 Pt was produced at the JAEA tandem accelerator [33] in a complete fusion reaction 36 Ar + 142 Nd → 178 Pt * . A 75 μg/cm 2 -thick 142 Nd target was made by sputtering of the 142 NdF 3 material (isotopically enriched to 99%) onto a thin (42 μg/cm 2 ) carbon backing facing the beam. Stability of the target performance with irradiation time was confirmed by the measurements of the 36 Ar ions scattered into a Si detector placed at backward angles, as well as by the constancy (within every beam energy setting) of the counting rate monitored during the experiment. The 36 Ar beam intensity was a few pnA, and the measurements were performed at three beam-energy settings (155, 170, and 180 MeV). Table 1 gives details on the energy balance of the formed CN.
The coincident fission fragments of 178 Pt were detected with a two-arm time-of-flight (TOF) setup placed downstream the target, with two TOF arms positioned symmetrically at ±60 • relative to the beam axis, with horizontal and vertical acceptance of ±15 • .
The chosen detection angles allowed for similar angular acceptance for both mass-symmetric and mass-asymmetric fission events and, thus, excluded influence of the setup geometry on the observed fis- were operated with isobutane gas at a pressure of 1.5 Torr and had a 2 μm aluminum-coated Mylar entrance window, whereas the MCP-based detectors were equipped with a thin (0.5 μm) Mylar foil coated with Au and CsI (100 Å and 20 Å of thickness, respectively). In addition to timing signals and spacial coordinates for the detected events, the MWPCs have also provided information on their partial energy loss in the isobutane.

Results
Figs. 1a-b give samples of recorded coincident data, in which experimental observables (timing signals and energies) are used without any preliminary treatment. Three groups of events are distinctly visible in the plots. Their identification as projectile/target scattering and fission events is obvious directly from the plotted raw data.
For the follow-up analysis, we select fission events by making use of two conditions on the observables, indicated in Figs. 1a-b as contours. 1 Angular information extracted from the MWPC impact coordinates (folding angles: see Ref. [19] for details) was used to check for the selection quality.
For every identified fission event, velocities of coincident FFs were derived from the measured TOF values and TOF distances calculated with help of the MWPC coordinates. They were then calibrated with the scattered 36 Ar beam and corrected for the reaction kinematics, as well as for attenuation in the target (calculated for a half of the thickness) and the TOF detectors' foils. Fig. 1c shows the obtained FF velocities for one of the TOF arms. The striking feature of these distributions is their pronounced nonsymmetric character. A good description of the velocity spectra is achieved with a two-Gaussian fit, as demonstrated in the inset of Fig. 1c. For coincident fragments, one finds a correlation of events from the low-and high-velocity groups in the velocity spectra from the two TOF arms. This inequality in velocities of coincident FFs allows one to conclude that the fission of 178 Pt produces fragments with different masses and is therefore predominantly asymmetric.
Importantly, the two-component velocity fits as in Fig. 1c deliver very different distribution widths and thus do not yield the same integral for the expected light and heavy fragment groups. 1 An alternative approach for the fission event selection is to extract from the measured data masses and total kinetic energies and to construct a corresponding correlation plot, as shown in Fig. 1d. This analysis does not necessitate any prior gating but uses two-body fission kinematics for all of the measured events.   Fig. 2b. Projection of the data in Fig. 2b on the TKE-axis gives the TKE distribution (Fig. 2a), whose average value TKE and width σ TKE are found to slightly change with the increasing beam energy ( TKE = −1.9(2) MeV, σ TKE = 1.2(2) MeV for the measured E beam range). This corroborates recent results on the TKE parameters' behavior in 180,190 Hg [19] and is generally inline with positive and negative slopes in dTKE , respectively, known for actinides (cf., e.g., [37]).
The TKE distribution in Fig. 2a is clearly skewed. The simulated FF energy straggling in the target and TOF detectors' foils could not reproduce the observed asymmetry effect in the TKE, unless unrealistic assumptions are made about the inhomogeneity of the MCP foil (thickness varying from zero till 10 times the nominal value of 0.5 μm). Similarly-skewed TKE distributions were obtained also at E beam = 155 and 180 MeV. Based on the velocity analysis, an unconstrained two-Gaussian fit was carried out to describe the TKE data. This fit, statistically reliable only at the two higher energies, yields two TKE components placed at TKE low (maximum of the shadowed-area curve in Fig. 2a) and TKE high (maximum of the other dashed curve); their numerical values are given in Table 1.
The TKE components TKE low and TKE high are linked to the symmetric and asymmetric fission modes. This is demonstrated by the difference in the shape of the partial MDs constructed with events in Fig. 2b in the regions below TKE low and above TKE high and projected on the mass-axis (cf. the dotted lines and arrows in the Figure): narrow and clearly symmetric in Fig. 2d and wide and flat-top in Fig. 2c. The best-fit descriptions of partial MDs in Figs. 2c-d are achieved with one-and two Gaussians, respectively. The latter determines the light ( A L = 79(1) amu) and heavy ( A H = 99(1) amu) FF peak positions. Thus, our experimental results shown in Fig. 2c-d offer the first direct experimental evidence of the co-existing symmetric and asymmetric fission modes in the 178 Pt nucleus and in the sub-lead region. Contrary to the Mulgin et al. [38] who interpreted earlier experimental data close to the β-stability line around A∼200 [27,28] within a liquid-drop model with phenomenological shell corrections added, our conclusion on the coexistence of two modes in 178 Pt is based on the assumption-free deconvolution of experimental TKE-mass data which makes the result unambiguous.
The experimental total FFMDs are shown in Figs. 2e-g by the black circles. One observes that the MD shape evolves with the excitation energy E * CN : it becomes wider when E * CN increases. The effect of the MD broadening is well-known for actinides (cf., e.g. Ref. [39]); it scales with the nuclear temperature. The expected linear dependence of the MD variance with E * CN for nuclei in the region of interest has already been demonstrated in fission of 180,190 Hg isotopes (cf. Fig. 3 of Ref. [19]); present experimental data follow the same trend.
Solid red and dashed lines drawn in Figs. 2e-g are results of the analysis in terms of two fission modes, with the fit function composed of three Gaussians with fixed positions as obtained above. Overall, a good description of the experimental data is achieved. The asymmetric mode is found to be dominant, in accordance with the velocity analysis. The weight of the symmetric mode amounts to ∼31% at the three considered beam energies. Thus, in contrast to actinides [37], the balance between symmetric and asymmetric modes in the FFMDs does not seem to be significantly affected by the excitation energy. This can be explained in terms of the energy considerations of Table 1: corrections to the excitation energy E * CN due to possible neutron emission 2Ē ν , rotational energy E rot of the CN and the rotation-dependent fission-barrier height B f ,¯ reduce the initial spread of 20 MeV in E * CN , resulting in practically identical (∼25 MeV) effective excitation energy E eff CN .

Interpretation
Nuclear density functional theory (DFT) calculations made prior the experiment within two Hartree-Fock-Bogolyubov frameworks employing the Skyrme UNEDF1-HFB [41] and Gogny D1S [42] energy density functionals (cf . Figs 3 and 4, respectively) help to interpret the obtained experimental results. 2 Proton emission has been neglected as it affects less than 10% of fission events at the highest excitation energy, as estimated with the statistical code GEF [40]. To illustrate the shapes on the way to fission, and the emergent pre-fragments, the neutron localization functions [43,44] corresponding to various intrinsic configurations along the asymmetric (ABCD) and symmetric (ABcd) paths are plotted. To understand the formation of fragments corresponding to the 178 Pt fission pathways, we use the concept of nucleon localization functions (NLFs) [43]. Within this framework, the elongated configurations on the way to scission are composed of two clusters (pre-fragments) connected by a neck. At scission, the neck nucleons are redistributed into pre-fragments, producing the final fission fragments. As shown in Ref. [44], NLFs quantify the appearance of pre-fragments more efficiently than nucleonic density distributions as the concentric patterns in NLFs -due to shell structure in the nuclear interior -are averaged out in density distributions. Fig. 3 displays the resulting NLFs along the two fission pathways: asymmetric (ABCD) and symmetric (ABcd). Based on the analysis of NLFs according to the procedure of Ref. [44], the asymmetric prescission configurations marked "C" and "D" in Fig. 3 are composed of a nearly-spherical cluster around 86 Sr and a lighter deformed pre-fragment. Such a structure results in FFs around 98 Mo and 80 Kr. As far as the symmetric configuration "c" is concerned, its pre-fragments can be associated with spherical 64 Ni nuclei.
The static fission valley in Figs. 3 and 4 evolves on a fairly flat landscape, in contrast to a typical situation in heavy actinides (see e.g. [17,23]). Absence of any ridge in the area of low octupole moments, along with a fairly small energy difference between the asymmetric and symmetric paths, suggests a possibility for a competition between different fission modes. At present, a detailed description of this competition is difficult to assess theoretically, as the post-scission configurations associated with fusion valleys [16] enter the picture and produce a sudden drop in PES at very large elongations (cf. Figs. 3 and 4a), which makes it practically impossible to follow adiabatically the original fission trajectory.
A detailed analysis of the PES in Fig. 4b shows that the plateau predicted for nearly-symmetric shapes around Q 20 = 190 b in the region between the paths CD and cd, has a rather complicated structure. Namely, at the same values of quadrupole and octupole moments, two local symmetric PES minima with similar energies but distinct hexadecapole moments and nuclear density distributions are found. One of these solutions, with Q 40 ∼ 60 b 2 , corresponds to compact fragments, while that with Q 40 ≈ 85 b 2 can be associated with very elongated fragments. In both models, the symmetric pathway associated with elongated-fragment configurations, expected to have lower TKE, is predicted to be energetically slightly more favored than that associated with compact fragments. Therefore, it cannot be excluded that the symmetric fission mode seen experimentally contains contributions from both structures. It is interesting to see that competing fission pathways involving similarly asymmetric, compact, or elongated shapes have been predicted for multimodally fissioning nuclei in the fermium region [45,46], i.e., for nuclei with much larger values of A C N and N/Z . Experimentally, we find that both symmetric and asymmetric fission modes follow the trend previously observed in heavier, trans-lead, nuclei [47]. In particular, higher values of TKE in the asymmetric mode (cf. Table 1) -which also match well the TKE = 135.9 MeV value expected from the Viola systematics [48] -are indicative of less deformed scission configurations, whereas for the symmetric mode, highly elongated FF shapes are expected from its lower TKE values. This finding is consistent with the shapes of nucleon localizations shown in Fig. 3: symmetric configuration "d" corresponds to highly deformed fragments without a well defined neck. As discussed above, a similar configuration associated with symmetric elongated fragments has been predicted in the D1S model: in Fig. 4b it is marked by a black dot at Q 40 ≈ 85 b 2 and Q 30 ≈ 0.

Conclusions
In summary, the FFMDs of 178 Pt produced in a complete fusion reaction 36 Ar + 142 Nd are found to be predominantly asymmetric, with the most probable mass division A L ≈ 79 and A H ≈ 99.
The combined analysis of the FFMDs and TKE distributions made it possible to separate asymmetric and symmetric fission modes. It is found that the asymmetric mode is associated with larger TKE values than the symmetric mode. Moreover, its average TKE follows the systematics [48] established for nuclei with N/Z ∼ 1.5, which suggests the asymmetric mode's insensitivity to the isospin of the CN, at least for A C N > 177.
The UNEDF1-HFB and D1S calculations support the experimental results. Namely, they correctly reproduce the measured mass division associated with the dominant asymmetric fission mode, and they predict highly elongated pre-scission configurations along the symmetric fission path, which is in accordance with the lower experimental TKE value for this mode.
The present work provides new experimental information on the extension of the recently-discovered island of asymmetric fission towards lower atomic numbers. For the first time, the interplay between different fission modes has been found in a nucleus from the sub-lead region. The result provides strong motivation for extending microscopic models of fission to FFMDs and TKE distributions at nonzero excitation energies. Finally, beyond-DFT extensions of the current formalism are needed, as the PESs predicted for pre-lead nuclei are generally very flat in the pre-scission region, resulting in possible interferences between asymmetric and symmetric fission modes.