Mass-asymmetric fission in the 40Ca+142Nd reaction

Shell effects play a major role in fission. Mass-asymmetric fission observed in the spontaneous and low energy fission of actinide nuclei was explained by incorporating the fragment shell properties in liquid drop model. Asymmetric fission has also been observed in the low energy fission of neutron-deficient 180Hg nuclei in recent β-delayed fission experiments. This low-energy β-delayed fission has been explained in terms of strong shell effects in pre-scission configurations associated with the system after capture. Calculations predicted asymmetric fission for heavier Hg isotopes as well, at compound nuclear excitation energy as high as 40 MeV. To explore the evolution of fission fragment mass distribution as a function of neutron and proton numbers and also with excitation energy, fission fragment mass distributions have been measured for the 40Ca+142Nd reaction forming the compound nucleus 182Hg at energies around the capture barrier, using the Heavy Ion Accelerator Facility and CUBE spectrometer at the Australian National University. Mass-asymmetric fission is observed in this reaction at an excitation energy of 33.6 MeV. The results are consistent with the β-delayed fission measurements and indicate the presence of shell effects even at higher exciation energies.


Introduction
Nuclear fission is a dynamic process involving large scale collective motion, often affected by a subtle interplay of macroscopic and microscopic effects during the transition of the fissioning nucleus from its ground state deformation to the scission point.Fragment mass distributions are an important observable in fission which provides crucial information about the potential-energy landscape of the fissioning system.Fragment mass distributions have been observed to be predominantly asymmetric in the spontaneous or low energy fission of most of the actinide nuclei [1], which could not be explained solely by using the liquid drop model (LDM) [2].The experimental observations were explained by incorporating the fragment shell properties near the scission configuration, particularly the spherical shell closure (Z = 50, N = 82) or deformed neutron shells (N = 88) [1,3], within the LDM frame work.a e-mail: prasad.edayillam@anu.edu.aub Permanent Address: Department of Physics, Central University of Kerala, Kasaragod, 671314, India.
c Presently at National Superconducting Cyclotron Laboratory, Michigan State University, Michigan, 48824, USA.
d Presently at Bhabha Atomic Research Center, Mumbai 400085, India.
f Institute for Nuclear Chemistry, Johannes Gutenberg University Mainz, 55128 Mainz, Germany.
Recent observations of mass-asymmertic fission of the Hg isotopes in β-delayed fission experiments [4,14] indicated the role of shell structures other than fragment shells in deciding the fission outcomes.The low yield of symmetric fission in 180 Hg populating 90 Zr (Z = 40, N = 50) led to the speculation that fragment shell effects, though significant in the potential energy surface near scission, must not play a major role in determining the mass split in this nucleus.
Even though β-delayed fission experiments allowed us to access the low energy fission regime of the neutrondeficient nuclei in the mass 180-200 region, the availability of nuclei undergoing this process is severely limited by the stringent conditions on β-decay Q-values and branching ratios [4].Also, the maximum available excitation energy for the fissioning system is restricted by the Qvalue of the parent nucleus [4].In the actinide region, it is observed that [1,5] the fragment mass division becomes symmetric with increasing excitation energy, as shell effects generally wash out at higher excitations.In order to understand the evolution of fission fragment mass distribution as a function of neutron and proton numbers (N and Z) of the fissioning system and the excitation energy in the neutron deficient Hg region, we measured the fission fragment mass distributions of 182 Hg populated through the fusion reaction 40 Ca+ 142 Nd at energies around the capture barrier.The results are compared with the latest experimental data available in the same mass region for the fis- sion of different Hg isotopes and also with the predictions of some of the theoretical calculations available.

Experimental details and data analysis
The experiment was performed using the 14UD Pelletron accelerator and superconducting linear accelerator facility at the Australian National University.Pulsed 40 Ca beams with a pulse seperation of 106.7 ns and full width at half-maximum (FWHM) of 0.7-1.5 ns were used to bombard the isotopically enriched 142 NdF 3 target of thickness 400 μg/cm 2 , with a 18 μg/cm 2 carbon backing facing downstream.The measurements were performed at 167.7, 194.9, 199.9, 210.0 and 221.1 MeV laboratory energies and the fission fragments were detected using the CUBE [6] fission spectrometer.CUBE consists of two large area position sensitive multiwire proportional counters, each with an active area of 279 × 357 mm 2 .These detectors were mounted at 45 • and 90 • scattering angles with respect to the beam direction, such that the normal to the central foil of both detectors was at 180 mm from the center of the target.The target normal was oriented at 60 • with respect to the beam axis to avoid shadowing of the detectors.Two silicon monitor detectors were mounted at θ = 30 • , at azimuthal angles of 90 • and 270 • , to detect the elastically scattered beam particles.
The CUBE detectors provide timing, position, and energy loss signals of the particles entering them.The calibrated position and time of flight information were used to obtain the fragment velocities and center-of-mass angles.The mass ratio (M R ) of the fragments is then obtained as, where m 1 and m 2 are the masses of fragments at scission and v 1 and v 2 are their center-of-mass velocities, respectively.Light particle evaporation from the fragments does not alter the centroids of the M R distribution, as the mass ratio is derived from the fragment velocities, which -on average -are not affected by the evaporation of light particles.
Mass-angle distribution (MAD) plots [7] of the fragments provide a direct indication of the presence of processes other than fusion-fission in heavy ion reactions.
MAD plots generally consist of groups originating from elastic, inelastic, fusion-fission and quasifission processes.Unlike the elastic and inelastic events, quasifission events overlap significantly with those from the fusion-fission making their separation impossible in most cases.However, in general, a strong component of quasifission may be inferred from the presence of mass-angle correlations in a MAD plot [7].

Results
MADs of the fragments were generated to probe the presence of processes other than fusion-fission in the 40  The width of the fragment M R distribution is obtained by fitting the distribution with a single Gaussian function.The standard deviations (σ MR ) of the Gaussian fit at different CN excitation energies are shown in Table 1.The σ MR values increase with increasing excitation energy.Even though the absence of mass-angle correlation rules out fast quasifission in the 40 Ca+ 142 Nd reaction, quasifission with longer sticking times may be contributing to larger σ MR values (σ MR ≥ 0.07 [7]) observed in this reaction.Slow quasifission could contribute to an increase in mass widths at higher energies and angular momenta, but the smallest contribution is expected at the lowest energy.Because of their longer sticking times in comparison with the fast quasifission events [7], slow quasifission is not expected to produce mass-angle correlations in the MAD plots.

Discussion
According to a recent macroscopic-microscopic finiterange liquid-drop model calculation [9], the zero angular momentum fission barrier height of 182 Hg is 10.85 MeV.Hence, the available excitation energy above the saddle point (E * s ) for 182 Hg nuclei formed in the 40 Ca+ 142 Nd reaction is 22.8 MeV at the lowest measured energy.The M R distributions from the fission of 180 Hg, 190 Hg and 195 Hg populated at similar or nearby excitation energies above the zero angular momentum saddle point, populated through the reactions 36 Ar+ 144,154 Sm [10] and 13 C+ 182 W [11,12], respectively, are compared with our present observation in Fig. 3. Different parameters of the reactions studied in this paper are given in Table 2.The fragment mass distributions reported in Ref. [10] for the 36 Ar+ 144,154 Sm reaction have been converted into M R distributions in this plot for a direct comparison.It is interesting to note that the fission from 180 Hg and 190 Hg nuclei produced in the 36 Ar+ 144,154 Sm reactions also show signatures of asymmetric mass split.However, a symmetric split has been observed in the fission of 195 Hg formed in the 13 C+ 182 W reaction, showing a transition from asymmetric to symmetric mass division with increase in neutron number in Hg isotopes.Similarly, a symmetric-peaked distribution has also been reported for the fission of 198 Hg [13].The observation of asymmetric mass division in the low energy fission of 180 Hg [4,14] in β-delayed fission experiments triggered special interest in the fission of nuclei in the neutron deficient Hg region.Soon after this observation, different theoretical explanations were put forward to explain the experimental results.Among these calculations, potential energy surface calculations [4,15] provided a qualitative explanation of the data and predicted similar observations for heavier isotopes of Hg.Microscopic calculations based on the Skyrme-HFB model [16] also reproduced the experimental observations in 180,198 Hg.Calculations based on a modified scission point model [17,18] also explained low energy fission results observed for 180 Hg.Interestingly, though based on different model assumptions, all these calculations reproduced the β delayed fission results reasonably well.
The M R distributions observed in the 40 Ca+ 142 Nd and 36 Ar+ 144,154 Sm reactions are thus compared with the results from β-delayed fission in Fig. 4. A striking feature is the similarity in mass division in all these reactions.It is reported that the asymmetric peaks in the fission of 180 Hg in Ref. [14] are centered around 80 Kr and 100 Ru, translating to M R values 0.46 and 0.54 for the light and heavy fragments, respectively.The M R peaks observed in the 40 Ca+ 142 Nd reaction are also consistent with these values.The peaks of the two Gaussian functions used to represent the mass distributions in the 36 Ar+ 144,154 Sm reactions in Ref. [10] also correspond to similar M R values, consistent with that of β-delayed fission results.
The observation of mass-asymmetric fission in the 40 Ca+ 142 Nd fusion-fission reaction appears to support the influence of shell effects up to this excitation energy.The relatively low fissility of 182 Hg suggests that the observed fission may be dominated by first chance fission of the CN itself.Fission yield calculations based on Brownian Shape Motion (BSM) by Moller [19] predicted asymmetric fission in Hg isotopes ( 176 Hg to 188 Hg) up to CN excitation energies as high as 40 MeV.Similarly, calculations based on finite-temperature density functional theory [20] also predicted the occurrence of mass-asymmetric fission in neutron deficient Hg isotopes at high CN excitation energies up to 30 MeV.We thus compared our results with the BSM predictions for the fission of 182 Hg in Fig. 5(a).Though both theoretical predictions and experimental results show similar trends in mass split, the mass centroids of the asymmetric peaks are different.Similar observations may also be made for the low energy [14] and high energy [10] fission of 180 Hg.However, the predicted results match with the experimental results for 190 Hg [10].In addition to the mismatch in mass centroids, significant difference in the FWHM of the asymmetric peaks was observed in the experimental results and BSM predictions.
On the other hand, pre-scission neutron multiplicity (ν pre ) estimates based on the systematics available in literature (ν pre =0.51 according to the systematics from Ref. [21] and 0.82 from [22]) indicate that multichance fission may be significant in the case of 182 Hg, leading to a possibility that low energy fission of 180  In a further step we used the empirical model GEF [23] to compare the experimental results observed in this work.The GEF model [23] uses a large body of experimental information, to develope an empirical, global description of fission quantities.In GEF, the quantitative predictions of fission fragment yields rely on the properties of the fragment shells that define quantum oscillators in mass asymmetry and charge polarisation on the fission path.The positions and shapes of the fission valleys of standard fission channels [24] were obtained by fitting the structures in the measured mass distributions.The potential at elongation is calculated as the sum of the macroscopic potential and the shell effects.Although GEF is not intended for nuclei lighter than Pb, the experimental M R distribution observed for the 40 Ca+ 142 Nd reaction at E * s =22.8 MeV has been compared with the GEF predictions for the fission of 182 Hg in Fig. 6 (a).The model predictions are in good agreement with the experimental results in terms of the mass centroids, peak to valley ratio and the FWHM of the mass-asymmetric peaks.The model predictions at different E * s values for the fission of 182 Hg are shown in Fig. 6 (b).It is quite clear that the distribution becomes a single Gaussian-like form at higher excitation energy for 182 Hg, resulting from the weakening of shell effects at such high excitations.The experimental M R distributions obtained for the fission of 195 Hg in the 13 C+ 182 W reaction at E * s = 23.0 and 28.6 MeV are compared with the GEF model predictions in Fig. 6 (c).The model results matches well with the experimental M R distribution predicting a much narrower M R distribution for the fission of 195 Hg compared with 182 Hg.However, GEF also predicts a slightly asymmetric mass-split for the fission of 195 Hg, which could not be explored in detail at the moment due to the limited statistics available.
Good agreement between the experimental data and GEF indicates the persistence of shell effects at excitation energies at least up to 34 MeV, consistent with the predictions of Refs.[19,20].The success of the GEF model to reproduce the experimental observables suggests that the asymmetric fission observed in the neutron deficient Hg region may also be explained using the same physics that is applicable in the fission of actinide nuclei.This needs further investigation.
From the present results for the 40 Ca+ 142 Nd reaction, it is difficult to make definitive statements about the nature of shell effects at excitation energies above E * =33.6 MeV.Unlike the observation at E * =33.6 MeV, the signature of mass-asymmetric fission is much weaker at higher excitation energies.The flat-topped M R distribution observed at E * =54.9 MeV and above may be indicating some asymmetric component underlying the dominant symmetric distribution.Such a flat-topped distribution has been represented by the sum of two Gaussian functions in Ref. [10] for the case of 36 Ar+ 144,154 Sm reactions at E * up to 65.5 and 70.5 MeV, respectively, for the fission of 180 Hg and 190 Hg nuclei.More experimental data are required at finer energy steps to conclusively establish the excitation energy dependence of mass division in the fission of neutron-deficient Hg nuclei.

Summary and conclusions
In this paper we discussed the fission fragment mass-angle and mass ratio distributions for the 40 Ca+ 142 Nd reaction at energies around the capture barrier.Fragment mass-angle and mass ratio distributions were extracted using twobody kinematics [6].The absence of a strong mass-angle correlations in the MAD clearly rules out the influence of fast quasifission in this reaction.The fission fragment M R distribution shows an asymmetric mass division The present results are compared with the fission fragment mass distributions from the 36 Ar+ 144,154 Sm and 13 C+ 182 W reactions populating 180,190,195 Hg nuclei, respectively.While the fragments from 180,190 Hg showed signatures of asymmetric mass split, a symmetric distrbution is observed for the fission of 195 Hg.While the observation of mass-asymmetric fission superficially support the existence of shell effects even at high excitation energies as claimed in [10] and predicted in Refs.[19,20], we also show empirically that the results could be explained by using a 25% fission contribution from 180 Hg.Even though the experimental results show similar trends as predicted in Ref. [19] in mass division, differences have been observed in the position of the mass centroids and FWHM of the peaks.On the otherhand, calculations based on an empirical [23] reproduced the results perfectly well, supporting the influence of shell effects at compound nuclear excitation energy at least up to 34 MeV.The success of this empirical model also hints that a global description of fission may possibly be able to represent the phenomenon of fission across the nuclear chart.

Figure 1 .
Figure 1.Experimental MAD scatter plots for the 40 Ca+ 142 Nd reaction at different beam energies.The Ec.m.V B values and CN excitation energies E * are given at the top of each plot.E * , E c.m. and V B are in units of MeV.

Figure 2 .
Figure 2. The fission M R distributions from the 40 Ca+ 142 Nd reaction at different CN excitation energies as indicated.The yields are scaled to show all energies in a single plot, scaling factors are shown inside the parantheses.

Figure 3 .
Figure 3.The scaled M R distributions of fission from different reaction populating isotopes of Hg.The excitation energy available above the zero angular momentum fission barrier (E * s

Figure 5 .
Figure 5. (a) The M R distributions of fission fragments from the 40 Ca+ 142 Nd reaction at E * =33.6 MeV compared with BSM predictions of 182 Hg [19] at E * =20 and 40 MeV.(b) M R distribution obtained by subtracting 25% contribution from the fission of 180 Hg.A Gaussian fit to this distribution is shown using the dot-dashed line (blue).Dashed line (red) represents the sum of the Gaussian fit values and 25% fission contribution from 180 Hg.
Hg may be contributing to the observed M R distribution in the 40 Ca+ 142 Nd reaction.Such a possibility is explored by first normalising the area under the M R distributions from the β-delayed fission study and 40 Ca+ 142 Nd reaction at E * =33.6 MeV and, then, subtracting a fraction of the M R distribution of 180 Hg from that of 182 Hg.It was observed DOI: 10.1051/ 03006 (2016) , Heavy Ion Accelerator Symposium 2015 123 EPJ Web of Conferences epjconf/201612303006 that subtracting a 25% contribution of fission of 180 Hg from that measured from the 40 Ca+ 142 Nd reaction leads to a distribution which can be represented by a single Gaussian centered at mass symmetry.This is shown in Fig. 5(b).While the dot-dashed curve represents the Gaussian fit to the symmetric distribution, the dashed line represents the sum of this Gaussian fit and 25% fraction of asymmetric fission from 180 Hg.

Figure 6 .
Figure 6.(a) The M R distributions of fission fragments from the 40 Ca+ 142 Nd reaction at E * s =22.8 MeV is compared with GEF model predictions.(b) GEF predictions of the M R distributions for the fission of 182 Hg at different E * s values.(c) GEF predictions of the M R distributions for the fission of 195 Hg at different E * s with peaks centered around M R values 0.45 and 0.55 at E * =33.6 MeV.These M R values are consistent with the asymmetric mass split observed in the low energy fission of180 Hg in β-delayed fission experiments.Flat-topped M R distributions have been observed at higher exciation energies, possibly indicating a small component of low E * asymmetric fission underlying a symmetric component.

Table 1 .
Single Gaussian widths (σ MR ) obtained for the M R distributions for the 40 Ca+ 142 Nd reaction at different CN excitation energies.

Table 2 .
The CN produced, CN excitation energy (E * ) and excitation energy available above the zero-angular momentum saddle point (E * s ) for different reactions studied in this paper.