Evidence for the general dominance of proton shells in low-energy fission
K. Mahata, C. Schmitt, Shilpi Gupta, A. Shrivastava, G. Scamps, K.-H. Schmidt
EEvidence for the general dominance of proton shells in low-energy fission
K. Mahata,
1, 2, ∗ C. Schmitt, † Shilpi Gupta,
1, 2
A. Shrivastava,
1, 2
G. Scamps, and K.-H. Schmidt Nuclear Physics Division, Bhabha Atomic Research Centre, Mumbai - 400085, India. Homi Bhabha National Institute, Anushaktinagar, Mumbai - 400094, India. Institut Pluridisciplinaire Hubert Curien, 23 rue du Loess, B.P. 28, 67037 Strasbourg Cedex 2, France Institut d’Astronomie et d’Astrophysique, Universite Libre de Bruxelles,Campus de la Plaine CP 226, 1050 Brussels, Belgium Rheinstraße 4, 64390 Erzhausen, Germany (Dated: August 3, 2020)A regular pattern, revealing the leading role of the light-fragment nuclear charge, is found to emergefrom a consistent analysis of the experimental information collected recently on low-energy asymmet-ric fission of neutron-deficient nuclei around lead. The observation is corroborated by a theoreticalinvestigation within a microscopic framework, suggesting the importance of proton configurationsdriven by quadrupole-octupole correlations. This is in contrast to the earlier theoretical interpre-tations in terms of dominant neutron shells. The survey of a wider area of the nuclear chart bya semi-empirical approach points to the lack of understanding of the competition between the dif-ferent underlying macroscopic and microscopic forces in a quantitative manner. Combined withpreviously identified stabilizing forces, the present finding shows a striking connection between the“old” (actinide) and “new” (pre-actinide) islands of asymmetric fission which could steer the strivefor an unified theory of fission.
PACS numbers:
Introduction.
Fission is among the most dramaticexamples of nuclear decay whereby a heavy nucleus splitsinto two fragments of comparable mass. Its discoveryin the 1930’s came as a surprize to the community, andrecognition required the irrefutable chemical and physi-cal evidence to be established [1, 2]. The fission processis important for various fields, including fundamentalphysics, astrophysics, and applied science [3].Although fission was unexpected, an explanation forits high probability in heavy nuclei came quickly. Itappeared that this re-arrangement of more than 200nucleons - which is a priori a complex many-bodyquantum-mechanical problem, can be explained in anessentially classical way [4, 5], in analogy with the divi-sion of a macroscopic liquid drop (LD) like a living cell.However, the LD model could not explain why, at lowexcitation energy, typical actinides predominantly splitin an asymmetric manner [6, 7]. The explanation had toawait the late 1950’s [8], and namely the introductionby Strutinsky of a method accounting for shell-structureeffects in the calculation of the potential energy of thefissioning-system [9], creating a complex landscape. Itwas then realized [10, 11] that strong fragment-drivenmicroscopic stabilization effects can supersede the gentlyevolving compound nucleus (CN) macroscopic energy,and dig deep valleys towards scission.Natural candidates for producing fission valleys arethe “standard” magic numbers [12]. For fission of ∗ Electronic address: [email protected] † Electronic address: [email protected] actinides around uranium, fragment mass distributionsof limited resolution (which constituted the main sourceof information for several decades) were interpreted asbeing due to the influence of shell effects, and namelyneutron shells [3]. The heavy-fragment mass distributionexhibiting a broad and robustly sitting structure around A H ≈
140 was found to be made up of two “standard”contributions: the so-named S A H ≈ S A H ≈ N = 82 spherical, and a N ≈
88 deformed,shell [13], respectively.At the beginning of the century, a novel experimentalmethod by Schmidt et al. [14] revealed, however, thatthe A H ≈
140 peak is characterized by a constancyof the heavy-fragment charge number at Z H ≈ S S S T KE , a lowneutron multiplicity for the heavy partner, and its yieldincreases with N CN /Z CN approaching that of Sn[3, 16, 17]. These observations suggested that the S Z = 50 shell aidedby N = 82. It is supported by the abrupt transitionfrom asymmetric to symmetric fission while approaching Fm [18, 19]. An interpretation for the S β stability, namely in Tl, was established inlight-ion induced fission by Itkis et al. [7]. The recentobservation of almost exclusively asymmetric fission inthe neutron-deficient
Hg, for which two doubly-magic Zr fragments were expected [21] has led to a resurgence a r X i v : . [ nu c l - t h ] J u l of interest in fissioning pre-actinides, and measurementsof additional systems [22–28] ascertained the occurenceof asymmetric fission over an enlarged domain aroundlead.Finally, a consistent understanding of the fragment prop-erties running from the “old” (actinide) to the “new”(pre-actinide) region of asymmetric fission is still missing[3, 29]. Advanced theories [20, 29–31] have proposeddifferent mechanisms to find an analogous origin. In thisletter, the experimental information collected duringthe last few years in the neutron-deficient region aroundlead is analyzed in detail with the aim to elucidate itsasymmetric fission properties, address the question ofits origin, and seek a connection between the “old” andthe “new” islands of asymmetric fission. Method.
The low excitation energy required for studyingasymmetric fission of neutron-deficient pre-actinides canbe ideally reached in β -delayed and electromagnetic-induced fission. Unfortunately, the number of systemsaccessible to these approaches is limited. A worldwideeffort is therefore invested since a few years based onthe alternative fusion-induced fission approach. Thedrawback of the method is the excitation energy im-parted to the CN, which implies a weakening of possibleshell-driven effects. The experimental informationfrom the various approaches are analyzed in a commonframework. The asymmetric components, clearly visiblein the β -delayed [21, 22] and electromagnetic-induced[23] fission experiments, in terms of the mean positionof the light and heavy partners, in either mass A L,H orcharge Z L,H depending on availability, are deduced fromthe measured fragment A (or Z ) distributions. As forthe fusion-induced fission approach, the location of theasymmetric peaks was determined in the correspondingreferences [24–28] based on the adjustment of the massdistribution by a superposition of Gaussian functions.The mean neutron and/or proton numbers of thefission partners are then derived in this work underthe Unchanged-Charge-Density (UCD) assumption [32].The uncertainty (wherever applicable) introduced bythis assumption was taken to be 0.8 unit. Results.
To elucidate the nature of the asymmetricsplit in the pre-actinide region, the deduced Z L,H and N L,H are displayed in Fig. 1 as a function of,respectively, the total number of available protons( Z CN ) and neutrons ( N CN ) in the fissioning system.Distinctly different behaviors, in the way the neutronsand protons are shared, are observed. Interestingly, thelight-fragment charge Z L is seen to be confined withina narrow range around 36. Comparison between the χ of the free (full) and horizontally-constrained (dashed)adjustment of the Z L points shows that the slope isnot very significant statistically. On the contrary, theheavy-fragment charge Z H exhibits a much stronger
30 35 40 45 5076 78 80 82 84 86 88 Z L o r Z H Z CN 30 35 40 45 5076 78 80 82 84 86 88 30 35 40 45 5076 78 80 82 84 86 88Slope χ Z H ± L ± L N L o r N H N CN Pt Au Hg Hg Hg Tl Po 40 45 50 55 60 65 7095 100 105 110 115 120 125 Hg Po Po Rn 40 45 50 55 60 65 7095 100 105 110 115 120 125Slope χ N H ± L ± Hg Tl Tl Bi Bi FIG. 1: Mean (a) proton Z L ( H ) and (b) neutron N L ( H ) num-bers of the light (heavy) fragment as a function of fission-ing system Z CN and N CN , respectively, from fusion- (red), β -delayed- (blue) and electromagnetic-induced (green) fis-sion [7, 21–28]. The best fits and Z L = 36 are shown as con-tinuous and dashed lines, respectively. dependence on Z CN , while both N L,H increase mono-tonically with increasing number of neutrons N CN to beshared.It is evident from the rather stable location of Z L ,inferred from the present investigation involving alarge diversity in ( A CN , Z CN ), that the light-fragmentproton configuration plays the leading role in governingasymmetric fission of neutron-deficient nuclei aroundlead. This is at variance with previous interpretationwhich suggested the leading role played by neutrons (see e.g. Refs. [23, 30, 31, 33]). A preliminary survey [29]based on four data points suggested that Z L indeed playsa specially intriguing role. Though no preference forspecific neutron sharing can be observed, it is interestingto note in Fig. 1(a) that the Z L values for N L (cid:38)
50 areconsistently higher ( ≈
37) than those ( ≈
35) for N L <
50 (see also Fig. 2). This is the primary reason for theobserved small slope in Z L as a function of Z CN . Comparison with theory.
State-of-the-art modelcalculations in the field provide a reasonable descriptionof asymmetric fission of
Hg [31, 35–37]. Ichikawaand Moller [30], based on a macroscopic-microscopicapproach, attribute the observed mass asymmetry toa shell gap developing at the outer saddle point inthe neutron sub-system. Using the microscopic energydensity functional (EDF) framework, Scamps andSimenel [31] have concluded the dominance of octupoleeffects, in most cases driven by neutron configurations.Another interpretation [36] relate the asymmetric splitsto prescission configurations involving molecular struc-tures, and namely a spherical Zr.For the systems presented in this letter we have per-formed calculations within the quantum-based EDFtheory of Ref. [31]. The experimental Z L ( H ) and N L ( H ) are compared in Fig. 2 with the predicted correspondingmost probable values as determined by the bottom ofthe asymmetric fission valley just before scission. Forodd-nuclei, the calculation corresponds to the averagefrom the neighboring even-even systems. A reasonablygood agreement between the experimental data andtheory is observed. In particular, the relative constancyof Z L is reproduced, highlighting the dominance ofproton configurations over the neutron effects proposedin Ref. [31]. Interestingly, the calculation seems also toexhibit a bunching of Z L into two subgroups, dependingon whether N L is below or above ≈
50. In Ref. [31],a detailed analysis of neutron-deficient system (namely
Pt) identified a shell gap at Z L = 34 for N L <
50 caused by a stabilized large quadrupole-octupoledeformation at scission from the single particle energylevels of Se . Intrigued by the present observation,a similar detailed analysis was performed for a lessneutron-deficient system i.e. , Pb. Another shell gapwas seen to be present at Z L = 38 when N L > Sr with the nascent light fragment infission of Pb. The last row of the figure displays themagnitude of the (c) proton and (d) neutron shell gap δ for this fragment in the ( β , β ) deformation plane.Interestingly, even though a large shell gap for N = 56 ispresent at smaller deformations ( β ∼ Z = 38 gap is found to dominate for the identified scissionshape. This corroborates that stabilized deformedproton configurations play the dominant role in decidingthe fission partition in pre-actinides, where theory wasoriginally [31] anticipating neutrons to play the leadingrole. Fission-fragment properties over the nuclear chart.
The pronounced double-humped mass distribution of
Hg being reminiscent of the distribution measuredaround uranium, it is very intriguing to search for aconnection between the “old” and “new” isolated regionsof asymmetric fission.The evolution of the fragment mass distribution asmeasured across the nuclear chart for low-energy fissionof isotopes between platinium ( Z CN =78) and ruther-fordium ( Z CN =104) is illustrated in Fig. 3. To coveran as wide as possible domain, the results from variousexperimental methods are included. That implies somespread ( ∼ Z=34Z=50 N=56N=50 N=52 Neutrons P r o t on s Rn Po Po Z=38 Po Bi Bi Tl Tl Tl Hg Hg Hg Hg Au Pt Pb Sr (a)(b) (d)(c) FIG. 2: (a) Comparison between the experimental Z L ( H ) and N L ( H ) values (filled black symbols) and calculations (corre-sponding open symbols) with the EDF framework of Ref. [31].The blue and the red colors represent compact and elongatedshapes of the fragments, respectively. The average experi-mental trends in Z L for N L below and above ≈
50 are shownin black dashed lines. (b) Identification of the nascent lightfragment with the quadrupole-octupole deformed Sr den-sity profile (green contour) in the energetically most favorablescission shape of Pb (black contour). Proton Z = 38 (c)and neutron N = 56 (d) shell gap δ in the ( β , β ) plane.Blue crosses correspond to the scission shape of (b). Experimentally, an asymmetric fission component startsto be visible in the actinide region for A CN above ≈ A CN ≈ Sn in the heaviest transfermiums.At the left of the domain (from radon to radium), sym-metric fission prevails for the lightest actinides due to thedominant influence of the macroscopic potential whichoutweights the Z H quantum effect that governs S S Z L ≈ Pt
180 182 184 186 188 190 192 194 196 198179 Au
181 183 185 187 189 191 193 195 197 199180 Hg
182 184 186 188 190 192 194 196 198 200181 Tl
183 185 187 189 191 193 195 197 199 201190 Pb
192 194 196 198 200 202191 Bi
193 195 197 199 201 203192 Po
194 196 198 200 202 204193 At
195 197 199 201 203 205194 Rn
196 198 200 202 204 206205 Fr Ra
220 222 224 226 228 230 232 234219 Ac
221 223 225 227 229 231 233 235220 Th
222 224 226 228 230 232 234 236221 Pa
223 225 227 229 231 233 235 237230 U
232 234 236 238 252 Cf
254 256253 Es
255 257254 Fm
256 258255 Md
257 259256 No
258 260259 Lr Rf -3 -2 -1
70 80 90 100 110 120 130 140 Po S S N e w s t ab ili z a t i on Y i e l d ( % ) Fragment Mass (u)N=126 Z=82
FIG. 3: Experimental fragment mass distributions across the nuclear chart [7, 14, 21–28, 42, 43] at low energy fission (blackhistograms). Wherever the fragment Z was measured, mass was obtained under the UCD assumption. The calculations bythe code GEF2019/V1.1 (red full lines) are done at the actual E ∗ for the measured systems. For fusion-fission, the GEFresult obtained at low energy is shown (black full dots), extrapolated from the overall reasonable description by the model ofmeasurements done at intermediate energy [28]. The inset shows the multi-Gaussian fit, using the “old” and “new” fissionmodes, to the experimental mass distribution of Po at an excitation energy 9.5 MeV above the fission barrier [7], see thetext. The red dashed line represent the fit without the “new” mode.
In the absence of calculations by a fundamentaltheory over the wide domain of Fig. 3, we consider thesemi-empirical GEneral Fission model (GEF2019/V1.1)[17, 29]. The GEF formalism casts the essential ideasabout the physics of fission, including the new stabiliza-tion in the preactinide region, into simplified equationswith a global set of parameters, obtained by fittingbenchmark experimental data. The calculated massdistributions are shown in Fig. 3 with red full lines.Overall, the model performs impressively well; in par-ticular, the most neutron-deficient pre-actinides, heavyactinides and the fermium region are nicely described.Thus, its predictions in the pre-actinide region, wherethe experimental information is still limited, can beconsidered as of reliable guidance for future studies.However, in the region of most neutron-deficient radiumto thorium, GEF fails to reproduce the experimentalobservations, indicating that the competition betweenthe structural effect(s) at play in a specific region and the macroscopic force is not fully understood yet. Thedetailed theoretical models [39–41] also fail to reproducethe experimental observations in this region.Since quantum effects are a property of the nucleus per se , if the nuclear structure of the nascent fragmentsindeed plays a key role, analogous stabilizations must be at play in the pre- and actinide islands. The mani-festation of a specific configuration in fission yields of agiven system is then a matter of competition. A weakpersistence of the S S Bi and
At was indeed seen by Itkis etal. [7], progressively dying out with increasing neutron-deficiency. The observation of sizeable asymmetriccomponents more close to symmetric split [7] was earlierattributed to neutron shells [33]. According to theoutcome of the present investigation, this finding isinstead proposed to be governed by the influence of thehere-evidenced Z L stabilization, and which is aided byspecific N configurations with increasing N CN [13, 33].The inset of fig. 3 shows that the experimental data on Po [7], which is ideally situated at the crossroads ofthe old and new islands, can be accurately describedonce all the identified effects, which we attribute toproton configurations, are taken into account.
30 35 40 45 50 55 60 75 80 85 90 95 100'New': Pre-actinide 'Old': ActinideS1S2Z ≈ S y m m e t r i c s p l i t ( Z C N / ) Z L o r Z H Z CN FIG. 4: Evolution of the average Z L ( H ) positions for the asym-metric fission channel as a function of Z CN from above rare-earth to very heavy elements. For clarity, isotopes of a sameelement are shifted according to mass. The points are fromRefs. [7, 15, 18, 19, 21–28] and therein. Finally, the evolution of the Z L ( H ) peak positions fromabove rare-earth to very heavy elements is presentedin Fig. 4, pointing to a natural connection between thetwo islands of asymmetry. As discussed earlier, in thepre-actinide region the light fragment position remainsfixed at Z ≈
36, and the heavy fragment charge increasessteadily till it merges with the S S S Z CN . It isinteresting to note that the role reversal of the light andheavy fragment occurs exactly at the boundary betweenpre-actinides and actinides. The observed geometricconnection between these two islands establishes thegeneral dominance of proton shells in low-energy fission.It raises fundamental questions like “Why is the influenceof the protons so dominant in the sharing of nucleons infission?”, “Is the neutron subsystem strongly disturbedby the neck, while the protons are pushed away into thefragments by the Coulomb repulsion allowing specificstabilized configurations to manifest?”. The presentfinding emphasizes the need for further experimentalstudies, both near the reversal boundary and towardsthe limits. On the low Z CN side, it would in particularbe interesting to see if fission becomes symmetric inthe region around neutron-deficient hafnium ( Z CN =2 × Z CN side, the abrupt resurgence of predominantly symmetricfission was already seen in heavy fermium-like elements.For still larger Z CN , linear continuity would suggest another role reversal, the light fragment formation beingthis time driven by the standard ( S S
2) fissionmodes. Such a picture was recently predicted within amacroscopic-microscopic prescission point model [44].Dynamical calculations based on either a microscopicmean-field [45] or a macro-microscopic [46] approachinstead predict a more asymmetric partitioning relatedto
Pb cluster radioactivity, and the matter is vividlydebated [47]. It is interesting to note that, for thesuper-heavy nuclei, the lead fragment cluster would beassociated with a light partner having Z L ≈ Conclusion.
The consistent analysis of the experi-mental information on fission of neutron-deficient nucleiaround lead reveals the leading role played by the lightfragment proton configuration, which is in contrast tothe predicted dominance of neutron shells in previoustheoretical studies. Detailed theoretical investigationusing the microscopic EDF framework attribute theexperimental observation to shell stabilizations at Z= 34 and 38 associated with more elongated shape( β (cid:38) N L <
50 and more compact shape( β (cid:46) N L (cid:38)
50, respectively. Combininga light-fragment-driven stabilizing effect identified inthis work with previously established leading effects, astriking connection between the old and new islands ofasymmetric fission is found to hold, explaining the maintrends from above rare-earth to very heavy elementfission in an essentially “simple” way for the first time,and establishing the general dominance of proton shellsin low-energy fission. Large-scale calculations within asemi-empirical model suggest that a major deficiency ofcurrent understanding is in the complex and quantitativeinterference of the various macroscopic and microscopicforces. The experimental evidence made available inthis work is essential for addressing this question, andguiding the necessary development towards a unifiedtheory of fission.
Acknowledgements