New fission fragment distributions and r-process origin of the rare-earth elements
S. Goriely, J.-L. Sida, J.-F. Lemaitre, S. Panebianco, N. Dubray, S. Hilaire, A. Bauswein, H.-Thomas Janka
NNew fission fragment distributions and r-process origin of the rare-earth elements
S. Goriely, J.-L. Sida, J.-F. Lemaˆıtre, S. Panebianco, N. Dubray, S. Hilaire, A. Bauswein,
4, 5 and H.-T. Janka Institut d’Astronomie et d’Astrophysique, CP-226,Universit´e Libre de Bruxelles, 1050 Brussels, Belgium C.E.A. Saclay, Irfu/Service de Physique Nucl´eaire, 91191 Gif-sur-Yvette, France CEA, DAM, DIF, F-91297 Arpajon, France Department of Physics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece Max-Planck-Institut f¨ur Astrophysik, Postfach 1317, 85741 Garching, Germany (Dated: September 7, 2018)Neutron star (NS) merger ejecta offer a viable site for the production of heavy r-process elementswith nuclear mass numbers
A > ∼ < ∼ A < ∼ A (cid:39)
278 mass region that is responsible for the final recycling of the fissioningmaterial. Using ejecta conditions based on relativistic NS merger calculations we show that thisspecific FFD leads to a production of the A (cid:39)
165 rare-earth peak that is nicely compatible withthe abundance patterns in the Sun and metal-poor stars. This new finding further strengthens thecase of NS mergers as possible dominant origin of r-nuclei with
A > ∼ PACS numbers: 26.30.Hj,24.75.+i, 25.85.-w,26.60.Gj
Introduction. —The rapid neutron-capture process (r-process) of stellar nucleosynthesis explains the produc-tion of the stable (and some long-lived radioactive)neutron-rich nuclides heavier than iron that are ob-served in stars of various metallicities and in the so-lar system (see review of [1]). While r-process theoryhas made progress in understanding possible mechanismsthat could be at the origin of the solar-system compo-sition, the cosmic site(s) of the r-process has (have) notbeen identified yet and the astrophysical sources and spe-cific conditions in which the r-process takes place are stillamong the most longstanding mysteries of nuclear astro-physics.Progress in modelling core-collapse supernovae (SNe)and γ -ray bursts has raised a lot of excitement about theso-called neutrino-driven wind environment [1–3]. Whilethe light r-elements up to the second abundance peak( A ∼ ∼ − –10 − M (cid:12) [9–18]. This mass, combined withthe predicted astrophysical event rate ( ∼ − yr − in theMilky Way [19, 20]) can account for the majority of r-material in our Galaxy [10, 12, 17, 18, 21, 22]. Nearly all of the ejecta are converted to r-process nuclei, whoseradioactive decay heating leads to potentially observ-able electromagnetic radiation in the optical and infraredbands [22, 23] with 100–1000 times fainter peak bright-nesses than those of typical SNe and durations of onlydays [13, 17, 18, 24–26]. These “macronovae” [27] or“kilonovae” [22] are intensely searched for (with a recent,possible first success [28, 29]) and their unambiguous dis-covery would constitute the first detection of r-materialin situ.In this specific r-process scenario, the number of freeneutrons per seed nucleus reach a few hundreds. Withsuch a neutron richness, fission plays a fundamental roleby recycling the matter during the neutron irradiationand by shaping the final r-abundance distribution in the110 < ∼ A < ∼
170 mass region at the end of the neutronirradiation. The final composition of the ejecta is thenrather insensitive to details of the initial abundances andthe astrophysical conditions, in particular the mass ra-tio of the two NSs, the quantity of matter ejected, andthe equation of state (EOS) [17, 18, 30]. This robust-ness, which is compatible with the uniform, solar-likeabundance pattern of the rare-earth elements observedin metal-poor stars [31], might point to the creation ofthese elements by fission recycling in NS merger (NSM)ejecta.However, the estimated abundance distribution re-mains sensitive to the adopted nuclear models. Theejecta are composed almost exclusively of
A >
140 nuclei,and in particular the A (cid:39)
195 third r-process peak ap-pears in proportions similar to those observed in the solarsystem, deviations resulting essentially from the still diffi-cult task to predict neutron capture and β -decay rates for a r X i v : . [ a s t r o - ph . S R ] N ov exotic neutron-rich nuclei. The situation for the lighter110 < ∼ A < ∼
170 species has been rather unclear up to nowand extremely dependent on fission properties, includ-ing in particular the fission fragment distribution (FFD).In the present paper, we apply a new state-of-the-artscission-point model, called SPY, to the determinationof the FFD of all neutron-rich fissioning nuclei of rele-vance during the r-process nucleosynthesis and analyzeits impact on the r-process abundance distribution.
NS merger simulations and the r-process. —Our NSMsimulations were performed with a general relativisticSmoothed Particle Hydrodynamics scheme [18, 32, 33]representing the fluid by a set of particles with constantrest mass, whose properties were evolved according toLagrangian hydrodynamics, conserving the electron frac-tion of fluid elements. The Einstein field equations weresolved assuming a conformally flat spatial metric. Ther-abundance distributions resulting from binary simula-tions with different mass ratios or different EOSs are vir-tually identical [18]. For this reason, in the present anal-ysis only symmetric 1.35 M (cid:12) –1.35 M (cid:12) systems with theDD2 EOS [34, 35], including thermal effects and a res-olution of ∼ ∼ × − M (cid:12) . In [18, 33] moredetails are given on gross properties of the ejecta, the in-fluence of the EOS and the postprocessing for the nucle-osynthesis calculations. Note that the 1.35 M (cid:12) –1.35 M (cid:12) case is of particular interest since, according to popula-tion synthesis studies and pulsar observations, it repre-sents the most abundant systems [36].Our nuclear network calculations were performed asin [17, 37], where the reaction network, temperaturepostprocessing, inclusion of pressure feedback by nuclearheating, and the density extrapolation beyond the endof the hydrodynamical simulations are described. Thereaction network includes all 5000 species from protonsup to Z = 110 that lie between the valley of β -stabilityand the neutron-drip line. All fusion reactions on lightelements as well as radiative neutron captures, photodis-integrations, α - and β -decays, and fission processes, areincluded. The corresponding rates are based on exper-imental data whenever available or on theoretical pre-dictions otherwise, as obtained from the BRUSLIB nu-clear astrophysics library [38]. In particular, the reactionrates are estimated with the TALYS code [39, 40] on thebasis of the Skyrme Hartree-Fock-Bogolyubov (HFB) nu-clear mass model, HFB-21 [41], and the β -decays with theGross Theory 2 (GT2) [42], employing the same HFB-21 Q -values.The neutron-induced, photo-induced, β -delayed andspontaneous fission rates are estimated on the basis ofthe HFB-14 fission paths [43]. The neutron- and photo-induced fission rates were calculated with the TALYScode for all nuclei with 90 ≤ Z ≤
110 [44]. Similarly,the β -delayed and spontaneous fission rates are estimatedwith the same TALYS fission barrier penetration calcu- SF > ββ df > β (n,f) > (n, γ )( γ ,f) > ( γ ,n) Z n-drip (a) ν <33 ≤ ν <66 ≤ ν <9 ν ≥ Z N (b) FIG. 1. (a) Dominant fission regions in the (
N, Z ) plane.Nuclei with spontaneous fission being faster than β -decaysare shown by full squares, those with β -delayed fission fasterthan β -decays by open squares, those with neutron-inducedfission faster than radiative neutron capture at T = 10 Kby open triangles, and those for which photo-fission at T =10 K is faster than photo-neutron emission by closed circles.For Z = 110, β -decay processes are not calculated. (b) SPYpredictions of the average number of emitted neutrons foreach fissioning nucleus in the ( N, Z ) plane. lation. The β -delayed fission rate takes into account thefull competition between the fission, neutron and photonchannels, weighted by the population probability givenby the β -decay strength function [45]. The main fissionregions by one of the four fission processes are illustratedin Fig. 1a. SPY fission fragment distribution. —To study preciselythe impact of the nascent fragment nuclear structure onthe mass distribution, a renewed statistical scission-pointmodel, called SPY, was developed [49]. It consists ofa parameter-free approach based on up-to-date micro-scopic ingredients extracted with a mean-field descrip-tion using the effective nucleon-nucleon Gogny interac-tion [50]. This renewed version of the Wilkins fissionmodel [51] estimates first the absolute energy availablefor all possible fragmentations at the scission point fora given fissioning nucleus [49]. The main ingredient inthese calculations is the individual potential energy ofeach fission fragment as a function of its axial deforma-tion, as compiled in the AMEDEE database [50] for morethan 8000 nuclei. Once the available energies are calcu-lated for each fragmentation, a microcanonical descrip-tion including nuclear Fermi gas state densities is usedto determine the main fission fragment observables, moreparticularly mass and charge yields, kinetic energy andexcitation energy of the fragments [52]. The number ofevaporated neutrons is deduced from the mean excitationenergy of each fragment. The scission-point models [51]have shown their ability to reproduce the general trendsof the fission yields for actinides, and the SPY model has A Y i e l d [ % ] FIG. 2. FFDs from the SPY model for eight A = 278 isobars. proven its capability to describe them up to exotic nucleiin the study of the mercury isotopes [49].SPY has now been applied to all the neutron-rich nu-clei of relevance for r-process nucleosynthesis. It is foundthat the A (cid:39)
278 fissioning nuclei, which are main pro-genitors of the 110 < ∼ A < ∼
170 nuclei in the decompres-sion of NS matter, present an unexpected doubly asym-metric fission mode with a characteristic four-hump pat-tern, as illustrated in Fig. 2. Such fragment distribu-tions have never been observed experimentally and canbe traced back to the predicted potential energies atlarge deformations of the neutron-rich fragments favoredby the A (cid:39)
278 fission. The two asymmetric fissionmodes can also be seen on the potential energy surface(Fig. 3) obtained from a detailed microscopic calculation[53] for
Cf in the deformation subspace (elongation (cid:104) ˆ Q (cid:105) , asymmetry (cid:104) ˆ Q (cid:105) ). This calculation uses a state-of-the-art mean-field model with the Gogny interaction.The two fission valleys indicated by arrows in Fig. 3 leadto asymmetries similar to the distributions presented inFig. 2 obtained with SPY. The symmetric valley, cor-responding to a nil octupole moment, is disfavored bya smaller barrier transmission probability linked to thepresence of a barrier, hidden in this subspace by a dis-continuity [54].Finally, we show in Fig. 1(b) the SPY prediction of theaverage number of evaporated neutrons for each sponta-neously fissioning nucleus. This average number is seento reach values of about four for the A (cid:39)
278 isobars andmaximum values of ∼
14 for the heaviest Z (cid:39)
110 nucleilying at the neutron drip line.
Nucleosynthesis calculations. —Due to the specific ini-tial conditions of high neutron densities (typically N n (cid:39) − cm − at the drip density), the nuclear flow duringmost of the neutron irradiation will follow the neutron-drip line and produce in milliseconds the heaviest drip-line nuclei. However, for drip-line nuclei with Z ≥ FIG. 3.
Cf potential energy surface as a function of thequadrupole (cid:104) ˆ Q (cid:105) and octupole (cid:104) ˆ Q (cid:105) deformations. Bothasymmetric fission valleys are depicted by the red arrows. and recycling the heavy material into lighter fragments,which restart capturing the free neutrons. Fission recy-cling can take place up to three times before the neutronsare exhausted, depending on the expansion timescales.When the neutron density drops below some 10 cm − ,the timescale of neutron capture becomes longer than afew seconds, and the nuclear flow is dominated by β -decays back to the stability line (as well as fission and α -decay for the heaviest species). The final abundancedistribution of the 3 × − M (cid:12) of ejecta during the NSMis compared with the solar system composition in Fig. 4.The similarity between the solar abundance pattern andthe prediction in the 140 < ∼ A < ∼
180 region is remark-able and strongly suggests that this pattern constitutesthe standard signature of r-processing under fission con-ditions.The 110 < ∼ A < ∼
170 nuclei originate exclusively fromthe spontaneous and β -delayed fission recycling thattakes place in the A (cid:39)
278 region at the time all neu-trons have been captured and the β -decays dominate thenuclear flow. The A (cid:39)
278 isobars correspond to thedominant abundance peak in the actinide region dur-ing the irradiation phase due to the turn-off point atthe N = 184 drip-line shell closure and the bottleneckcreated by β -decays along the nuclear flow. The nucleithat β -decay along the A = 278 isobar fission asymmet-rically according to the SPY FFD model, as illustratedin Fig. 2, leading to a similar quadruple hump patternvisible in Fig. 4 (red squares). The asymmetric A (cid:39) A (cid:39)
278 fission-ing nuclei and hence an underproduction of the A (cid:39) -4 -3 -2 -1
80 100 120 140 160 180 200 220 240 M a ss fr ac ti on ASolar -4 -3
140 150 160 170 180
FIG. 4. Final abundance distribution vs. atomic mass forejecta from 1.35–1.35 M (cid:12)
NS mergers. The red squares arefor the newly derived SPY predictions of the FFDs and theblue circles for essentially symmetric distributions based onthe 2013 GEF model [46]. The abundances are compared withthe solar ones [48] (dotted circles). The insert zooms on therare-earth elements. semi-empirical GEF model [46], also leading to an un-derproduction of rare-earth elements, as shown in Fig. 4and also discussed in Ref. [47]. Our NSM scenario thusoffers a consistent explanation of the creation of the rare-earth elements connected to r-processing, different fromalternative suggestions for production sites of these el-ements, e.g. at freeze-out conditions in high-entropy r-process environments [55] with all the associated astro-physical problems [1–3].In addition, with the SPY FFDs the r-abundance dis-tribution is rather robust for different sets of fission barri-ers. As explained above, the 110 < ∼ A < ∼
170 abundancesoriginate essentially from the fission of the nuclei that β -decay along the A (cid:39)
278 isobars at the end of theneutron irradiation. The corresponding fissioning nucleiare all predicted by the SPY model to fission basicallywith the same doubly asymmetric distribution (Fig. 2),leading to similar r-distributions, independent of the fis-sioning element along the isobar.The emission of prompt neutrons also affects the r-abundance distribution. According to the SPY model,the fission of the most abundant nuclei around A = 278is accompanied with the emission of typically 4 neutrons(Fig. 1b). These neutrons are mainly re-captured by theabundant nuclei forming the N = 126 peak. For thisreason, not only the abundance distribution for A < ∼ A = 196 peak is shifted to higher masses by a few units.The impact, however, remains small due to the small av-erage number of emitted neutrons. This even improvesthe agreement with the solar distribution for A (cid:39)
145 and A (cid:39)
172 nuclei but distorts slightly the A = 195 peak.However, the global abundance pattern for A > -4 -3 -2
120 140 160 180 200HFB-21 & TDAFRDM & GT2D1M & GT2 M a ss fr ac ti on ASolar
FIG. 5. Same as Fig. 4 but with abundance distributions ob-tained with three additional sets of nuclear rates, namely re-action rates obtained with the D1M [56] or FRDM [57] massesand β -decay rates from the GT2 or Tamm-Dancoff approxi-mation (TDA) [58]. particular the A = 195 peak, can also be affected by thestill uncertain neutron-capture and β -decay rates. Nev-ertheless, the production of the rare-earth peak remainsqualitatively rather robust (Fig. 5), at least for the threeadditional sets of nuclear models tested here. Conclusions. —The decompression of NS matter re-mains a promising site for the r-process. This site isextremely robust with respect to many astrophysical un-certainties. We demonstrated here that the newly derivedFFD based on the SPY model can consistently explainthe abundance pattern in the rare-earth peak within thisr-process scenario, in contrast to results with more phe-nomenological models predicting symmetric mass yieldsfor the fissioning A (cid:39)
278 nuclei. Our new finding pro-vides an even stronger hint to NSMs as possibly dominantsite for the origin of
A >
140 r-nuclei in the Universe. Inparticular the robustness of the ejecta conditions and as-sociated fission recycling as well as the good quantitativeagreement of the theoretical and solar abundances arefully compatible with the amazing uniformity of the rare-earth abundance patterns observed in many metal-poorstars [31].The unexpected doubly asymmetric FFD predictedby SPY also opens new perspectives in theoretical andexperimental nuclear physics concerning specific fissionmodes related to the nuclear structure properties of ex-otic nuclei. Dynamical mean field calculations [59] shouldquantitatively confirm the fission yields predicted bySPY, and future experiments producing fission fragmentssimilar to those predicted by the doubly asymmetric fis-sion mode could reveal the nuclear properties of the cor-responding fission fragments.S.G. acknowledges financial support of F.N.R.S. and“Actions de recherche concert´ees (ARC)” from the“Communaut´e fran¸caise de Belgique”. 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