Korneev, I Y

Panov, I

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PoS(NIC-IX)156Fission recycling in the r-process and formation ofthe second peak with A ∼ 130I.V.Panov∗Institute for Theoretical and Experimental Physics, B. Cheremushkinskaja 25, Moscow, 117259,Russia.E-mail: Igor.Panov@itep.ruI.Yu.KorneevInstitute for Theoretical and Experimental Physics, B. Cheremushkinskaja 25, Moscow, 117259,Russia.E-mail: chronomaster@inbox.ruWe discuss the influence of mass predictions and mass distribution of fission products on theformation of heavy elements on the final stages of the r-process in a very high neutron densityenvironment (e.g. neutron star mergers), when the recycling of the r-process due to fission hasoccurred. Different evolution models as well as observations give the evidence of the existenceat least two different astrophysical scenario for the r-process. All the models can be dividedby duration of neutron exposition into two groups, in which the r-process nucleosynthesis isresponsible for the formation of different nuclei. Scenario, in which the long-time solution isrealized can be main for the formation of the most heavy nuclei. In such a scenario the importantrole belongs to fission, which is responsible in part to the recycling r-process into the regionof nuclei with A= 120-140. But the utilization of new mass predictions and consistent reactionrates in the r-process calculations leads to the strong disagreement with observations, especiallyfor nuclei in the vicinity of second peak at the abundance curve. We showed that the agreementbetween calculations and observations can be achieved due to prompt fission neutrons, consideredas a part of the model of mass distribution of fission fragments.International Symposium on Nuclear Astrophysics — Nuclei in the Cosmos — IXJune 25-30 2006CERN, Geneva, Switzerland∗Speaker.c© Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. http://pos.sissa.it/PoS(NIC-IX)156Fission recycling... I.V.Panov1. r-process in transuranium region and mass predictions.The fission recycling is expected to be of significance [1] when the r-process duration becomeslong enough to transform the major part of seeds into the transuranium nuclei and to give back thefission fragments into the r-process.As a result of long duration of the r-process (long-time solution [1]) fission recycling occursand fission products became new seeds with masses in the vicinity of the second peak on the r-element abundance curve and quasi equilibrium in formation of abundances between second peakand fission region can be reached. In this case the mass distribution of fission products (along withthe consistent nuclear data such as the mass excess, fission barriers and reaction rates) is importantfor the production of nuclei with A∼130.As a model realizing the long-time solution we used one of the model calculations of neutronstar merger [2] with the average initial value of neutron excess, defined by Ye=0.1. In the r-processprocessing for this model the number of species due to fission recycling was approximately dou-bled.In our r-process calculations, along with the neutron rates [5, 4] we use new set of fissionrates [3]. The fission barrier predictions, used in calculations of the fission rates [3], were based onthe new improvement of Extended Thomas-Fermi model with Strutinsky integral (ETFSI) [8], orThomas-Fermi model [6], and mass predictions in accordance with [7, 9]. These data unfortunatelymade worse the agreement between observations of nuclear abundances and calculations, especiallyfor mass region 120 < A < 140 and strong shift of the calculated second peak on the abundancecurve from position around A∼130 in the region of bigger masses occurs (Fig.1) in compare withprevious calculations [11], where the agreement with observations was good enough. The explana-tion is rather obvious - in comparison to the previously used mass formulae [13, 14], based on Hilfet al. mass predictions [13] and FRDM rates [12] the utilization of discussed consistent mass andfission barrier predictions (ETFSI or Thomas-Fermi) shifts the neutron drip line in the direction ofheavier masses. For example, the mass prediction of [13] defines the atomic mass of the heaviestCf isotope A=279, while the other mass model discussed above (ETFSI) predicts the existence ofCf isotopes heavier than A=300.Problem is that for very high neutron density environments, when the r-process passes along(or near) the neutron drip-line, even the mass of light fission fragment when new mass predictions[6, 8] is applied can be greater than 130. Previously introduced mass distribution of fission frag-ments in the model of binary fission [10] was sufficiently good for getting the agreement betweencalculations and observation of heavy element abundances when FRDM mass predictions wereused. In case when new mass predictions is applied, the neutron drip-line (and the r-process pathalso) turns out to be shifted to the region of more heavier isotopes.The previous calculations of the r-process used a very simple models of binary fission, whenonly two fragments were taken into account in model of symmetric [5] or asymmetric [1] fissionand prompt fission neutrons were not taken into account. As a result, the r-process in actinoideregion goes on nuclei with atomic masses 280-300 instead of 250-260 when HM barrier and masspredictions were used [15].When the calculations of the r-process with new rates but with old model of mass distributionof fission products have been done, the average masses of the or fission fragments increase, mostly2PoS(NIC-IX)156Fission recycling... I.V.Panovexceed 130 and the position of the second peak on the calculated abundance curve does not re-produce the observed one. One of the possible explanation of the shift - incomplete description ofmass distribution of fission fragments. Adopted in our previous works [11, 10, 3] model of fissionproducts mass distribution, included in part the symmetric fission into to equal fission fragmentsfor all nuclei with atomic masses A > 260, was not contradict the experimental data, thou did nottake into account the prompt fission neutrons. But for up-to-date nucleosynthesis calculations withnew nuclear rates, mass excesses and fission barriers predictions the introduction of prompt fissionneutrons into the model of fission products mass predictions is urgent and should remove away "theexcess of mass" and restore the agreement between calculations and observations.-7-6-5-4-3-2Lg YA100 150 200AFigure 1: Calculated r-process abundances, used FRDM-data (line) and ETFSI mass-predictions (dashedline); circles - ss-abundance. Simple mass distribution model without prompt neutrons is used.2. Mass distribution of fission fragments and calculations.Previously [10] it was shown that combination of symmetric and asymmetric fission applied tothe model of binary fission gave better agreement with observations especially with utilization massdistribution of Itkis et al. [18] for asymmetric fission instead of the expansion mass distributionfor U235 for all nuclei [1]. Only two fission products were considered neglecting prompt fissionneutrons with "averaged" values of fission product masses, defined as A1 = 130,Z1 = 52− (Z f −3PoS(NIC-IX)156Fission recycling... I.V.Panov80)∗2/20 and A2 =A f −A1,Z2 = Z f −Z1 in case when atomic number of mother nucleus A f < 260and symmetric fission otherwise. But for the r-process modelling with rates on the base of new masspredictions this model turns out too reductive.According to the nuclear systematics [19, 20, 21] the multiplicity of prompt neutrons increaseswith increasing of both atomic number and mass number. The simple model of binary fission, whenonly fission fragments were considered we enriched by the emission of prompt neutrons.In our present calculations we also added prompt fission neutrons into the mass model distri-bution and increased the number of fission products up to 40 daughter nuclei, with weight functionsof isotope yields based on nuclear systematics. Thus we considered (Z f ,A f )→∑i, j pi j ∗ [(Zi,Ai)+(Z j,A j)+νi j ∗n], where ∑i, j pi j = 1 and Z f = Zi+Z j, A f = Ai+A j+νi j for any i, j. Neutron mul-tiplicity per fission νi j is the linear function of A f and A f −Z f . It is equal neutron multiplicity forexperimentally known nuclei νp ≈ 2− 4 and is extrapolated into neutron rich region up to valuesν ≈ 20 near neutron drip-line. The extreme number of free neutrons is in agreement with publishedresults [16] of neutron multiplicities, based on semi-empirical Monte-Carlo calculations [17].-7-6-5-4-3-2Lg YA100 150 200AFigure 2: r-process abundances: circles - ss-abundance; line - present calculations with mass distributionmodel included prompt and delayed neutrons. ETFSI mass and rates predictions are used.The details of fission of very neutron rich nuclei are not known, because such nuclei can not beinvestigated experimentally and theory predictions have a very short range. It is difficult to say whatkind of emission - prompt or delayed neutrons will be important during fission of such an exotic4PoS(NIC-IX)156Fission recycling... I.V.Panovnuclei. But no doubts the neutrons should be emitted - mass predictions show that fission fragmentsafter the fission of very neutron rich nuclei in number of cases are unbound and only evaporationof neutrons or other light particles can lead to the bound nuclear configurations. For simplicity weconsider all neutrons are prompt, because this proposition does not influence significantly upon ther-process yields.Described above model of mass distribution of fission fragments with taking into accountprompt fission neutrons was included in our calculations and received r-element abundances agreewell with the observations (Fig.2). Of course the extrapolation accuracy of calculated neutronmultiplicity in the region of very neutron rich nuclei may be not very high, but it is the problemof all nuclear data for experimentally unknown nuclei. Only the development of theory and futureexperiments can clarify the problem.3. ConclusionsIn numerical calculations of the r-process it was shown that utilization of self-consistent nu-clear data (mass predictions and reaction rates on the base of ETFSI or Thomas-Fermi models)and simple model of binary fission leads to the disagreement between observations and calculatedabundances.When the fission model was enriched by taking into account the neutron multiplicity, themasses of fission fragments decreased and agreement between observations and calculations wasrestored. For the majority cases at least one of the fragments became lighter than 130 and recyclingof the r-process occurs into the region before the second peak, that restored the agreement withobservations for the nuclear yields in the vicinity of A ∼ 130.Consideration of detailed mass distribution with taking into account up to 20 different speciesfor every fission product leads to smoothing effect of yields for nuclei around 130 and below. Theutilized model of mass distribution is confirmed by detailed calculations of fission product massdistribution for different nuclei, at least for atomic mass numbers A≥ 260 [16]. We consider thefurther understanding of mass distribution of fission fragments will lead to the more accurate fissionmodel. In asymptotic case this model should approach the mass distribution of experimentallyknown nuclei.Acknowledgments. The authors thank E. Kolbe, K.-L.Kratz, K.Langanke, G.Martinez-Pinedo,P.Möller D.K. Nadyozhin, B. Pfeiffer, T. Rauscher, F.-K. Thielemann for useful discussions. Thiswork was supported in part by grant RFBR 04-02-16793 and grant SNSF No. IB7320-110996.References[1] P.A. Seeger, W.A. Fowler, D.D. Clayton, Suppl., Nucleosynthesis of heavy elements by neutroncapture. Astrophys. J., Suppl. 97, 121 (1965).[2] C. Freiburghaus, S. Rosswog, F.-K. Thielemann, R-Process in Neutron Star Mergers. Astrophys. J.Lett. 525, L121 (1999).[3] I.V. Panov, E. Kolbe, B. Pfeiffer, T. Rauscher, K.-L. Kratz, F.-K. Thielemann, Calculations of fissionrates for r-process nucleosynthesis. Nuclear Physics A. 747, 633 (2005).5PoS(NIC-IX)156Fission recycling... I.V.Panov[4] T. Rauscher, F.-K. Thielemann, Astrophysical Reaction Rates From Statistical Model Calculations.Atomic Data and Nuclear Data Tables. 75, 1 (2000).[5] J.J. Cowan, F.-K. Thielemann, J.W. Truran, The R-process and nucleochronology. Phys. Rep. 208, 267(1991).[6] W.D. Myers, W.J.Swiatecki, Thomas-Fermi fission barriers. Phys. Rev. C. 60, 014606-1 (1999).[7] W.D. 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Fission recycling in the r-process and formation of the second peak with A ~ 130.

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