The beta-Oslo method: experimentally constrained ( n,γ ) reaction rates relevant to the r -process
A. C. Larsen, S. N. Liddick, A. Spyrou, M. Guttormsen, F. L. Bello Garrote, J. E. Midtbø, T. Renstrøm
TThe beta-Oslo method:experimentally constrained ( n, γ ) reaction ratesrelevant to the r -process A. C. Larsen , S. N. Liddick , A. Spyrou , , , M. Guttormsen ,F. L. Bello Garrote , J. E. Midtbø , and T. Renstrøm Department of Physics, University of Oslo, Norway, [email protected] , National Superconducting Cyclotron Laboratory, Michigan State University, USA, Department of Chemistry, Michigan State University, USA, Department of Physics and Astronomy, Michigan State University, USA, Joint Institute for Nuclear Astrophysics, Michigan State University, USA
Abstract.
Unknown neutron-capture reaction rates remain a significantsource of uncertainty in state-of-the-art r -process nucleosynthesis reac-tion network calculations. As the r -process involves highly neutron-richnuclei for which direct ( n, γ ) cross-section measurements are virtuallyimpossible, indirect methods are called for to constrain ( n, γ ) cross sec-tions used as input for the r -process nuclear network. Here we discussthe newly developed beta-Oslo method, which is capable of provding ex-perimental input for calculating ( n, γ ) rates of neutron-rich nuclei. Thebeta-Oslo method represents a first step towards constraining neutron-capture rates of importance to the r -process. Keywords:
Nucleosynthesis, r -process, neutron-capture reaction rates,level density, γ -decay strength On August 17, 2017, the LIGO and Virgo gravitational-wave detectors mea-sured, for the first time, a direct signal from two colliding neutron stars [1].Follow-up measurements with telescopes sensitive to electromagnetic radiationconfirmed that the rapid neutron-capture process ( r -process) [2,3] had indeedtaken place in the collision ( e.g. , Ref. [4]). Hence, a long-standing question innuclear astrophysics was at least partly solved; one astrophysical r -process siteis now confirmed.However, the uncertain nuclear-physics input remains a huge obstacle in mod-eling the r -process yields in large-scale nucleosynthesis network calculations [5,6].The r -process involves highly neutron-rich nuclei, where there is a severe lack ofrelevant nuclear data such as masses, β -decay rates and neutron-capture crosssections. As shown in, e.g. , Ref. [5], one cannot rely on the assumption of ( n, γ )–( γ, n ) equilibrium for typical r -process temperatures and neutron densities in a r X i v : . [ nu c l - e x ] A ug A.C. Larsen et al. a neutron-star merger event, at least not at all times and for all trajectoriesas demonstrated in Ref. [7]. As a consequence, neutron-capture rates will im-pact the final abundances and must be included in the nucleosynthesis calcula-tions. Moreover, it is an unfortunate fact that different theoretical predictionsfor neutron-capture rates may vary by several orders of magnitude.In this work, a recently developed method to address this issue is presented:The beta-Oslo method [8,9] provides data on the nuclear level density and av-erage γ -decay strength of moderately neutron-rich nuclei. These quantities arecrucial input for calculations of neutron-capture rates [5]. The beta-Oslo methodpresents a first step towards constraining neutron-capture rates of importanceto the r -process. The principles behind the beta-Oslo method are very similar to those of the Oslomethod, which will be briefly outlined in the following. The starting point is aset of excitation-energy tagged γ -ray spectra containing γ rays from all possiblecascades originating at a given initial excitation energy. In the Oslo method,this has been achieved by charged-particle– γ -ray coincidence measurements. The γ -ray spectra are corrected for the NaI detector response using the methoddescribed in Ref. [10], and the distribution of primary γ rays is determined by aniterative subtraction technique [11]. Finally, the nuclear level density (NLD) and γ -ray strength function ( γ SF) are simultaneously extracted from the primary γ -ray distribution [12] and normalized to auxiliary data [13]. The level-density and γ -strength data can then be used as input for ( n, γ ) cross-section calculations asshown, e.g. , in Ref. [14].In 2004, a surprising increase in the low- γ -energy region of the γ -decaystrength of , Fe was discovered [15]. This upbend has later been discoveredin many nuclei and has been confirmed with an independent measurement tech-nique [16,17] and shown to be dominantly of dipole nature [18,19]. If the upbendis indeed present in very neutron-rich nuclei such as those involved in the r -process, it could increase ( n, γ ) reaction rates by 1-2 orders of magnitude [20].Hence, it is critical to measure the γ SF in neutron-rich nuclei to see whetherthe upbend exists in these exotic systems. To address this question and to pro-vide indirect measurement of ( n, γ ) reaction rates, the beta-Oslo method [8] wasrecently invented.The method exploits the high Q -value for beta decay of neutron-rich nuclei,so that excited states in a broad energy range will be populated in the daughternucleus. Further, using a segmented total-absorption spectrometer such as theSuN detector [21], one obtains the sum of all γ rays in the cascades giving theinitial excitation energy, while the single segments give the individual γ rays. Inthis way, one can generate a matrix of excitation-energy tagged γ -ray spectraand apply the Oslo method to extract NLD and γ SF for the daughter nucleus.The beta-Oslo method was first applied on Ga beta-decaying into Ge [8].The experiment was performed at the National Superconducting Cyclotron Lab- he beta-Oslo method 3 (MeV) g E ) - ) ( M e V g f ( E - - - - Ni SuN data, Ni, Rossi et al. exp. error bandQRPAQTBA (a) K) T (10 -
10 1 10 ) - m o l - s ( c m æ v sÆ A N Exp. JINA REACLIB JINA REACLIB x 10 (0.1) (b)
Fig. 1. (Color online) Gamma-decay strength function of Ni [23] (a) and the Ni( n, γ ) Ni reaction rate from Ref. [9] (b), where we follow Ref. [24] and comparewith the JINA REACLIB rate [25] (dashed line) scaled with a factor of 10 up anddown (light-shaded band). oratory (NSCL), Michigan State University (MSU), using a 130-MeV/nucleon Ge beam producing Ga by fragmentation on a thick beryllium target. The Ga secondary beam was implanted on an Si surface-barrier detector mountedinside SuN, which was used to measure the subsequent γ -ray cascades in thedaughter nucleus Ge. The resulting data set enabled a significant improve-ment on the Ge( n, γ ) Ge reaction rate, which has not been measured directlyand so relied on purely theoretical estimates.Further, the beta-Oslo method has recently been applied on the neutron-rich Co isotope, beta-decaying into Ni [9]. The experiment was performedat NSCL, MSU, where a primary 140-MeV/nucleon Kr beam hit a berylliumtarget to produce Co that was delivered to the experimental setup, this timewith a double-sided Si strip detector inside SuN. Again, SuN was used to detectthe γ -ray cascades from the daughter nucleus, Ni. Complementary data fromGSI on the Ni γ SF [22] above the neutron separation energy allowed for awell-determined absolute normalization of the full γ SF as shown in Fig. 1a. Thelow-energy upbend is indeed present in the Ni γ SF and is likely due to stronglow-energy M Ni data, the Ni( n, γ ) Ni reaction rate is deduced with an un-certainty of a factor ∼ − A.C. Larsen et al.
The beta-Oslo method is capable of extracting NLDs and γ SFs of neutron-richnuclei, enabling an indirect way to experimentally constrain ( n, γ ) reaction ratesof relevance to the r -process. So far, three reaction rates have been inferred: Ge( n, γ ) Ge [8], Ni( n, γ ) Ni [9] and Ni( n, γ ) Ni [26]. In the future, manymore rates will be constrained with this technique, to the benefit of r -processnucleosynthesis calculations and our understanding of NLDs and γ SFs.
Acknowledgments
A. C. L. gratefully acknowledges funding through ERC-STG-2014 under grantagreement no. 637686. Support from the ChETEC COST Action (CA16117),supported by COST (European Cooperation in Science and Technology) is ac-knowledged. This work was supported by the National Science Foundation underGrants No. PHY 1102511 (NSCL) and No. PHY 1430152 (JINA Center for theEvolution of the Elements), and PHY 1350234 (CAREER). This material isbased upon work supported by the US Department of Energy National NuclearSecurity Administration through under Award No. de-na0003180, No. DE-NA-0000979 and No. DE-NA-0003221.
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