Low Energy measurement of the 96 Zr(α,n ) 99 Mo reaction cross section and its impact on weak r-process nucleosynthesis
G. G. Kiss, T. N. Szegedi, P. Mohr, M. Jacobi, Gy. Gyürky, R. Huszánk, A. Arcones
DDraft version September 29, 2020
Preprint typeset using L A TEX style emulateapj v. 08/22/09
LOW ENERGY MEASUREMENT OF THE ZR( α, N ) MO REACTION CROSS SECTION AND ITS IMPACTON WEAK R-PROCESS NUCLEOSYNTHESIS
G. G. Kiss
Institute for Nuclear Research (ATOMKI), H-4026 Debrecen, Bem t´er 18/c, Hungary
T. N. Szegedi
Institute for Nuclear Research (ATOMKI), H-4026 Debrecen, Bem t´er 18/c, HungaryUniversity of Debrecen, H-4001 Debrecen, Egyetem t´er 1, Hungary
P. Mohr
Institute for Nuclear Research (ATOMKI), H-4026 Debrecen, Bem t´er 18/c, Hungary
M. Jacobi
Institut f¨ur Kernphysik, Technische Universit¨at Darmstadt, Schlossgartenstr. 2, D-64289 Darmstadt, Germany
Gy. Gy¨urky
Institute for Nuclear Research (ATOMKI), H-4026 Debrecen, Bem t´er 18/c, Hungary
R. Husz´ank
Institute for Nuclear Research (ATOMKI), H-4026 Debrecen, Bem t´er 18/c, Hungary
A. Arcones
Institut f¨ur Kernphysik, Technische Universit¨at Darmstadt, Schlossgartenstr. 2, D-64289 Darmstadt, GermanyGSI Helmholtzzentrum fr Schwerionenforschung GmbH, Planckstr. 1, D-64291 Darmstadt, GermanyHelmholtz Forschungsakademie Hessen f¨ur FAIR, GSI Helmholtzzentrum fr Schwerionenforschung, 64291 Darmstadt, Germany
Draft version September 29, 2020
ABSTRACTLighter heavy elements beyond iron and up to around silver can form in neutrino-driven ejecta incore-collapse supernovae and neutron star mergers. Slightly neutron-rich conditions favour a weakr-process that follows a path close to stability. Therefore, the beta decays are slow compared to theexpansion time scales, and ( α ,n) reactions become critical to move matter towards heavier nuclei.The rates of these reactions are calculated with the statistical model and their main uncertainty, atenergies relevant for the weak r-process, is the α +nucleus optical potential. There are several sets ofparameters to calculate the α +nucleus optical potential leading to large deviations for the reactionrates, exceeding even one order of magnitude. Recently the Zr( α ,n) Mo reaction has been identifiedas a key reaction that impacts the production of elements from Ru to Cd. Here, we present the firstcross section measurement of this reaction at energies (6.22 MeV ≤ E c . m . ≤ Z = 44 −
48 isotopesunder different neutrino-driven wind conditions.
Subject headings: nucleosynthesis, weak r-process, cross section measurement, optical model, statisticalmodel INTRODUCTION
Half of the stable isotopes heavier than iron are pro-duced by the rapid neutron capture process (r-process)when neutron captures are faster than beta decays. Thisprocess requires extreme neutron densities and explo-sive environments, therefore the two favourite candidatesare: core-collapse supernovae, where neutron stars areborn, and neutron star mergers. After a successful core-collapse supernova, there is a neutrino-driven wind con-
Electronic address: [email protected] sisting of matter ejected by neutrinos emitted from thehot proto-neutron star. For many years, this was the pre-ferred scenario for the r-process, even if the conditionswere only slightly neutron rich or proton rich and thusnot enough for the r-process (for a review see Arcones &Thielemann (2013) and reference therein). In contrast,the r-process has been observed in neutron star merg-ers. After the gravitational wave detection of GW170817(Abbott et al. 2017), there was an observation of the kilo-nova light curve produced by the radioactive decay of theneutron-rich nuclei formed during the r-process (Metzger a r X i v : . [ nu c l - e x ] S e p et al. 2010; Abbott et al. 2017). Also Sr was directly ob-served in the kilonova spectrum (Watson et al. 2019).Still there are many open questions concerning the as-trophysical site and the nuclear physics involved.Observations of the oldest stars in our galaxy and inneighbour dwarf galaxies (see e.g., Frebel 2018; Reichertet al. 2020a; Cˆot´e et al. 2019) indicate that the r-processoccurred already very early, even before neutron starmergers could significantly contribute. This points torare supernovae, and recent investigations have shownthat magneto-rotational supernovae could account forthis early r-process contribution (see e.g., Winteler et al.2012; Nishimura et al. 2017; M¨osta et al. 2018; Reichertet al. 2020b). Another hint from observations is thatthe elements between Sr and Ag may be produced by aseparate or additional process to the r-process (Travaglioet al. 2004; Qian & Wasserburg 2000; Montes et al. 2007;Hansen et al. 2014). One possibility to explain these ob-servations is the neutrino-driven ejecta from core-collapsesupernovae (Qian & Woosley 1996; Wanajo et al. 2011;Arcones & Montes 2011; Arcones & Bliss 2014).In neutrino-driven, neutron-rich supernova ejecta, theweak r-process can form the lighter heavy elements be-tween Sr and Ag (see e.g., Bliss et al. 2018). Initiallythe matter is close to the neutron star and very hot,therefore a nuclear statistical equilibrium (NSE) is es-tablished. As matter expands the temperature dropsand individual nuclear reactions become important. Blisset al. (2018) have investigated all possible conditions ex-pected in neutrino-driven, neutron-rich supernova ejectaand identified those where nuclear reactions are impor-tant. In the weak r-process, the nucleosynthesis pathis determined by (n, γ )-( γ ,n) equilibrium and stays closeto stability. Consequently, compared to the expansiontimescale, β decays are too slow to move matter to higherproton numbers and ( α ,n) and (p,n) reactions becomeimportant as they are faster (Bliss et al. 2017).Therefore, in order to use observations to understandthe astrophysical conditions where lighter heavy elementsare produced, one has to reduce the nuclear physicsuncertainties of the key reactions. In a broad sensi-tivity study (Bliss et al. 2020), several ( α ,n) reactionshave been identified as critical because of their impacton the abundances under different astrophysical condi-tions. These reactions rates are calculated from the crosssections computed with the Hauser-Feshbach statisticalmodel which relies on nuclear physics inputs. Recently, aseries of sensitivity calculations were performed to eval-uate the theoretical uncertainty of these cross sectioncalculations (Pereira & Montes 2016; Mohr 2016; Blisset al. 2017). These works identified different α +nucleusoptical potential parameter sets ( α OMP’s) as the mainsource of uncertainty. The difference between the crosssection based on various α OMP’s can exceed even an or-der of magnitude (Pereira & Montes 2016). Therefore,experiments are critical to reduce the uncertainties ofthe rates. Low energy alpha-induced reaction cross sec-tion measurements were frequently used to constrain theparameters of the α OMP’s used in astrophysical calcu-lations (Sauerwein et al. 2011; Scholz et al. 2014; Kisset al. 2015). However, such precise experimental data,reaching sub-Coulomb energies are typically missing forisotopes located at or close to the weak r-process path(Bliss et al. 2017).
TABLE 1Decay parameters of the reaction product Mo and itsdaughter Tc m , taken from Browne & Tuli (2017);Goswamy et al. (1992). Residual Half- Energy Relativenucleus life [h] [keV] intensity [%] Mo 65.924 ± ± ± ± ± ± Tc m ± ± Here we contribute to a more reliable weak r-processcalculation by measuring the Zr( α ,n) Mo reactioncross section for the first time at energies relevant for theweak r-process nucleosynthesis and by using the precisedata to evaluate the α OMP’s used in the nucleosynthe-sis network. This reaction is one of the bottlenecks thatsensitively affects the production of nuclei between 44 ≤ Z ≤
47 (Bliss et al. 2020). We demonstrate that reducingthe nuclear physics uncertainty to a 30% level is criticaland enough to get accurate abundance predictions.This paper is structured as follows. In Sect. 2, wepresent our experimental approach. The results includ-ing a theoretical analysis are in Sect. 3, and the impactof those on the weak r-process is in Sect. 4. Finally, weprovide a short summary and conclusions are given inSect. 5. EXPERIMENTAL APPROACH
The cross section measurement was carried out at theInstitute for Nuclear Research (Atomki) using the acti-vation technique. The targets were prepared by electronbeam evaporation of metallic Zr onto 6 µ m thick Al foilbacking. Similarly to our previous cross section measure-ments (Korkulu et al. 2018; Kiss et al. 2018), the absolutenumber of target atoms was determined with the Ruther-ford Backscattering technique using the Oxford-type Nu-clear Microprobe Facility at Atomki (Huszank et al.2016). The energy and the diameter of the beamspotof the He + beam provided by the Van de Graff acceler-ator was 2.0 MeV and 2.5 µ m, respectively. Two Siliconion-implanted detectors (50 mm sensitive area and 18keV energy resolution) were used to measure the yield ofthe backscattered ions, one of them was placed at a scat-tering angle of 165 ◦ and the other one was set to 135 ◦ .Target thicknesses between 1.23 x 10 and 1.54 x 10 Zr atom/cm were found with an uncertainty of typically5%.The Zr targets were irradiated with α beams from theMGC cyclotron of Atomki. The energy of the α beamwas between E lab = 6.5 MeV and E lab = 13.0 MeV, thisenergy range was scanned with energy steps of 0.5 MeV- 1.0 MeV. The length of the irradiations varied between t irrad = 6 h to t irrad = 48 h with beam currents of 0.5 - 1.4 µ A. Longer irradiations were carried out at lower energiesto (partially) compensate the lower cross sections. Thenumber of the impinging α particles was obtained fromcurrent measurement. After the beam-defining aperture,the chamber was insulated and secondary electron sup-pression voltage of −
300 V was applied at the entranceof the chamber. From the last beam-defining aperturethe whole chamber served as a Faraday cup. The col- -3 -2 -1 . k e V . k e V . k e V . k e V . k e V . k e V . k e V C oun t s [ / ( k e V x s e c ) ] E [keV]
100 200 300 400 500 600 700 80010 -3 -2 -1 . k e V E = 9.0 MeVdetB, close geometry
E [keV]
E = 11.0 MeVdetA, far geometry . k e V Fig. 1.— γ -ray spectra, measured for one hour, taken on detA, t waiting = 9.5 h after the 11 MeV irradiation (left panel); and on detB,t waiting = 62.6 h after the 9 MeV irradiation (right panel). The peaks used for the analysis are marked. lected charge was measured with a current integrator,the counts were recorded in multichannel scaling mode,stepping the channel in every minute to take into accountthe possible changes in the beam current.The cross sections were measured using the activationtechnique (Gy¨urky et al. 2019). The decay parametersof the Mo reaction product are summarized in Table 1.The β − decay of Mo is followed by the emission of nu-merous, relatively intense γ -rays, which were detectedby two Germanium detectors: a Low Energy PhotonSpectrometer (detA) and a 50% relative efficiency HPGedetector (detB), both equipped with a 4 π lead shield.DetA has low laboratory background (about 0.585 1/sin the 50-2000 keV energy region), its resolution is ex-cellent, but with increasing γ -ray energies its detectionefficiency decreases sharply. Accordingly, this detectorwas used to measure the yield of the E γ = 40.58 keV, E γ = 140 .
51 keV (belonging to the daughter isotope Tc m ), E γ = 181 .
07 keV and E γ = 366 .
42 keV tran-sitions. The laboratory background of detB is higher(about 5.071 1/s in the 100-2000 keV energy region),however, its detection efficiency is much higher for thehigher energy γ -rays, therefore, this detector was usedto measure the yield of the E γ = 739 .
50 keV and E γ = 777 .
92 keV γ -rays, also. After the irradiations, t waiting ≈ . γ -countings were two-to-six days in the caseof each irradiation and the spectra were saved in everyhour. Typical off-line γ spectra, measured with detA(left panel) and detB (right panel), can be seen in Fig. 1.The activity of the samples irradiated at E lab = 8 MeVand higher were measured with both detectors, the re-sulting cross sections were found to be always consistent.The half-life of the Mo is known from large numberof experiments with uncertainty less than 0.01% (Stone2014). The activity of the samples irradiated with alphabeams of E lab = 12 MeV and E lab = 13 MeV energieswere measured for more than 2 weeks, the deadtime andrelative intensity corrected peak areas were fitted withexponential using the least square method. The resultedhalf-lives, having χ always below 1.3, are in agreement with the literature value within their uncertainties, whichproves that no other γ transitions pollutes the peaks usedfor cross section determination.The low yields measured in the present work necessi-tated the use of short source-to-detector distances for the γ -countings carried out after the irradiation of the Zr tar-gets with alpha beams of E lab = 9 . Co,
Ba,
Cs,
Eu, and
Am sources, the abso-lute detector efficiency was measured in far geometry: at15 cm and 21 cm distance from the surface of detA anddetB, respectively. Since the calibration sources (espe-cially
Ba,
Eu) emit multiple γ -radiations from cas-cade transitions, in close geometry no direct efficiencymeasurement was carried out. Instead, in the case ofthe high energy irradiations (at and above 10 MeV) theyield of the investigated γ -rays was measured both inclose and far geometry. Taking into account the timeelapsed between the two countings, a conversion factorof the efficiencies between the two geometries could bedetermined and used henceforward in the analysis. RESULTS AND THEORETICAL ANALYSIS
The measured Zr( α ,n) Mo cross section values arelisted in Table 2. The effective center-of-mass energy inthe second column takes into account the energy loss ofthe beam in the target. The quoted uncertainty in the E c . m . values corresponds to the energy stability of the α -beam and to the uncertainty of the energy loss in the tar-get, which was calculated using the SRIM code (Ziegleret al. 2008). The activity of several targets were mea-sured using both detA and detB, in these cases the crosssections were derived from the averaged results weightedby the statistical uncertainty of the measured values.The uncertainty of the cross sections is the quadraticsum of the following partial errors: detection efficiency(5%), far-to-close detection efficiency correction factor( ≤ ≤ ≤ TABLE 2Measured cross sections of the Zr( α ,n) Mo reaction.The last five rows show the average results (weighted bythe statistical uncertainties) of the measurements carriedout at the same energy. E c . m . Cross section[MeV] [mbarn]6.22 ± ± · − ± ± · − ± ± · − ± ± · − ± ± · − ± ± · − ± ± · − ± ± · − ± ± · − ± ± · − ± ± · ± ± · ± ± · ± ± · ± ± · ± ± · ± ± · ± ± · − ± ± · − ± ± · − ± ± · − ± ± · ± ± · made.The Zr( α ,n) Mo reaction was already studied inseveral works (Chowdhury et al. 1995; Pupillo et al. 2015;Hagiwara et al. 2018; Murata et al. 2019). However, be-cause the literature data do not reach the lowest energies,and because of the significant scatter of the literaturedata below 11 MeV, the further analysis is restricted toour new experimental results.The new experimental data for the Zr( α ,n) Mo re-action have been analyzed in the statistical model (SM),complemented by the recently suggested pure barriertransmission model (PTBM) (Mohr et al. 2020). In aschematic notation, the cross section of an α -induced( α , X ) reaction is given by σ ( α, X ) ∼ T α, T X (cid:80) T i = T α, × b X (1)with the transmission coefficients T α, of the incoming α -particle, T i for the outgoing particles ( i = γ, p, n, α, n ,etc.), and the branching ratio b X = T X / (cid:80) i T i for thebranching into the X channel. Usually, the transmissions T i are calculated from optical model potentials for theparticle channels and from the γ -ray strength functionfor the ( α , γ ) capture channel. For further details, seee.g. Rauscher & Thielemann (2000); Rauscher (2011).For the Zr( α ,n) Mo reaction in the energy range un-der study (see Fig. 2) the neutron channel is dominatingbecause the proton channel is closed or suppressed bythe Coulomb barrier and the γ -channel is typically muchweaker than the neutron channel. Thus, the branchingratio to the neutron channel is b n ≈
1, and the ( α ,n) crosssection is almost identical to the total α -induced reactioncross section σ reac . From Eq. (1) it can be seen that the( α ,n) cross section is essentially defined by the trans- -1 Present work McFadden [30] Demetriou-I [31] PBTM [36] Avrigeanu 2014 [32] PBTM x 0.65 S f a c t o r [ M e V b ] E c.m. [MeV] Zr( ,n) Mo Fig. 2.—
Comparison of experimental and theoretical astrophys-ical S-factors of Zr( α ,n) Mo reaction as a function of the energy(the inset shows the same data on linear scale). Excellent agree-ment with χ /N < mission T α, which in turn depends only on the chosen α OMP. Other ingredients of the statistical model affectthe branching ratios b X , but have only minor influence onthe ( α ,n) cross section because of b n ≈
1. For complete-ness we note that below the ( α ,n) threshold at 5.1 MeV,we find b γ ≈
1, and the ( α , γ ) cross section approachesthe total cross section σ reac .It is obvious from Fig. 2 that predictions of the ( α ,n)cross sections in the SM vary over more than one orderof magnitude at the lowest energies whereas at energiesabove 10 MeV most predictions agree nicely. For betterreadability of Fig. 2, we restrict ourselves to the pre-sentation of the widely used α OMP’s by McFadden &Satchler (1966), Demetriou et al. (2002), and Avrigeanuet al. (2014); the latter is the default α OMP in TALYS(which is a widely used nuclear reaction code; the cal-culations shown in Fig. 2 were carried out using version1.9).The reason for the wide range of predictions was iden-tified and discussed in Mohr et al. (2020). The usual SMcalculations show a dramatic sensitivity to the tail of theimaginary potential. To avoid this sensitivity, an alter-native approach was suggested in Mohr et al. (2020) touse the PBTM model for the calculation of the total re-action cross section σ reac . The Supplement of Mohr et al.(2020) provides the new ATOMKI-V2 α OMP which re-produces measured ( α ,n) cross sections over a wide rangeof masses and energies with deviations below a factor oftwo. This holds also for the present Zr( α ,n) Mo re-action (see Fig. 2). However, there is a slight overesti-mation of the experimental results over the full energyrange under study (dotted line in Fig. 2). Therefore thecalculation from the ATOMKI-V2 potential was scaledby a factor of 0.65 to obtain best agreement with the newexperimental data. These scaled cross sections were usedto calculate the astrophysical reaction rate N A (cid:104) σv (cid:105) (seebelow).Although the scaling factor of 0.65 is within the esti-mated uncertainty of the new approach of Mohr et al.(2020), a brief discussion of this factor is appropriate:( i ) Technically, the ATOMKI-V2 potential is a com-plex α OMP which approximates the calculations in thePBTM with small deviations. In the present case, theATOMKI-V2 calculation of the total cross section σ reac is about 10% higher than the underlying PBTM calcula-tion.( ii ) The ATOMKI-V2 potential distinguishes betweensemi-magic and non-magic target nuclei; the latter (like Zr in this work) require a deeper potential with volumeintegrals of J R = 371 MeV fm whereas the semi-magictargets are characterized by a lower J R = 342 . .Depending on energy, the lower J R for semi-magic tar-gets increases the effective barrier and thus reduces σ reac by about 15 − Zr( α , α ) Zr elas-tic scattering at 35 MeV (Lund et al. 1995; Lahanaset al. 1986) requires volume integrals around J R ≈ , thus indicating that Zr behaves more like asemi-magic nucleus. As a consequence, the usage of theglobal value J R = 371 MeV fm instead of the locallyoptimized J R ≈
350 MeV fm leads to an overestimationof σ reac by about 10 − i ) and ( ii ) providesa reasonable explanation for the obtained scaling factorof 0.65 for the ATOMKI-V2 result using the global J R =371 MeV fm for non-magic target nuclei.Finally, the agreement of the scaled ATOMKI-V2 cal-culation with the experimental data is excellent with χ per point of about 0.6 whereas calculations with the dif-ferent α OMPs within TALYS show a different energy de-pendence (see Fig. 2) and cannot reach χ /N < N A (cid:104) σv (cid:105) .The lowest experimental data point at about 6.2 MeVis located only 1.1 MeV above the ( α ,n) threshold at5.1 MeV. The astrophysical reaction rate N A (cid:104) σv (cid:105) resultsfrom the folding of a Maxwell-Boltzmann velocity dis-tribution with the energy-dependent cross section σ ( E ).At higher temperatures, the folding integral is essentiallydetermined by the new experimental data. At lowertemperatures, the calculation of the rate has to rely onthe calculated cross section between the threshold at 5.1MeV and the lowest data point at 6.2 MeV. Because ofthe excellent reproduction of the energy dependence ofthe ( α ,n) cross section we estimate an overall uncertaintyof less than 30% for all temperatures. The obtained re-action rates are listed in Table 3. Compared to previ-ously recommended rates, e.g. from REACLIB (REA-CLIB 2015; Cyburt et al. 2010), STARLIB (STARLIB2017; Sallaska et al. 2013), or NON-SMOKER (Rauscher& Thielemann 2000) which vary by more than one or-der of magnitude, the uncertainty of the present recom-mended rate is reduced significantly to about 30%. IMPACT ON WEAK R-PROCESS
We investigate the impact of the new experimentaldata on the nucleosynthesis of lighter heavy elementsin neutron-rich supernova ejecta. We use astrophysicaltrajectories based on the neutrino-driven wind model ofBliss et al. (2018). Each trajectory corresponds to a com-bination of astrophysical parameters which are expectedfor neutrino-driven winds. The 36 trajectories under con-
TABLE 3Recommended astrophysical reaction rate N A (cid:104) σv (cid:105) of the Zr( α ,n) Mo reaction. T N A (cid:104) σv (cid:105) (cm s − mole − )1.0 2.09 × − × − × − × − × − × − × − sideration (see Table I of Bliss et al. (2020)) cover elec-tron fractions between 0.40 and 0.49, entropies between32 and 175 k B per nucleon, and expansion timescalesfrom 9.7 to 63.8 ms. In that work, the authors identifiedthe conditions for which ( α ,n) reactions have a significantimpact on the final abundances. Under such conditions,Bliss et al. (2020) used 36 trajectories to identify key( α ,n) reactions. The reaction Zr( α ,n) Mo is in theirlist of key reactions. Our nucleosynthesis calculations areperformed with the WinNet reaction network (Winteleret al. 2012). Reaction rates are taken from the JINAREACLIBV2.0 (REACLIB 2015; Cyburt et al. 2010) li-brary except for ( α ,n) reactions for which TALYS 1.6with the GAOP α OMP was used (for more details seeBliss et al. (2018, 2020)). Replacing the Zr( α ,n) Moreaction rate with the values from Tab. 3 results in a re-duction of the final abundances by more than 10% in 17and by more than 20% in 6 of the 36 trajectories. Moreimportantly, the reduced reaction-rate uncertainty leadsto a significant improvement in the accuracy of the nucle-osynthesis predictions. Following Bliss et al. (2020) weestimate the uncertainty of the Zr( α ,n) Mo reactionrate calculated with the GAOP with the factors 0.1 and10 and the uncertainty of the updated (PBTM) reactionrate with 30% (see Sect. 3).
25 30 35 40 45 50 55 Z l o g ( Y ) MC1MC8 MC14MC18
Fig. 3.—
Elemental abundances for four trajectories from Blisset al. (2020). The lightly shaded regions correspond to the un-certainties due to variations of the previously used Zr( α ,n) Moreaction rate by factors 10 and 0.1. The solid bands correspond tothe uncertainties due to variations of the updated reaction rate by30%.
In Fig. 3, we present the impact of the reduced uncer-tainty of the new experimentally based reaction rate forfour representative trajectories from Bliss et al. (2020).Changes of the final abundances resulting from the vari-ation of the GAOP and PBTM Zr( α ,n) Mo reactionrate are represented by the shaded and solid bands, re-spectively (note that the figure shows solid colored bandsand not thick lines). If large amounts of elements heavierthan Tc are produced (e.g., trajectory MC1 in Fig. 3),the abundances are not sensitive to Zr( α ,n) Mo, be-cause the nucleosynthesis path runs along more neutron-rich nuclei. Trajectories that do not produce any ele-ments beyond Mo (e.g., trajectory MC14 in Fig. 3) arenot sensitive either. For roughly half of the 36 trajecto-ries, the variation of the previously used Zr( α ,n) Moreaction rate leads to a significant spread (up to a factorof 6 between the lower and upper estimate) in the ele-mental abundances between Ru and Xe (e.g., trajectoriesMC8 and MC18 in Fig. 3). In all of these trajectories,the lower uncertainty of the PBTM reaction rate leadsto greatly improved accuracy in the final abundances.In Fig. 4, we show the abundances for trajectory MC8in detail. The orange and blue bands represent the un-certainty as estimated for the GAOP and the PBTMreaction rate, respectively. The dashed and dotted linesin the upper panel show the abundance pattern calcu-lated with upper and lower uncertainty estimation of theGAOP reaction rate, respectively. In the bottom panel,we show the uncertainty for each element relative to theabundances calculated with the unvaried GAOP reactionrate, Y base . Since Zr( α ,n) Mo forms a bottleneck forthis trajectory, an increase of the reaction rate resultsin higher abundances of elements heavier than Tc. ThePBTM reaction rate is slightly lower than the GAOP re-action rate and thus the abundances are slightly lowerthan Y base . An exception is the abundance of Rhodiumwhich is not sensible to Zr( α ,n) Mo. Rhodium pos-sesses only one stable isotope,
Rh, which in all tra-jectories is mainly produced by the decay of
Nb. Itsabundance is therefore not correlated to Zr( α ,n) Mo.In summary, the reduction of the uncertainty to 30%is sufficient to get very accurate abundances. This accu-racy is crucial for comparing theoretical nucleosynthesiscalculations with observations. A similar reduction of theuncertainties for other reactions is necessary to reliablycompare nucleosynthesis calculations with observations.The PBTM should allow for such a reduction of uncer-tainties; a detailed investigation is in preparation. Thiswill allow to constrain the astrophysical site of the weakr-process and to further understand core-collapse super-novae and the origin of the lighter heavy elements. SUMMARY AND CONCLUSIONS
In a recent sensitivity study of the weak r-process (Blisset al. 2020), the Zr( α ,n) Mo reaction was identified asa bottleneck for the nucleosynthesis between rutheniumand cadmium, i.e. for nuclei with Z = 44 −
48. Thetypically assumed uncertainties of ( α ,n) reaction ratesof a factor of 10 lead to significant uncertainties for thenucleosynthetic yields in the weak r-process of about afactor of 5; thus the nuclear uncertainties prevent anyrobust astrophysical conclusion.In the present study, the cross section of the Zr( α ,n) Mo reaction has been measured for the firsttime from energies close above the reaction threshold at5.1 MeV up to about 12.5 MeV, thus covering the regionrelevant for the weak r-process. The chosen activationtechnique provides the total production cross section of l o g ( Y ) MC8
GAOP rate uncertaintyPBTM rate uncertainty44 45 46 47 48 Z Y / Y b a s e Fig. 4.—
Influence of the Zr( α ,n) Mo rate on trajectory MC8.Upper panel: Abundance uncertainty of elements between Ru andCd. The orange and blue bands correspond to the previously used(GAOP) and the updated (PBTM) reaction rate, respectively. Thedashed and dotted lines show the abundance pattern calculatedwith upper and lower uncertainty estimation of the GAOP rate,respectively. Lower panel: Abundance uncertainties relative to theunvaried GAOP reaction rate, Y base , in a linear scale. Mo which is an excellent basis for the calculation ofthe astrophysical production rate of molybdenum from Zr by α -induced reactions. The high precision experi-mental data have been analyzed in the statistical model,using global α OMP’s and complemented by the recentlysuggested PBTM model. It was found that the PBTMmodel — re-scaled by 0.65 — excellently reproduces thenew experimental data. The best-fit from the scaledPBTM was used to calculate the astrophysical reactionrates as a function of temperature. For the full tem-perature range of the weak r-process, the uncertainty ofthe reaction rate could be drastically reduced from theusually assumed factor of 10 down to about 30%.A repetition of the nucleosynthesis calculations ofBliss et al. (2020) with the new experimentally based Zr( α ,n) Mo reaction rate and its small uncertaintiesleads to very well-constrained nucleosynthesis yields forthe Z = 44 −
48 range. As the PBTM is typically able topredict α -induced reaction cross sections with uncertain-ties below a factor of two, a re-calculation of the full weakr-process network with updated rates from the PBTMwill lead to more robust nucleosynthesis yields which inturn should enable a major step towards stringent con-straints for the astrophysical conditions and the site ofthe weak r-process.The authors thank Julia Bliss, Fernando Montes, JorgePereira, and Zs. F¨ul¨op for valuable discussions. Thiswork was supported by NKFIH (NN128072, K120666,K134197), and by the ´UNKP-20-5-DE-2 New NationalExcellence Program of the Ministry of Human Capac-ities of Hungary. G. G. Kiss acknowledges supportfrom the J´anos Bolyai research fellowship of the Hun-garian Academy of Sciences. MJ and AA were sup-ported by the ERC Starting Grant EUROPIUM-677912, Deutsche Forschungsgemeinschaft through SFB 1245,and Helmholtz Forschungsakademie Hessen fr FAIR.This work has benefited from the COST Action ChETEC(CA16117) supported by COST (European Cooperationin Science and Technology). The nucleosynthesis com-putations were performed on the Lichtenberg High Per-formance Computer (TU Darmstadt).-induced reaction cross sections with uncertain-ties below a factor of two, a re-calculation of the full weakr-process network with updated rates from the PBTMwill lead to more robust nucleosynthesis yields which inturn should enable a major step towards stringent con-straints for the astrophysical conditions and the site ofthe weak r-process.The authors thank Julia Bliss, Fernando Montes, JorgePereira, and Zs. F¨ul¨op for valuable discussions. Thiswork was supported by NKFIH (NN128072, K120666,K134197), and by the ´UNKP-20-5-DE-2 New NationalExcellence Program of the Ministry of Human Capac-ities of Hungary. G. G. Kiss acknowledges supportfrom the J´anos Bolyai research fellowship of the Hun-garian Academy of Sciences. MJ and AA were sup-ported by the ERC Starting Grant EUROPIUM-677912, Deutsche Forschungsgemeinschaft through SFB 1245,and Helmholtz Forschungsakademie Hessen fr FAIR.This work has benefited from the COST Action ChETEC(CA16117) supported by COST (European Cooperationin Science and Technology). The nucleosynthesis com-putations were performed on the Lichtenberg High Per-formance Computer (TU Darmstadt).