Goriely, Stéphane

Hayakawa, Takehito

Mohr, Peter

Shizuma, Toshiyuki

DI-fusion

The s-process branching at 186Re revised

Mohr, P

Goriely, S

Shizuma, T

Hayakawa, T

CERN Document Server

PoS(NIC-IX)142The s-process branching at 186Re revisedP. Mohr∗Diakoniekrankenhaus, D-74523 Schwäbisch Hall, GermanyE-mail: WidmaierMohr@compuserve.deS. GorielyInstitute d’Astronomie et d’Astrophysique, Universite Libre de Bruxelles, BelgiumT. Shizuma and T. HayakawaAdvanced Photon Research Center, JAERI, JapanRecent experimental data for the 187Re(γ ,n)186Re reaction are reviewed, and the contributionof the (8+) isomer in 186Re is discussed. Statistical model calculations are used to derive the186Re(n,γ)187Re capture cross section from the photodisintegration data, and σMACS = 1070±370 mb is obtained at kT = 30 keV. The s-process branching at 186Re remains small.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)142s-process branching at 186Re revised P. Mohr1. IntroductionThe s-process branching at 186Re is important for the understanding of the s-process nucleo-synthesis pattern in this mass region, and it affects the 187Re-187Os cosmochronology [1, 2]. Adirect measurement of the neutron capture cross section of 186Re is extremely difficult becauseof its short half-life of t1/2 = 3.72 d. Instead, two recent experiments have measured the inversephotodisintegration cross section of 187Re(γ ,n)186Re, and statistical model calculations were usedto derive the 186Re(n,γ)187Re capture cross section [2, 3]. Here we compare the experimentalapproaches and discuss the reliability of the extraction of (n,γ) cross sections from experimental(γ ,n) data. Special attention is given to the role of the (8+) isomer in the photodisintegrationreaction which is located in 186Re at E = 149 keV with the much longer half-life of t1/2 = 2.0×105 y. It has been shown that the role of the (8+) isomer in the 185Re(n,γ)186Re capture reactionremains negligible because of the minor population in the (n,γ) reaction [4].2. Available experimental data of 187Re(γ ,n)186ReThree data sets exist for the 187Re(γ ,n)186Re reaction: bremsstrahlung photons and directneutron detection were used for measurements around the giant dipole resonance (GDR) by [5].Measurements above the threshold at Sn = 7.363 MeV up to about 11 MeV were performed usingmonochromatic photons and direct neutron detection [2], and [3, 6] have used bremsstrahlung forphotoactivation measurements from threshold to about 10 MeV. The results are shown in Fig. 1.8 9 10 11E (MeV)050100150(mb)Muller 2004Goryachev 1973Shizuma 20058 9 10 11E (MeV)-1001020304050(mb)(data with E < 10 MeV)0 = 107 99 mb; p = 1.90(all data points)0 = 1256 858 mb; p = 3.63Sn(eff) = Sn + 149 keVFigure 1: Experimental data for the 187Re(γ ,n)186Re reaction (cross section data [2, 5] and a parametrizationof the cross section [6]) compared to statistical model calculations (black lines) with various parameter setsfrom [2, 7] (left). Difference ∆σ between the direct measurements of [2] and the photoactivation data of[6] (right); the difference may be attributed to the population of the (8+) isomer in 186Re (see text). Theanalysis of [3] combines the direct data of [5] (including the isomer contribution) and photoactivation data(excluding the isomer contribution); it is thus questionable and not shown in this figure.There are a priori two arguments for a noticeable contribution of the (8+) isomer in the187Re(γ ,n)186Re reaction. (i) In the 185Re(γ ,n)184Re reaction a significant isomer population of2PoS(NIC-IX)142s-process branching at 186Re revised P. Mohrabout 20 % around 10 MeV has been reported in [6]; the same spins and parities are involved inboth reactions: Jpi (187Reg.s.)= Jpi (185Reg.s.)= 5/2+, the lowest states in 184Re and 186Re have lowspins and negative parity, and there is a 8(+) isomer at E = 188 keV in 184Re and a (8+) isomerin 186Re at E = 149 keV. So one expects a similar isomer contribution in both reactions. (ii) Themeasured average neutron energy remains below 1 MeV in the 187Re(γ ,n)186Re reaction [2] up toEγ = 11 MeV, and thus 186Re is produced at excitation energies of a few MeV at higher photonenergies. Here a sufficient number of states with higher spins and significant decay branches to the(8+) isomer can be expected.In [6] an upper limit for the decay activity of the (8+) isomer of ract = Aiso/Ag.s. = 10−5 isderived from the measured spectra. Using the half-lives of the ground state and the (8+) isomer, thisupper limit for the activity translates to an upper limit of the production yield of ryield = Yiso/Yg.s. ≈200; nevertheless, the (8+) isomer in 186Re has been ignored in [6, 3].The isomer contribution can be determined from the difference between measurements withdirect neutron detection and photoactivation. Unfortunately, the error bars prevent a precise deter-mination but a clear trend can be seen in Fig. 1. If one uses the parametrizationσ(E) = σ0×(E−SeffnSeffn)p(2.1)one can fit the isomer contribution in Fig. 1 (right part) by adjusting σ0 and p and with Seffn =Sn +149 keV. Depending on the treatment of the data points close above threshold (where one findsunphysically negative cross sections) and depending on the number of data points which are takeninto account (see below), one finds in any case values for σ0 which are significantly positive andvalues for p between 1.9 and 3.6 which are typical for large involved angular momenta (p≈ l +1/2)for the states feeding the (8+) isomer.The experimental result of [3, 6] is a parametrization of the cross section which also usesEq. (2.1) with Seffn = Sn = 7.363 MeV: σ0 = 80.4± 9.6 mb and p = 0.5; the validity is restrictedto E < 8.55 MeV in [3] because the lowest directly measured data points of [5] around 9 MeV arehigher than the parametrization of [3]. It is concluded in [3] that this difference is due to the tail ofthe GDR. However, the measured values of σ0 in [3] (see their Fig. 5) do not increase with energy.Therefore, the deviation between the photoactivation data of [3] and the data of [5] must probably –at least partly – be attributed to a noticeable isomer contribution. Unfortunately, [3] do not comparetheir data to the precise data of [2]; surprisingly, [2] is not even referenced in [3].3. Theoretical predictions of isomer contributions of (γ ,n) reactionsThe theoretical prediction of isomer contributions in (γ ,n) reactions is difficult because ofseveral reasons: (i) The isomer contribution depends sensitively on the level density of high-spinstates in the residual nucleus. At low energies, it is particularly difficult to estimate the level densityespecially for high-spin states, since the statistical approach is not valid anymore. Combinatorialor shell-model models are therefore required. In addition, there is a clear lack of experimental datathat can be used to constrain such models. It has been suggested to use experimental data of theisomer contribution in (γ ,n) reactions to study the high-spin level density [8]. (ii) Small branchingratios of low-spin states to the isomer may contribute noticeably to the total isomer cross section.3PoS(NIC-IX)142s-process branching at 186Re revised P. Mohr(iii) The neutron emission probability with large angular momenta l depends on the interplay of theattractive nuclear potential and the repulsive centrifugal barrier.For the 187Re(γ ,n)186Re reaction the theoretical isomer contribution increases from about 1 %to 15 % in the energy range of about 10 MeV to 20 MeV. As expected from the similarity of theinvolved spins and parities (see above), a similar result is obtained for the isomer contribution ofthe 185Re(γ ,n)184Re reaction.The comparison of the experimental result and the theoretical prediction of the 185Re(γ ,n)184Rereaction [6] shows that the theoretical prediction underestimates the experimental data significantly.In contrast, for the isomer contribution in the 181Ta(γ ,n)180Ta reaction theoretical and experimentalresults agree very well [8]. Only very few experimental data are available at energies close abovethe relevant thresholds, e.g. for the 13/2+ isomer in the 198Hg(γ ,n)197Hg reaction [9].At the present stage there is a clear discrepancy between the theoretical isomeric contributionpredicted for the 185Re(γ ,n)184Re reaction (around 1 % at 10 MeV) and the experimental resultsin [6], and a similar discrepancy is found for the 187Re(γ ,n)186Re reaction as shown in Fig. 1(right part). Further theoretical studies and improved and extended experimental data for isomercontributions in (γ ,n) reactions are urgently needed to shed light on this issue.4. Relation between (γ ,n) and (n,γ) data in the lab and under stellar conditionsIt has been stated in [3] that “the 187Re(γ ,n)186Re cross section and the cross section of theinverse reaction 186Re(n,γ)187Re are related via the principle of detailed balance”. However, thedetailed balance (as usually defined in nuclear astrophysics) relates reaction rates (not cross sec-tions):λ ?〈σv〉 ∼(G1G2G3) (A1A2A3)3/2T 3/2 exp(− QkT)(4.1)The total neutron capture cross section σ(n,γ) in the lab is given by the sum over all final states iin 187Re:σ(n,γ) = ∑iσ(n0,γi) (4.2)whereas the photodisintegration cross section σ(γ ,n) in the lab has to be summed over all finalstates j in 186Re:σ(γ ,n) = ∑jσ(γ0,n j) (4.3)Time reversal symmetry links the cross sectionsσ(n j,γi) and σ(γi,n j) (4.4)From the relation in Eq. (4.4) the detailed balance principle for reaction rates in Eq. (4.1) canbe derived; for the example of the 16O(α ,γ)20Ne reaction this has been shown explicitly in [10].However, there is no simple way to relate the capture and photodisintegration cross sections in thelab as defined in Eqs. (4.2) and (4.3).Photodisintegration data of the 187Re(γ ,n)186Re reaction can be used to test statistical modelcalculations and/or to adjust the parameters of the calculations. It has been shown in [2] thatdifferent parameter sets lead to comparable agreement with the experimental data (see also Fig. 1).4PoS(NIC-IX)142s-process branching at 186Re revised P. MohrA careful comparison between experimental 187Re(γ ,n)186Re data and theoretical predictions isalso given in [11].It turns out that the predicted neutron capture cross sections of the 186Re(n,γ)187Re reactionshow significant variations from 560 mb to 1460 mb [2, 7, 12, 13] at kT = 30 keV. This leads toan average cross section of σ = 1070± 370 mb which is slightly lower than the adopted value of1550±250 mb [12, 13]. This result is based on statistical model calculations using parameter setswhich are able to reproduce the 187Re(γ ,n)186Re cross section. Note that the large value in the listof calculations in [13] of σ = 2011 mb is based on a parameter set which is not able to describe therecent 187Re(γ ,n)186Re data [2] and should not be used for the 186Re(n,γ)187Re reaction.5. ConclusionsThe (8+) isomer in 186Re plays a significant role in the 187Re(γ ,n)186Re photodisintegrationreaction and has to be taken into account in the analysis of photoactivation data. The parametersof statistical model calculations can be restricted using the experimental 187Re(γ ,n)186Re data; thisleads to an improved neutron capture cross section of 186Re at kT = 30 keV of σ = 1070±370 mb.Further experimental data are required for isomer contributions in (γ ,n) reactions to improve thetheoretical description of high-spin level densities and isomer cross sections. Using the very sim-plistic assumption of a constant neutron density of Nn = 4×108 cm−3 the s-process path proceedsmainly via β -decay of 186Re (95 %), and the neutron capture branch via 186Re(n,γ)187Re remainssmall (5 %). Extremely small branching ratios of (2.1−5.4)×10−4 as quoted in [3] are not under-standable because any definition of the astrophysical s-process parameters is missing in [3]. Furtherdetails and information on the Re/Os chronometer can be found in the contributions of [14, 15, 16]to this conference.AcknowledgmentsWe thank S. Chiba for providing his calculations of the isomer contribution.References[1] F. Käppeler, S. Jaag, Z. Y. Bao, and G. Reffo, Astrophys. J. 366, 605 (1991).[2] T. Shizuma et al., Phys. Rev. C 72, 025808 (2005).[3] S. Müller et al., Phys. Rev. C 73, 025804 (2006).[4] T. Hayakawa et al., Astrophys. J. 628, 533 (2005).[5] A. M. Goryachev et al., Sov. J. Nucl. Phys. 17, 236 (1973).[6] S. Müller, diploma thesis, Technische Universität Darmstadt (2004).[7] T. Rauscher and F.-K. Thielemann, At. Data Nucl. Data Tables 88, 1 (2004).[8] S. Goko et al., Phys. Rev. Lett. 96, 192501 (2006).[9] K. Vogt, Ph.D. thesis, TU Darmstadt (2003).[10] P. Mohr et al., Europ. Phys. J. A 27, 75 (2006).5PoS(NIC-IX)142s-process branching at 186Re revised P. Mohr[11] T. Rauscher, Phys. Rev. C 74, 019801 (2006); Comment on [3].[12] Z. Y. Bao et al., At. Data Nucl. Data Tables 76, 70 (2000).[13] Data base KADoNiS, http://nuclear-astrophysics.fzk.de/kadonis/.[14] M. Segawa et al., these proceedings, PoS(NIC-IX)054.[15] M. Mosconi et al., these proceedings, PoS(NIC-IX)055.[16] F. G. Kondev et al., these proceedings, PoS(NIC-IX)127.[17] T. Hayakawa et al., Phys. Rev. C, submitted.[18] S. Mueller, private communication during NIC-IX.[19] S. Chiba, private communication.Notes added in Proof:In a recent experiment Hayakawa et al. [17] have measured the half-life of 184Re populatedby the the 185Re(γ ,n)184Re reaction at energies around the giant dipole resonance using the pho-toactivation technique. By a careful analysis of the decay curve they find an exponential decay ofthe activity with a half-life of t1/2(184Re) = 35.4± 0.7 days which is somewhat smaller than theadopted value of 38.0±0.5 days. No long-living component was found, and an upper limit of about3 % for the isomer contribution in the 185Re(γ ,n)184Re cross section is derived in [17]. In addition,the result of [6] has been revised by the author: the stated isomer contribution of 20.8 % shouldbe read as an upper limit [18]. Thus, the theoretical predictions for the isomer contribution of theorder of a few per cent in the 185Re(γ ,n)184Re reaction are in agreement now with the availableexperimental data.The similarity of the 187Re(γ ,n)186Re and 185Re(γ ,n)184Re reactions is confirmed by an addi-tional Hauser-Feshbach calculation [19]. This similarity indicates that the isomer contribution inthe 187Re(γ ,n)186Re reaction may be smaller than derived in Sect. 2 although low-lying levels in186Re with decay branches to the (8+)isomer have been identified [16]. The origin of the discrep-ancy between the directly measured data of [2, 5] and the photoactivation data of [3, 6] (as shownin Fig. 1) remains unclear.6

The s-process branching at $^{186}Re$ revised

Recent experimental data for the 187Re(γ ,n) 186Re reaction are reviewed, and the contribution of the (8 +) isomer in 186Re is discussed. Statistical model calculations are used to derive the 186Re(n,γ)187Re capture cross section from the photodisintegration data, and σMACS = 1070±370mb is obtained at κT = 30 keV. The s-process branching at 186Re remains small. © Copyright owned by the author(s).SCOPUS: cp.pinfo:eu-repo/semantics/publishe

The s-process branching at 186Re revised

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