Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike LicenceIn this work we present the results from the analysis of the experimentally measured angular distributions of the reaction 106Cd(α , α )106 Cd at several different energies around the Coulomb barrier. The difficulties that arise in the study of 106Cd-α -nuclear potential and the so called Family Problem are addressed in this work

Fueloep, Zs.

Galaviz, D.

Gyuerky, Gy.

Kiss, G. G.

Mate, Zs.

Mohr, P.

Ornelas, A.

Rauscher, T.

Somorjai, E.

Sonnabend, K.

Zilges, A.

English

University of Hertfordshire Research Archive

PoS(NIC XI)241How important is the Family? Alpha nuclearpotentials and p-process nucleosynthesis ∗A. Ornelas†a, D. Galaviza, Zs. Fülöpb, Gy. Gyürkyb, G. Kissb, Zs. Mátéb, P. Mohrc, T.Rauscherd, E. Somorjaib, K. Sonnabende and A. Zilges faCentro de Física Nuclear, University of Lisbon, 1649-003 Lisbon, PortugalbATOMKI, H-4001 Debrecen, POB. 51, HungarycDiakonie-Klinikum, D-74523 Schwäbisch Hall, GermanydDepartement für Physik und Astronomie, Universität Basel, CH-4056 Basel, SwitzerlandeInstitut für Kernphysik, TU-Darmstadt, D-64289 Darmstadt, Germanyf Institut für Kernphysik, Universität zu Köln, D-50937, Köln, GermanyE-mail: ornelas@cii.fc.ul.ptIn this work we present the results from the analysis of the experimentally measured angulardistributions of the reaction 106Cd(α , α)106Cd at several different energies around the Coulombbarrier. The difficulties that arise in the study of 106Cd-α-nuclear potential and the so calledFamily Problem are addressed in this work.11th Symposium on Nuclei in the Cosmos19-23 July 2010Heidelberg, Germany.∗Work supported by FCT grant PTDC/FIS/103902/2008, ERC StG No. 203175 and OTKA NN83261 (EuroGEN-ESIS)†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 XI)241How important is the Family? Alpha nuclear potentials and p-process nucleosynthesis A. Ornelas1. IntroductionThe story of nucleosynthesis beyond the iron peak is that of neutron capture reactions in theastrophysical s and r-process. However, there are 35 stable isotopes located in the proton-rich sidewhose production cannot be explained in the framework of the slow and rapid neutron captureprocess. One of the most accepted mechanisms for the synthesis of the so-called p-nuclei is basedon photodisintegration reactions on neutron-rich seed nuclei [1, 2]. The reaction rates sensitivityto the nuclear input in a p-process network calculation has been considered [1, 3].Whereas thelow mass p-nuclei (70≤A≤120) show a stronger dependence on the (γ ,p) reaction rates, the heavymass stable proton-rich isotopes are very sensitive to variations on the (γ ,α) reaction rates, whichdirectly depend on the considered α-nucleus potential.By measuring the angular distribution of alpha particles at energies close above the Coulomb barrierit is possible to extract information on the α-nucleus potential. However, as shown for 144Sm [4]and 92Mo [5], at these energies several “families“ of the potential (characterized by different depthsof the real nuclear potential) provide an equally good description of the scattering data.Here we present the first results obtained in the analysis of the potential families extracted from theangular distribution of the reaction 106Cd(α ,α)106Cd [6] measured at the ATOMKI laboratory atenergies around the Coulomb barrier. The sensitivity of the families to the description of α particlecapture reactions measured close to p-process relevant energies [7] is also shown.2. Systematic Study: The family problemThe analysis of the elastic scattering cross section of the reaction 106Cd(α ,α)106Cd was per-formed within the optical model:U(r) =VC(r)+VR f (r,RR,aR),+iWV f (r,RV ,aV )+ iWS g(r,RS,aS) (2.1)with the Coulomb potential (VC):VC(r) =ZP ZT e23−(rRC)22 RC f or r < RCZP ZT e2rf or r ≥ RC(2.2)and a complex nuclear potential, for which we adopted different volume and surface parameter-izations of the Woods-Saxon form V (r) = V0 fV (r) and W (r) = WV fV (r)+WS g(r,RS,aS) withfi =(1+ exp(r−Riai))−1, Ri = riA1/3 , i = V,S and g(r,RS,aS) = −4 aS d fS(r)dr as described in[8, 9, 10]. The optical model is designed to simplify the interaction between two nuclei, such thatan otherwise difficult to solve many-body problem is simplified to the interaction between two inertnuclei using an effective potential.The main goal of this work was to obtain the potential that accurately describes the measured cross-section data. As shown in previous works [4, 5] there are several potential families, correspondingto different depths of the real part of the nuclear potential, that describe with similar quality theelastic scattering data at energies around the Coulomb barrier. Following a similar approach wehave performed a systematic variation of the real part of the nuclear potential studying the angular2PoS(NIC XI)241How important is the Family? Alpha nuclear potentials and p-process nucleosynthesis A. Ornelasdistribution measured at the highest energy (Elab = 19.6 MeV) in order to obtain all the families ofthe 106Cd-α potential. We adopted the code a0 [11] to iteratively calculate the angular distributionfor each potential. In our approach, the diffuseness (ar) and radius (Rr) of the real part of the poten-tial were fixed, while the real depth potential (V0) was successively decreased and the imaginarypotential adjusted for each case. The results are presented in Figure 1. We obtained 14 differentpotentials that equally describe the 106Cd(α ,α)106Cd interaction, i.e, their χ2/F is very similar(lower part of the figure). The variations of the volume integrals for both real (JR) and imaginary(JI) parts of the potential are shown as well. As indicated, all families describe with similar quality1 2 3 4 5 6 7 8 9 10 11 12 13 14)3 (MeV/fmRJ020040060080010001200)3 (MeV/fmIJ50100150200250300Family No.1 2 3 4 5 6 7 8 9 10 11 12 13 14/F2 χ11.21.41.61.82Figure 1: Obtained χ2/F (bottom) for the different families of the potential extracted from the analysis ofthe 106Cd(α,α)106Cd reaction at Elab = 19.6 MeV. The resulting volume integrals for the real (JR, top) andimaginary (JI , center) potentials are shown as well.the experimental results. We present as an example Family No. 6 in Figure 2 together with theexperimental data for the three considered angular distributions [6].The 14 different potentials that we encountered are a consequence of the family problem thatarises from the fact that the scattering cross section is only sensitive to the asymptotic properties ofthe wave function (reflexion coefficients ηL and phase shifts δL).3. Description of existing capture dataOnce finished the analysis of the elastic scattering data, the obtained families of the potential3PoS(NIC XI)241How important is the Family? Alpha nuclear potentials and p-process nucleosynthesis A. OrnelasFigure 2: Experimental Rutherford normalized angular distributions for the reaction 106Cd(α,α)106Cd atElab = 16.1, 17.7 and 19.6 MeV [6]. In addition, the results obtained using Family No. 6 are shown. Allthree angular distributions are accurately described by the extracted families.were used to calculate the cross section for the processes 106Cd(α ,γ)110Sn, 106Cd(α ,n)109Sn, and106Cd(α ,p)109In. For this purpose, the NON-SMOKERWEB [12] application was employed.The resulting astrophysical S-factors are presented in Figure 3 together with the experimentaldata from [7] .As it can be observed, all derived potentials overestimate the experimental data for 106Cd(α ,γ)110Snand 106Cd(α ,n)109Sn processes, but describe the 106Cd(α ,p)109In reasonably well. More remark-able is the fact that all families of the potential, despite the large range of the nuclear potentialdepths for both real and imaginary parts, provide almost the same output. This indicates that thereal part of the potentials derived in this work is very insensitive in the description of radiativecapture of α particles by the nucleus 106Cd.Figure 3: Astrophysical S-factor of the 106Cd (α,γ) 110Sn, 106Cd(α ,n)109Sn and 106Cd(α ,p)109In reactionstogether with the results obtained from the 14 different potential families obtained in this study.4PoS(NIC XI)241How important is the Family? Alpha nuclear potentials and p-process nucleosynthesis A. Ornelas4. ConclusionsIn this work we have performed a systematic study of the potential families of the system α-106Cd analyzing the angular distribution of the reaction 106Cd(α ,α)106Cd at energies aroundthe Coulomb barrier. We obtained 14 different potential parameterizations, which were usedin the calculation of the astrophysical S-factor for the 106Cd(α ,γ)110Sn, 106Cd(α ,n)109Sn, and106Cd(α ,p)109In reactions. An almost equal result was obtained in describing the compound re-actions at energies of astrophysical interest. Further investigations are underway to clarify the sen-sitivity of the real and imaginary parts of the nuclear potential in the description of these processesand will be the topic of a dedicated paper.References[1] T. Rauscher. Branchings in the gamma process path revisited. Phys. Rev. C, 73(1),015804, 2006.[2] M. Arnould and S. Goriely. The p-process of stellar nucleosynthesis: astrophysics and nuclearphysics status. Phys. Rep., 384,1, 2003.[3] W. Rapp, J. Görres, M. Wiescher, H. Schatz, and F. Käppeler. Sensitivity of p-Process Nucleosynthesisto Nuclear Reaction Rates in a 25 M⊙ Supernova Model. Astrophys. J., 653,474, 2006.[4] P. Mohr, T. Rauscher, H. Oberhummer, Z. Máté, Z. Fülöp, E. Somorjai, M. Jaeger, and G. Staudt.144Sm–α optical potential at astrophysically relevant energies derived from 144Sm(α ,α)144Sm elasticscattering. Phys. Rev. C, 55,1523, 1997.[5] Z. Fülöp, G. Gyürky, Z. Máté, E. Somorjai, L. Zolnai, D. Galaviz, M. Babilon, P. Mohr, A. Zilges,T. Rauscher, H. Oberhummer, and G. Staudt. 92Mo(α,α)92Mo scattering, the 92Mo−α opticalpotential, and the 96Ru(γ,α)92Mo reaction rate at astrophysically relevant energies. Phys. Rev. C,64(6),065805, Nov 2001.[6] D. Galaviz. Systematic study of α-nucleus potentials for neutron-deficient nuclei and it’sastrophysical applications. PhD thesis, Technischen Universität Darmstadt, 2004.[7] G. Gyürky, G. G. Kiss, Z. Elekes, Z. Fülöp, E. Somorjai, A. Palumbo, J. Gorres, H. Y. Lee, W. Rapp,M. Wiescher, N. Özkan, R. T. Guray, G. Efe, and T. Rauscher. Alpha-induced cross sections of 106Cdfor the astrophysical p process. Phys. Rev. C, 74(2),025805, 2006.[8] M. Avrigeanu, W. von Oertzen, A. J. M. Plompen, and V. Avrigeanu. Optical model potentials foralpha-particles scattering around the coulomb barrier on A ∼ 100 nuclei. Nucl. Phys., A723,104,2003.[9] M. Avrigeanu, W. von Oertzen, and V. Avrigeanu. On temperature dependence of the optical potentialfor alpha-particles at low energies. Nucl. Phys., A764,246, 2006.[10] M. Avrigeanu, A. Obreja, F. Roman, V. Avrigeanu, and W. von Oertzen. Complementaryoptical-potential analysis of α-particle elastic scattering and induced reactions at low energies.Atomic Data and Nuclear Data Tables, 95,501 – 532, 2009.[11] H. Abele and P. Mohr. code a0− version 1.50, 2010. (unpublished).[12] T. Rauscher and F.-K. Thielemann. Astrophysical reaction rates from statistical model calculations.At. Data Nucl. Data Tab., 75,1–352, 2000.5

144Sm–α optical potential at astrophysically relevant energies derived from 144Sm(α ,α)144Sm elastic scattering.

92Mo(α,α)92Mo scattering, the 92Mo−α optical potential, and the 96Ru(γ,α)92Mo reaction rate at astrophysically relevant energies.

Alpha-induced cross sections of 106Cd for the astrophysical p process.

Astrophysical reaction rates from statistical model calculations.

Branchings in the gamma process path revisited.

code a0− version 1.50,

Complementary optical-potential analysis of α-particle elastic scattering and induced reactions at low energies.

On temperature dependence of the optical potential for alpha-particles at low energies.

Optical model potentials for alpha-particles scattering around the coulomb barrier on A ∼ 100 nuclei.

Sensitivity of p-Process Nucleosynthesis to Nuclear Reaction Rates in a 25 M⊙ Supernova Model.

Systematic study of α-nucleus potentials for neutron-deficient nuclei and it’s astrophysical applications.

The p-process of stellar nucleosynthesis: astrophysics and nuclear physics status.

How important is the Family? : Alpha nuclear potentials and p-process nucleosynthesis

How important is the Family? : Alpha nuclear potentials and p-process nucleosynthesis

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