Test of statistical model cross section calculations for α -induced reactions on 107 Ag at energies of astrophysical interest
C. Yalcin, Gy. Gyürky, T. Rauscher, G. G. Kiss, N. Özkan, R. T. Güray, Z. Halász, T. Szücs, Zs. Fülöp, Z. Korkulu, E. Somorjai
aa r X i v : . [ nu c l - e x ] A p r Test of statistical model cross section calculations for α -induced reactions on Ag atenergies of astrophysical interest
C. Yal¸cın,
1, 2, ∗ Gy. Gy¨urky, T. Rauscher,
3, 4
G. G. Kiss, † N. ¨Ozkan, R. T. G¨uray, Z. Hal´asz, T. Sz¨ucs, ‡ Zs. F¨ul¨op, J. Farkas, Z. Korkulu, and E. Somorjai Kocaeli University, Department of Physics, Umuttepe 41380, Kocaeli, Turkey Institute for Nuclear Research (MTA Atomki), H-4001 Debrecen, POB.51., Hungary Centre for Astrophysics Research, University of Hertfordshire, Hatfield AL10 9AB, United Kingdom Department of Physics, University of Basel, 4056 Basel, Switzerland (Dated: April 8, 2015)
Background:
Astrophysical reaction rates, which are mostly derived from theoretical cross sections, are necessaryinput to nuclear reaction network simulations for studying the origin of p nuclei. Past experiments have founda considerable difference between theoretical and experimental cross sections in some cases, especially for ( α , γ )reactions at low energy. Therefore, it is important to experimentally test theoretical cross section predictions atlow, astrophysically relevant energies. Purpose:
The aim is to measure reaction cross sections of
Ag( α , γ ) In and
Ag( α ,n) In at low energiesin order to extend the experimental database for astrophysical reactions involving α particles towards lower massnumbers. Reaction rate predictions are very sensitive to the optical model parameters and this introduces alarge uncertainty into theoretical rates involving α particles at low energy. We have also used Hauser-Feshbachstatistical model calculations to study the origin of possible discrepancies between prediction and data. Method:
An activation technique has been used to measure the reaction cross sections at effective center of massenergies between 7.79 MeV and 12.50 MeV. Isomeric and ground state cross sections of the ( α ,n) reaction weredetermined separately. Results:
The measured cross sections were found to be lower than theoretical predictions for the ( α , γ ) reaction.Varying the calculated averaged widths in the Hauser-Feshbach model, it became evident that the data for the( α , γ ) and ( α ,n) reactions can only be simultaneously reproduced when rescaling the ratio of γ - to neutron widthand using an energy-dependent imaginary part in the optical α + Ag potential.
Conclusions:
The new data extend the range of measured charged-particle cross sections for astrophysical ap-plications to lower mass numbers and lower energies. The modifications in the model predictions required toreproduce the present data are fully consistent with what was found in previous investigations. Thus, our resultsconfirm the previously suggested energy-dependent modification of the optical α +nucleus potential. PACS numbers: 25.55.-e, 27.60.+j, 29.30.Kv
I. INTRODUCTION
The synthesis of elements heavier than iron proceedsvia different processes. The so-called s and r processesinvolve neutron capture reactions. The s process is theslow neutron capture process responsible for the produc-tion of stable isotopes along the valley of beta stability inthe chart of isotopes. The r process is the rapid neutroncapture process and approximately half of the heavy el-ements with mass number A >
70 and all the actinidesin the solar system are believed to have been producedby the r process. These two processes were found to beunable, however, to create 35 neutron-deficient, naturalisotopes between Se and
Hg, which were called “ p nuclei” or “excluded isotopes” [1, 2]. Recently, it hasbeen shown, on the other hand, that Er,
Gd and ∗ Corresponding author: [email protected] † Present address: RIKEN Nishina Center, 2-1 Hirosawa, Wako,Saitama 351-0198, Japan ‡ Present address: Helmholtz-Zentrum Dresden-Rossendorf(HZDR), D-01328 Dresden, Germany
Ta may have large s -process contributions, neverthe-less, and that the ν -process may contribute to La and
Ta (see, e.g., [3] and references therein). The remain-ing p nuclei are thought to be produced in the γ -processwhich includes combination of ( γ ,n), ( γ ,p) and ( γ , α ) re-actions [1–9].The γ -process nucleosynthesis is modeled by using anextended nuclear reaction network, for which – amongothers – reaction rate information of thousands of neu-tron, proton and α -induced reactions as well as their in-verse reactions are needed [10–12]. Experimental studiesof reactions important in this context have been per-formed in recent years [13–35] but despite this effort,experimental cross sections are still very scarce at as-trophysically interesting, low energies. The full list ofthe experiments can be found in the KADoNiS p -processdatabase [36]. The experiments performed so far haveshown that there can be considerable differences betweentheoretical and experimental cross sections in some casesat energies close around the Coulomb barrier. In orderto get rid of this discrepancy, there is also strong effortto obtain a global α +nucleus optical potential [37] via α -elastic scattering experiments [38–40]. Theoretical cross TABLE I. Decay parameters of reaction products taken from[42, 43]. Only the γ -transitions used for the analysis are listed.Reaction Half-life E γ I γ (keV) (%) Ag( α, γ ) In 2.8047 ± ± Ag( α ,n) g In 4.92 ± ± ± ± Ag( α ,n) m In 69.1 ± ± ± sections are used in γ -process network calculations anda deficiency in reaction rates can perhaps be responsi-ble for the failure of γ -process models in reproducingthe observed p isotope abundances in the mass range150 ≤ A ≤ Ag is not a p nucleus and mostly pro-duced by the s and r processes, in order to further testthe reliability of statistical model predictions in this massrange, the α -capture cross sections of Ag have beenmeasured in the effective center of mass energy rangebetween 7.79 MeV and 12.50 MeV using the activationmethod. These energies are close to the astrophysicallyrelevant energy range (the Gamow window) which ex-tends from 5.83 MeV to 8.39 MeV at 3 GK temperaturetypical for the γ -process [41]. The results were comparedwith Hauser-Feshbach statistical model calculations.Details of the experiment are given in Sec. II. The ex-perimental results are presented in Sec. III A. A compar-ison to statistical model calculations and a detailed dis-cussion is given in Sec. III B. The final Sec. IV providesconclusions and a summary. II. EXPERIMENT
Reaction cross sections of
Ag( α, γ ) In and
Ag( α, n ) In have been measured at the laboratoryenergies between 8.16 MeV and 13.00 MeV. Since thereaction products are radioactive and their half-lives areconvenient, the activation method was used to determinethe cross sections. Detailed information about the acti-vation method can be found, e.g., in [15].In the case of
Ag( α ,n) the reaction product Inhas a long-lived isomeric state. The partial cross sectionsleading to the ground as well as the isomeric states canbe determined separately owing to the different decaypatterns of the two states. The decay parameters usedfor the analysis are summarized in Table I.
A. Target preparation
Natural silver and isotopically enriched
Ag targetswere produced by vacuum evaporation onto high puritythin aluminum foils (from 1.8 µ m to 2.5 µ m). The back-ing aluminum foils were thick enough to stop the heavyreaction products. Enriched targets were produced from99.50% isotopically enriched Ag available in metal-lic powder form (obtained from the company ISOFLEXUSA, Certificate No: 47-02-107-2999). Both naturaland enriched Ag metal powders were evaporated from amolybdenum crucible heated by DC current. The back-ing foil was placed 7 cm above the crucible in a holderdefining a circular spot with a diameter of 12 mm on thefoil for Ag deposition.The target thicknesses were determined with weightmeasurement. Before and after the evaporation theweight of the foils were measured with a precision bet-ter than 5 µ g and then from the difference the Ag arealdensity could be determined. Enriched and natural tar-gets were prepared with thicknesses varying between410 µ g/cm and 1042 µ g/cm . The targets were onlyirradiated once or cooled for more than 20 half-lives be-tween two subsequent activations of the same target.Reused targets were checked by γ -measurement beforethe second irradiation to determine any remaining activ-ity. B. Activations
The targets were irradiated with α beams from thecyclotron accelerator of MTA Atomki. In total thir-teen irradiations were made at different energies betweenE lab = 8.16 MeV and E lab = 13.00 MeV laboratory en-ergies. For 11.00 MeV and 11.50 MeV, two irradiationswere carried out with enriched and natural targets totest systematic uncertainty related to the targets. Theresults were compatible with each other (see Table II).Some energies were measured with an energy degraderfoil because the cyclotron could not produce these beamenergies directly (see Table II). Aluminum and nickel foilswere used as energy degraders. The thicknesses of the en-ergy degrader foils were determined by energy loss mea-surement of α particle emitted from a Am source. Inorder to calculate thickness of the degrader foils, ThiMeTcode [44] was used which takes into account energy de-pendence of stopping power through the degrader foil.A diagram of the target chamber is shown in Fig. 1.After the last beam defining aperture the whole chamberwas isolated and used as a Faraday cup to determine thenumber of projectiles by charge collection. A suppressionvoltage of −
300 V was applied at the entrance of thechamber to suppress the secondary electrons. The beamcurrent was recorded using a current integrator in multichannel scaling mode in order to take into account thepossible changes in the beam current. The integratedcurrent was recorded every 10 or 60 seconds.
FIG. 1. (Color online) A schematic drawing of the targetchamber used for the irradiations.
In addition, in order to monitor target stability duringthe irradiation, an ion-implanted Si detector was placedinto the target chamber at 165 ◦ relative to the beam di-rection. The elastic backscattering spectra were contin-uously taken and there were no substantial backgroundpeaks besides Ag and Al observed in the spectra. If thereis no target deterioration then the ratio of the numberof backscattered particle to those of incoming particlesshould be constant in time. Target stability was regularlychecked and no target deterioration was observed duringthe irradiations. Because the target stability could notbe monitored when an energy degrader foil was used, thebeam current was limited to 800 nA in these cases. Thisvalue was tested before the experiment using a naturaltarget and found that there was no target deterioration.The beam stop was placed 10 cm behind the target fromwhere no backscattered particles could reach the parti-cle detector. The beam stop was directly water cooledduring the irradiation. The typical current was between150 nA and 800 nA. The length of irradiation was chosenin the range of 1.5 h − C. Gamma counting and analysis
After each irradiation the target was taken from the re-action chamber and placed into a low-background count-ing setup to measure the
In and
In activities pro-duced through the
Ag( α, γ ) In and
Ag( α ,n) Inreactions, respectively. According to the actual countrate of the reaction products the target was placed at adistance of 10 cm or 1 cm from the end cap of a HPGedetector having 100% relative efficiency. To reduce theroom background the HPGe detector was placed into 4 π
100 200 300 400 500 600 700 800 900 10001000200030006000080000 k e V k e V k e V C oun t s / . k e V k e V (a) k e V C oun t s / . k e V Energy (MeV) k e V (b) FIG. 2. (a) Low and (b) high energy parts of the γ spectrumtaken after an 8.7 h irradiation of a target with a 10 MeV α beam. The γ -lines used for analysis are indicated on the spec-trum. The other peaks are from either laboratory backgroundor the other γ -transitions. (1 Channel=0.204 keV) commercial 10 cm thick lead shield with 1 mm cadmiumand 1 mm copper layers.As an example, Fig. 2 shows an off-line γ -ray spectrumtaken after a 8.7 h long irradiation with an α beam of10.00 MeV for a counting time of 16.5 h indicating the γ -lines used for cross section measurements (Table I).Owing to the very different half-lives of the reactionproducts (2.8047 d, 4.92 h and 69.1 min) and the differ-ent expected cross sections, the counting periods weresegmented into several parts. The γ -spectra were storedregularly in every 10 minutes near the beginning ofthe counting and in every 30 minutes after one hour.The ratio of the cross sections of Ag( α ,n) In to
Ag( α, γ ) In reactions is about 30 at 10.5 MeV andabout 95 at 12.5 MeV. At the beginning of the count-ing the spectra were thus dominated by the intense γ -radiations from the Ag( α ,n) In decay products. Themeasurement of the activity of the
Ag( α, γ ) In re-action product was therefore started only after about sixhours when the activity of at least the
In isomericstate decreased substantially. The reaction product ofthe
Ag( α, γ ) In reaction has a short lived (7.7 min)isomeric state decaying completely by isomeric transi-tion (IT) to the ground state. Starting the γ -countingfor this reaction several hours after the end of the irradi-ation guarantees that this short lived isomer has decayedcompletely to the ground state and hence the total crosssection can be obtained.The product of the Ag( α, γ ) In reaction emits twostrong γ -lines at 171.28 keV and 245.35 keV with rela-tive intensities of 90.7% and 94.1%, respectively. Butthere are contributions to the 245.35 keV peak from otherdecays. First, the ( α, γ ) reaction product In decaysto
Cd which has an isomeric state with a half-life of
FIG. 3. Decay of the isotopes produced on natural silvertargets by α irradiation. γ -ray. When natural targets areused, m Cd is also produced by the
Ag( α ,d) Cd re-action above the threshold (10.552 MeV). A second con-tribution to the 245.35 keV peak comes from the
Inisotope which is produced by the
Ag( α, n ) In reac-tion when natural targets are used. The energy of thegamma line is 244.8 keV and it cannot be distinguishedfrom the 245.35 keV transition. There is no data forthe gamma intensity of this line in literature [45–47] butthe cross section is rather high (according to theoreti-cal calculation with e.g. the NON-SMOKER code [48],for 12.21 MeV center of mass energy the cross sectionis 43.26 mb). Because of these contributions only the171.28 keV γ -line was used for the cross section calcula-tion.In the case of the Ag( α ,n) In reaction high inten-sity gammas at 657 keV and 884 keV are common forthe decay of the isomeric and ground states. There-fore they were not used for the analysis. Unique gam-mas with high intensity for the
In( α, n ) g In reac-tion are at 641.68 keV, 707.40 keV and 937.16 keV, andfor the
Ag( α, n ) m In reaction at 2129.40 keV and2211.33 keV. These lines were chosen to determine sep-arately the partial cross sections to the ground and iso-meric states.
D. Detector efficiency calibration and truecoincidence summing corrections
Absolute efficiency calibration of the detection sys-tem was done at 10 cm detector-target distance at whichthe true coincidence summing effect is negligible. Cali-brated Na, Mn, Co, Co, Zn,
Ba, and
Cssources were used for the efficiency measurement. Theefficiency at 171.28 keV was determined by using a 4 th order polynomial fitted to the calibration gamma linesin the energy range from 122.1 keV to 1332.5 keV. Forthe Ag( α ,n) In case, gammas lines are located be-
TABLE II. Measured cross sections of the
Ag( α, γ ) Inand
Ag( α ,n) In reactions.E beam E eff c . m . Cross section [ µ b][MeV] [MeV] Ag( α, γ ) In Ag( α ,n) In8.16 b ± ± ab ± ± a ± ± ± a ± ± ± b ± ± ± b ± ± ± a ± ± ± ± ± ± a ± ± ± ± ± ± ± ±
16 12568 ± ± ±
25 24567 ± ± ±
34 37066 ± a measured with enriched target. b measured with an energy degrader foil. tween 642.68 keV and 2211.33 keV. In this energy rangethe efficiency curve has power-law like behavior, there-fore in log-log scale linear fit used between 276.4 keV and1332.5 keV energies and then extrapolated to higher en-ergies in order to find the efficiency at 2129.40 keV and2211.33 keV. The validity of the linear extrapolation waschecked with an uncalibrated Co source emitting highenergy gammas.The efficiencies at the 1 cm geometry used for some ofthe cross section measurements was determined by scal-ing the measured efficiencies at 10 cm. In order to find ascaling factor for all studied γ -rays, one of the natural tar-get was irradiated at 12.50 MeV lab energy and countedboth at 10 cm and 1 cm. Taking into account the lengthsof the two countings and the time elapsed between them,scaling factors were determined which include both thedifference in efficiency and the true coincidence summingeffect in the decay of the studied In isotopes [23, 49]. III. RESULTS AND DISCUSSIONA. Measured cross sections
The
Ag( α, γ ) In and
Ag( α ,n) In reactioncross sections have been measured in the laboratory ener-gies range between 8.16 MeV and 13.00 MeV, which in-cludes a part of the astrophysically relevant energy range.Laboratory energies have been converted into effectivecenter-of-mass energies ( E effc . m . ) that correspond to beamenergies in the target at which half of the yield of the fulltarget thickness is obtained [50]. The experimental crosssection results for Ag( α, γ ) In and
Ag( α ,n) Inreactions are presented in Tables II and Fig. 4 and Fig. 5. -1 Exp ( , ) Baglin et al. Theo ( , ) Theo (mod) ( , ) C r o ss S ec ti on ( b ) E eff.c.m. (MeV) FIG. 4. (Color online) Measured cross section of
Ag( α , γ )compared to theory using the SMARAGD code [64] (see textfor details). Previous results from Baglin [51] are also includedin the figure. Previous results from Baglin [51] and Stelson [52] arealso included in the figures. For
Ag( α, γ ) In reac-tion, disagreement with Baglin [51] is not understood,but the comparison with theory makes the Baglin valuesvery unlikely. For
Ag( α ,n) In reaction, the agree-ment is good with Stelson [52] but our energy range ismuch wider.The uncertainty of the measured cross sections com-prise the following partial components added quadrati-cally: counting statistics (between 0.6% and 14.0%), de-tection efficiency (7%) (including the conversion factorbetween the two counting geometries), decay parameters(less than 3.1%) and target thickness (7%). The uncer-tainty of the beam energy is governed by the energy lossin the targets determined with the SRIM code [53] (be-tween 0.6% and 1%), uncertainties in the energy degraderfoil thickness (1%) and the energy calibration and stabil-ity of the cyclotron (0.5%). In order to check systematicuncertainties, measurements at 11 MeV and 11.5 MeVenergies were carried out with two different targets. Thecross section results of the two measurements are in agood agreement (Table II).The ( α ,n) reactions on Ag populate the ground state( T / = 4.92 h) and isomeric state ( T / = 69.1 min) of In. Partial cross sections leading to these two statesare listed separately in the Table III. The total cross sec-tion of the
Ag( α ,n) In reaction was determined bysumming the partial cross sections. In those cases wherethe cross section was determined based on the countingof more than one γ -line (see Table I), the final cross sec-tion quoted in the tables and shown in the figures wereobtained by weighted average. Exp ( ,n) Stelson et al. Theo ( ,n) Theo (mod) ( ,n) C r o ss S ec ti on ( b ) E eff.c.m. (MeV) FIG. 5. (Color online) Measured cross section of
Ag( α ,n)compared to theory using the SMARAGD code [64] (see textfor details). Previous results from Stelson [52] are also in-cluded in the figure.TABLE III. Partial cross sections of the Ag( α ,n) reactionleading to the ground and isomeric states of In.E beam E eff c . m . Cross Section [ µ b][MeV [MeV] g In (4.92 h) m In (69.1 min)9.00 a ± ± ± a ± ± ± b ± ± ± b ± ± ± a ± ±
11 1821 ± ± ±
11 1883 ± a ± ±
31 4949 ± ± ±
31 4911 ± ± ±
90 12443 ± ± ±
176 21663 ± ± ±
281 32398 ± a measured with enriched target. b measured with an energy degrader foil. B. Comparison with Hauser-Feshbach predictions
The Hauser-Feshbach model of compound nuclear re-actions makes use of averaged widths describing particleor photon emission from the formed compound nucleus[10, 54, 55]. These averaged widths comprise sums overtransition widths connecting the compound state and in-dividual final states, determined by computing transmis-sion coefficients from the solution of a time-independentSchr¨odinger equation for each transition energeticallypossible and allowed by quantum mechanical selectionrules [54, 55]. In addition to binding energies of the in-volved nuclei, optical potentials and low-lying, discreteexcited states have to be known for the calculation of av- -1-0.5 0 0.5 1 7 8 9 10 11 12 13 s en s i t i v i t y E c.m. (MeV) γ n α FIG. 6. (Color online) Sensitivity of the
Ag( α , γ ) In re-action cross sections to variations in various averaged reactionwidths as function of energy [56]. The cross sections are in-sensitive to a variation of the proton width across the shownenergy range. eraged particle-widths, and the γ -strength function, dis-crete excited states, and nuclear level density enter thecomputation of the γ -width.For a correct interpretation of the differences betweendata and predictions, it is necessary to study the sensi-tivities of the cross sections to the calculated averagedwidths which, in turn, depend on different nuclear prop-erties. These sensitivities are not only different for dif-ferent reaction types but they are also energy dependentand, in consequence, variations of certain nuclear prop-erties may have different impact on the resulting crosssections at lower and higher energy. Sensitivities as atool to understand the origin of discrepancies betweendata and theory have been thoroughly discussed in [56]and have been used in previous investigations similar tothe present one (e.g., see [30–33, 35, 57–60]).In general, the cross sections may be sensitive to sev-eral properties at a given energy. In this case, it is anadvantage to have consistent data for two or more re-action channels at the same energy. Here, we are ableto simultaneously consider ( α , γ ) and ( α ,n) data whichallows to reduce ambiguities. The sensitivity factors ofthe cross sections of both reactions to variations in theaveraged widths are shown in Figs. 6 and 7. A sensitivityfactor − ≤ s ≤ f = | s | ( v −
1) + 1, when the corresponding widthis changed by a factor of v [56, 61]. For s ≥
0, the originalcross section has to be multiplied by f whereas for s < f . This means that a negativesensitivity shows that the cross section will change in theopposite direction than the width, i.e., it will increasewhen the width decreases and vice versa. As can be seenin Figs. 6 and 7, the cross sections of both reactions aresensitive to the α width in the same manner across theinvestigated energy range but the sensitivity to neutron-and γ -widths are different and opposite. Both reactions -1-0.5 0 0.5 1 7 8 9 10 11 12 13 s en s i t i v i t y E c.m. (MeV) γ n α FIG. 7. (Color online) Same as Fig. 6 but for
Ag( α ,n) In. are insensitive to a change of the proton width at theshown energies.It should be noted that astrophysically relevant en-ergies are located below the ( α ,n) threshold and there-fore the astrophysically interesting width is the α width.This led to the series of investigations to better constrainthis width at low energy, as mentioned in Sec. I. It wasfound that the previous data could be described usingan energy-dependent modification of the α width whichonly acts at low energy [14, 27, 32, 35, 57, 59]. The α width was calculated using the well-known optical po-tential by [62] with one modification: the depth of thevolume imaginary part W was made energy-dependent.It has to approach the value given in [62] (25 MeV) athigh energy but has to be shallower at energies below theCoulomb barrier energy E C . A Fermi-type function wasused to achieve this: W = 251 + e (0 . E C − E α c . m . ) /a E MeV . (1)In previous work, the value a E for the “diffuseness” ofthe Fermi-type function has been found to be between2 and 5 MeV, depending on the reaction. Using such amodified, effective optical potential it remains an openquestion whether the modification is really due to a re-quired change in the optical potential, which affects thetotal reaction cross section, or due to the neglection ofdirect processes in the entrance channel [63].Here, we use a similar approach to be able to reproducethe experimental data. Figure 4 and 5 compares calcula-tions performed with the SMARAGD code [64] with thedata. It can be seen that the prediction using the opticalpotential by [62] (labeled “Theo”) follows the ( α ,n) dataquite well except at the lowest measured energy. On theother hand, the energy dependence of the ( α , γ ) data isreproduced well but the calculation gives cross sectionswhich are about 2 − α ,n) reaction is only sensitive to the α width. Since the data are reproduced at these energies,the α widths have to be accurately predicted there. Atthe same energies the ( α , γ ) reaction is sensitive not onlyto the α width but also to the γ - and neutron widths.Since these widths have exactly opposite impact on thecross sections, only the change in the ratio q = Γ γ / Γ n ofaverage γ width Γ γ to average neutron width Γ n can bedetermined from the requirement to reproduce the ( α , γ )data simultaneously with the ( α ,n) data. Rescaling q by afactor of 0.5 shifts the predicted cross sections down andexcellent agreement with the experimental ( α , γ ) crosssections is achieved at the higher energies.Even with the adjusted ratio q , cross sections at thelowest measured energies remain overpredicted. Accord-ing to the sensitivities, the only way to mend this isto alter the α width. The α width, however, describeswell the data at higher energies and therefore an energy-dependent modification is required. We chose the sameparameterization as used in previous work and given inEq. (1). We found that the best fit to the data can be ob-tained with a E = 5 MeV. The resulting excitation func-tions are also shown in Figure 4 and 5 and labeled “Theo(mod)”. These results are fully consistent with previousinvestigations, where a similar a E was found and a simi-lar rescaling of the γ width relative to the neutron widthwas necessary. IV. SUMMARY AND CONCLUSION
The
Ag( α, γ ) In and
Ag( α ,n) In reactioncross sections have been measured in the effective cen- ter of mass energies between 7.79 MeV and 12.50 MeV,with the aim to extend the available database for im-proving predictions of the averaged α widths at low en-ergy. Experimental results were compared with Hauser-Feshbach statistical model calculations. It was foundthat an energy-dependent modification of the α widthand a rescaling of the γ - to neutron-width ratio is neces-sary. This is completely consistent with previous works.This finding confirms the applicability of the previouslysuggested parameterization of the optical α +nucleus po-tential also at mass numbers lower than studied so far. ACKNOWLEDGMENTS
This work was partially supported by the Scientific andTechnological Research Council of Turkey (TUBITAK),Grants No. 109T585 (under the EUROGENESIS re-search program) and Grants No. 108T508 and by OTKAgrants K101328 and K108459. CY acknowledges sup-port through the Scientific and Technological ResearchCouncil of Turkey (TUBITAK), under the programmeof BIDEB-2219. GGK acknowledges support from theBolyai grant. TR is supported by the BRIDGCE grantfrom the UK Science and Technology Facilities Council(grant ST/M000958/1), by the Swiss NSF, and the Eu-ropean Research Council (grant GA 321263-FISH). [1] E. M. Burbidge, G. R. Burbidge, W. A. Fowler, and F.Hoyle, Rev. Mod. Phys. , 547 (1957).[2] A. G. W. Cameron, Pub. Astron. Soc. Pac. , 201(1957).[3] T. Rauscher, N. Dauphas, I. Dillmann, C. Fr¨ohlich, Zs.F¨ul¨op and Gy. Gy¨urky, Rep. Prog. Phys. , 066201,(2013).[4] S. E. Woosley and W. M. Howard, Astrophys. J. Suppl.Ser. , 285 (1978).[5] M. Rayet, N. Prantzos, and M. Arnould, Astron. Astro-phys. , 271 (1990).[6] J. J. Cowan, F. K. Thielemann, and J. W. Truran, Phys.Rep. , 267 (1991).[7] G. Wallerstein et al., Rev. Mod. Phys. , 995 (1997).[8] M. Arnould, S. Goriely, and K. Takahashi, Phys. Rep. , 97 (2007).[9] R. Baruah, K. Duorah, H. L. Duorah, J. Astrophys. Astr. , 165, (2009).[10] T. Rauscher and F. K. Thielemann, At. Data Nucl. DataTables , 1 (2000).[11] T. Rauscher and F. K. Thielemann, At. Data Nucl. DataTables , 47 (2001).[12] T. Rauscher, Phys. Rev. C , 015804 (2006). [13] Zs. F¨ul¨op, ´A. Z. Kiss, C. E. Rolfs, H. P. Trautvetter, U.Greife, M. Junker, S. Goriely, M. Arnould, T. Rauscher,and H. Oberhummer, Z. Phys. A , 203 (1996).[14] E. Somorjai, Zs. F¨ul¨op, ´A. Z. Kiss, C. E. Rolfs, H.P. Trautvetter, U. Greife, M. Junker, S. Goriely, M.Arnould, M. Rayet, T. Rauscher, and H. Oberhummer,Astron. Astrophys. , 1112 (1998).[15] N. ¨Ozkan et al., Nucl. Phys. A710 , 469 (2002).[16] W. Rapp, M. Heil, D. Hentschel, F. K¨appeler, R. Rei-farth, H. J. Brede, H. Klein, and T. Rauscher, Phys.Rev. C , 015803 (2002).[17] M.S. Basunia, E. B. Norman, H. A. Shugart, A. R. Smith,M. J. Dolinski, and B. J. Quiter, Phys. Rev. C , 035801(2005).[18] S. Harissopulos, A. Lagoyannis, A. Spyrou, Ch. Zarkadas,G. Galanopoulos, G. Perdikakis, H-W Becker, C. Rolfs etal., J. Phys. G.: Nucl. Part. Phys. , S1417 (2005).[19] Gy. Gy¨urky, G. G. Kiss, Z. Elekes, Zs. F¨ul¨op, E. Somor-jai, A. Palumbo, J. G¨orres, H. Y. Lee, W. Rapp, M. Wi-escher, N. ¨Ozkan, R.T. G¨uray, G. Efe, and T. Rauscher,Phys. Rev. C , 025805 (2006).[20] N. ¨Ozkan, G. Efe, R.T. G¨uray, A. Palumbo, J. G¨orres, H.-Y. Lee, L. O. Lamm, W. Rapp, E. Stech, M. Wiescher,G. Gy¨urky, Zs. F¨ul¨op, E. Somorjai, Phys. Rev. C , , 025804 (2008).[22] I. Cata-Danil et al., Phys. Rev. C , 035803 (2008).[23] C. Yal¸cın et al., Phys. Rev. C , 065801 (2009).[24] R.T. G¨uray et al. Phys. Rev. C , 035804 (2009).[25] G. Gy¨urky et al., J. Phys. G , 115201 (2010).[26] G. G. Kiss et al., Phys. Lett. B , 419 (2011).[27] A. Sauerwein et al., Phys. Rev. C , 045808 (2011).[28] I. Dillmann et al., Phys. Rev. C 84, 015802 (2011).[29] A. Palumbo et al., Phys. Rev. C , 028801 (2012).[30] Z. Hal´asz et al., Phys. Rev. C , 025804 (2012).[31] G. G. Kiss et al., Phys. Rev. C , 035801 (2012).[32] T. Rauscher et al., Phys. Rev. C , 015804 (2012).[33] A. Sauerwein et al., Phys. Rev. C , 035802 (2012).[34] L. Netterdon et al., Nuclear Physics A , 149 (2013).[35] G. G. Kiss, T. Sz¨ucs, T. Rauscher, Zs. T¨or¨ok, Zs. F¨ul¨op,Gy. Gy¨urky, Z. Hal´asz, and E. Somorjai, Phys. Lett. B , 40 (2014).[36] T. Sz¨ucs, I. Dillmann, R. Plag, and Zs.F¨ul¨op, Nuclear Data Sheets , 651(2013).[38] G. G. Kiss et al., Phys. Rev. C , 045804 (2013).[39] Gy. Gy¨urky et al., Phys. Rev. C , 041601 (2012).[40] G. G. Kiss et al., Phys. Rev. C , 065807 (2011).[41] T. Rauscher, Phys. Rev. C , 045807 (2010).[42] J. Blachot, Nuclear Data Sheets, , 1239 (2009).[43] G. G¨urdal and F.G. Kondev, Nuclear Data Sheets, , 587 (1980).[46] D. De Frenne, E. Jacobs and M. Verboven, Nuclear DataSheets , 443 (1989).[47] D. De Frenne and E. Jacobs, Nuclear Data Sheets ,639 (1996).[48] T. Rauscher, NON-SMOKER code,http://nucastro.org/nonsmoker.html.[49] K. Debertin and R.G. Helmer, Gamma-And X-ray Spec-trometry With Semiconductor Detectors (North-Holland,Amsterdam, 1989).[50] C.E. Rolfs and W.S. Rodney,
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