Comprehensive test of the Brink-Axel hypothesis in the energy region of the pygmy dipole resonance
M. Markova, P. von Neumann-Cosel, A. C. Larsen, S. Bassauer, A. Görgen, M. Guttormsen, F. L. Bello Garrote, H. C. Berg, M. M. Bjørøen, T. Dahl-Jacobsen, T. K. Eriksen, D. Gjestvang, J. Isaak, M. Mbabane, W. Paulsen, L. G. Pedersen, N. I. J. Pettersen, A. Richter, E. Sahin, P. Scholz, S. Siem, G. M. Tveten, V. M. Valsdottir, M. Wiedeking, F. Zeiser
CComprehensive Test of the Brink-Axel Hypothesis in the Energy Region of thePygmy Dipole Resonance
M. Markova, ∗ P. von Neumann-Cosel, † A. C. Larsen, ‡ S. Bassauer, A. G¨orgen, M. Guttormsen, F. L. Bello Garrote, H. C. Berg, M. M. Bjørøen, T. Dahl-Jacobsen, T. K. Eriksen, D. Gjestvang, J. Isaak, M. Mbabane, W. Paulsen, L. G. Pedersen, N. I. J. Pettersen, A. Richter, E. Sahin, P. Scholz,
3, 4
S. Siem, G. M. Tveten, V. M. Valsdottir, M. Wiedeking,
5, 6 and F. Zeiser Department of Physics, University of Oslo, N-0316 Oslo, Norway Institut f¨ur Kernphysik, Technische Universit¨at Darmstadt, D-64289 Darmstadt, Germany Institut f¨ur Kernphysik, Universit¨at zu K¨oln, D-50937 K¨oln, Germany Department of Physics, University of Notre Dame, Indiana 46556-5670, USA Department of Subatomic Physics, iThemba LABS, Somerset West 7129, South Africa School of Physics, University of the Witwatersrand, Johannesburg 2050, South Africa (Dated: December 23, 2020)The validity of the Brink-Axel hypothesis, which is especially important for numerous astrophys-ical calculations, is addressed for , , Sn below the neutron separation energy by means ofthree independent experimental methods. The γ -ray strength functions (GSFs) extracted from pri-mary γ -decay spectra following charged-particle reactions with the Oslo method and with the Shapemethod demonstrate excellent agreement with those deduced from forward-angle inelastic protonscattering at relativistic beam energies. In addition, the GSFs are shown to be independent of exci-tation energies and spins of the initial and final states. The results provide the most comprehensivetest of the generalized Brink-Axel hypothesis in heavy nuclei so far, demonstrating its applicabilityin the energy region of the pygmy dipole resonance. Introduction. − Gamma-ray strength functions (GSFs)describe the average γ decay and absorption probabilityof nuclei as a function of γ energy. Besides their gen-uine interest and importance for basic nuclear physics,they are required for applications in astrophysics [1], re-actor design [2], and waste transmutation [3] based onstatistical nuclear reaction theory. A particular exam-ple is large-scale reaction network calculations of neutroncapture reactions in the r -process nucleosynthesis. Ac-cordingly, there are considerable efforts to collect data onthe GSF in many nuclei [4] and extract systematic pa-rameterization [5] which allows extrapolation to unknowncases.Although all electromagnetic multipoles can in princi-ple contribute, the GSF is dominated by E M r -process involves nuclei with extreme neutron-to-proton ratios, the impact of low-energy E n, γ ) reaction rates and the resulting r -processabundances can be significant [8–11].The GSFs used in large-scale astrophysical networkcalculations of the r -process [12] are based on model cal-culations of ground state photoabsorption. Their appli-cation requires the validity of the Brink-Axel (BA) hy- pothesis [13, 14], which in its generalized form states thatthe GSF is independent of the energies, spins, and pari-ties of the initial and final states and depends on the γ energy only. However, recent theoretical studies [15–17]put that into question, demonstrating that strength func-tions of collective modes built on excited states gener-ally do show dependence on the excitation energy. Shell-model calculations in light nuclei [16] found E γ -width distributionsobserved in s - and p -wave neutron capture experiments[26] would also represent proof against the BA hypothesis[27].There are two major sources of GSF data [4]. Oneclass of experiments determines the ground-state pho-toabsorption by measuring the subsequent γ or particledecay [23, 28]. Alternatively, the primary γ decay distri-bution is extracted in light-ion induced compound reac-tions (the so-called Oslo method [29–32]). In principle, acomparison of both methods for the same nucleus shouldprovide a test of the validity of the BA hypothesis, butis complicated by assumptions necessary to extract theGSF. For ( γ, γ (cid:48) ) experiments with broad bremsstrahlungbeams, one needs to model the experimentally inaccessi-ble ground state branching ratios and the significant con- a r X i v : . [ nu c l - e x ] D ec tributions to the spectra due to atomic scattering. Theanalysis of Oslo-type data is based on the validity of theBA hypothesis, and assumptions have to be made aboutthe intrinsic spin distribution and the reaction-dependentspin population.In such comparisons, differences have been observed inheavy deformed nuclei at excitation energies of 2–3 MeV,where the GSF is dominated by the orbital M < E E ◦ [39]. Such data also permit extraction of the M γ emission in Osloexperiments based on large-volume LaBr (Ce) detectorsallows qualitatively new tests of the BA hypothesis asdescribed below including resolved coincidence studies ofdecay to the ground state and low-lying excited states.Combining data from the two methods allows for test-ing the generalized BA hypothesis with respect to theenergy and spin independence of initial and final statesin the PDR region. Here we present a case study for , , Sn. The choice is based on the following consid-erations. (i) Data for E M p, p (cid:48) ) experiments haverecently become available [41, 42]. (ii) The isotopes havehigh neutron threshold energies providing a large overlapregion between the GSFs deduced from the ( p, p (cid:48) ) andthe Oslo experiments. (iii) While their low-energy struc-ture is very similar, the GSFs of the Sn isotopes showa distinct dependence on neutron excess in the PDR re-gion [43]. Experimental details and data analysis. − The inelasticproton scattering experiments and the methods to ex-tract the E M Sn experiment at theOslo Cyclotron Laboratory (OCL) has previously been g E0246810 ( M e V ) x E N u m b e r o f c oun t s Sn S + + FIG. 1. Experimental primary γ -ray matrix P ( E γ , E x ),Eq. (1), for Sn. The yellow dashed line indicates the neu-tron threshold S n , while the dashed red and blue lines (regions1 and 2) confine transitions to the ground state and the firstexcited J π = 2 + state at E x = 1 .
171 MeV. The solid bluelines (region 3) mark the region 4.5 MeV ≤ E x ≤ . E γ ≥ . reported in Refs. [44, 45]. The reaction Sn( He, αγ )was used to produce Sn nuclei, where the charged par-ticles were measured with eight collimated Si detectors at45 ◦ and the γ rays with the NaI(Tl) array CACTUS [46].We provide here a brief description of the , Snexperiments at OCL. A 16-MeV proton beam of in-tensity I = 3 − , Sn. The target thicknesses and enrichmentswere 2.0 mg/cm , 99.6% ( Sn) and 0.47 mg/cm , 95.3%( Sn). The reactions of interest were , Sn( p, p (cid:48) γ ).The targets were placed in the center of the Oslo SCintil-lator ARray (OSCAR) [47, 48], consisting of 30 cylindri-cal LaBr (Ce) γ -ray detectors of size 3 . × .
5” mountedon a truncated icosahedron frame. Charged particleswere registered with 64 Si particle ∆ E − E telescopes(SiRi) [49], covering angles 126 ◦ − ◦ . The energy res-olution of OSCAR is ≈ .
7% at E γ = 662 keV. Thefront-end of the LaBr (Ce) crystals were placed 16 cmfrom the center of the target. Particle- γ coincidenceswere recorded using XIA digital electronics [50]. Ap-proximately 5 . × and 1 . × proton- γ coincidenceswere measured in the excitation energy range up to theneutron thresholds for Sn and
Sn, respectively.The proton energy deposited in the SiRi telescopes wastransformed to initial excitation energy E x in the resid- - - - ) - G SF ( M e V Oslo method, tot. err.Oslo method(p,p') Sn (MeV) g E ) - M e V - G SF ( - - - Sn (MeV) g E ) - G SF ( M e V Sn (MeV) g E ) - G SF ( M e V FIG. 2. Comparison of the GSFs for , , Sn obtained from the Oslo method (blue) and from the ( p, p (cid:48) ) experiments [42](orange). The total error bands for the Oslo method (light blue) are asymmetric and include all uncertainties. The dark blueband represents statistical and systematic uncertainties from the unfolding and the extraction of primary γ rays. The E γ binwidths are 128 keV and 200 keV for the Oslo data and the ( p, p (cid:48) ) measurements respectively. ual nucleus using the reaction kinematics, and the datawere arranged in an E x vs. γ -ray energy matrix. The γ -ray spectra for each E x bin were unfolded with thetechnique described in Ref. [29] using the response func-tion of the OSCAR detectors [51]. The distribution ofprimary γ rays (the first emitted γ rays in the decay cas-cades) for each E x bin was obtained through an iterativesubtraction method [30]. The resulting primary γ -raymatrix for the example of Sn is displayed in Fig. 1.With the primary γ -ray matrix P ( E γ , E x ) at hand, wecan use the ansatz [31] P ( E γ , E x ) ∝ ρ ( E f ) T ( E γ ) (1)to simultaneously extract the level density ρ ( E f ) at thefinal excitation energy E f = E x − E γ and the γ -raytransmission coefficient T ( E γ ). For dipole decay, the γ -ray transmission coefficient is connected to the γ -raystrength function f ( E γ ) through the expression T ( E γ ) =2 πE γ f ( E γ ). The application of Eq. (1) assumes thatthe generalized form of the BA hypothesis holds. Giventhis expression, both ρ and T can be extracted from a χ minimization of a chosen area of the primary γ -raymatrix [31]. For Sn, the area confined by the bluelines (area 3) in Fig. 1 was chosen for the decomposi-tion. The minimization yields the functional forms ofboth the ρ ( E f ) and f ( E γ ), except for the absolute valueand the slope (see the Supplemental Material for details).The level density at low excitation energies is normalizedusing available information on low-lying discrete levels, while the value ρ ( S n ), obtained from the s -wave neu-tron resonance spacing D or from systematics, is usedto further constrain the normalization. Finally, the GSFis normalized to the value of the average total radiativewidth from s -wave neutron resonance experiments. De-tails of the normalization procedure, a presentation ofall parameters as well as the choice of the primary γ -raymatrix area for , , Sn can be found in the Supple-mental Material.
Results and discussion. − Figure 2 compares the GSFsfor , , Sn extracted using the Oslo method (blue)and from inelastic proton scattering [42] (orange). Inthe energy regions where both results overlap, the twofundamentally different methods yield agreement withinthe estimated uncertainty bands for all three nuclei insupport of the BA hypothesis. Peak-like structures at E γ ≈ . p, p (cid:48) )data [42, 52] as highlighted in the lower part of Fig. 2.The strength at the peak shows an increase from 1 × − MeV − to 2 . × − MeV − with the increasing neu-tron number from Sn to
Sn. A concentration ofisoscalar E Sn [53, 54]. The mutual observation in re-actions probing the isoscalar and isovector response isconsidered a signature of the PDR [6, 7]. The present re-sults from the Oslo method for , Sn find comparablestructures indicating that the PDR is also imprinted onthe quasi-continuum and is not a feature solely connectedto the ground state. We note that although systematic - - - Oslo method = 5.6 MeV i E(a) g -ray energy E g - - - ) - G SF ( M e V = 6.3 MeV i E(b) (MeV) g E - - -
10 = 7.4 MeV i E(c) Sn FIG. 3. GSF of
Sn for several narrow initial excitationenergy bins with width of 256 keV (red data points) comparedto the Oslo method result for the full excitation energy range4 . ≤ E x ≤ . E γ bin widthof 128 keV is used. uncertainties are larger for Sn due to the absence oflevel density information from neutron capture reactions,variations of the level density may shift the GSF up ordown but the peak around 6.5 MeV remains. The PDRstructure is not seen in the
Sn Oslo results, most prob-ably hindered by the limited energy resolution of the pre-viously used experimental setup. Photoabsorption crosssections for
Sn deduced from a recent ( γ, γ (cid:48) ) experi-ment exceed the present results in the energy region ofthe PDR [55]. However, we reiterate the model depen-dence of such an extraction pointed out above.An alternative way to test the BA hypothesis withOslo-type data is to study the GSF as a function of theinitial and final excitation energy as outlined in Ref. [18].From the primary γ -ray matrix, we extract the GSF for256-keV wide excitation-energy bins. This way, we caninvestigate the possible variation of the GSF as a func-tion of initial excitation energy. The results of applyingthis procedure to the Sn data are illustrated in Fig. 3, (MeV) g E - - - ) - G SF ( M e V -rays to the ground state g Shape method, -rays to the first excited state g Shape method, Oslo methodSn(p,p') Sn FIG. 4. Comparison of the GSFs for
Sn extracted with theOslo method (blue band) from selective decay to the groundstate and the first excited 2 + state utilizing the Shape method(red and green triangles) and from the ( p, p (cid:48) ) data [42] (orangeband). The E γ bin widths are 128 keV for the Oslo andShape-method data and 200 keV for the ( p, p (cid:48) ) data. where the GSFs for three narrow initial excitation en-ergies are compared to the Oslo-method data extractedfrom the full E x range. Each GSF was scaled to the Oslo-method results by a χ fit. There is overall good agree-ment, but the GSFs for the selected initial energy binsexhibit stronger fluctuations compared to the standardOslo method strength. This can be traced back to thereduced number of levels in the initial state bins whichlead to an increase of fluctuations of the Porter-Thomasintensity distribution expected for statistical decay [56].An analog analysis of the final-state energy dependenceshows comparable agreement.Finally, we test the spin independence of the present re-sults by applying a novel approach to extract the energydependence of the GSF in a largely model-independentway (the so-called Shape method [57]). Here, we use thecapability of the OSCAR array to resolve the decay tothe ground state and to the first excited 2 + state study-ing again the case of the Sn isotope (regions 1 and 2in Fig. 1). Compared to the much broader spin rangecontributing to the full Oslo data set, this defines ini-tial spin windows J = 1–3 and J = 1 for levels directlyfeeding the 2 + state and 0 + ground state, respectively.As the dipole GSF is given by [58] f ( E i , E f , E γ , J πi ) = (cid:104) Γ γ ( E i , E f , E γ , J πi ) (cid:105) ρ ( E i , J πi ) /E γ , one can extract infor-mation on the shape of the γ strength from the intensities N D proportional to the average, partial radiative width (cid:104) Γ γ ( E i , E f , E γ , J πi ) (cid:105) in the diagonals [57].The GSF deduced from the Shape method is shownin Fig. 4 together with those extracted from the Oslomethod and from the ( p, p (cid:48) ) data. Data points from de-cay to the 0 + and 2 + state are shown by red and greentriangles, respectively. The error bars include only statis-tical errors, which are typically smaller than the symbolsizes. Since the Shape method does not provide an abso-lute normalization of the strength, the results were scaledto the ( p, p (cid:48) ) data by a least-squares fit. The shapes of allthree GSFs agree within their uncertainties, demonstrat-ing independence from the particular spin distribution ofthe initial and final states. The comparison of the GSFfrom inelastic proton scattering with the Shape-methoddata points from ground state decay illustrates the di-rect correspondence between “upward” and “downward”strengths. Summary and conclusions. − We present the most com-prehensive test of the generalized BA hypothesis in heavynuclei in the energy region below the neutron thresh-old so far. It is based on a comparison of the GSFs in , , Sn deduced from relativistic Coulomb excita-tion in forward-angle inelastic proton scattering [39] andfrom Oslo-type experiments. The agreement of the twosets of GSFs demonstrates that the generalized BA hy-pothesis holds for the energy region of the PDR in thestudied cases, and experiments based on ground statephotoabsorption indeed provide the same information onGSFs in nuclei as Oslo-type experiments. The specificevolution with neutron excess in these data also high-lights the impact of the PDR on the GSFs. Despite theobservation of non-statistical decay of the PDR in recent( γ, γ (cid:48) ) experiments [37, 38], the PDR structure around6.5 MeV seems to be also present in the quasi-continuum.Further tests of the BA hypothesis include a demonstra-tion of the independence of the GSFs from the energiesand spins of initial and final states. The latter utilizes thenovel Shape method [57] which allows a largely model-independent extraction of the energy dependence of theGSF from the selective decay to specific final states.It remains an open question to what extent these re-sults can be generalized. Since we are discussing aver-aged properties, the most critical parameter is a suffi-ciently large level density. The examples studied here aresemimagic nuclei with correspondingly low level-densityvalues. Thus, we expect that our conclusion on the BAhypothesis may hold in general for heavy nuclei withground state deformation (and thus higher level densi-ties) [19] except for doubly magic cases [59]. Future workshould explore the limits of ground state photoabsorptionexperiments to extract the GSF as a function of γ energy,level density, and mass number.The authors express their thanks to J. C. M¨uller,P. A. Sobas, and J. C. Wikne at the Oslo Cyclotron Labo-ratory for operating the cyclotron and providing excellentexperimental conditions. A. Zilges is thanked for stim-ulating discussions and providing the , Sn targets.This work was supported in part by the National ScienceFoundation under Grant No. OISE-1927130 (IReNA),by the Deutsche Forschungsgemeinschaft (DFG, Ger-man Research Foundation) under Grant No. SFB 1245(project ID 279384907), by the Norwegian Research Council Grant 263030, and by the National ResearchFoundation of South Africa (Grant No. 118846). A. C. L.acknowledges funding by the European Research Coun-cil through ERC-STG-2014 under Grant Agreement No.637686, from the “ChETEC” COST Action (CA16117),supported by COST (European Cooperation in Scienceand Technology), and from JINA-CEE (JINA Center forthe Evolution of the Elements) through the National Sci-ence Foundation under Grant No. PHY-1430152. ∗ [email protected] † [email protected] ‡ [email protected][1] M. Arnould and S. Goriely, Prog. Part. Nucl. Phys. ,103766 (2020).[2] M. B. Chadwick, M. Herman, P. Oblo˘zinsk´y, M. E. Dunn,Y. Danon, A. C. Kahler, D. L. Smith, B. Pritychenko,G. Arbanas, R. Arcilla, et al. , Nucl. Data Sheets ,2887 (2011), special Issue on ENDF/B-VII.1 Library.[3] M. Salvatores and G. Palmiotti, Prog. Part. Nucl. Phys. , 144 (2011).[4] S. Goriely, P. Dimitriou, M. Wiedeking, T. Belgya,R. Firestone, J. Kopecky, M. Krtiˇcka, V. Plujko,R. Schwengner, S. Siem, et al. , Eur. Phys. J. A , 172(2019).[5] S. Goriely and V. Plujko, Phys. Rev. C , 014303 (2019).[6] D. Savran, T. Aumann, and A. Zilges, Prog. Part. Nucl.Phys. , 210 (2013).[7] A. Bracco, E. Lanza, and A. Tamii, Prog. Part. Nucl.Phys. , 360 (2019).[8] S. Goriely, Phys. Lett. B , 10 (1998).[9] S. Goriely, E. Khan, and M. Samyn, Nucl. Phys. A ,331 (2004).[10] E. Litvinova, H. Loens, K. Langanke, G. Mart´ınez-Pinedo, T. Rauscher, P. Ring, F.-K. Thielemann, andV. Tselyaev, Nucl. Phys. A , 26 (2009).[11] I. Daoutidis and S. Goriely, Phys. Rev. C , 034328(2012).[12] M. Wiescher, F. K¨appeler, and K. Langanke, Annu. Rev.Astron. Astroph. , 165 (2012).[13] D. M. Brink, Ph.D. thesis, University of Oxford (1955),doctoral thesis.[14] P. Axel, Phys. Rev. , 671 (1962).[15] G. W. Misch, G. M. Fuller, and B. A. Brown, Phys. Rev.C , 065808 (2014).[16] C. W. Johnson, Phys. Lett. B , 72 (2015).[17] N. Q. Hung, N. D. Dang, and L. T. Q. Huong, Phys. Rev.Lett. , 022502 (2017).[18] M. Guttormsen, A. C. Larsen, A. G¨orgen, T. Renstrøm,S. Siem, T. G. Tornyi, and G. M. Tveten, Phys. Rev.Lett. , 012502 (2016).[19] D. Martin, P. von Neumann-Cosel, A. Tamii, N. Aoi,S. Bassauer, C. A. Bertulani, J. Carter, L. Donaldson,H. Fujita, Y. Fujita, et al. , Phys. Rev. Lett. , 182503(2017).[20] L. C. Campo, M. Guttormsen, F. L. B. Garrote, T. K.Eriksen, F. Giacoppo, A. G¨orgen, K. Hadynska-Klek,M. Klintefjord, A. C. Larsen, T. Renstrøm, E. Sahin,S. Siem, A. Springer, T. G. Tornyi, and G. M. Tveten, Phys. Rev. C , 054303 (2018).[21] P. Scholz, M. Guttormsen, F. Heim, A. C. Larsen,J. Mayer, D. Savran, M. Spieker, G. M. Tveten, A. V.Voinov, J. Wilhelmy, F. Zeiser, and A. Zilges, Phys. Rev.C , 045806 (2020).[22] C. T. Angell, S. L. Hammond, H. J. Karwowski, J. H.Kelley, M. Krtiˇcka, E. Kwan, A. Makinaga, and G. Ru-sev, Phys. Rev. C , 051302 (2012).[23] J. Isaak, D. Savran, M. Krtiˇcka, M. Ahmed, J. Beller,E. Fiori, J. Glorius, J. Kelley, B. L¨oher, N. Pietralla,C. Romig, G. Rusev, M. Scheck, L. Schnorrenberger,J. Silva, K. Sonnabend, A. Tonchev, W. Tornow,H. Weller, and M. Zweidinger, Phys. Lett. B , 361(2013).[24] L. Netterdon, A. Endres, S. Goriely, J. Mayer, P. Scholz,M. Spieker, and A. Zilges, Phys. Lett. B , 358 (2015).[25] J. Isaak, D. Savran, B. L¨oher, T. Beck, M. Bhike,U. Gayer, Krishichayan, N. Pietralla, M. Scheck,W. Tornow, V. Werner, A. Zilges, and M. Zweidinger,Phys. Lett. B , 225 (2019).[26] P. E. Koehler, A. C. Larsen, M. Guttormsen, S. Siem,and K. H. Guber, Phys. Rev. C , 041305(R) (2013).[27] P. Fanto, Y. Alhassid, and H. A. Weidenm¨uller, Phys.Rev. C , 014607 (2020).[28] S. Bassauer, P. von Neumann-Cosel, P.-G. Reinhard,A. Tamii, S. Adachi, C. A. Bertulani, P. Y. Chan,A. D’Alessio, H. Fujioka, H. Fujita, et al. , arXiv (2020).[29] M. Guttormsen, T. S. Tveter, L. Bergholt, F. Ingebret-sen, and J. Rekstad, Nucl. Instrum. Methods Phys. Res.A , 371 (1996).[30] M. Guttormsen, T. Ramsøy, and J. Rekstad, Nucl. In-strum. Methods Phys. Res. A , 518 (1987).[31] A. Schiller, L. Bergholt, M. Guttormsen, E. Melby,J. Rekstad, and S. Siem, Nucl. Instrum. Methods Phys.Res. A , 498 (2000).[32] A. C. Larsen, M. Guttormsen, M. Krtiˇcka, E. Bˇet´ak,A. B¨urger, A. G¨orgen, H. T. Nyhus, J. Rekstad,A. Schiller, S. Siem, H. K. Toft, G. M. Tveten, A. V.Voinov, and K. Wikan, Phys. Rev. C , 034315 (2011).[33] K. Heyde, P. von Neumann-Cosel, and A. Richter, Rev.Mod. Phys. , 2365 (2010).[34] M. Guttormsen, L. A. Bernstein, A. B¨urger, A. G¨orgen,F. Gunsing, T. W. Hagen, A. C. Larsen, T. Renstrøm,S. Siem, M. Wiedeking, and J. N. Wilson, Phys. Rev.Lett. , 162503 (2012).[35] A. Voinov, E. Algin, U. Agvaanluvsan, T. Belgya,R. Chankova, M. Guttormsen, G. E. Mitchell, J. Rekstad,A. Schiller, and S. Siem, Phys. Rev. Lett. , 142504(2004).[36] A. C. Larsen, M. Guttormsen, N. Blasi, A. Bracco,F. Camera, L. C. Campo, T. K. Eriksen, A. G¨orgen,T. W. Hagen, V. W. Ingeberg, et al. , J. Phys. G ,064005 (2017).[37] C. Romig, D. Savran, J. Beller, J. Birkhan, A. Endres,M. Fritzsche, J. Glorius, J. Isaak, N. Pietralla, M. Scheck,L. Schnorrenberger, K. Sonnabend, and M. Zweidinger,Phys. Lett. B , 369 (2015).[38] B. L¨oher, D. Savran, T. Aumann, J. Beller, M. Bhike,N. Cooper, V. Derya, M. Duchˆene, J. Endres, A. Hennig, et al. , Phys. Lett. B , 72 (2016).[39] P. von Neumann-Cosel and A. Tamii, Eur. Phys. J. A , 110 (2019). [40] J. Birkhan, H. Matsubara, P. von Neumann-Cosel,N. Pietralla, V. Y. Ponomarev, A. Richter, A. Tamii,and J. Wambach, Phys. Rev. C , 041302(R) (2016).[41] S. Bassauer, P. von Neumann-Cosel, P.-G. Reinhard,A. Tamii, S. Adachi, C. A. Bertulani, P. Y. Chan,G. Col`o, A. D’Alessio, H. Fujioka, et al. , Phys. Lett. B , 135804 (2020).[42] S. Bassauer, P. von Neumann-Cosel, P.-G. Reinhard,A. Tamii, S. Adachi, C. A. Bertulani, P. Y. Chan,A. D’Alessio, H. Fujioka, H. Fujita, et al. , Phys. Rev.C , 034327 (2020).[43] S. Bassauer, Doctoral thesis D17, Technische Uni-versit¨at Darmstadt (2019); http://tuprints.ulb.tu-darmstadt.de/9668.[44] H. K. Toft, A. C. Larsen, A. B¨urger, M. Guttormsen,A. G¨orgen, H. T. Nyhus, T. Renstrøm, S. Siem, G. M.Tveten, and A. Voinov, Phys. Rev. C , 044320 (2011).[45] U. Agvaanluvsan, A. C. Larsen, M. Guttormsen,R. Chankova, G. E. Mitchell, A. Schiller, S. Siem, andA. Voinov, Phys. Rev. C , 014320 (2009).[46] M. Guttormsen, A. Atac, G. Løvhøiden, S. Messelt,T. Ramsøy, J. Rekstad, T. Thorsteinsen, T. Tveter, andZ. Zelazny, Phys. Scripta T32 , 54 (1990).[47] V. W. Ingeberg et al. , in preparation (2020).[48] F. Zeiser, G. M. Tveten, F. L. B. Garrote, M. Gut-tormsen, A. C. Larsen, V. W. Ingeberg, A. G¨orgen,and S. Siem, Nucl. Instrum. Methods Phys. Res. A ,164678 (2021).[49] M. Guttormsen, A. B¨urger, T. E. Hansen, and N. Lietaer,Nucl. Instrum. Methods Phys. Res. A , 168 (2011).[50]
Pixie-16 User Manual, Version 3.06 , XIA (2019).[51] F. Zeiser and G. M. Tveten, oslocyclotronlab/ocl geant4:Geant4 model of oscar (2018).[52] A. M. Krumbholz, P. von Neumann-Cosel, T. Hashimoto,A. Tamii, T. Adachi, C. A. Bertulani, H. Fujita, Y. Fu-jita, E. Ganioglu, K. Hatanaka, et al. , Phys. Lett. B ,7 (2015).[53] J. Endres, D. Savran, P. A. Butler, M. N. Harakeh,S. Harissopulos, R.-D. Herzberg, R. Kr¨ucken, A. Lagoy-annis, E. Litvinova, N. Pietralla, V. Y. Pono-marev, L. Popescu, P. Ring, M. Scheck, F. Schl¨uter,K. Sonnabend, V. I. Stoica, H. J. W¨ortche, and A. Zilges,Phys. Rev. C , 064331 (2012).[54] L. Pellegri, A. Bracco, F. C. L. Crespi, S. Leoni, F. Cam-era, E. G. Lanza, M. Kmiecik, A. Maj, R. Avigo, G. Ben-zoni, et al. , Phys. Lett. B , 519 (2014).[55] M. M¨uscher, J. Wilhelmy, R. Massarczyk,R. Schwengner, M. Grieger, J. Isaak, A. R. Jung-hans, T. K¨ogler, F. Ludwig, D. Savran, D. Symochko,M. P. Tak´acs, M. Tamkas, A. Wagner, and A. Zilges,Phys. Rev. C , 014317 (2020).[56] C. E. Porter and R. G. Thomas, Phys. Rev. , 483(1956).[57] M. Wiedeking, M. Guttormsen, A. C. Larsen, F. Zeiser,A. G¨orgen, S. N. Liddick, D. M¨ucher, S. Siem, andA. Spyrou, arXiv:2010.15696.[58] G. A. Bartholomew, E. D. Earle, A. J. Ferguson, J. W.Knowles, and M. A. Lone, Adv. Nucl. Phys. , 229(1973).[59] S. Bassauer, P. von Neumann-Cosel, and A. Tamii, Phys.Rev. C94