Investigation of pair-correlated 0^+ states in ^{134}Ba via the ^{136}Ba(p,t) reaction
J. C. Nzobadila Ondze, B. M. Rebeiro, S. Triambak, L. Atar, G. C. Ball, V. Bildstein, C. Burbadge, A. Diaz Varela, T. Faestermann, P. E. Garrett, R. Hertenberger, M. Kamil, R. Lindsay, J. N. Orce, A. Radich, H.-F. Wirth
aa r X i v : . [ nu c l - e x ] J a n Investigation of pair-correlated 0 + states in Ba via the
Ba( p, t ) reaction
J. C. Nzobadila Ondze, B. M. Rebeiro, ∗ S. Triambak, † L. Atar, G. C. Ball, V. Bildstein, C. Burbadge, A. Diaz Varela, T. Faestermann, P. E. Garrett,
2, 1
R. Hertenberger, M. Kamil, R. Lindsay, J. N. Orce, A. Radich, and H. -F. Wirth Department of Physics and Astronomy, University of the Western Cape, P/B X17, Bellville 7535, South Africa Department of Physics, University of Guelph, Guelph, Ontario N1G 2W1, Canada TRIUMF, 4004 Wesbrook Mall, Vancouver, British Columbia V6T 2A3, Canada. Physik Department, Technische Universit¨at M¨unchen, D-85748 Garching, Germany Fakult¨at f¨ur Physik, Ludwig-Maximilians-Universit¨at M¨unchen, D-85748 Garching, Germany (Dated: February 1, 2021)We performed a high resolution study of 0 + states in Ba using the
Ba( p, t ) two-neutrontransfer reaction. Our experiment shows a significant portion of the L = 0 pair-transfer strengthconcentrated at excited 0 + levels in Ba. Potential implications in the context of Xe → Baneutrinoless double beta decay matrix element calculations are briefly discussed.
The even-mass barium isotopic chain ( Z = 56) is a fertiletesting ground for nuclear structure models and also im-portant for nuclear astrophysics studies and tests of fun-damental symmetries. For example, theory calculationspredict an enhanced octupole collectivity around Ba,which is located on the N = Z line [1, 2]. Possible oc-tupole correlations have been observed in the neutron-deficient Ba [3] and
Ba [4] isotopes, while thereis clear experimental evidence of octupole deformationin the ground states of neutron-rich Ba nuclei around N = 88 [5, 6]. Furthermore, for N ≤
82, in the A ∼ N = 82) to γ -soft [8], wherethe shape changes are characterized by quantum phasetransitions (QPTs) [9, 10]. Within the interacting bosonmodel (IBM), the Ba isotope was identified as a poten-tial E (5) symmetry critical point [11] for a second-orderQPT. Independently, from a nuclear astrophysics per-sective, fractional abundance ratios of odd-to-even bar-ium isotopes as well as relative elemental ratios such as[Ba/Fe] and [Ba/Eu] etc, offer insight into the r and s -process neutron capture contributions [12, 13] to heavyelement nucleosynthesis in stellar environments. This isparticularly relevant in metal-poor stars, where the dom-inant contribution to elemental abundances is expectedto be from the r -process [14]. One interesting exampleis the subgiant HD140283, in which case the fractionalbarium abundances obtained from independent spectralanalyses have yielded inconsistent results. These discrep-ancies have stirred a debate on the assumed r -processorigin of the odd Ba isotopes during the early stages ofgalactic evolution [15–19].In the context of fundamental symmetries, Ba is thedaughter nucleus in
Xe double beta decay, an attrac-tive candidate to search for the lepton-number-violating ∗ Present address: Univ Lyon, Univ Claude Bernard Lyon 1,CNRS/IN2P3, IP2I Lyon, UMR 5822, F-69622, Villeurbanne,France † [email protected] neutrinoless double beta (0 ν β ) transformation. Obser-vation of such decays would unequivocally show that theneutrinos are their own antiparticles (i.e. they are Majo-rana fermions). In such a scenario, other useful informa-tion on lepton-number-violating new physics or the abso-lute neutrino mass scale, etc. can only be obtained if thenuclear matrix element (NME) for the decay is accuratelyknown [20, 21]. To this end, a variety of many-body tech-niques are used to evaluate 0 ν β decay NMEs in severalcandidate nuclei. These calculations have yielded signif-icantly discrepant results for individual cases [20]. Ad-dressing this apparent model dependence in all doublebeta decaying nuclei remains an important issue. Wefocus on this aspect here.The dominant contribution to a 0 ν β decay NMEarises from the transformation of nucleon pairs that cou-ple to total angular momentum J = 0 [22–24]. Sucha decay corresponds to spherical superfluid parent anddaughter nuclei. The J = 0 contributions to the matrixelement arise from higher seniority [22, 23] componentsin the wavefunctions, due to broken Cooper pairs of nu-cleons. These lead to cancellations and effectively reducethe 0 ν β decay amplitude. An additional reduction inthe NME is expected if there is a seniority mismatch be-tween the initial and the final wavefunctions [25]. Thiswould be the case if the parent and the daughter havedifferent intrinsic shapes [26], that are driven by multi-pole correlations. It is now established that these col-lective correlations (other than pairing) play an impor-tant role in 0 ν β NME calculations [20] and could furtherquench calculated NMEs [26]. As examples, one can lookat two traditionally used many-body methods, the Inter-acting Shell Model (ISM) and the Quasiparticle RandomPhase Approximation (QRPA). In the former, the treat-ment of correlations is exact, with comparatively smallervalence spaces. On the other hand, the QRPA calcu-lations use larger model spaces, with relatively simplerconfigurations for the valence nucleons. Here, the pair-ing between like nucleons is treated via a transformationto the quasiparticle regime, within the Bardeen-Cooper-Schrieffer (BCS) approximation [27]. Such BCS pairingsmears the Fermi surfaces in the parent and the daugh-ter (as one would expect in a superfluid), while the RPAcorrelations admix higher seniority components in thewavefunctions [23, 25]. In this context, ( p, t ) [28–31] and( He , n ) [32] two-nucleon transfer experiments offer valu-able insight into pairing correlations between like nucle-ons [33]. For reactions on even-even nuclei, strong popu-lation of the ground states (relative to excited 0 + states)would imply that both the target and residual nucleusground states are nearly superfluid, and well describedby BCS wavefunctions [28, 33].For the case of Xe → Ba, the 0 ν β decay NMEdiffers more than a factor of four, depending on the many-body technique used [34]. This is an important issue as Xe decay is a promising candidate to search for 0 ν β decays [34]. In fact, several planned large-scale time pro-jection chamber (TPC)-based experiments aim to mea-sure Xe 0 ν β decay [35–38]. From a nuclear structureperspective this is an interesting case, because of its lo-cation in a shape-transitional region of the Segr`e chart.While the nearly spherical Xe has a closed shell at N = 82, the daughter Ba has N = 80.In light of the above, we recently benchmarked the J = 0 part of the Xe 0 ν β decay NME, via a studyof neutron pairing correlations using the Ba( p, t ) reac-tion [34]. Contrary to what one would expect for spheri-cal superfluid systems [33], we observed for the first timea strong population of higher lying 0 + states, relative tothe ground state in Ba. About 53% of the groundstate L = 0 ( p, t ) strength was distributed over excited0 + states, with ∼
35% concentrated at the 0 +2 , 0 +3 and0 +4 levels. This was clear evidence of a breakdown of theBCS approximation for neutrons in Ba. The resultsalso implied significantly different ground state wave-functions for the spherical
Ba and the (final-state)
Ba nucleus. If this were the case, because one canexpect nearly identical ground state wavefunctions forthe N = 82 Ba and
Xe nuclei, a sizable differencein deformation (seniority mismatch) between the parentand the daughter in Xe → Ba ββ decay cannot beruled out.Further investigations of shape-transitional barium iso-topes around A ∼
130 are relevant in context of theabove. Previous data from ( p, t ) reactions on barium iso-topes show inconclusive evidence in this regard. For the
Ba( p, t ) case, Cˇata-Danil et al. [39] observe around34% of the ground state strength distributed over ex-cited 0 + states in Ba. However their measured L = 0strength distribution was around a factor of two largerthan what was reported in subsequent work by Pascu etal. [40]. Similarly, for the Ba( p, t ) reaction, Ref. [39]report ∼
27% of the ground state strength distributedover excited 0 + states, while Ref. [40] claim this valueis much smaller, at around 10%. Adequate Ba( p, t )angular distribution data were not presented in both ref-erences. In comparison, measured , Ba( p, t ) crosssections do not show a similar fragmentation of themonopole strength [41, 42].
FIG. 1. Particle identification spectra using energy losses reg-istered in the two proportional counters and the total energydeposited in the plastic scintillator. The triton groups arehighlighted. The other particles are mainly deuterons.
Considering the aforementioned discrepancies andgiven the importance of the measured results, in thisLetter we report remeasurements of the relative popula-tion of 0 + states in Ba, with the
Ba( p, t ) reaction.The experiment was performed at the Maier-Leibnitz-Laboratorium (MLL), operated jointly by the Ludwig-Maximilian Universit¨at (LMU) and Technische Univer-sit¨at M¨unchen (TUM), in Garching, Germany. 22 MeVprotons from the MLL tandem accelerator were directedonto a 40 µg/ cm , 93% isotopically enriched BaO tar-get, that was evaporated on a thin carbon foil. Thelight reaction products were momentum analyzed withthe high-resolution Q3D magnetic spectrograph [43, 44].The focal plane detector for the spectrograph comprisedtwo gas proportional counters and a 7-mm-thick plasticscintillator [44]. The energy losses of the charged ejec-tiles in the proportional counters and the residual energydeposited in the plastic scintillator were used to discrim-inate the tritons from other ejectiles (as shown in Fig. 1).A cathode strip foil in the second proportional counter
800 1000 1200 1400 160010 Excitation Energy (keV) C oun t s / k e V + + + * + + * * * * *** * + ** + * FIG. 2. Triton spectra corresponding to states in
Ba, at θ lab = 25 ◦ . Peaks from contaminants in the target are markedwith asterisks. The 0 + states observed in this experiment arelabeled. The state at ∼ provided high-resolution position information for the tri-tons.We collected triton spectra at five magnetic field set-tings and at ten angles, ranging from 5 ◦ to 50 ◦ (in 5 ◦ increments). The Q3D field settings allowed us to studystates in Ba up to ∼ .
10 keV for thetriton peaks. The triton energies were calibrated in-situ ,using well known states in
Ba [47]. A sample spectrumis shown in Fig. 2.During the course of the experiment, we also col-lected
Ba( p, p ) data over an angular range of 10 ◦ -60 ◦ . These data allowed us to accurately determinethe effective Ba areal density in the target foil, forsmall angle scattering. In addition, both the ( p, p ) andthe ( p, t ) data sets from this work were analyzed as de-scribed in Ref. [34], given the similarity between the twoexperiments. We performed distorted wave Born ap-
Scattering angle ( θ c.m. ) -1 d σ / d Ω ( m b / s r) E x = 0 keVLi, Liang and CaiBecchetti and Greenless FIG. 3. Measured
Ba ground state angular distributioncompared with normalized DWBA predictions obtained usingdifferent triton OMPs [45, 46]. -1 -2 -1 -2 -1 -3 -2 d σ / d Ω ( m b / s r) -2 -1
10 20 30 40 50 θ c.m. (deg) -3 -2
10 20 30 40 50 θ c.m. (deg) -2 -1 Ground state1760 keV2159 keV d σ / d Ω ( m b / s r) FIG. 4.
Ba( p, t ) angular distributions for observed 0 + states in Ba, compared with normalized DWBA predic-tions for L = 0 transfer. proximation (DWBA) calculations of angular distribu-tions using the DWUCK4 code [48] and compared themto our experimental results. The DWBA analysis usedWoods-Saxon potentials and global optical model poten-tial (OMP) parameters. Based on the agreement withour measured Ba( p, p ) cross sections and a compari-son with previous
Ba( p, p ) data obtained over a largeangular range [34], we chose the global OMP parame-ters recommended by Varner et al. [49] for the incomingproton channel in the DWUCK4 calculations. For thetriton channel we chose the OMPs recommended by Li,
TABLE I. Measured L = 0 Ba( p, t ) strength distributionover excited 0 + states in Ba, relative to the ground state. a For comparison we also list the results from previous work [39,40].Ref. [39] Ref. [40] This work E x ǫ i E x ǫ i E x ǫ i (keV) (%) (keV) (%) (keV) (%)1759 3 .
73 1760 . . . . .
85 2159 . . . . ≤ . ... ... . ≤ . .
52 2380 . b . . ≤ . .
67 2488 . . . . .
99 2727 . . . . .
81 2883 . . . . ... . b . ... ... .
63 3000 . . ... ... . ... ... ... ... ... ... . . ... ... .
47 3505 . . ... ... ... ... ... ... . ... . b . ... ... .
22 3623 . b . ... ... ... ... . b . ... ... P ǫ i = 34% P ǫ i = 17.1(4)% P ǫ i = 44.9(9)% a The 0 + assignments for states above 2488 keV were onlymade from Ba( p, t ) measurements. b These states were tentatively assigned spin-parity J π = (0 + ). Liang, and Cai [45], as they yielded better agreementwith our measured ground state angular distribution for
Ba. This is shown in Fig. 3. The two-neutron transferform factor was obtained using the OMPs from Ref. [50],assuming a (0 h / ) configuration. For each state, thedepth of the potential was adjusted such that each trans-ferred neutron had a binding energy ( S n + E x ) /
2, where S n is the two neutron separation energy of Ba and E x is the excitation energy in the residual Ba nucleus.The above DWBA prescription was used to performan angular distribution analysis of all the peaks shownin Fig. 2, that corresponded to states in
Ba. We iden-tify seven 0 + states in Ba. These include the groundstate and a previously unreported level at 3528 keV. The measured angular distributions are shown in Fig. 4.These data determined the monopole ( p, t ) strengths toexcited 0 + states, using the ratio [34] ǫ i = " (cid:0) dσd Ω (cid:1) data0 + ex (cid:0) dσd Ω (cid:1) DWBA0 + ex i " (cid:0) dσd Ω (cid:1) DWBAG . S . (cid:0) dσd Ω (cid:1) dataG . S . , (1)so that the Q value dependence on the cross sections wasremoved. An independent confirmation of this state would be welcome.
The results are shown in Table I. We find that our ex-tracted value for the integrated strength is more consis-tent with the result of Cˇata-Danil et al. [39] and disagreessignificantly with the later work of Pascu et al. [40]. Itis also apparent that there are some large discrepanciesbetween our work and Ref. [40] for individual states, andthat we observe fewer excited 0 + states than either ofthese measurements. We briefly discuss a few aspects ofthis comparison below.The Nuclear Data Sheets (NDS) for A = 134 [51] list adoublet of states at 2334.76(6) and 2336.82(3) keV. Theselevels are assigned spin-parity (1 , + ) and 0 + respec-tively. The Q3D spectrograph (also used in Refs. [39, 40])is limited by energy resolution to differentiate betweenthese two states. We observe a single triton peak cor-responding to E x = 2334 . L = 2transition. This indicates that the population of the2337 keV level was below our experimental sensitivity.We encounter a similar situation near 2.4 MeV, with twoknown closely-spaced states at 2379.112(18) keV [51] and2377.1(4) keV [51, 52]. The former is an established 0 + level, while the latter was assigned a tentative spin valueof J = (6) [51]. Our spectrum shows a triton peak cor-responding to 2379.0(4) keV, whose measured angulardistribution agrees well with L = 2 transfer.As a result of the above, we measured cross sections at5 ◦ to place upper limits on the possible L = 0 strengthsfor the 2337 and 2379 keV levels. Several of the otherweakly populated 0 + states at higher excitation energywere not observed in this work. A probable explanationfor this can be invoked from the fact that the previousmeasurements were carried out at a higher beam energyof 25 MeV. Due to the large negative Q value for this re-action ( − . L = 0 cross section at the mostforward angles decreases more rapidly with increase inexcitation energy for 22 MeV protons as compared to25 MeV. Our DWBA calculations show that at 22 MeV,the forward angle differential cross sections are arounda factor of 2 smaller at 1.8 MeV excitation energy, com-pared to those at 25 MeV. This factor increases to ap-proximately 5 and 10 at excitation energies of 2.5 and3.5 MeV, respectively. In contrast, large changes in for-ward angle differential cross sections are not predictedfor L = 2 transitions.It is difficult to comment further since both Refs. [39,40] reported meager Ba( p, t ) angular distribution data.Cˇata-Danil et al. [39] acquired data at only two anglesand chose to identify the L = 0 transitions using a sin-gle number, the ratio of the cross sections at θ lab = 6 ◦ and 15 ◦ . In comparison, Pascu et al. acquired data atonly three angles [40] and do not explicitly show angular The results of Refs. [39, 40] are also discordant with one another,for both , Ba( p, t ) data. A detailed analysis of the full data set will be presented in afuture publication. distributions for excited 0 + states. They identified the0 + states using the same procedure as in Ref. [39]. Ade-quate descriptions regarding the choice of OMP param-eters for their analyses and the procedure to determinetarget thicknesses were not provided in these references.However, since both these works provided more complete Ba( p, t ) angular distribution plots, we are able to ad-dress the discrepancy for this reaction. In particular, ourestimated values of ǫ i (via inspection and from DWBAcalculations) show better agreement with the results ofRef. [39] and significantly disagree with the results inRef. [40]. This gives credence to the former results overthe latter.It is evident from our results in Table I that a sig-nificant portion of the ( p, t ) strength is distributed overexcited 0 + levels in Ba. This is similar to our pre-viously reported
Ba( p, t ) results [34] and clearly indi-cates a breakdown of the BCS approximation for neu-trons in
Ba. The persistence of such behavior as onemoves away from the N = 82 shell closure, with inte- grated , , Ba( p, t ) strengths being ∼ Ba,
Ba and
Ba and a mis-match between the wavefunctions for the initial and finalstates in Xe ββ decay. Such a curtailed overlap offersa possible explanation for the comparatively long 2 ν β decay half-life [55] measured for Xe. It would also re-duce its calculated 0 ν β decay NME compared to a sce-nario in which both the parent and daughter are nearlyspherical (or similarly deformed). Both experimental in-vestigations of quadrupole correlations in Ba as wellas theoretical studies of deformation effects on the NME(along the lines of Refs. [56, 57]) will be useful to furthershed light in this regard.This work was partially funded by the National Re-search Foundation (NRF), South Africa under Grant No.85100. J.C.N.O thanks the NRF funded MaNuS/MatSciprogram at UWC for financial support during the courseof his M.Sc. [1] J. Skalski, Physics Letters B , 6 (1990).[2] P.-H. Heenen, J. Skalski, P. Bonche, and H. Flocard,Phys. Rev. C , 802 (1994).[3] J. F. Smith et al. , Phys. Rev. C , R1037 (1998).[4] P. Mason et al. , Phys. Rev. C , 064315 (2005).[5] B. Bucher et al. , Phys. Rev. Lett. , 112503 (2016).[6] B. Bucher et al. , Phys. Rev. Lett. , 152504 (2017).[7] E. Marshalek, L. W. Person, and R. K. Sheline,Rev. Mod. Phys. , 108 (1963).[8] R. Casten and P. Von Brentano,Physics Letters B , 22 (1985).[9] P. Cejnar, J. Jolie, and R. F. Casten,Rev. Mod. Phys. , 2155 (2010).[10] K. Nomura, T. Nikˇsi´c, and D. Vretenar,Phys. Rev. C , 014304 (2017).[11] R. F. Casten and N. V. Zamfir,Phys. Rev. Lett. , 3584 (2000).[12] L. Mashonkina, T. Gehren, and I. Bikmaev, Astronomyand Astrophysics , 249 (2000).[13] T. Tsujimoto, T. Shigeyama, and Y. Yoshii,The Astrophysical Journal , L33 (2000).[14] J. W. Truran, Astronomy and Astrophysics , 391(1981).[15] Gallagher, A. J., Ryan, S. G.,Garc´ıa P´erez, A. E., and Aoki, W.,Astronomy and Astrophysics , A24 (2010).[16] P. Magain, Astronomy and Astrophysics , 686 (1995).[17] P. Francois, Astronomy and Astrophysics , 229(1996).[18] R. Collet, M. Asplund, and P. E. Nissen,Publications of the Astronomical Society of Australia , 330–334 (2009).[19] D. L. Lambert and C. Allende Prieto,Monthly Notices of the Royal Astronomical Society , 325 (2002).[20] Jonathan Engel and Javier Men´endez, Reports onProgress in Physics , 046301 (2017).[21] H. Ejiri, J. Suhonen, and K. Zuber,Physics Reports , 1 (2019). [22] E. Caurier, J. Men´endez, F. Nowacki, and A. Poves,Phys. Rev. Lett. , 052503 (2008).[23] F. ˇSimkovic, A. Faessler, V. Rodin, P. Vogel, and J. En-gel, Phys. Rev. C , 045503 (2008).[24] Y. Iwata, N. Shimizu, T. Otsuka, Y. Ut-suno, J. Men´endez, M. Honma, and T. Abe,Phys. Rev. Lett. , 112502 (2016).[25] E. Caurier, F. Nowacki, and A. Poves,The European Physical Journal A , 195 (2008).[26] Alfredo Poves, “Neutrinoless double beta decay pairingmatters,” in Fifty Years of Nuclear BCS , edited by R. A.Broglia and V. Zelevinsky (World Scientific, 2013) pp.297–308.[27] F. T. Avignone, S. R. Elliott, and J. Engel,Rev. Mod. Phys. , 481 (2008).[28] S. J. Freeman, J. P. Schiffer, A. C. C. Villari, J. A.Clark, C. Deibel, S. Gros, A. Heinz, D. Hirata, C. L.Jiang, B. P. Kay, A. Parikh, P. D. Parker, J. Qian,K. E. Rehm, X. D. Tang, V. Werner, and C. Wrede,Phys. Rev. C , 051301 (2007).[29] T. Bloxham, B. P. Kay, J. P. Schiffer, J. A. Clark, C. M.Deibel, S. J. Freeman, S. J. Freedman, A. M. Howard,S. A. McAllister, P. D. Parker, D. K. Sharp, and J. S.Thomas, Phys. Rev. C , 027308 (2010).[30] J. S. Thomas, S. J. Freeman, C. M. Deibel, T. Faester-mann, R. Hertenberger, B. P. Kay, S. A. McAllister, A. J.Mitchell, J. P. Schiffer, D. K. Sharp, and H.-F. Wirth,Phys. Rev. C , 047304 (2012).[31] D. K. Sharp, S. J. Freeman, B. D. Cropper, P. J.Davies, T. Faestermann, T. M. Hatfield, R. Hertenberger,S. J. F. Hughes, P. T. MacGregor, and H.-F. Wirth,Phys. Rev. C , 024329 (2019).[32] A. Roberts, A. M. Howard, J. J. Kolata, A. N. Vil-lano, F. D. Becchetti, P. A. DeYoung, M. Febbraro, S. J.Freeman, B. P. Kay, S. A. McAllister, A. J. Mitchell,J. P. Schiffer, J. S. Thomas, and R. O. Torres-Isea,Phys. Rev. C , 051305 (2013). [33] R. A. Broglia, O. Hansen, and C. Riedel, “Two-neutrontransfer reactions and the pairing model,” in Advances inNuclear Physics: Volume 6 , edited by M. Baranger andE. Vogt (Springer US, Boston, MA, 1973) pp. 287–457.[34] B. M. Rebeiro, S. Triambak, P. E. Garrett, B. A.Brown, G. C. Ball, R. Lindsay, P. Adsley, V. Bild-stein, C. Burbadge, A. Diaz Varela, T. Faestermann,D. L. Fang, R. Hertenberger, M. Horoi, B. Jigmed-dorj, M. Kamil, K. G. Leach, P. Z. Mabika, J. C.Nzobadila Ondze, J. N. Orce, and H.-F. Wirth,Physics Letters B , 135702 (2020).[35] J. B. Albert et al. (nEXO Collaboration),Phys. Rev. C , 065503 (2018).[36] D. S. Akerib et al. (LUX-ZEPLIN Collaboration),Phys. Rev. C , 014602 (2020).[37] F. Agostini et al. (DARWIN Collaboration),The European Physical Journal C , 808 (2020).[38] J. J. Gomez-Cadenas, Nuclear and Particle Physics Proceedings , 1732 (2016),37th International Conference on High Energy Physics(ICHEP).[39] G. Cˇata-Danil, D. Bucurescu, L. Trache, A. M. Oros,M. Jaskola, A. Gollwitzer, D. Hofer, S. Deylitz, B. D.Valnion, and G. Graw, Phys. Rev. C , 2059 (1996).[40] S. Pascu, G. Cˇata-Danil, D. Bucurescu,N. M˘arginean, C. M¨uller, N. V. Zamfir, G. Graw,A. Gollwitzer, D. Hofer, and B. D. Valnion,Phys. Rev. C , 014304 (2010).[41] S. Pascu, G. Cˇata-Danil, D. Bucurescu, N. M˘arginean,N. V. Zamfir, G. Graw, A. Gollwitzer, D. Hofer, andB. D. Valnion, Phys. Rev. C , 064323 (2009).[42] G. Suliman, D. Bucurescu, R. Hertenberger, H. F. Wirth,T. Faestermann, R. Kr¨ucken, T. Behrens, V. Bild-stein, K. Eppinger, C. Hinke, M. Mahgoub, P. Meier- beck, M. Reithner, S. Schwertel, and N. Chauvin,Eur. Phys. J. A , 243 (2008).[43] M. L¨offler, H. Scheerer, and H. Vonach,Nuclear Instruments and Methods , 1 (1973).[44] G. Dollinger and T. Faestermann, Nuclear Physics News , 5 (2018).[45] X. Li, C. Liang, and C. Cai,Nuclear Physics A , 103 (2007).[46] R. Capote et al. , Nuclear Data Sheets , 3107 (2009),Special Issue on Nuclear Reaction Data.[47] .[48] P. D. Kunz, DWUCK4 DWBA Program (University ofColorado, unpublished, 1978).[49] R. Varner, W. Thompson, T. McAbee, E. Ludwig, andT. Clegg, Physics Reports , 57 (1991).[50] F. D. Becchetti and G. W. Greenlees,Phys. Rev. , 1190 (1969).[51] A. A. Sonzogni, Nuclear Data Sheets , 1 (2004).[52] B. Fazekas, T. Belgya, G. Moln´ar, ´A. Veres,R. Gatenby, S. Yates, and T. Otsuka,Nuclear Physics A , 249 (1992).[53] V. S. Aleksandrov, B. S. Dzhelepov, A. I. Medvedev,V. E. Ter-Nersesyants, I. F. Uchevatkin, and S. A.Shestopalova, Bull. Acad. Sci. USSR, Phys. Ser. , 106(1974).[54] R. A. Meyer, R. D. Griffioen, J. G. Lefler, and W. B.Walters, Phys. Rev. C , 2024 (1976).[55] R. Saakyan, Annual Review of Nuclear and Particle Science , 503 (2013).[56] P. K. Rath, R. Chandra, K. Chaturvedi, P. K. Raina,and J. G. Hirsch, Phys. Rev. C , 044303 (2009).[57] D.-L. Fang, A. Faessler, V. Rodin, and F. ˇSimkovic,Phys. Rev. C83