Preliminary experimental data for nucleon transfer reactions of the 40Ca + 58Ni and 40Ca + 64Ni systems are analyzed with the coupled-channels approach. It is shown that a simple treatment for the transfer in the coupled-channels method cannot reproduce simultaneously the transfer probabilities and the subbarrier enhancement of fusion cross sections

Bourgin, D.

Courtin, S.

Haas, F.

Hagino, K.

Scamps, G.

arXiv

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DOI 10.1393/ncc/i2016-16414-7Colloquia: IWM-EC 2016IL NUOVO CIMENTO 39 C (2016) 414Coupled-channels description of the 40Ca + 58,64Ni transferand fusion reactionsG. Scamps(1), D. Bourgin(2)(3), K. Hagino(1), F. Haas(2)(3)and S. Courtin(2)(3)(4)(1) Department of Physics, Tohoku University - Sendai 980-8578, Japan(2) IPHC, Université de Strasbourg - F-67037 Strasbourg, France(3) CNRS, UMR7178 - F-67037 Strasbourg, France(4) USIAS - F-67083 Strasbourg, Francereceived 10 January 2017Summary. — Preliminary experimental data for nucleon transfer reactions ofthe 40Ca + 58Ni and 40Ca + 64Ni systems are analyzed with the coupled-channelsapproach. It is shown that a simple treatment for the transfer in the coupled-channelsmethod cannot reproduce simultaneously the transfer probabilities and the sub-barrier enhancement of fusion cross sections.An extra enhancement of fusion cross sections at low energies is often attributed todifferent transfer processes. Several approaches have been employed in order to reproducethis enhancement. In our previous analysis [1], we attempted to reproduce simultaneouslythe experimental transfer probabilities and the fusion cross sections for the reaction96Zr + 40Ca [2]. The strategy was to adjust the transfer coupling to the experimentaltransfer data and to compare the fusion cross sections obtained with this approach tothe experimental data. A slight underestimation of the fusion cross sections was foundat low energies. On the other hand, Esbensen et al. [3] showed that it was possible toreproduce perfectly the fusion cross sections if one takes into account in addition theproton transfer channels.In this contribution, we test this approach on the 40Ca+58Ni and 40Ca+64Ni systems,for which the fusion cross sections have been measured in ref. [4]. The TDHF theory [5]has shown that the major difference between these two systems is due to the neutrontransfer. It is expected that the transfer probability for the 40Ca + 64Ni system is byabout one order of magnitude higher than that for the 40Ca + 58Ni system. In thepresent contribution, we shall try to reproduce the neutron and proton transfer channelssimultaneously with the enhancement of the fusion cross sections at low energies.The experiment has been recently performed at LNL in inverse kinematics at energiesaround and below the Coulomb barrier. 64Ni and 58Ni beams were delivered by the XTUTandem accelerator (Elab = 174, 190 and 210 MeV for 64Ni, and Elab = 170 and 201 MeVCreative Commons Attribution 4.0 License (http://creativecommons.org/licenses/by/4.0) 12 G. SCAMPS et al.Table I. – The values of Woods-Saxon real and imaginary potentials employed in the coupled-channels calculations.System V0 [MeV] r0 [fm] a [fm] W0 [MeV] rW [fm] aW [fm]40Ca + 58Ni 60.41 1.17 0.66 35 1.1 0.240Ca + 64Ni 68.70 1.16 0.66 35 1.1 0.2for 58Ni) onto a 100 micro g/cm2 strip 40Ca target deposited on a 15 micro g/cm2 12Cbacking. The 40Ca target-like ions were detected and identified by the large acceptance(±5◦) PRISMA magnetic spectrometer around θlab = 45◦. Four transfer channels wereidentified: +1n, +2n, −1p and −2p, where the + sign means a transfer from the Nifragment to the 40Ca one.The coupled-channels calculations have been carried out with the program CC-FULL [6], that has been modified in order to compute the neutron and proton transferprobabilities.The same method as in ref. [1] has been used, with values for the nucleus-nucleuspotential given in table I and with the coupling parameters to the transfer channel intable II. This model assumes that the pair transfer is a sum of two processes, that is, adirect pair transfer and a sequential transfer. The sequential transfer coupling is assumedto be equal to the single transfer, i.e. a12=a01. As in ref. [4], we take into account theexcitation to the first 3− state in 40Ca at energy 3.736 MeV with a coupling strength ofβ = 0.4, the 2+ state in 58Ni at 1.454 MeV with β = 0.18, and the 2+ state in 58Ni at1.346 MeV with β = 0.16.The transfer probabilities are computed as the ratio of the transfer cross sections tothe elastic plus inelastic cross sections. The coupling parameters have been adjusted inorder to reproduce the experimental transfer results as shown on the left part of figs. 1and 2. In these figures, the transfer probabilities are shown as a function of the distanceof closest approach D based on the Rutherford trajectory. As expected from the Q-value,the transfer probabilities are by one order of magnitude less for the 40Ca + 58Ni systemthan for the 40Ca + 64Ni system. In the former system, the coupled-channels reproduceswell the fusion cross sections because the transfer effect is too small to enhance the fusioncross sections.Table II. – Coupling constants for the transfer channels in the coupled-channels calculations.The parameters a are given in fm, β in MeV fm and Q in MeV.System n,p a01 β01 Q01 a02 β02 Q0240Ca + 58Ni n 1.96 −6 −3.85 1.06 −3 −2.6240Ca + 58Ni p 1.96 −16 −4.909 1.06 −12 −6.1940Ca + 64Ni n 1.16 −37 −1.29 1.06 −27.39 040Ca + 64Ni p 1.16 −30 −0.874 1.06 −20.39 0COUPLED-CHANNELS DESCRIPTION OF THE 40Ca +58,64 Ni TRANSFER ETC. 310−310−210−1Ptr11 12 13 14 15 16D [fm]1n2n-1p-2p10−310−110103σf[mb]65 70 75 80 85 90 95Ec.m. [MeV]trsfno trsfexpFig. 1. – Left: The transfer probabilities obtained experimentally (marker) and with the coupled-channels method (lines) for the 40Ca+58Ni reaction. Right: Corresponding fusion cross sectionsobtained experimentally and with the coupled-channels method with and without taking intoaccount the couplings to the transfer channels (lines).For the 40Ca + 64Ni fusion reaction, the coupled-channels method predicts a smalleffect of the transfer. In contrast, experimentally the fusion cross sections are enhancedat energies below the barrier. Note that we can also invert the procedure, that is, byfitting the transfer coupling in order to reproduce the fusion cross sections and thencomparing the transfer probabilities to the experimental data. In that case, the fusioncross sections will be well reproduced but the predicted transfer probabilities would beoverestimated by about a factor of 10. In either way, it does not seem possible withthis approach to reproduce simultaneously the transfer probabilities and the sub-barrierenhancement of fusion cross sections.In conclusion, this analysis has shown a possible limitation of the present coupled-channels method. One possibility is the coupling scheme used in refs. [1, 3, 7], thatassumes that couplings to collective states are identical before and after the transfer.That is, the collective excitations and the transfer channels are treated as independentdegrees of freedom. More complex models may be necessary in order to reproduce theenhancement of fusion cross sections with the coupling strengths which reproduce theexperimental transfer probabilities.10−310−210−1Ptr12 13 14 15 16D [fm]1n2n-1p-2p10−310−110103σf[mb]60 65 70 75 80 85 90 95 100Ec.m. [MeV]trsfno trsfexpFig. 2. – Same as fig. 1 for the 40Ca + 64Ni reaction.4 G. SCAMPS et al.∗ ∗ ∗GS acknowledges the Japan Society for the Promotion of Science for the JSPS post-doctoral fellowship for foreign researchers. This work was supported by Grant-in-Aid forJSPS Fellows No. 14F04769.REFERENCES[1] Scamps G. and Hagino K., Phys. Rev. C, 92 (2015) 054614.[2] Corradi L. et al., Phys. Rev. C, 84 (2011) 034603.[3] Esbensen H., Montagnoli G. and Stefanini A. M., Phys. Rev. C, 93 (2016) 034609.[4] Bourgin D. et al., Phys. Rev. C, 90 (2014) 044610.[5] Bourgin D., Simenel C., Courtin S. and Haas F., Phys. Rev. C, 93 (2016) 034604.[6] Hagino K., Rowley N. and Kruppa A. T., Comput. Phys. Commun., 123 (1999) 143;Hagino K. and Takigawa N., Prog. Theor. Phys., 128 (2012) 1061.[7] Esbensen H. and Landowne S., Nucl. Phys. A, 492 (1989) 473.

Coupled-channels description of the 40Ca + 58,64Ni transfer and fusion reactions

International audiencePreliminary experimental data for nucleon transfer reactions of the 40Ca+58Ni and 40Ca+64Ni systems are analyzed with the coupled- channels approach. It is shown that a simple treatment for the transfer in the coupled-channels method cannot reproduce simultaneously the transfer probabilities and the sub-barrier enhancement of fusion cross sections

Coupled-channels description of the 40Ca + 58,64Ni transfer and fusion reactions

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