Investigation of the Calculation of Coupled Channels for Some Halo Systems
Keywords:one halo nuclei, weakly bound nuclei, breakup channel
The fusion reaction for systems involving halo nuclei are investigated by two- and multicoupled channel calculations for the systems 8B+58Ni, 11Be+209Bi, and 15C+232Th. The effect of coupling between the breakup channel and the elastic channel have been considered using the Continuum Discretized Coupled Channels (CDCC) method in full quantum and semiclassical approaches. The calculation of the fusion cross-section qfus (mb), fusion barrier distribution Dfus (mb/MeV) and fusion probability Pfus reproduces the measured data for the systems under study quite well above and below the Coulomb barrier VB. In the case of two-channel coupling both in semiclassical and quantum mechanical approaches, the measured data above the Coulomb barrier VB are overestimated.
C.A. Bertulani, M.S. Hussein, G . M¨unzenberg. Physics of Radioactive Beams (Nova Science, 2001).
N. Takigawa, M. Kuratani, H. Sagawa. Effect of breakup reactions on the fusion of a halo nucleus. Phys. Rev. C 47, 2470 (1993). https://doi.org/10.1103/PhysRevC.47.R2470
R.N. Boyd, I. Tanihata. Physics with radioactive nuclear beams. Phys. Today 45 44 (1992). https://doi.org/10.1063/1.881311
S. Nakayama, T. Yamagata, H. Akimune, I. Daito, H. Fujimura, Y. Fujita, M. Fujiwara, K. Fushimi, T. Inomata, H. Kohri, N. Koori, K. Takahisa, A. Tamii, M. Tanaka, H. Toyokawa. Soft dipole resonance in the neutron-skin nucleus 6He. Phys. Rev. Lett. 85, 262 (2000). https://doi.org/10.1103/PhysRevLett.85.262
M.Y.M. Hassan, M.Y.H. Farag, E.H. Esmael, H.M. Maridi. Elastic scattering and breakup effect analysis of 11Be+12C at 38.4 MeV/nucleon. Phys. Rev. C 79, 064608 (2009). https://doi.org/10.1103/PhysRevC.79.064608
R. Kumari. On the fusion probabilities of halo nuclei. Proceedings of the DAE Symp. Nucl. Phys. 58, 340 (2013).
C. SignoriniZ, H. LiuZ, C. LiK, E.G. L¨obner, L. M¨uller, M. Ruan, K. Rudolph, F. Soramel, C. Zotti, A. Andrighetto, L. Stroe, A. Vitturi, H.Q. Zhang. Does break-up affect 9Be+209Bi fusion at the barrier. Eur. Phys. J. A 5, 7 (1999). https://doi.org/10.1007/s100500050250
C. Signorini. Interaction at the barrier in the systems 9,10,11Be+209Bi: Well-established facts and open questions. Eur. Phys. J. A 13, 129 (2002). https://doi.org/10.1140/epja1339-24
J.J. Kolata, V. GuimarГJes, D. Peterson, P. Santi, R.White-Stevens, P.A. DeYoung, G.F. Peaslee, B. Hughey, B. Atalla, M. Kern, P.L. Jolivette, J.A. Zimmerman, M.Y. Lee, F.D. Becchetti, E.F. Aguilera, E. Martinez-Quiroz, J.D. Hinnefeld. Sub-barrier fusion of 6He with 209Bi. Phys. Rev. Lett. 81, 4580 (1998). https://doi.org/10.1103/PhysRevLett.81.4580
K.E. Rehm, H. Esbensen, C.L. Jiang, B.B. Back, F. Borasi, B. Harss, R.V.F. Janssens, V. Nanal, J. Nolen, R.C. Pardo, M. Paul, P. Reiter, R.E. Segel, A. Sonzogni, J. Uusitalo, A.H. Wuosmaa. Fusion cross sections for the proton drip line nucleus 17F at energies below the Coulomb barrier. Phys. Rev. Lett. 81, 3341 (1998). https://doi.org/10.1103/PhysRevLett.81.3341
F.A. Majeed, Y.A. Abdul-Hussien. Semiclassical treatment of fusion and breakup processes of 6;8He halo nuclei. J. Theo. Appl. Phys. 10, 107 (2016). https://doi.org/10.1007/s40094-016-0207-y
F.A.Majeed, R.S. Hamodi, F.M. Hussain. Effect of coupled channels on semiclassical and quantum mechanical calculations for heavy ion fusion reactions. J. Comp. and Theo. Nanosci. 14, 2242 (2017). https://doi.org/10.1166/jctn.2017.6816
F.A. Majeed. The role of the breakup channel on the fusion reaction of light and weakly bound nuclei. Int. J. Nucl. Energ. Sci. Tech. 11, 218 (2017). https://doi.org/10.1504/IJNEST.2017.10009085
F.A. Majeed, F.A. Mahdi. Quantum mechanical calculations of a fusion reaction for some selected halo systems. Ukr. J. Phys. 64, 11 (2019). https://doi.org/10.15407/ujpe64.1.11
H.D.Marta, L.F. Canto, R. Donangelo, P. Lotti. Validity of the semiclassical approximation for the breakup of weakly bound nuclei. Phys. Rev. C 66, 024605 (2002). https://doi.org/10.1103/PhysRevC.66.024605
M. Dasgupta, D.J. Hinde, N. Rowley, A.M. Stefanini. Measuring barriers to fusion. Annu. Rev. Nucl. Part. Sci. 48, 401 (1998). https://doi.org/10.1146/annurev.nucl.48.1.401
G.R. Satchler, M.A. Nagarajan, J.S. Lilley, I.J. Thompson. Heavy-ion fusion: Channel-coupling effects, the barrier penetration model, and the threshold anomaly for heavy-ion potentials. Ann. Phys. 178, 110 (1987). https://doi.org/10.1016/S0003-4916(87)80015-5
A.M.S. Breitschaft, V.C. Barbosa, L.F. Canto, M.S. Hussein, E.J. Moniz, J. Christley, I.J. Thompson. Coupled-channel effects on heavy-ion sub-barrier fusion within the doorway expansion method. Ann. Phys. 243, 420 (1995). https://doi.org/10.1006/aphy.1995.1103
W.H.Z. C'ardenas, L.F. Canto, R. Donangelo, N. Carlin, M.S. Hussein. Schematic coupled-channel calculations for nuclear reactions with unstable beams. Braz. J. Phys. 34, 1254 (2004). https://doi.org/10.1590/S0103-97332004000600017
K. Hagino, A. Vitturi, C.H. Dasso, S.M. Lenzi. Role of breakup processes in fusion enhancement of drip-line nuclei at energies below the Coulomb barrier. Phys. Rev. C 61, 037602 (2000). https://doi.org/10.1103/PhysRevC.61.037602
A. Diaz-Torres, I.J. Thompson. Effect of continuum couplings in fusion of halo 11Be on 208Pb around the Coulomb barrier. Phys. Rev. C 65, 024606 (2002). https://doi.org/10.1103/PhysRevC.65.024606
M.S. Hussein, M.P. Pato, L.F. Canto, R. Donangelo. Near-barrier fusion of 11Li with heavy spherical and deformed targets. Phys. Rev. C 46, 377 (1992). https://doi.org/10.1103/PhysRevC.46.377
A. Kumari, R. Kharab. Role of projectile breakup in 6He and 6Li induced fusion reactions around barrier energies. Nucl. Phys. A 941, 38 (2015). https://doi.org/10.1016/j.nuclphysa.2015.05.007
M.S. Hussein, M.P. Pato, L.F. Canto, R. Donangelo. Real part of the polarization potential for 11Li induced fusion reactions. Phys. Rev. C 47, 2398 (1993). https://doi.org/10.1103/PhysRevB.47.2398
N. Rowley, G. Satchler, P. Stelson. On the "distribution of barriers" interpretation of heavy-ion fusion. Phys. Lett. B 254, 25 (1991). https://doi.org/10.1016/0370-2693(91)90389-8
E.F. Aguilera, P. Amador-Valenzuela, E. Martinez-Quiroz, D. Lizcano, P. Rosales, H. Garc' ia-Mart' inez, A. G'omez-Camacho, J.J. Kolata, A. Roberts, L.O. Lamm, G. Rogachev, V. Guimar˜aes, F.D. Becchetti, A. Villano, M. Ojaruega, M. Febbraro, Y. Chen, H. Jiang, P.A. De-Young, G.F. Peaslee, C. Guess, U. Khadka, J. Brown, J.D. Hinnefeld, L. Acosta, E.S. Rossi Jr, J.F.P. Huiza, T.L. Belyaeva. Near-barrier fusion of the 8B+58Ni proton-halo system. Phys. Rev. Lett. 107, 092701 (2011). https://doi.org/10.1103/PhysRevLett.107.092701
M. Mazzocco, C. Signorini, M. Romoli, A. De Francesco, M. Di Pietro, E. Vardaci, K. Yoshida, A. Yoshida, R. Bonetti, A. De Rosa, T. Glodariu, A. Guglielmetti, G. Inglima, M. La Commara, B. Martin, D. Pierroutsakou, M. Sandoli, F. Soramel, L. Stroe, R. Kanungo, N. Khai, T. Motobayashi, T. Nomura, T. Ishikawa, H. Ishiyama, S. Jeong, H. Miyatake, M.H. Tanaka, I. Sugai, Y. Watanabe. Scattering of 11Be halo nucleus from 209Bi at the Coulomb barrier. Eur. Phys. J. A 28, 295 (2006). https://doi.org/10.1140/epja/i2006-10058-0
M. Alcorta, K.E. Rehm, B.B. Back, S. Bedoor, P.F. Bertone, C.M. Deibel, B. DiGiovine, H. Esbensen, J.P. Greene, C.R. Hoffman, C.L. Jiang, J.C. Lighthall, S.T. Marley, R.C. Pardo, M. Paul, A. Rogers, C. Ugalde, A.H. Wuosmaa. Fusion reactions with the one-neutron halo nucleus 15C. Phys. Rev. Lett. 106, 172701 (2011). https://doi.org/10.1103/PhysRevLett.106.172701
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