Abstract
The problem of the calculation of inclusive breakup cross sections in nuclear reactions is reexamined. For that purpose, the theory proposed by Ichimura et al. (Phys Rev C 32:431, 1985) is revisited, both in its prior and post representations. We briefly outline the connection of this theory with that proposed by Udagawa and Tamura (Phys Rev C 24:1348, 1981) and apply both theories to the inclusive breakup of \(^6\)Li on \(^{209}\)Bi at near-barrier energies, comparing also with available data. The relative importance of elastic versus non-elastic breakup, as a function of the incident energy and of the projectile separation energy, is also investigated.
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References
Austern, N., Vincent, C.M.: Inclusive breakup reactions. Phys. Rev. C 23, 1847 (1981)
Austern, N., Iseri, Y., Kamimura, M., Kawai, M., Rawitscher, G., Yahiro, M.: Continuum-discretized coupled-channels calculations for three-body models of deuteron-nucleus reactions. Phys. Rep. 154, 125 (1987)
Baur, G., Shyam, R., Rösel, F., Trautmann, D.: Importance of the breakup mechanism for composite particle scattering. Phys. Rev. C 21, 2668 (1980)
Baur, G., Shyam, R., Rösel, F., Trautmann, D.: Calculation of proton–neutron coincidence cross sections in 56 MeV deuteron-induced breakup reactions by post form distorted-wave born approximation. Phys. Rev. C 28, 946 (1983)
Beck, C., Keeley, N., Diaz-Torres, A.: Coupled-channel effects in elastic scattering and near-barrier fusion induced by weakly bound nuclei and exotic halo nuclei. Phys. Rev. C 75, 054605 (2007)
Bohr, N.: Neutron capture and nuclear constitution. Nature 137(3461), 344 (1936)
Budzanowski, A., et al.: Observation of the \(\alpha \)-particle breakup process at \(E_\alpha \)(lab) = 172.5 MeV. Phys. Rev. Lett. 41, 635 (1978)
Camacho, J.G., Moro, A.M.: A pedestrian approach to the theory of transfer reactions: application to weakly-bound and unbound exotic nuclei. In: The Euroschool on Exotic Beams, Vol. IV, pp. 39–66. Springer, Berlin (2014)
Canto, L., Gomes, P., Lubian, J., Chamon, L.C., Crema, E.: Dynamic effects of breakup on fusion reactions of weakly bound nuclei. Nucl. Phys. A 821, 51 (2009)
Capel, P., Goldstein, G., Baye, D.: Time-dependent analysis of the breakup of \(^{11}\)Be on \(^{12}\)C at 67 MeV/nucleon. Phys. Rev. C 70, 064605 (2004)
Carlson, B.V., Capote, R., Sin, M.: Elastic and inelastic breakup of deuterons with energy below 100 MeV. (2015) arXiv:1508.01466
Cook, J.: Global optical-model potentials for the elastic scattering of \(^{6,7}\)Li projectiles. Nucl. Phys. A 388, 153 (1982)
Cotanch, S.R.: Coupled channels optical theorem and non-elastic cross section sum rule. Nucl. Phys. A 842, 48 (2010)
Crespo, R., Deltuva, A., Moro, A.M.: Core excitation contributions to the breakup of the one-neutron halo nucleus \(^{11}\)Be on a proton. Phys. Rev. C 83, 044622 (2011)
Cubero, M., et al.: Do Halo nuclei follow Rutherford elastic scattering at energies below the barrier? The case of \(^{11}\)Li. Phys. Rev. Lett. 109, 262701 (2012)
Dasgupta, M., et al.: Effect of breakup on the fusion of \(^{6}\)Li, \(^{7}\)Li, and \(^{9}\)Be with heavy nuclei. Phys. Rev. C 70(024), 606 (2004)
de Diego, R., Arias, J.M., Lay, J.A., Moro, A.M.: Continuum-discretized coupled-channels calculations with core excitation. Phys. Rev. C 89, 064609 (2014)
Deltuva, A.: Deuteron stripping and pickup involving the halo nuclei \(^{11}\)Be and \(^{15}\)C. Phys. Rev. C 79, 054603 (2009)
Deltuva, A., Moro, A.M., Cravo, E., Nunes, F.M., Fonseca, A.C.: Three-body description of direct nuclear reactions: comparison with the continuum discretized coupled channels method. Phys. Rev. C 76, 064602 (2007)
Di Pietro, A., et al.: Experimental study of the collision \(^{11}\)Be + \(^{64}\)Zn around the Coulomb barrier. Phys. Rev. C 85, 054607 (2012)
Diaz-Torres, A.: Modelling incomplete fusion dynamics of weakly bound nuclei at near-barrier energies. J. Phys. G Nucl. Part. Phys. 37, 075109 (2010)
Diaz-Torres, A., Thompson, I.: Effect of continuum couplings in fusion of halo \(^{11}\)Be on \(^{208}\)Pb around the Coulomb barrier. Phys. Rev. C 65, 024606 (2002)
Diaz-Torres, A., Hinde, D., Tostevin, J., Dasgupta, M., Gasques, L.: Relating breakup and incomplete fusion of weakly bound nuclei through a classical trajectory model with stochastic breakup. Phys. Rev. Lett. 98, 152701 (2007)
Esbensen, H., Bertsch, G.F.: Effects of E2 transitions in the Coulomb dissociation of \(^{8}\)B. Nucl. Phys. A 600, 37 (1996)
Faddeev, L.D.: Mathematical aspects of the three-body problem in quantum scattering theory (Davey, New york, 1965). (1960). Zh Eksp Teor Fiz 39:1459, [Sov. Phys. JETP 12, 1014 (1961)]
Fernández-García, J.P., et al.: Simultaneous analysis of the elastic scattering and breakup channel for the reaction \(^{11}\)Li+\(^{208}\)Pb at energies near the Coulomb barrier. Phys. Rev. C 92, 044608 (2015)
Glöckle, W.: The Quantum Mechanical Few-Body Problem. Springer, Berlin (1983)
Hirabayashi, Y., Sakuragi, Y.: Anomalous renormalization of cluster-folding interactions for \(^{6}\)Li-nucleus scattering at low energies. Phys. Lett. B 258, 11 (1991)
Huby, R., Mines, J.R.: Distorted-wave born approximation for stripping to virtual levels. Rev. Mod. Phys. 37, 406 (1965)
Hussein, M., McVoy, K.: Inclusive projectile fragmentation in the spectator model. Nucl. Phys. A 445, 124 (1985)
Hussein, M., Frederico, T., Mastroleo, R.: Faddeev and DWBA description of inclusive break-up and incomplete fusion reactions. Nucl. Phys. A 511, 269 (1990)
Ichimura, M.: Relation among theories of inclusive breakup reactions. Phys. Rev. C 41, 834 (1990)
Ichimura, M., Austern, N., Vincent, C.M.: Equivalence of post and prior sum rules for inclusive breakup reactions. Phys. Rev. C 32, 431 (1985)
Ichimura, M., Austern, N., Vincent, C.M.: Comparison of approximate formalisms for inclusive breakup reactions. Phys. Rev. C 34, 2326 (1986). doi:10.1103/PhysRevC.34.2326
Ichimura, M., Austern, N., Vincent, C.M.: Approximate sum rules for inclusive breakup reactions. Phys. Rev. C 37, 2264 (1988). doi:10.1103/PhysRevC.37.2264
Johnson, R., Tandy, P.: An approximate three-body theory of deuteron stripping. Nucl. Phys. A 235, 56 (1974)
Johnson, R.C., Soper, P.J.R.: Contribution of deuteron breakup channels to deuteron stripping and elastic scattering. Phys. Rev. C 1, 976 (1970)
Kasano, A., Ichimura, M.: A new formalism of inclusive breakup reactions and validity of the surface approximation. Phys. Lett. 115B, 81 (1982)
Kido, T., Yabana, K., Suzuki, Y.: Coulomb breakup mechanism of neutron drip-line nuclei. Phys. Rev. C 50, R1276–R1279 (1994)
Lei, J., Moro, A.M.: Numerical assessment of post-prior equivalence for inclusive breakup reactions. Phys. Rev. C 92, 061602(R) (2015)
Lei, J., Moro, A.M.: Reexamining closed-form formulae for inclusive breakup: application to deuteron- and \(^{6}\)Li-induced reactions. Phys. Rev. C 92, 044616 (2015)
Li, X.H., Udagawa, T., Tamura, T.: Assessment of approximations made in breakup-fusion descriptions. Phys. Rev. C 30, 1895 (1984)
Marta, H.D., Canto, L.F., Donangelo, R.: Complete and incomplete fusion of weakly bound nuclei. Phys. Rev. C 89, 034625 (2014)
Moro, A.M., Crespo, R.: Core excitation effects in the breakup of the one-neutron halo nucleus \(^{11}\)Be on a proton target. Phys. Rev. C 85, 054613 (2012)
Moro, A.M., Lay, J.A.: Interplay between valence and core excitation mechanisms in the breakup of halo nuclei. Phys. Rev. Lett. 109, 232502 (2012)
Potel, G., Nunes, F.M., Thompson, I.J.: Establishing a theory for deuteron-induced surrogate reactions. Phys. Rev. C 92, 034611 (2015)
Sánchez-Benítez, A., et al.: Study of the elastic scattering of \(^{6}\)He on \(^{208}\)Pb at energies around the Coulomb barrier. Nucl. Phys. A 803, 30 (2008)
Santra, S., Kailas, S., Ramachandran, K., Parkar, V.V., Jha, V., Roy, B.J., Shukla, P.: Reaction mechanisms involving weakly bound \(^{6}{\rm Li}\) and \(^{209}{\rm Bi}\) at energies near the Coulomb barrier. Phys. Rev. C 83, 034616 (2011)
Santra, S., Kailas, S., Parkar, V.V., Ramachandran, K., Jha, V., Chatterjee, A., Rath, P.K., Parihari, A.: Disentangling reaction mechanisms for \(\alpha \) production in the \(^{6}\)Li + \(^{209}\)Bi reaction. Phys. Rev. C 85, 014612 (2012)
Santra, S., et al.: Resonant breakup of \(^{6}\)Li by \(^{209}\)Bi. Phys. Lett. B 677, 139 (2009)
Satchler, G.: Direct Nuclear Reactions. International Series of Monographs on Physics. Clarendon Press, Oxford (1983)
Shyam, R., Baur, G., Rösel, F., Trautmann, D.: Elastic and inelastic breakup of the \(^{3}\)He particle. Phys. Rev. C 22, 1401 (1980)
Summers, N.C., Nunes, F.M.: Core excitation in the elastic scattering and breakup of \(^{11}\)Be on protons. Phys. Rev. C 76, 014611 (2007)
Summers, N.C., Nunes, F.M., Thompson, I.J.: Extended continuum discretized coupled channels method: core excitation in the breakup of exotic nuclei. Phys. Rev. C 74, 014606 (2006)
Thompson, I.J.: The theory of partial fusion. J. Phys. Conf. Ser. 312, 082041 (2011)
Thompson, I.J., Nunes, F.M.: Nuclear Reactions for Astrophysics Nuclear Reactions for Astrophysics, 1st edn. Cambridge University Press, Cambridge (2009)
Typel, S., Baur, G.: Coulomb dissociation of \(^{8}\)B into \(^{7}\)Be + p: effects of multiphoton exchange. Phys. Rev. C 50, 2104 (1994)
Udagawa, T., Tamura, T.: Derivation of breakup-fusion cross sections from the optical theorem. Phys. Rev. C 24, 1348 (1981)
Udagawa, T., Li, X.H., Tamura, T.: Breakup-fusion description of nonequilibrium protons from (\(\alpha \), p) reactions. Phys. Lett. 135B, 333 (1984)
Vincent, C.M.: Gell–Mann–Goldberger relation for reactions of the form \((d, pn)\). Phys. Rev. 175, 1309 (1968)
Vincent, C.M., Fortune, H.T.: New method for distorted-wave analysis of stripping to unbound states. Phys. Rev. C 2, 782 (1970)
Watanabe, S., Matsumoto, T., Minomo, K., Ogata, K., Yahiro, M.: Effects of four-body breakup on \(^{6}\)Li elastic scattering near the Coulomb barrier. Phys. Rev. C 86, 031601 (2012)
Yahiro, M., Iseri, Y., Kameyama, H., Kamimura, M., Kawai, M.: Chapter III. Effects of deuteron virtual breakup on deuteron elastic and inelastic scattering. Prog. Theor. Phys. Suppl. 89, 32 (1986)
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Moro, A.M., Lei, J. Recent Advances in Nuclear Reaction Theories for Weakly Bound Nuclei: Reexamining the Problem of Inclusive Breakup. Few-Body Syst 57, 319–330 (2016). https://doi.org/10.1007/s00601-016-1085-1
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DOI: https://doi.org/10.1007/s00601-016-1085-1