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The angular momentum dependence of nuclear optical potentials

  • R. S. MackintoshEmail author
Open Access
Review
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Abstract.

The nuclear optical model potential (OMP) is generally assumed to be independent of the orbital angular momentum, l , of the interacting nuclei. Nucleon-nucleus and nucleus-nucleus interactions are customarily l independent in calculations of nuclear elastic scattering and in standard reaction codes. The evidence for various forms of l dependence of OMPs is reviewed and the importance of implementing these forms is evaluated. Existing arguments and evidence for l dependence are reviewed and new arguments and calculations are introduced. The relationship is examined between i) l dependence, and, ii) the undularity (waviness) of l -independent potentials that are S -matrix equivalent to l -dependent potentials. Such undularity is a property of the dynamic polarisation potential (DPP) generated by the coupling to reaction channels, or by coupling to excited states of the target or projectile nuclei. Various examples, particularly involving weakly bound projectile nuclei, are reviewed. Undularity is also a property of l -independent potentials that have been found in model-independent fits to precise, wide angular range, elastic scattering angular distributions; such undularity therefore indicates underlying l dependence. Cases of such phenomenological undularity, for both light and heavy ions, are referenced and shown to be related to undulatory properties of the dynamic polarisation potentials (DPPs) arising from channel coupling. Other forms of l dependence, that could be standard options in direct reaction codes, are also reviewed. The case is made that reaction-induced l dependence is a general property of nucleon-nucleus and nucleus-nucleus interactions and represents a valid extension of the nuclear optical model. A particular form of l dependence, parity dependence, arises due to the exchange of identical particles.

Notes

References

  1. 1.
    P. Darriulat, G. Igo, H.G. Pugh, H.D. Holmgren, Phys. Rev. 137, B315 (1965)ADSCrossRefGoogle Scholar
  2. 2.
    R.S. Mackintosh, arXiv:1705.07003v6 (2019)Google Scholar
  3. 3.
    A.J. Koning, J.P. Delaroche, Nucl. Phys. A 713, 231 (2003)ADSCrossRefGoogle Scholar
  4. 4.
    W.W. Daehnick, J.D. Childs, Z. Vrcelj, Phys. Rev. C 21, 2253 (1980)ADSCrossRefGoogle Scholar
  5. 5.
    D.Y. Pang, P. Roussel-Chomaz, H. Savajols, R.L. Varner, R. Wolski, Phys. Rev. C 79, 024615 (2009)ADSCrossRefGoogle Scholar
  6. 6.
    T. Furumoto, K. Tsubakihara, S. Ebata, W. Horiuchi, Phys. Rev. C 99, 034605 (2019)ADSCrossRefGoogle Scholar
  7. 7.
    R.S. Mackintosh, Eur. Phys. J. A 53, 66 (2017)ADSCrossRefGoogle Scholar
  8. 8.
    H. Feshbach, C.E. Porter, V.F. Weisskopf, Phys. Rev. 96, 448 (1954)ADSCrossRefGoogle Scholar
  9. 9.
    R.D. Woods, D.S. Saxon, Phys. Rev. 95, 577 (1954)ADSCrossRefGoogle Scholar
  10. 10.
    L.C. Gomes, J.D. Walecka, V.F. Weisskopf, Ann. Phys. (N.Y.) 3, 241 (1958)ADSCrossRefGoogle Scholar
  11. 11.
    H. Feshbach, Ann. Phys. 5, 357 (1958)ADSCrossRefGoogle Scholar
  12. 12.
    H. Feshbach, Ann. Phys. 19, 287 (1962)ADSCrossRefGoogle Scholar
  13. 13.
    J.S. Bell, E.J. Squires, Phys. Rev. Lett. 3, 96 (1959)ADSCrossRefGoogle Scholar
  14. 14.
    J.P. Jeukenne, A. Lejeune, C. Mahaux, Phys. Rev. C 10, 1391 (1974)ADSCrossRefGoogle Scholar
  15. 15.
    J.P. Jeukenne, A. Lejeune, C. Mahaux, Phys. Rev. C 15, 10 (1977)ADSCrossRefGoogle Scholar
  16. 16.
    C. Mahaux, R. Sartor, Advances in Nuclear Physics, Vol. 20, edited by J.W. Negele, E. Vogt (Plenum, New York, 1991) p. 1Google Scholar
  17. 17.
    F.A. Brieva, J.R. Rook, Nucl. Phys. A 291, 299 (1977)ADSCrossRefGoogle Scholar
  18. 18.
    F.A. Brieva, J.R. Rook, Nucl. Phys. A 291, 317 (1977)ADSCrossRefGoogle Scholar
  19. 19.
    F.A. Brieva, J.R. Rook, Nucl. Phys. A 297, 206 (1978)ADSCrossRefGoogle Scholar
  20. 20.
    C. Mahaux, G.R. Satchler, Nucl. Phys. A 560, 5 (1993)ADSCrossRefGoogle Scholar
  21. 21.
    H. Guo, Y. Xu, H. Liang, Y. Han, Q. Shen, Phys. Rev. C 83, 064618 (2011)ADSCrossRefGoogle Scholar
  22. 22.
    K. Wildermuth, Y.C. Tang, A Unified Theory of the Nucleus (Vieweg, Braunschweig, 1977)Google Scholar
  23. 23.
    P. Descouvement, M. Dufour, in Clusters in Nuclei, Vol. 2, edited by C. Beck, Lect. Notes Phys., Vol. 848 (Springer, 2012) p. 1Google Scholar
  24. 24.
    Y. Suzuki, R.G. Lovas, K. Yabana, K. Varga, Structure and Reactions of Light Exotic Nuclei (Taylor and Francis, London, 2003)Google Scholar
  25. 25.
    C.L. Rao, M. Reeves, G.R. Satchler, Nucl. Phys. A 207, 182 (1973)ADSCrossRefGoogle Scholar
  26. 26.
    C.A. Coulter, G.R. Satchler, Nucl. Phys. A 293, 269 (1977)ADSCrossRefGoogle Scholar
  27. 27.
    G.H. Rawitscher, Nucl. Phys. A 475, 519 (1987)ADSCrossRefGoogle Scholar
  28. 28.
    N.K. Glendenning, D.L. Hendrie, O.N. Jarvis, Phys. Lett. B 26, 131 (1968)ADSCrossRefGoogle Scholar
  29. 29.
    R.S. Mackintosh, Nucl. Phys. A 164, 398 (1971)ADSCrossRefGoogle Scholar
  30. 30.
    G.R. Satchler, Direct Nuclear Reactions (Clarendon Press, Oxford, 1983)Google Scholar
  31. 31.
    R.S. Mackintosh, N. Keeley, Phys. Rev. C 81, 034612 (2010)ADSCrossRefGoogle Scholar
  32. 32.
    R.S. Mackintosh, N. Keeley, Phys. Rev. C 85, 064603 (2012)ADSCrossRefGoogle Scholar
  33. 33.
    N. Keeley, R.S. Mackintosh, Phys. Rev. C 97, 014605 (2018)ADSCrossRefGoogle Scholar
  34. 34.
    R.S. Mackintosh, N. Keeley, Phys. Rev. C 98, 069901(E) (2018)ADSCrossRefGoogle Scholar
  35. 35.
    N. Keeley, R.S. Mackintosh, Phys. Rev. C 99, 034614 (2019)ADSCrossRefGoogle Scholar
  36. 36.
    R.S. Mackintosh, N. Keeley, Phys. Rev. C 90, 044601 (2014)ADSCrossRefGoogle Scholar
  37. 37.
    E. Bauge, J.P. Delaroche, M. Girod, Phys. Rev. C 58, 1118 (1998)ADSCrossRefGoogle Scholar
  38. 38.
    E. Bauge, J.P. Delaroche, M. Girod, Phys. Rev. C 63, 024607 (2001)ADSCrossRefGoogle Scholar
  39. 39.
    N. Vinh Mau, Microscopic Optical Potentials, edited by H.V. von Geramb, Lecture Notes in Physics, Vol. 89 (Springer Verlag, New York, 1979) p. 104Google Scholar
  40. 40.
    N. Vinh Mau, A. Boussy, Nucl. Phys. A 257, 189 (1976)ADSCrossRefGoogle Scholar
  41. 41.
    F. Osterfeld, J. Wambach, V.A. Madsen, Phys. Rev. C 23, 179 (1981)ADSCrossRefGoogle Scholar
  42. 42.
    J. Wambach, V.K. Mishra, Li Chu-Hsia, Nucl. Phys. A 380, 285 (1982)ADSCrossRefGoogle Scholar
  43. 43.
    V.A. Madsen, P. Osterfeld, Phys. Rev. C 39, 1215 (1989)ADSCrossRefGoogle Scholar
  44. 44.
    M. Pignanelli, H.V. von Geramb, R. DeLeo, Phys. Rev. C 24, 369 (1981)ADSCrossRefGoogle Scholar
  45. 45.
    J.P. Delaroche, M.S. Islam, R.W. Finlay, Phys. Rev. C 33, 1826 (1986)ADSCrossRefGoogle Scholar
  46. 46.
    G.M. Honoré, W. Tornow, C.R. Howell, R.S. Pedroni, R.C. Byrd, R.L. Walter, J.P. Delaroche, Phys. Rev. C 33, 1129 (1986)ADSCrossRefGoogle Scholar
  47. 47.
    C. Mahaux, H. Weidenmüller, Shell-Model Approach to Nuclear Reactions (North Holland Publishing Co., Amsterdam, 1969)Google Scholar
  48. 48.
    N. Austern, Phys. Rev. B 137, 752 (1965)ADSMathSciNetCrossRefGoogle Scholar
  49. 49.
    N. Keeley, R.S. Mackintosh, Phys. Rev. C 90, 044602 (2014)ADSCrossRefGoogle Scholar
  50. 50.
    B. Buck, Phys. Rev. 130, 712 (1963)ADSCrossRefGoogle Scholar
  51. 51.
    F.G. Perey, Phys. Rev. 131, 745 (1963)ADSCrossRefGoogle Scholar
  52. 52.
    R.S. Mackintosh, Phys. Lett. B 44, 437 (1973)ADSCrossRefGoogle Scholar
  53. 53.
    R.S. Mackintosh, Nucl. Phys. A 230, 195 (1974)ADSCrossRefGoogle Scholar
  54. 54.
    A.M. Kobos, R.S. Mackintosh, Phys. Lett. B 62, 127 (1976)ADSCrossRefGoogle Scholar
  55. 55.
    R.S. Mackintosh, N. Keeley, Phys. Rev. C 98, 024624 (2018)ADSCrossRefGoogle Scholar
  56. 56.
    R.S. Mackintosh, A.M. Kobos, J. Phys. G: Nucl. Part. Phys. 5, 359 (1979)ADSCrossRefGoogle Scholar
  57. 57.
    M.A. Franey, P.J. Ellis, Phys. Rev. C 23, 787 (1981)ADSCrossRefGoogle Scholar
  58. 58.
    I.J. Thompson, Comput. Phys. Rep. 7, 167 (1988)ADSCrossRefGoogle Scholar
  59. 59.
    L.W. Owen, G.R. Satchler, Phys. Rev. Lett. 25, 1720 (1970)ADSCrossRefGoogle Scholar
  60. 60.
    B.Z. Georgiev, R.S. Mackintosh, Phys. Lett. B 73, 250 (1978)ADSCrossRefGoogle Scholar
  61. 61.
    B.T. Kim, M.C. Kyum, S.W. Hong, M.H. Park, T. Udagawa, Comput. Phys. Commun. 71, 150 (1992)ADSCrossRefGoogle Scholar
  62. 62.
    B.T. Kim, T. Udagawa, Phys. Rev. C 42, 1147 (1990)ADSCrossRefGoogle Scholar
  63. 63.
    F.G. Perey, B. Buck, Nucl. Phys. 32, 353 (1962)CrossRefGoogle Scholar
  64. 64.
    R.S. Mackintosh, S.G. Cooper, J. Phys. G: Nucl. Part. Phys. 23, 565 (1997)ADSCrossRefGoogle Scholar
  65. 65.
    D. Lukaszek, G.H. Rawitscher, Phys. Rev. C 50, 968 (1994)ADSCrossRefGoogle Scholar
  66. 66.
    C.H. Johnson, C. Mahaux, Phys. Rev. C 38, 2589 (1988)ADSCrossRefGoogle Scholar
  67. 67.
    M.A. Nagarajan, C. Mahaux, G.R. Satchler, Phys. Rev. Lett. 54, 1136 (1985)ADSCrossRefGoogle Scholar
  68. 68.
    S. Ait-Tahar, R.S. Mackintosh, M.A. Russell, J. Phys. G: Nucl. Part. Phys. 21, 577 (1995)ADSCrossRefGoogle Scholar
  69. 69.
    R.S. Mackintosh, Inverse scattering: Applications in nuclear physics (Scholarpedia, 2012)Google Scholar
  70. 70.
    D. Baye, Nucl. Phys. A 460, 581 (1986)ADSCrossRefGoogle Scholar
  71. 71.
    F.K. Vosniakos, N.E. Davison, W.R. Falk, O. Abou-Zeid, S.P. Kwan, Nucl. Phys. A 332, 157 (1979)ADSCrossRefGoogle Scholar
  72. 72.
    R.S. Mackintosh, Nucl. Phys. A 742, 3 (2004)ADSCrossRefGoogle Scholar
  73. 73.
    R.S. Mackintosh, S.G. Cooper, Nucl. Phys. A 589, 377 (1995)ADSCrossRefGoogle Scholar
  74. 74.
    S.G. Cooper, R.S. Mackintosh, Nucl. Phys. A 592, 338 (1995)ADSCrossRefGoogle Scholar
  75. 75.
    V.I. Kukulin, R.S. Mackintosh, J. Phys. G: Nucl. Part. Phys. 30, R1 (2004)ADSCrossRefGoogle Scholar
  76. 76.
    F. Michel, G. Reidemeister, Z. Phys. A 333, 331 (1989)ADSGoogle Scholar
  77. 77.
    S.G. Cooper, R.S. Mackintosh, Z. Phys. A 337, 357 (1990)ADSGoogle Scholar
  78. 78.
    N.N.T. Phuc, N.H. Phuc, D.T. Khoa, Phys. Rev. C 98, 024613 (2018)ADSCrossRefGoogle Scholar
  79. 79.
    N.N.T. Phuc, R.S. Mackintosh, N.H. Phuc, D.T. Khoa, in preparationGoogle Scholar
  80. 80.
    D.R. Thompson, Y.C. Tang, Phys. Rev. C 4, 306 (1971)ADSCrossRefGoogle Scholar
  81. 81.
    D.R. Thompson, Y.C. Tang, R.E. Brown, Phys. Rev. C 5, 1939 (1972)ADSCrossRefGoogle Scholar
  82. 82.
    G.W. Greenlees, W. Makofske, Y.C. Tang, D.R. Thompson, Phys. Rev. C 6, 2057 (1972)ADSCrossRefGoogle Scholar
  83. 83.
    S.G. Cooper, R.S. Mackintosh, Phys. Rev. C 54, 3133 (1996)ADSCrossRefGoogle Scholar
  84. 84.
    S.G. Cooper, Nucl. Phys. A 618, 87 (1997)ADSCrossRefGoogle Scholar
  85. 85.
    H. Heiberg-Andersen, R.S. Mackintosh, J.S. Vaagen, Nucl. Phys. A 713, 63 (2003)ADSCrossRefGoogle Scholar
  86. 86.
    S.G. Cooper, R.S. Mackintosh, Nucl. Phys. A 517, 285 (1990)ADSCrossRefGoogle Scholar
  87. 87.
    A.A. Ioannides, R.S. Mackintosh, Nucl. Phys. A 438, 354 (1985)ADSCrossRefGoogle Scholar
  88. 88.
    R.S. Mackintosh, A.A. Ioannides, in Advanced Methods in the Analysis of Nuclear Scattering Data, Lect. Notes Phys., Vol. 236 (Springer Verlag, Berlin, 1985) p. 283Google Scholar
  89. 89.
    R.S. Mackintosh, A.M. Kobos, Phys. Lett. B 116, 95 (1982)ADSCrossRefGoogle Scholar
  90. 90.
    A.A. Ioannides, R.S. Mackintosh, Nucl. Phys. A 467, 482 (1987)ADSCrossRefGoogle Scholar
  91. 91.
    S.G. Cooper, R.S. Mackintosh, Inverse Probl. 5, 707 (1989)ADSCrossRefGoogle Scholar
  92. 92.
    R.S. Mackintosh, arXiv:1205.0468 (2012)Google Scholar
  93. 93.
    R.S. Mackintosh, A.M. Kobos, Phys. Lett. B 116, 95 (1982)ADSCrossRefGoogle Scholar
  94. 94.
    R.S. Mackintosh, Scholarpedia 7, 12032 (2012)  https://doi.org/10.4249/scholarpea.12032 ADSCrossRefGoogle Scholar
  95. 95.
    S.G. Cooper, Notes for Imago users, Open University report (1999) unpublished, available upon requestGoogle Scholar
  96. 96.
    M. Ermer, H. Clement, P. Grabmayr, G.J. Wagner, L. Friedrich, E. Huttel, Phys. Lett. B 188, 17 (1987)ADSCrossRefGoogle Scholar
  97. 97.
    M. Ermer, H. Clement, G. Holetzke, W. Kabitzke, G. Graw, R. Hertenberger, H. Kader, F. Merz, P. Schiemenz, Nucl. Phys. A 533, 71 (1991)ADSCrossRefGoogle Scholar
  98. 98.
    A.M. Kobos, R.S. Mackintosh, Ann. Phys. (N.Y.) 123, 296 (1979)ADSCrossRefGoogle Scholar
  99. 99.
    R. Alarcon, J. Rapaport, R.W. Finlay, Nucl. Phys. A 462, 413 (1987)ADSCrossRefGoogle Scholar
  100. 100.
    R.E. Shamu, J. Barnes, S.M. Ferguson, G. Haouat, J. Lachkat, J. Phys. G: Nucl. Part. Phys. 17, 525 (1991)ADSCrossRefGoogle Scholar
  101. 101.
    A.M. Kobos, R.S. Mackintosh, J.R. Rook, Nucl. Phys. A 389, 205 (1982)ADSCrossRefGoogle Scholar
  102. 102.
    R.S. Mackintosh, J. Phys. G: Nucl. Part. Phys. 5, 1587 (1979)ADSCrossRefGoogle Scholar
  103. 103.
    R.S. Mackintosh, L.A. Cordero-L., Phys. Lett B 68, 213 (1977)ADSCrossRefGoogle Scholar
  104. 104.
    A.M. Kobos, R.S. Mackintosh, J. Phys. G: Nucl. Part. Phys. 5, 97 (1979)ADSCrossRefGoogle Scholar
  105. 105.
    A.M. Kobos, R.S. Mackintosh, Acta Phys. Pol. B 12, 1029 (1981)Google Scholar
  106. 106.
    R.S. Mackintosh, unpublished (2016) postscript files available on requestGoogle Scholar
  107. 107.
    R.S.Mackintosh, unpublished (1978) scanned copy available on requestGoogle Scholar
  108. 108.
    Y.-W. Lui, O. Karban, S. Roman, R.K. Bhowmik, J.M. Nelson, E.C. Pollacco, Nucl. Phys. A 333, 205 (1980)ADSCrossRefGoogle Scholar
  109. 109.
    M.E. Cage, D.L. Clough, A.J. Cole, J.B.A England, G.J. Pyle, P.M. Rolph, L.H. Watson, D.H. Worledge, Nucl. Phys. A 183, 449 (1972)ADSCrossRefGoogle Scholar
  110. 110.
    R.S. Mackintosh, S.G. Cooper, A.A. Ioannides, Nucl. Phys. A 476, 287 (1987)ADSCrossRefGoogle Scholar
  111. 111.
    R.S. Mackintosh, K. Rusek, Phys. Rev. C 67, 034607 (2003)ADSCrossRefGoogle Scholar
  112. 112.
    N. Keeley, R.S. Mackintosh, Phys. Rev. C 83, 044608 (2011)ADSCrossRefGoogle Scholar
  113. 113.
    F. Skaza et al., Phys. Lett. B 619, 82 (2005)ADSCrossRefGoogle Scholar
  114. 114.
    R.S. Mackintosh, N. Keeley, Phys. Rev. C 83, 057601 (2011)ADSCrossRefGoogle Scholar
  115. 115.
    R.S. Mackintosh, N. Keeley, Phys. Rev. C 76, 024601 (2007)ADSCrossRefGoogle Scholar
  116. 116.
    D.Y. Pang, R.S. Mackintosh, Phys. Rev. C 84, 064611 (2011)ADSCrossRefGoogle Scholar
  117. 117.
    G. Marquíinez-Durán, N. Keeley, K.W. Kemper, R.S. Mackintosh, I. Martel, K. Rusek, A.M. Sánchez-Benéz, Phys. Rev. C 95, 024602 (2017)ADSCrossRefGoogle Scholar
  118. 118.
    A.A. Ioannides, R.S. Mackintosh, Phys. Lett. B 169, 113 (1986)ADSCrossRefGoogle Scholar
  119. 119.
    R.S. Mackintosh, D.Y. Pang, Phys. Rev. C 86, 047602 (2012)ADSCrossRefGoogle Scholar
  120. 120.
    N. Keeley, R.S. Mackintosh, C. Beck, Nucl. Phys. A 834, 792c (2010)ADSCrossRefGoogle Scholar
  121. 121.
    R.S. Mackintosh, D.Y. Pang, Phys. Rev. C 88, 014608 (2013)ADSCrossRefGoogle Scholar
  122. 122.
    N. Keeley, R.S. Mackintosh, Phys. Rev. C 77, 054603 (2008)ADSCrossRefGoogle Scholar
  123. 123.
    R.S. Mackintosh, A.A. Ioannides, S.G. Cooper, Nucl. Phys. A 483, 173 (1988)ADSCrossRefGoogle Scholar
  124. 124.
    R.S. Mackintosh, A.A. Ioannides, S.G. Cooper, Nucl. Phys. A 483, 195 (1988)ADSCrossRefGoogle Scholar
  125. 125.
    R.S. Mackintosh, S.G. Cooper, Nucl. Phys. A 494, 123 (1989)ADSCrossRefGoogle Scholar
  126. 126.
    S.G. Cooper, R.S. Mackintosh, Nucl. Phys. A 511, 29 (1990)ADSCrossRefGoogle Scholar
  127. 127.
    R. Crespo, R.C. Johnson, J.A. Tostevin, R.S. Mackintosh, S.G. Cooper, Phys. Rev. C 49, 1091 (1994)ADSCrossRefGoogle Scholar
  128. 128.
    F.G. Perey, in Direct interactions and nuclear reaction mechanisms, edited by E. Clemental, C. Villi (Gordon and Breach, New York, 1963)Google Scholar
  129. 129.
    R.S. Mackintosh, unpublished preprint, availableGoogle Scholar
  130. 130.
    E.E. Gross, R.H. Bassel, L.N. Blumberg, B.J. Morton, A. van der Woude, A. Zucker, Nucl. Phys. A 102, 673 (1967)ADSCrossRefGoogle Scholar
  131. 131.
    D.J. Horen, C.H. Johnson, A.D. MacKellar, Phys. Lett. B 161, 217 (1085)ADSCrossRefGoogle Scholar
  132. 132.
    D.J. Horen, C.H. Johnson, J.L. Fowler, A.D. MacKellar, B. Castel, Phys. Rev. C 34, 429 (1986)ADSCrossRefGoogle Scholar
  133. 133.
    C.H. Johnson, D.J. Horen, C. Mahaux, Phys. Rev. C 36, 2252 (1987)ADSCrossRefGoogle Scholar
  134. 134.
    C.H. Johnson, R.R. Winters, Phys. Rev. C 37, 2340 (1988)ADSCrossRefGoogle Scholar
  135. 135.
    J.-P. Jeukenne, C.H. Johnson, C. Mahaux, Phys. Rev. C 38, 2573 (1988)ADSCrossRefGoogle Scholar
  136. 136.
    T. Wada, H. Horiuchi, Prog. Theor. Phys. 80, 488 (1988)ADSCrossRefGoogle Scholar
  137. 137.
    T. Wada, H. Horiuchi, Prog. Theor. Phys. 80, 502 (1988)ADSCrossRefGoogle Scholar
  138. 138.
    H. Horiuchi, in Proceedings of the International Conference on Clustering Aspects of Nuclear Structure and Nuclear Reactions (Chester, 1984), edited by J.S. Lilley, M.A. Nagarajan (Reidel, Dordrecht, 1984) p. 35Google Scholar
  139. 139.
    S. Ait-Tahar, R.S. Mackintosh, S.G. Cooper, T. Wada, Nucl. Phys. A 562, 101 (1993)ADSCrossRefGoogle Scholar
  140. 140.
    Y. Kondo, B.A. Robson, R. Smith, Phys. Lett. B 227, 310 (1989)ADSCrossRefGoogle Scholar
  141. 141.
    S. Ait-Tahar, S.G. Cooper, R.S. Mackintosh, Nucl. Phys. A 542, 499 (1992)ADSCrossRefGoogle Scholar
  142. 142.
    R.A. Chatwin, J.S. Eck, D. Robson, A. Richter, Phys. Rev. C 1, 795 (1970)ADSCrossRefGoogle Scholar
  143. 143.
    A.E. Bisson, R.H. Davis, Phys. Rev. Lett. 22, 542 (1969)ADSCrossRefGoogle Scholar
  144. 144.
    A.E. Bisson, K.A. Eberhard, R.H. Davis, Phys. Rev. C 1, 539 (1970)ADSCrossRefGoogle Scholar
  145. 145.
    C. Gao, G. He, Phys. Lett. B 282, 16 (1992)ADSCrossRefGoogle Scholar
  146. 146.
    S. Ait-Tahar, R.S. Mackintosh, S.G. Cooper, Nucl. Phys. A 561, 285 (1993)ADSCrossRefGoogle Scholar
  147. 147.
    H. Bohn, K.A. Eberhart, R. Vandenbosch, K.G. Bernhardt, R. Bangert, Y.-d. Chan, Phys. Rev. C 16, 665 (1977)ADSCrossRefGoogle Scholar
  148. 148.
    D.E. Trcka, A.D. Frawley, K.W. Kemper, D. Robson, J.D. Fox, E.G. Myers, Phys. Rev. C 41, 2134 (1990)ADSCrossRefGoogle Scholar
  149. 149.
    E.L. Reber, K.W. Kemper, P.V. Green, P.L. Kerr, A.J. Mendez, E.G. Myers, B.G. Schmidt, Phys. Rev. C 49, R1 (1994)ADSCrossRefGoogle Scholar
  150. 150.
    S. Ohkubo, Y. Hirabayashi, Phys. Rev. C 89, 051601 (2014)ADSCrossRefGoogle Scholar
  151. 151.
    R.S. Mackintosh, Y. Hirabayashi, S. Ohkubo, Phys. Rev. C 91, 024616 (2015)ADSCrossRefGoogle Scholar
  152. 152.
    S. Ohkubo, Y. Hirabayashi, Phys. Rev. C 89, 061601 (2014)ADSCrossRefGoogle Scholar
  153. 153.
    R.S. Mackintosh, Phys. Rev. C 94, 034602 (2016)ADSCrossRefGoogle Scholar
  154. 154.
    S.Y. Lee, Nucl. Phys. A 311, 518 (1978)ADSCrossRefGoogle Scholar
  155. 155.
    R.S. Mackintosh, A.M. Kobos, Phys. Lett. B 92, 59 (1980)ADSCrossRefGoogle Scholar
  156. 156.
    A.M. Kobos, G.R. Satchler, R.S. Mackintosh, Nucl. Phys. A 395, 248 (1983)ADSCrossRefGoogle Scholar
  157. 157.
    A.M. Kobos, R.S. Mackintosh, Phys. Rev. C 26, 1766 (1982)ADSCrossRefGoogle Scholar
  158. 158.
    S. Ohkubo, Y. Hirabayashi, A.A. Ogloblin, Phys. Rev. C 92, 051601 (2015)ADSCrossRefGoogle Scholar
  159. 159.
    D.Y. Pang, Y.L. Ye, F.R. Xu, Phys. Rev. C 83, 064619 (2011)ADSCrossRefGoogle Scholar
  160. 160.
    F.M. Nunes, A. Lovell, A. Ross, L.J. Titus, R.J. Charity, W.H. Dickhoff, M.H. Mahzoon, J. Sarich, S.M. Wild, arXiv:1509.047001Google Scholar
  161. 161.
    B.W. Ridley, J.F. Turner, Nucl. Phys. 58, 497 (1964)CrossRefGoogle Scholar
  162. 162.
    V. Hnizdo, O. Karban, J. Lowe, G.W. Greenlees, W. Makofske, Phys. Rev. C 3, 1560 (1971)ADSCrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.School of Physical SciencesThe Open UniversityMilton KeynesUK

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