Abstract
The most general procedure to describe the emission of deformed fragments within a phenomenological approach is the coupled channels method. We analyze various methods to integrate the coupled channels system of differential equations describing emission processes, namely (a) numerical integration, (b) diagonalisation method, (c) analytical continuation method, (d) distorted wave approach and (e) two potential method. These methods are general, not depending upon the concrete structure of the emitted fragments. We then discuss the intrinsic system of coordinate, adiabatic approach, emission from triaxial nuclei, the coupling with rotation and vibration of the heavy fragment.
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References
Fröman, P.P.: Alpha decay from deformed nuclei. Mat. Fys. Skr. Dan. Vid. Selsk. 1(3) (1957)
Gyarmati, B., Vertse, T.: On the normalisation of Gamow functions. Nucl. Phys. A 160, 523–528 (1971)
Vertse, T., Pál, K.F., Balogh, A.: GAMOW, a program for calculating the resonant state solution of the Radial Schrödinger Equation in an arbitrary optical potential. Comput. Phys. Commun. 27, 309–322 (1982)
Ixaru, L., Rizea, M., Vertse, T.: Piecewiese perturbation methods for calculating Eigensolutions of complex optical potential. Comput. Phys. Commun. 85, 217–230 (1995)
Ferreira, L.S., Maglione, E., Liotta, R.J.: Nucleon resonances in deformed nuclei. Phys. Rev. Lett. 78, 1640–1643 (1997)
Kukulin, V.I., Krasnopol’sly, V.M., Horáček, J.: Theory of Resonances. Kluwer Academic Press, Dordrecht (1989)
Tanaka, N., Suzuki, Y., Varga, K.: Exploration of resonances by analytic continuation in the coupling constant. Phys. Rev. C 56, 562–565 (1997)
Tanaka, N., Suzuki, Y., Varga, K., Lovas, R.G.: Unbound states by analytic continuation in the coupling constant. Phys. Rev. C 59, 1391–1399 (1999)
Taylor, J.R.: Scattering Theory. Wiley, New York (1972)
Cattapan, G., Maglione, E.: From bound states to resonances: analytic continuation of the wave function. Phys. Rev. C 61, 067301/1–4 (2000)
Davids, C.N., Esbensen, H.: Decay rates of spherical and deformed proton emitters. Phys. Rev. C 61, 044302/1–5 (2000)
Satchler, G.R.: Direct Nuclear Reactions. Clarendon Press, Oxford (1983)
Bugrov, V.P., Kadmensky, S.G., Furman, V.I., Khlebostroev, V.G.: Multiparticle variant of proton and neutron radioactivity—the case of diagonal transitions. Yad. Fiz. 41, 1123 (1985) [Sov. J. Nucl. Phys. 41, 717–723 (1985)]
Bugrov, V.P., Kadmensky, S.G.: Proton decay of deformed nuclei. Yad. Fiz. 49, 1562 (1989) [Sov. J. Nucl. Phys. 49, 967–972 (1989)]
Kadmensky, S.G.: On absolute values of α-widths for heavy spherical nuclei. Z. Phys. A 312, 113–120 (1983)
Becchetti, F.D. Jr., Greenlees, G.W.: Nucleon-nucleon optical-model parameters, A > 40, E < 50 MeV. Phys. Rev. 182, 1190–1209 (1969)
Kadmensky, S.G., Bugrov, V.P.: Yad. Fiz. 59, 424 (1996) [Phys. At. Nucl. 59, 399 (1996)]
Gurvitz, S.A., Kalbermann, G.: Decay width and shift of a quasistationary state. Phys. Rev. Lett. 59, 262–265 (1987)
Gurvitz, S.A.: New approach to tunneling problems. Phys. Rev. A 38, 1747–1759 (1988)
Jackson, D.F., Rhoades-Brown, M.: Theories of alpha-decay. Ann. Phys. 105, 151 (1977)
Berggren, T., Olanders, P.: Alpha decay from deformed nuclei: (I) formalism and application to ground-state cedays. Nucl. Phys. A 473, 189–220 (1987)
Berggren, T.: Anisotropic alpha decay from oriented odd-mass isotopes of some light actinides. Phys. Rev. C 50, 2494–2507 (1994)
Esbensen, H., Davids, C.N.: Coupled-channels treatment of deformed proton emitters. Phys. Rev. C 63, 014315/1–13 (2000)
Nilsson, S.G.: Binding state of individual nucleons in strongly deformed nuclei. Kgl. Danske Videnskab. Selskab Mat. Fys. Medd. 29(16) (1955)
Fiorin, G., Maglione, E., Ferreira, L.S.: Theoretical description of deformed proton emitters: nonadiabatic quasiparticle method. Phys. Rev. C 67, 054302/1–4 (2003)
Maglione, E., Ferreira, L.S., Liotta, R.J.: Nucleon decay from deformed nuclei. Phys. Rev. Lett. 81, 538–541 (1998)
Maglione, E., Ferreira, L.S., Liotta, R.J.: Proton emission from deformed nuclei. Phys. Rev. C 59, R589–R592 (1999)
Cwiok, S., Dudek, J., Nazarewicz, W., Skalski, J., Werner, T.: Single-particle energies, wave functions, quadrupole moments and g-factors in an axially deformed Woods-Saxon potential with applications to the two-centre-type nuclear problem. Comput. Phys. Commun. 46, 379–399 (1987)
Ferreira, L.S., Maglione, E.: 151Lu: spherical or deformed? Phys. Rev. C 61, 021304(R)/1–3 (2000)
Möller, P., Nix, R.J., Myers, W.D., Swiatecki, W.: Nuclear ground-state masses and deformations. At. Data Nucl. Data Tables 59, 185–381 (1995)
Maglione, E., Ferreira, L.S.: Fine structure in proton emission from deformed 131Eu. Phys. Rev. C 61, 047307/1–3 (2000)
Sonzogni, A.A., Davids, C.N., Woods, P.J., et al.: Fine structure in the decay of the highly deformed proton emitter 131Eu. Phys. Rev. Lett. 83, 1116–1118 (1999)
Ferreira, L.S., Maglione, E., Fernandes, D.E.P.: Dependence of the decay widths for proton emission on the single particle potential. Phys. Rev. C 65, 024323/1–9 (2002)
Cherpunov, V.A.: Yad. Fiz. 6, 955 (1967)
Blomqvist, J., Wahlborn, S.: Shell model calculations in the Lead region with a diffuse nuclear potential. Ark. Fys. 16, 545–566 (1960)
Rost, E.: Protron shell-model potentials for Lead and the stability of superheavy nuclei. Phys. Lett. 26 B, 184–187 (1968)
Dudek, J., Szymanski, Z., Werner, T., Faessler, A., Lima, C.: Description of high spin states in 146Gd using the optimized Woods-Saxon potential. Phys. Rev. C 26, 1712–1718 (1982)
Kruppa, A.T., Barmore, B., Nazarewicz, W., Vertse, T.: Fine structure in the decay of deformed proton emitters: nonadiabatic approach. Phys. Rev. Lett. 84, 4549–4552 (2000)
Barmore, B., Kruppa, A.T., Nazarewicz, W., Vertse, T.: Theoretical description of deformed proton emitters: nonadiabatic coupled-channel method. Phys. Rev. C 62, 054315/1–12 (2000)
Barmore, B., Kruppa, A.T., Nazarewicz, W., Vertse, T.: A new approach to deformed proton emitters: non-adiabatic coupled-channels. Nucl. Phys. A 682, 256c–263c (2001)
Delion, D.S., Liotta, R.J., Wyss, R.: High-spin proton emitters in odd-odd nuclei and shape changes. Phys. Rev. C 68, 054603(R)/1–5 (2003)
Ferreira, L.S., Maglione, E.: Odd-odd deformed proton emitters. Phys. Rev. Lett. 86, 1721–1724 (2001)
Bohr, A., Mottelson, B.: Nuclear Structure. Benjamin, New York (1975)
Davids, C.N., Esbensen, H.: Decay rate of triaxially deformed proton emitters. Phys. Rev. C 69, 043314/1–9 (2004)
Davids, C.N., Woods, P.J., Mahmud, H., et al.: Proton decay of the highly deformed odd-odd nucleus 130Eu. Phys. Rev. C 69, 011302(R)/1–3 (2004)
Delion, D.S., Wyss, R., Karlgren, D., Liotta, R.J.: Proton emission from triaxial nuclei. Phys. Rev. C 70, 061301(R)/1–5 (2004)
Kruppa, A.T., Nazarewicz, W.: Gamow and R-Matrix approach to proton emitting nuclei. Phys. Rev. C 69, 054311/1–11 (2004)
Kadmensky, S.G., Sonzogni, A.A.: Proton angular distributions from oriented proton-emitting nuclei. Phys. Rev. C 62, 054601/1–5 (2000)
Rafiqullah, A.K.: Alpha decay of nonaxial nuclei. Phys. Rev. 127, 905–913 (1962)
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Delion, D.S. (2010). Coupled Channels Methods. In: Theory of Particle and Cluster Emission. Lecture Notes in Physics, vol 819. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14406-6_4
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DOI: https://doi.org/10.1007/978-3-642-14406-6_4
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