Abstract
A model for quantum tunnelling of a cluster comprising A identical particles, coupled by oscillator-type potential, through short-range repulsive potential barriers is introduced for the first time in the new symmetrized-coordinate representation and studied within the s-wave approximation. The symbolic-numerical algorithms for calculating the effective potentials of the close-coupling equations in terms of the cluster wave functions and the energy of the barrier quasistationary states are formulated and implemented using the Maple computer algebra system. The effect of quantum transparency, manifesting itself in nonmonotonic resonance-type dependence of the transmission coefficient upon the energy of the particles, the number of the particles A = 2,3,4, and their symmetry type, is analyzed. It is shown that the resonance behavior of the total transmission coefficient is due to the existence of barrier quasistationary states imbedded in the continuum.
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References
Pen’kov, F.M.: Quantum transmittance of barriers for composite particles. JETP 91, 698–705 (2000)
Pijper, E., Fasolino, A.: Quantum surface diffusion of vibrationally excited molecular dimers. J. Chem. Phys. 126, 014708-1–014708-10 (2007)
Bondar, D.I., Liu, W.-K., Ivanov, M.Y.: Enhancement and suppression of tunneling by controlling symmetries of a potential barrier. Phys. Rev. A 82, 052112-1–052112-9 (2010)
Shegelski, M.R.A., Pittman, J., Vogt, R., Schaan, B.: Time-dependent trapping of a molecule. European Phys. J. Plus 127, 17-1–17-13 (2012)
Ershov, S.N., Danilin, B.V.: Breakup of two-neutron halo nuclei. Phys. Part. Nucl. 39, 1622–1720 (2008)
Nesterov, A.V., Arickx, F., Broeckhove, J., Vasilevsky, V.S.: Three-cluster description of properties of light nuclei with neutron and proton access within the algebraic version of the resonating group method. Phys. Part. Nucl. 41, 1337–1426 (2010)
Hofmann, H.: Quantummechanical treatment of the penetration through a two-dimensional fission barrier. Nucl. Phys. A 224, 116–139 (1974)
Krappe, H.J., Möhring, K., Nemes, M.C., Rossner, H.: On the interpretation of heavy-ion sub-barrier fusion data. Z. Phys. A 314, 23–31 (1983)
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 problems. Comput. Phys. Communications 46, 379–399 (1987)
Hagino, K., Rowley, N., Kruppa, A.T.: A program for coupled-channel calculations with all order couplings for heavy-ion fusion reactions. Comput. Phys. Commun. 123, 143–152 (1999)
Zagrebaev, V.I., Samarin, V.V.: Near-barrier fusion of heavy nuclei: coupling of channels. Phys. Atom. Nucl. 67, 1462–1477 (2004)
Ahsan, N., Volya, A.: Quantum tunneling and scattering of a composite object reexamined. Phys. Rev. C 82, 064607-1–064607-19 (2010)
Shotter, A.C., Shotter, M.D.: Quantum mechanical tunneling of composite particle systems: Linkage to sub-barrier nuclear reactions. Phys. Rev. C 83, 054621-1–054621-11 (2011)
Shilov, V.M.: Sub-barrier fusion of intermediate and heavy nuclear systems. arXiv:1012.3683 [nucl-th] Phys. Atom. Nucl. 75, 485–490 (2012)
Chuluunbaatar, O., Gusev, A.A., Derbov, V.L., Krassovitskiy, P.M., Vinitsky, S.I.: Channeling problem for charged particles produced by confining environment. Phys. Atom. Nucl. 72, 768–778 (2009)
Gusev, A.A., Vinitsky, S.I., Chuluunbaatar, O., Gerdt, V.P., Rostovtsev, V.A.: Symbolic-numerical algorithms to solve the quantum tunneling problem for a coupled pair of ions. In: Gerdt, V.P., Koepf, W., Mayr, E.W., Vorozhtsov, E.V. (eds.) CASC 2011. LNCS, vol. 6885, pp. 175–191. Springer, Heidelberg (2011)
Gusev, A.A., Chuluunbaatar, O., Vinitsky, S.I.: Computational scheme for calculating reflection and transmission matrices, and corresponding wave functions of multichannel scattering problems. In: Uvarova, L.A. (ed.) Proc. Second International Conference “The Modeling of Non-linear Processes and Systems”, Yanus, Moscow, pp. 978–975 (2011)
Gusev, A., Vinitsky, S., Chuluunbaatar, O., Rostovtsev, V., Hai, L., Derbov, V., Góźdź, A., Klimov, E.: Symbolic-numerical algorithm for generating cluster eigenfunctions: identical particles with pair oscillator interactions. In: Gerdt, V.P., Koepf, W., Mayr, E.W., Vorozhtsov, E.V. (eds.) CASC 2013. LNCS, vol. 8136, pp. 155–168. Springer, Heidelberg (2013)
Vinitsky, S.I., Gerdt, V.P., Gusev, A.A., Kaschiev, M.S., Rostovtsev, V.A., Samoilov, V.N., Tupikova, T.V., Chuluunbaatar, O.: A symbolic-numerical algorithm for the computation of matrix elements in the parametric eigenvalue problem. Programming and Computer Software 33, 105–116 (2007)
Bunge, C.F.: Fast eigensolver for dense real-symmetric matrices. Comput. Phys. Communications 138, 92–100 (2001)
Chuluunbaatar, O., Gusev, A.A., Vinitsky, S.I., Abrashkevich, A.G.: KANTBP 2.0: New version of a program for computing energy levels, reaction matrix and radial wave functions in the coupled-channel hyperspherical adiabatic approach. Comput. Phys. Commun. 179, 685–693 (2008)
Chuluunbaatar, O., Gusev, A.A., Vinitsky, S.I., Abrashkevich, A.G.: KANTBP 3.0 - New version of a program for computing energy levels, reflection and transmission matrices, and corresponding wave functions in the coupled-channel adiabatic approach, Program library “JINRLIB”, http://wwwinfo.jinr.ru/programs/jinrlib/kantbp/indexe.html
de Carvalho, C.A.A., Nussenzweig, H.M.: Time delay. Phys. Rept. 364, 83–174 (2002)
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Vinitsky, S. et al. (2013). Symbolic-Numerical Algorithm for Generating Cluster Eigenfunctions: Tunneling of Clusters through Repulsive Barriers. In: Gerdt, V.P., Koepf, W., Mayr, E.W., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2013. Lecture Notes in Computer Science, vol 8136. Springer, Cham. https://doi.org/10.1007/978-3-319-02297-0_35
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DOI: https://doi.org/10.1007/978-3-319-02297-0_35
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