Symbolic-Numerical Algorithm for Generating Cluster Eigenfunctions: Tunneling of Clusters through Repulsive Barriers

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.

[1]  Quantum transmittance of barriers for composite particles , 1999, hep-ph/9912546.

[2]  Fernando Porcelli,et al.  On the black hole’s thermodynamics and the entropic origin of gravity , 2010 .

[3]  Ochbadrakh Chuluunbaatar,et al.  Channeling problem for charged particles produced by confining environment , 2009 .

[4]  M. Shegelski,et al.  Time-dependent trapping of a molecule , 2012 .

[5]  A. Volya,et al.  Quantum tunneling and scattering of a composite object reexamined , 2010, 1010.3973.

[6]  A. Fasolino,et al.  Quantum surface diffusion of vibrationally excited molecular dimers. , 2007, The Journal of chemical physics.

[7]  Ochbadrakh Chuluunbaatar,et al.  KANTBP: A program for computing energy levels, reaction matrix and radial wave functions in the coupled-channel hyperspherical adiabatic approach , 2007, Comput. Phys. Commun..

[8]  Ochbadrakh Chuluunbaatar,et al.  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 , 2014, Comput. Phys. Commun..

[9]  Ochbadrakh Chuluunbaatar,et al.  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 , 2008, Comput. Phys. Commun..

[10]  S. Ershov,et al.  Breakup reactions of two-neutron halo nuclei , 2008 .

[11]  A. Shotter,et al.  Quantum mechanical tunneling of composite particle systems: Linkage to sub-barrier nuclear reactions , 2011 .

[12]  B. A. Brown,et al.  Experimental determination of an I{sup {pi}=}2{sup -} ground state in {sup 72,74}Cu , 2010 .

[14]  M. Nemes,et al.  On the interpretation of heavy-ion sub-barrier fusion data , 1983 .

[15]  Ochbadrakh Chuluunbaatar,et al.  Erratum to: Program ADZH_v2_0, "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" [Computer Physics Communications 179 (2008) 685] , 2009, Comput. Phys. Commun..

[16]  H. Hofmann.  Quantummechanical treatment of the penetration through a two-dimensional fission barrier , 1974 .

[17]  Vladimir P. Gerdt,et al.  Symbolic-Numerical Algorithms to Solve the Quantum Tunneling Problem for a Coupled Pair of Ions , 2011, CASC.

[18]  Enhancement and suppression of tunneling by controlling symmetries of a potential barrier , 2010, 1006.0905.

[19]  J. Broeckhove,et al.  Three-cluster description of properties of light neutron- and proton-rich nuclei in the framework of the algebraic version of the resonating group method , 2010 .

[20]  Vladimir P. Gerdt,et al.  A symbolic-numerical algorithm for the computation of matrix elements in the parametric eigenvalue problem , 2007, Programming and Computer Software.

[21]  Ochbadrakh Chuluunbaatar,et al.  Symbolic-Numerical Algorithm for Generating Cluster Eigenfunctions: Identical Particles with Pair Oscillator Interactions , 2013, CASC.

[22]  V. Zagrebaev,et al.  Near-barrier fusion of heavy nuclei: Coupling of channels , 2004 .

[23]  Witold Nazarewicz,et al.  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 , 1987 .

[24]  C. F. Bunge.  Fast eigensolver for dense real-symmetric matrices , 2001 .