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Manuscript Title: 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. | ||

Authors: O. Chuluunbaatar, A.A. Gusev, S.I. Vinitsky, A.G. Abrashkevich | ||

Program title: KANTBP | ||

Catalogue identifier: ADZH_v2_0Distribution format: tar.gz | ||

Journal reference: Comput. Phys. Commun. 179(2008)685 | ||

Programming language: FORTRAN 77. | ||

Computer: Intel Xeon EM64T, Alpha 21264A, AMD Athlon MP, Pentium IV Xeon, Opteron 248, Intel Pentium IV. | ||

Operating system: OC Linux, Unix AIX 5.3, SunOS 5.8, Solaris, Windows XP. | ||

RAM: This depends on
- the number of differential equations;
- the number and order of finite elements;
- the number of hyperradial points; and
- the number of eigensolutions required
| ||

Keywords: eigenvalue and multi-channel scattering problems, Kantorovich method, finite element method, R-matrix calculations, hyperspherical coordinates, multi-channel adiabatic approximation, ordinary differential equations, high-order accuracy approximations. | ||

PACS: 02.30.Hq, 02.60.Jh, 02.60.Lj, 03.65.Nk, 31.15.Ja, 31.15.Pf, 34.50.-s, 34.80.Bm. | ||

Classification: 2.1, 2.4. | ||

External routines: GAULEG and GAUSSJ [2] | ||

Nature of problem:In the hyperspherical adiabatic approach [3 5], a multidimensional Schrödinger equation for a two-electron system [6] or a hydrogen atom in magnetic field [7 9] is reduced by separating radial coordinate ρ from the angular variables to a system of the second-order ordinary differential equations containing the potential matrix elements and first-derivative coupling terms. The purpose of this paper is to present the finite element method procedure based on the use of high-order accuracy approximations for calculating approximate eigensolutions of the continuum spectrum for such systems of coupled differential equations on finite intervals of the radial variable ρ ∈ [ρ _{min}, ρ_{max}]. This approach can be used in the calculations of effects of electron screening on low-energy fusion cross sections [10 12]. | ||

Solution method:The boundary problems for the coupled second-order differential equations are solved by the finite element method using high-order accuracy approximations [13]. The generalized algebraic eigenvalue problem AF = EBF with respect to pair unknowns (E,F) arising after the replacement of the differential problem by the finite-element approximation is solved by the subspace iteration method using the SSPACE program [14]. The generalized algebraic eigenvalue problem (A -EB)F = λDF with respect to pair unknowns (λ,F) arising after the corresponding replacement of the scattering boundary problem in open channels at fixed energy value, E, is solved by the LDL^{T} factorization of symmetric matrix and back-substitution methods using the DECOMP and REDBAK programs, respectively [14]. As a test desk, the program is applied to the calculation of the reaction matrix and corresponding radial wave functions for 3D-model of a hydrogen-like atom in a homogeneous magnetic field described in [9] on finite intervals of the radial variable ρ ∈ [ρ_{min}, ρ_{max}]. For this benchmark model the required analytical expressions for asymptotics of the potential matrix elements and first-derivative coupling terms, and also asymptotics of radial solutions of the boundary problems for coupled differential equations have been produced with help of a MAPLE computer algebra system. | ||

Restrictions:The computer memory requirements depend on: - the number of differential equations;
- the number and order of finite elements;
- the total number of hyperradial points; and
- the number of eigensolutions required.
| ||

Running time:The running time depends critically upon: - the number of differential equations;
- the number and order of finite elements;
- the total number of hyperradial points on interval [ρ
_{min}, ρ_{max}]; and - the number of eigensolutions required.
| ||

References: | ||

[1] | O. Chuluunbaatar, A.A. Gusev, A.G. Abrashkevich, A. Amaya-Tapia, M.S. Kaschiev, S.Y. Larsen and S.I. Vinitsky, Comput. Phys. Commun. 177 (2007) 649 675; http://cpc.cs.qub.ac.uk/summaries/ADZH v1 0.html. | |

[2] | W.H. Press, S.A. Teukolsky, W.T. Vetterling and B.P. Flannery, Numerical Recipes: The Art of Scientific Computing, Cambridge University Press, Cambridge, 1986. | |

[3] | J. Macek, J. Phys. B 1 (1968) 831 843. | |

[4] | U. Fano, Rep. Progr. Phys. 46 (1983) 97 165. | |

[5] | C.D. Lin, Adv. Atom. Mol. Phys. 22 (1986) 77 142. 3 | |

[6] | A.G. Abrashkevich, D.G. Abrashkevich and M. Shapiro, Comput. Phys. Commun. 90 (1995) 311 339. | |

[7] | M.G. Dimova, M.S. Kaschiev and S.I. Vinitsky, J. Phys. B 38 (2005) 2337 2352. | |

[8] | O. Chuluunbaatar, A.A. Gusev, V.L. Derbov, M.S. Kaschiev, L.A. Melnikov, V.V. Serov and S.I. Vinitsky, J. Phys. A 40 (2007) 11485 11524. | |

[9] | O. Chuluunbaatar, A.A. Gusev, V.P. Gerdt, V.A. Rostovtsev, S.I. Vinitsky, A.G. Abrashkevich, M.S. Kaschiev and V.V. Serov, Comput. Phys. Commun. 178 (2007) 301 330; http://cpc.cs.qub.ac.uk/summaries/AEAA v1 0.html. | |

[10] | H.J. Assenbaum, K. Langanke and C. Rolfs, Z. Phys. A 327 (1987) 461 468. | |

[11] | V. Melezhik, Nucl. Phys. A 550 (1992) 223 234. | |

[12] | L. Bracci, G. Fiorentini, V.S. Melezhik, G. Mezzorani and P. Pasini, Phys. Lett. A 153 (1991) 456 460. | |

[13] | A.G. Abrashkevich, D.G. Abrashkevich, M.S. Kaschiev and I.V. Puzynin, Comput. Phys. Commun. 85 (1995) 40 64. | |

[14] | K.J. Bathe, Finite Element Procedures in Engineering Analysis, Englewood Cli s, Prentice Hall, New York, 1982. |

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