KANTBP: A program for computing energy levels, reaction matrix and radial wave functions in the coupled-channel hyperspherical adiabatic approach

A FORTRAN 77 program is presented which calculates energy values, reaction matrix and corresponding radial wave functions in a coupled-channel approximation of the hyperspherical adiabatic approach. In this approach, a multi-dimensional Schrödinger equation is reduced to a system of the coupled second-order ordinary differential equations on the finite interval with homogeneous boundary conditions of the third type. The resulting system of radial equations which contains the potential matrix elements and first-derivative coupling terms is solved using high-order accuracy approximations of the finite-element method. As a test desk, the program is applied to the calculation of the energy values and reaction matrix for an exactly solvable 2D-model of three identical particles on a line with pair zero-range potentials.

Program summary

Program title: KANTBPCatalogue identifier: ADZH_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADZH_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 4224No. of bytes in distributed program, including test data, etc.: 31 232Distribution format: tar.gzProgramming language: FORTRAN 77Computer: Intel Xeon EM64T, Alpha 21264A, AMD Athlon MP, Pentium IV Xeon, Opteron 248, Intel Pentium IVOperating system: OC Linux, Unix AIX 5.3, SunOS 5.8, Solaris, Windows XPRAM: depends on (a) the number of differential equations; (b) the number and order of finite-elements; (c) the number of hyperradial points; and (d) the number of eigensolutions required. Test run requires 30 MBClassification: 2.1, 2.4External routines: GAULEG and GAUSSJ [W.H. Press, B.F. Flanery, S.A. Teukolsky, W.T. Vetterley, Numerical Recipes: The Art of Scientific Computing, Cambridge University Press, Cambridge, 1986]Nature of problem: In the hyperspherical adiabatic approach [J. Macek, J. Phys. B 1 (1968) 831-843; U. Fano, Rep. Progr. Phys. 46 (1983) 97-165; C.D. Lin, Adv. Atom. Mol. Phys. 22 (1986) 77-142], a multi-dimensional Schrödinger equation for a two-electron system [A.G. Abrashkevich, D.G. Abrashkevich, M. Shapiro, Comput. Phys. Comm. 90 (1995) 311-339] or a hydrogen atom in magnetic field [M.G. Dimova, M.S. Kaschiev, S.I. Vinitsky, J. Phys. B 38 (2005) 2337-2352] is reduced by separating the radial coordinate ρ from the angular variables to a system of second-order ordinary differential equations which contain 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 for such systems of coupled differential equations.Solution method: The boundary problems for coupled differential equations are solved by the finite-element method using high-order accuracy approximations [A.G. Abrashkevich, D.G. Abrashkevich, M.S. Kaschiev, I.V. Puzynin, Comput. Phys. Comm. 85 (1995) 40-64]. 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 [K.J. Bathe, Finite Element Procedures in Engineering Analysis, Englewood Cliffs, Prentice-Hall, New York, 1982]. 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 LDLT factorization of symmetric matrix and back-substitution methods using the DECOMP and REDBAK programs, respectively [K.J. Bathe, Finite Element Procedures in Engineering Analysis, Englewood Cliffs, Prentice-Hall, New York, 1982]. As a test desk, the program is applied to the calculation of the energy values and reaction matrix for an exactly solvable 2D-model of three identical particles on a line with pair zero-range potentials described in [Yu. A. Kuperin, P.B. Kurasov, Yu.B. Melnikov, S.P. Merkuriev, Ann. Phys. 205 (1991) 330-361; O. Chuluunbaatar, A.A. Gusev, S.Y. Larsen, S.I. Vinitsky, J. Phys. A 35 (2002) L513-L525; N.P. Mehta, J.R. Shepard, Phys. Rev. A 72 (2005) 032728-1-11; O. Chuluunbaatar, A.A. Gusev, M.S. Kaschiev, V.A. Kaschieva, A. Amaya-Tapia, S.Y. Larsen, S.I. Vinitsky, J. Phys. B 39 (2006) 243-269]. For this benchmark model the needed analytical expressions for the potential matrix elements and first-derivative coupling terms, their asymptotics and 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:

•

(a) the number of differential equations;

•

(b) the number and order of finite-elements;

•

(c) the total number of hyperradial points; and

•

(d) the number of eigensolutions required.

Restrictions due to dimension sizes may be easily alleviated by altering PARAMETER statements (see Long Write-Up and listing for details). The user must also supply subroutine POTCAL for evaluating potential matrix elements. The user should supply subroutines ASYMEV (when solving the eigenvalue problem) or ASYMSC (when solving the scattering problem) that evaluate the asymptotics of the radial wave functions at the right boundary point in case of a boundary condition of the third type, respectively.Running time: The running time depends critically upon:

•

(a) the number of differential equations;

•

(b) the number and order of finite-elements;

•

(c) the total number of hyperradial points on interval [0,ρmax]; and

•

(d) the number of eigensolutions required.

The test run which accompanies this paper took 28.48 s without calculation of matrix potentials on the Intel Pentium IV 2.4 GHz.     

POTHMF: A program for computing potential curves and matrix elements of the coupled adiabatic radial equations for a hydrogen-like atom in a homogeneous magnetic field

A FORTRAN 77 program is presented which calculates with the relative machine precision potential curves and matrix elements of the coupled adiabatic radial equations for a hydrogen-like atom in a homogeneous magnetic field. The potential curves are eigenvalues corresponding to the angular oblate spheroidal functions that compose adiabatic basis which depends on the radial variable as a parameter. The matrix elements of radial coupling are integrals in angular variables of the following two types: product of angular functions and the first derivative of angular functions in parameter, and product of the first derivatives of angular functions in parameter, respectively. The program calculates also the angular part of the dipole transition matrix elements (in the length form) expressed as integrals in angular variables involving product of a dipole operator and angular functions. Moreover, the program calculates asymptotic regular and irregular matrix solutions of the coupled adiabatic radial equations at the end of interval in radial variable needed for solving a multi-channel scattering problem by the generalized R-matrix method. Potential curves and radial matrix elements computed by the POTHMF program can be used for solving the bound state and multi-channel scattering problems. As a test desk, the program is applied to the calculation of the energy values, a short-range reaction matrix and corresponding wave functions with the help of the KANTBP program. Benchmark calculations for the known photoionization cross-sections are presented.

Program summary

Program title:POTHMFCatalogue identifier:AEAA_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEAA_v1_0.htmlProgram obtainable from:CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions:Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.:8123No. of bytes in distributed program, including test data, etc.:131 396Distribution format:tar.gzProgramming language:FORTRAN 77Computer:Intel Xeon EM64T, Alpha 21264A, AMD Athlon MP, Pentium IV Xeon, Opteron 248, Intel Pentium IVOperating system:OC Linux, Unix AIX 5.3, SunOS 5.8, Solaris, Windows XPRAM:Depends on

1.

the number of radial differential equations;

2.

the number and order of finite elements;

3.

the number of radial points.

Test run requires 4 MBClassification:2.5External routines:POTHMF uses some Lapack routines, copies of which are included in the distribution (see README file for details).Nature of problem:In the multi-channel adiabatic approach the Schrödinger equation for a hydrogen-like atom in a homogeneous magnetic field of strength γ (γ=B/B₀, B₀≅2.35×¹⁰⁵ T is a dimensionless parameter which determines the field strength B) is reduced by separating the radial coordinate, r, from the angular variables, (θ,φ), and using a basis of the angular oblate spheroidal functions [3] to a system of second-order ordinary differential equations which contain first-derivative coupling terms [4]. The purpose of this program is to calculate potential curves and matrix elements of radial coupling needed for calculating the low-lying bound and scattering states of hydrogen-like atoms in a homogeneous magnetic field of strength 0<γ?1000 within the adiabatic approach [5]. The program evaluates also asymptotic regular and irregular matrix radial solutions of the multi-channel scattering problem needed to extract from the R-matrix a required symmetric shortrange open-channel reaction matrix K [6] independent from matching point [7]. In addition, the program computes the dipole transition matrix elements in the length form between the basis functions that are needed for calculating the dipole transitions between the low-lying bound and scattering states and photoionization cross sections [8].Solution method:The angular oblate spheroidal eigenvalue problem depending on the radial variable is solved using a series expansion in the Legendre polynomials [3]. The resulting tridiagonal symmetric algebraic eigenvalue problem for the evaluation of selected eigenvalues, i.e. the potential curves, is solved by the LDL^T factorization using the DSTEVR program [2]. Derivatives of the eigenfunctions with respect to the radial variable which are contained in matrix elements of the coupled radial equations are obtained by solving the inhomogeneous algebraic equations. The corresponding algebraic problem is solved by using the LDL^T factorization with the help of the DPTTRS program [2]. Asymptotics of the matrix elements at large values of radial variable are computed using a series expansion in the associated Laguerre polynomials [9]. The corresponding matching points between the numeric and asymptotic solutions are found automatically. These asymptotics are used for the evaluation of the asymptotic regular and irregular matrix radial solutions of the multi-channel scattering problem [7]. As a test desk, the program is applied to the calculation of the energy values of the ground and excited bound states and reaction matrix of multi-channel scattering problem for a hydrogen atom in a homogeneous magnetic field using the KANTBP program [10].Restrictions:The computer memory requirements depend on:

1.

the number of radial differential equations;

2.

the number and order of finite elements;

3.

the total number of radial points.

Restrictions due to dimension sizes can be changed by resetting a small number of PARAMETER statements before recompiling (see Introduction and listing for details).Running time:The running time depends critically upon:

1.

the number of radial differential equations;

2.

the number and order of finite elements;

3.

the total number of radial points on interval [rmin,rmax].

The test run which accompanies this paper took 7 s required for calculating of potential curves, radial matrix elements, and dipole transition matrix elements on a finite-element grid on interval [rmin=0, rmax=100] used for solving discrete and continuous spectrum problems and obtaining asymptotic regular and irregular matrix radial solutions at rmax=100 for continuous spectrum problem on the Intel Pentium IV 2.4 GHz. The number of radial differential equations was equal to 6. The accompanying test run using the KANTBP program took 2 s for solving discrete and continuous spectrum problems using the above calculated potential curves, matrix elements and asymptotic regular and irregular matrix radial solutions. Note, that in the accompanied benchmark calculations of the photoionization cross-sections from the bound states of a hydrogen atom in a homogeneous magnetic field to continuum we have used interval [rmin=0, rmax=1000] for continuous spectrum problem. The total number of radial differential equations was varied from 10 to 18.References:

[1]

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

[2]

http://www.netlib.org/lapack/.

[3]

M. Abramovits, I.A. Stegun, Handbook of Mathematical Functions, Dover, New York, 1965.

[4]

U. Fano, Colloq. Int. C.N.R.S. 273 (1977) 127; A.F. Starace, G.L. Webster, Phys. Rev. A 19 (1979) 1629-1640; C.V. Clark, K.T. Lu, A.F. Starace, in: H.G. Beyer, H. Kleinpoppen (Eds.), Progress in Atomic Spectroscopy, Part C, Plenum, New York, 1984, pp. 247-320; U. Fano, A.R.P. Rau, Atomic Collisions and Spectra, Academic Press, Florida, 1986.

[5]

M.G. Dimova, M.S. Kaschiev, S.I. Vinitsky, J. Phys. B 38 (2005) 2337-2352; O. Chuluunbaatar, A.A. Gusev, V.L. Derbov, M.S. Kaschiev, V.V. Serov, T.V. Tupikova, S.I. Vinitsky, Proc. SPIE 6537 (2007) 653706-1-18.

[6]

M.J. Seaton, Rep. Prog. Phys. 46 (1983) 167-257.

[7]

M. Gailitis, J. Phys. B 9 (1976) 843-854; J. Macek, Phys. Rev. A 30 (1984) 1277-1278; S.I. Vinitsky, V.P. Gerdt, A.A. Gusev, M.S. Kaschiev, V.A. Rostovtsev, V.N. Samoylov, T.V. Tupikova, O. Chuluunbaatar, Programming and Computer Software 33 (2007) 105-116.

[8]

H. Friedrich, Theoretical Atomic Physics, Springer, New York, 1991.

[9]

R.J. Damburg, R.Kh. Propin, J. Phys. B 1 (1968) 681-691; J.D. Power, Phil. Trans. Roy. Soc. London A 274 (1973) 663-702.

[10]

O. Chuluunbaatar, A.A. Gusev, A.G. Abrashkevich, A. Amaya-Tapia, M.S. Kaschiev, S.Y. Larsen, S.I. Vinitsky, Comput. Phys. Comm. 177 (2007) 649-675.

     

ODPEVP: A program for computing eigenvalues and eigenfunctions and their first derivatives with respect to the parameter of the parametric self-adjoined Sturm-Liouville problem

A FORTRAN 77 program is presented for calculating with the given accuracy eigenvalues, eigenfunctions and their first derivatives with respect to the parameter of the parametric self-adjoined Sturm-Liouville problem with the parametric third type boundary conditions on the finite interval. The program calculates also potential matrix elements - integrals of the eigenfunctions multiplied by their first derivatives with respect to the parameter. Eigenvalues and matrix elements computed by the ODPEVP program can be used for solving the bound state and multi-channel scattering problems for a system of the coupled second-order ordinary differential equations with the help of the KANTBP programs [O. Chuluunbaatar, A.A. Gusev, A.G. Abrashkevich, A. Amaya-Tapia, M.S. Kaschiev, S.Y. Larsen, S.I. Vinitsky, Comput. Phys. Commun. 177 (2007) 649-675; O. Chuluunbaatar, A.A. Gusev, S.I. Vinitsky, A.G. Abrashkevich, Comput. Phys. Commun. 179 (2008) 685-693]. As a test desk, the program is applied to the calculation of the potential matrix elements for an integrable 2D-model of three identical particles on a line with pair zero-range potentials, a 3D-model of a hydrogen atom in a homogeneous magnetic field and a hydrogen atom on a three-dimensional sphere.

Program summary

Program title: ODPEVPCatalogue identifier: AEDV_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEDV_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC license, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 3001No. of bytes in distributed program, including test data, etc.: 24 195Distribution format: tar.gzProgramming language: FORTRAN 77Computer: Intel Xeon EM64T, Alpha 21264A, AMD Athlon MP, Pentium IV Xeon, Opteron 248, Intel Pentium IVOperating system: OC Linux, Unix AIX 5.3, SunOS 5.8, Solaris, Windows XPRAM: depends on

1.

the number and order of finite elements;

2.

the number of points; and

3.

the number of eigenfunctions required.

Test run requires 4 MBClassification: 2.1, 2.4External routines: GAULEG [3]Nature of problem: The three-dimensional boundary problem for the elliptic partial differential equation with an axial symmetry similar to the Schrödinger equation with the Coulomb and transverse oscillator potentials is reduced to the two-dimensional one. The latter finds wide applications in modeling of photoionization and recombination of oppositively charged particles (positrons, antiprotons) in the magnet-optical trap [4], optical absorption in quantum wells [5], and channeling of likely charged particles in thin doped films [6,7] or neutral atoms and molecules in artificial waveguides or surfaces [8,9]. In the adiabatic approach [10] known in mathematics as Kantorovich method [11] the solution of the two-dimensional elliptic partial differential equation is expanded over basis functions with respect to the fast variable (for example, angular variable) and depended on the slow variable (for example, radial coordinate ) as a parameter. An averaging of the problem by such a basis leads to a system of the second-order ordinary differential equations which contain potential matrix elements and the first-derivative coupling terms (see, e.g., [12,13,14]). The purpose of this paper is to present the finite element method procedure based on the use of high-order accuracy approximations for calculating eigenvalues, eigenfunctions and their first derivatives with respect to the parameter of the parametric self-adjoined Sturm-Liouville problem with the parametric third type boundary conditions on the finite interval. The program developed calculates potential matrix elements - integrals of the eigenfunctions multiplied by their derivatives with respect to the parameter. These matrix elements can be used for solving the bound state and multi-channel scattering problems for a system of the coupled second-order ordinary differential equations with the help of the KANTBP programs [1,2].Solution method: The parametric self-adjoined Sturm-Liouville problem with the parametric third type boundary conditions is solved by the finite element method using high-order accuracy approximations [15]. The generalized algebraic eigenvalue problem AF=EBF with respect to a pair of unknown (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 [16]. First derivatives of the eigenfunctions with respect to the parameter which contained in potential matrix elements of the coupled system equations are obtained by solving the inhomogeneous algebraic equations. As a test desk, the program is applied to the calculation of the potential matrix elements for an integrable 2D-model of three identical particles on a line with pair zero-range potentials described in [1,17,18], a 3D-model of a hydrogen atom in a homogeneous magnetic field described in [14,19] and a hydrogen atom on a three-dimensional sphere [20].Restrictions: The computer memory requirements depend on:

1.

the number and order of finite elements;

2.

the number of points; and

3.

the number of eigenfunctions required.

Restrictions due to dimension sizes may be easily alleviated by altering PARAMETER statements (see sections below and listing for details). The user must also supply DOUBLE PRECISION functions POTCCL and POTCC1 for evaluating potential function U(ρ,z) of Eq. (1) and its first derivative with respect to parameter ρ. The user should supply DOUBLE PRECISION functions F1FUNC and F2FUNC that evaluate functions f₁(z) and f₂(z) of Eq. (1). The user must also supply subroutine BOUNCF for evaluating the parametric third type boundary conditions.Running time: The running time depends critically upon:

1.

the number and order of finite elements;

2.

the number of points on interval [zmin,zmax]; and

3.

the number of eigenfunctions required.

The test run which accompanies this paper took 2 s with calculation of matrix potentials on the Intel Pentium IV 2.4 GHz.References:

[1]

O. Chuluunbaatar, A.A. Gusev, A.G. Abrashkevich, A. Amaya-Tapia, M.S. Kaschiev, S.Y. Larsen, S.I. Vinitsky, Comput. Phys. Comm. 177 (2007) 649-675

[2]

O. Chuluunbaatar, A.A. Gusev, S.I. Vinitsky, A.G. Abrashkevich, Comput. Phys. Comm. 179 (2008) 685-693.

[3]

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

[4]

O. Chuluunbaatar, A.A. Gusev, S.I. Vinitsky, V.L. Derbov, L.A. Melnikov, V.V. Serov, Phys. Rev. A 77 (2008) 034702-1-4.

[5]

E.M. Kazaryan, A.A. Kostanyan, H.A. Sarkisyan, Physica E 28 (2005) 423-430.

[6]

Yu.N. Demkov, J.D. Meyer, Eur. Phys. J. B 42 (2004) 361-365.

[7]

P.M. Krassovitskiy, N.Zh. Takibaev, Bull. Russian Acad. Sci. Phys. 70 (2006) 815-818.

[8]

V.S. Melezhik, J.I. Kim, P. Schmelcher, Phys. Rev. A 76 (2007) 053611-1-15.

[9]

F.M. Pen'kov, Phys. Rev. A 62 (2000) 044701-1-4.

[10]

M. Born, X. Huang, Dynamical Theory of Crystal Lattices, The Clarendon Press, Oxford, England, 1954.

[11]

L.V. Kantorovich, V.I. Krylov, Approximate Methods of Higher Analysis, Wiley, New York, 1964.

[12]

U. Fano, Colloq. Int. C.N.R.S. 273 (1977) 127;

A.F. Starace, G.L. Webster, Phys. Rev. A 19 (1979) 1629-1640.

[13]

C.V. Clark, K.T. Lu, A.F. Starace, in: H.G. Beyer, H. Kleinpoppen (eds.), Progress in Atomic Spectroscopy, Part C, Plenum, New York, 1984, pp. 247-320.

[14]

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

[15]

A.G. Abrashkevich, D.G. Abrashkevich, M.S. Kaschiev, I.V. Puzynin, Comput. Phys. Comm. 85 (1995) 40-64.

[16]

K.J. Bathe, Finite Element Procedures in Engineering Analysis, Englewood Cliffs, Prentice-Hall, New York, 1982.

[17]

O. Chuluunbaatar, A.A. Gusev, M.S. Kaschiev, V.A. Kaschieva, A. Amaya-Tapia, S.Y. Larsen, S.I. Vinitsky, J. Phys. B 39 (2006) 243-269.

[18]

Yu.A. Kuperin, P.B. Kurasov, Yu.B. Melnikov, S.P. Merkuriev, Ann. Phys. 205 (1991) 330-361.

[19]

O. Chuluunbaatar, A.A. Gusev, V.P. Gerdt, V.A. Rostovtsev, S.I. Vinitsky, A.G. Abrashkevich, M.S. Kaschiev, V.V. Serov, Comput. Phys. Comm. 178 (2008) 301-330.

[20]

A.G. Abrashkevich, M.S. Kaschiev, S.I. Vinitsky, J. Comp. Phys. 163 (2000) 328-348.

     

fgh, a code for the calculation of Coulomb radial wave functions from series expansions

The code fgh is an up-dated version of a code coulfg (see [Seaton, Comput. Phys. Comm. 25 (1982) 87]), used for the calculation of the Coulomb functions f and g, analytic in the energy, for attractive potentials. The new code works for attractive and repulsive potentials and also gives the functions h which have simple asymptotic forms. There is an option to use either the variables (?,r) customary in atomic physics, or (for positive energies) (η,ρ) customary in nuclear physics. When (η,ρ) are used, the code also gives the functions F_?(η,ρ) and G_?(η,ρ).Use of series solutions can lead to loss of accuracy due to cancellation effects. fgh provides an indication of the number of significant figures lost due to cancellations.     

An improved version of ISICS: a program for calculating K-, L- and M-shell cross sections from PWBA and ECPSSR theory using a personal computer

The C program, ISICS [Z. Liu, S.J. Cipolla, Comput. Phys. Comm. 97 (1996) 315-330], which calculates ionization and X-ray production cross-sections using PWBA and ECPSSR theory, has been enhanced to include new options, correct some minor flaws, and to make the program more versatile.

Program summary

Title of program: ISICSCatalog identifier: ADDS_v2_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADDS_v2_0Program available from: CPC Program Library, Queen's University of Belfast, N. IrelandOperating system under which the program has been tested: WINDOWS XPProgram language used: CComputer: 80486 or higher-level PCsNo. of lines in distributed program, including test data, etc.: 5343No. of bytes in distributed program, including test data, etc.: 151 838Distribution format: tar.gzCatalogue identifier of previous version: ADDSJournal reference of previous version: Comput. Phys. Comm. 97 (1996) 315-330Does the new version supersede the previous version: YesNature of the physical problem: Ionization and X-ray production cross-section calculations for ion-atom collisions.Reasons for new version: Increased functionality and new options.Summary of revisions: Option for the united-atom approximation for binding-energy correction; easier inputting of updated atomic parameters; extension of projectile energy down to eV range; accounting for DHS wave function in K-shell ionization; other miscellaneous changes.Method of solution: Numerical integration of form factor using a logarithmic transform and Gaussian quadrature, plus exact integration limits.Restrictions on the complexity of the problem: The consumed CPU time increases with the atomic shell (K, L, M), but execution is still very fast.Typical running time: No change from previous version.Unusual features of the program: No     

An improved version of ISICS: A program for calculating K-, L- and M-shell cross sections from PWBA and ECPSSR theory using a personal computer

The formatting of the M-shell atomic parameters imbedded in file XCSC.H in ISICS has been corrected. The problem only affected cross section calculations for Uranium and heavier elements. The corrected version of ISICS has been re-compiled and is now available.

New version program summary

Program title: ISICSCatalogue identifier: ADDS_v3_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADDS_v3_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 4645No. of bytes in distributed program, including test data, etc.: 106 731Distribution format: tar.gzProgramming language: C++Computer: 80486 or higher-level PCsOperating system: WINDOWS 98 through WINDOWS XPClassification: 16.7Does the new version supersede the previous version?: YesNature of problem: Ionization and X-ray production cross section calculations for ion-atom collisions.Solution method: Numerical integration of form factor using a logarithmic transform and Gaussian quadrature, plus exact integration limits.Reasons for new version: The formatting of the M-shell atomic parameters involving cross section calculations for Uranium and heavier elements needed to be corrected.Summary of revisions: The affected file XCSC.H in ISICS has been corrected and ISICS has been recompiled.Restrictions: The consumed CPU time increases with the atomic shell (K, L, M), but execution is still very fast.Running time: This depends on which shell and the number of different energies to be used in the calculation. For example, to calculate K-shell cross sections for protons striking carbon for 19 different proton energies it took less than 10 s; to calculate M-shell cross sections for protons on gold for 21 proton energies it took 4.2 min.