Efficient fitting algorithms applied to analysis of coincidence γ-ray spectra

In the paper efficient nonlinear fitting algorithms without matrix inversion are described. The algorithms were applied to the analysis of two- and three-fold coincidence γ-ray spectra. They were used to process coincidence matrices from fission data from the multidetector GAMMASPHERE spectrometer.     

Relativistic central-field Green's functions for the Ratip package

From perturbation theory, Green's functions are known for providing a simple and convenient access to the (complete) spectrum of atoms and ions. Having these functions available, they may help carry out perturbation expansions to any order beyond the first one. For most realistic potentials, however, the Green's functions need to be calculated numerically since an analytic form is known only for free electrons or for their motion in a pure Coulomb field. Therefore, in order to facilitate the use of Green's functions also for atoms and ions other than the hydrogen-like ions, here we provide an extension to the Ratip program which supports the computation of relativistic (one-electron) Green's functions in an—arbitrarily given—central-field potential V(r). Different computational modes have been implemented to define these effective potentials and to generate the radial Green's functions for all bound-state energies E<0. In addition, care has been taken to provide a user-friendly component of the Ratip package by utilizing features of the Fortran 90/95 standard such as data structures, allocatable arrays, or a module-oriented design.

Program summary

Title of program:XgreensCatalogue number: ADWMProgram summary URL:http://cpc.cs.qub.ac.uk/summaries/ADWMProgram obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandLicensing provisions:NoneComputer for which the new version has been tested: PC Pentium II, III, IV, AthlonInstallations: University of Kassel (Germany)Operating systems: SuSE Linux 8.2, SuSE Linux 9.0Program language used in the new version: ANSI standard Fortran 90/95Memory required to execute with typical data: On a standard grid (400 nodes), one central-field Green's function requires about 50 kBytes in RAM while approximately 3 MBytes are needed if saved as two-dimensional array on some external disc spaceNo. of bits in a word: Real variables of double- and quad-precision are usedPeripheral used: Disk for input/outputCPU time required to execute test data: 2 min on a 450 MHz Pentium III processorNo. of lines in distributed program, including test data etc.: 82 042No. of bytes in distributed program, including test data etc.: 814 096Distribution format: tar.gzNature of the physical problem: In atomic perturbation theory, Green's functions may help carry out the summation over the complete spectrum of atom and ions, including the (summation over the) bound states as well as an integration over the continuum [R.A. Swainson, G.W.F. Drake, J. Phys. A 24 (1991) 95]. Analytically, however, these functions are known only for free electrons (V(r)≡0) and for electrons in a pure Coulomb field (V(r)=−Z/r). For all other choices of the potential, in contrast, the Green's functions must be determined numerically.Method of solution: Relativistic Green's functions are generated for an arbitrary central-field potential V(r)=−Z(r)/r by using a piecewise linear approximation of the effective nuclear charge function Z(r) on some grid : Zi(r)=Z0i+Z1ir. Then, following McGuire's algorithm [E.J. McGuire, Phys. Rev. A 23 (1981) 186], the radial Green's functions are constructed from the (two) linear-independent solutions of the homogeneous equation [P. Morse, H. Feshbach, Methods of Theoretical Physics, McGraw-Hill, New York 1953 (Part 1, p. 825)]. In the computation of these radial functions, the Kummer and Tricomi functions [J. Spanier, B. Keith, An Atlas of Functions, Springer, New York, 1987] are used extensively.Restrictions onto the complexity of the problem: The main restrictions of the program concern the shape of the effective nuclear charge Z(r)=−rV(r), i.e. the choice of the potential, and the allowed energies. Apart from obeying the proper boundary conditions for a point-like nucleus, namely, Z(r→0)=Znuc>0 and Z(r→∞)=Znuc−Nelectrons?0, the first derivative of the charge function Z(r) must be smaller than the (absolute value of the) energy of the Green's function, .Unusual features of the program:Xgreens has been designed as a part of the Ratip package [S. Fritzsche, J. Elec. Spec. Rel. Phen. 114-116 (2001) 1155] for the calculation of relativistic atomic transition and ionization properties. In a short dialog at the beginning of the execution, the user can specify the choice of the potential as well as the energies and the symmetries of the radial Green's functions to be calculated. Apart from central-field Green's functions, of course, the Coulomb Green's function [P. Koval, S. Fritzsche, Comput. Phys. Comm. 152 (2003) 191] can also be computed by selecting a constant nuclear charge Z(r)=Zeff. In order to test the generated Green's functions, moreover, we compare the two lowest bound-state orbitals which are calculated from the Green's functions with those as generated separately for the given potential. Like the other components of the Ratip package, Xgreens makes careful use of the Fortran 90/95 standard.     

TiReX: Replica-exchange molecular dynamics using Tinker

We present a driver program for performing replica-exchange molecular dynamics simulations with the Tinker package. Parallelization is based on the Message Passing Interface, with every replica assigned to a separate process. The algorithm is not communication intensive, which makes the program suitable for running even on loosely coupled cluster systems. Particular attention is paid to the practical aspects of analyzing the program output.

Program summary

Program title: TiReXCatalogue identifier: AEEK_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEEK_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.: 43 385No. of bytes in distributed program, including test data, etc.: 502 262Distribution format: tar.gzProgramming language: Fortran 90/95Computer: Most UNIX machinesOperating system: LinuxHas the code been vectorized or parallelized?: parallelized with MPIClassification: 16.13External routines: TINKER version 4.2 or 5.0, built as a libraryNature of problem: Replica-exchange molecular dynamics.Solution method: Each replica is assigned to a separate process; temperatures are swapped between replicas at regular time intervals.Running time: The sample run may take up to a few minutes.     

Revised and extended Utilities for the Ratip package

During the last years, the Ratip package has been found useful for calculating the excitation and decay properties of free atoms. Based on the (relativistic) multiconfiguration Dirac-Fock method, this program is used to obtain accurate predictions of atomic properties and to analyze many recent experiments. The daily work with this package made an extension of its Utilities [S. Fritzsche, Comput. Phys. Comm. 141 (2001) 163] desirable in order to facilitate the data handling and interpretation of complex spectra. For this purpose, we make available an enlarged version of the Utilities which mainly supports the comparison with experiment as well as large Auger computations. Altogether 13 additional tasks have been appended to the program together with a new menu structure to improve the interactive control of the program.

Program summary

Title of program: RATIPCatalogue identifier: ADPD_v2_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADPD_v2_0Program obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandLicensing provisions: noneReference in CPC to previous version: S. Fritzsche, Comput. Phys. Comm. 141 (2001) 163Catalogue identifier of previous version: ADPDAuthors of previous version: S. Fritzsche, Department of Physics, University of Kassel, Heinrich-Plett-Strasse 40, D-34132 Kassel, GermanyDoes the new version supersede the original program?: yesComputer for which the new version is designed and others on which it has been tested: IBM RS 6000, PC Pentium II-IVInstallations: University of Kassel (Germany), University of Oulu (Finland)Operating systems: IBM AIX, Linux, UnixProgram language used in the new version: ANSI standard Fortran 90/95Memory required to execute with typical data: 300 kBNo. of bits in a word: All real variables are parameterized by a selected kind parameter and, thus, can be adapted to any required precision if supported by the compiler. Currently, the kind parameter is set to double precision (two 32-bit words) as used also for other components of the Ratip package [S. Fritzsche, C.F. Fischer, C.Z. Dong, Comput. Phys. Comm. 124 (2000) 341; G. Gaigalas, S. Fritzsche, Comput. Phys. Comm. 134 (2001) 86; S. Fritzsche, Comput. Phys. Comm. 141 (2001) 163; S. Fritzsche, J. Elec. Spec. Rel. Phen. 114-116 (2001) 1155]No. of lines in distributed program, including test data, etc.:231 813No. of bytes in distributed program, including test data, etc.: 3 977 387Distribution format: tar.gzip fileNature of the physical problem: In order to describe atomic excitation and decay properties also quantitatively, large-scale computations are often needed. In the framework of the Ratip package, the Utilities support a variety of (small) tasks. For example, these tasks facilitate the file and data handling in large-scale applications or in the interpretation of complex spectra.Method of solution: The revised Utilities now support a total of 29 subtasks which are mainly concerned with the manipulation of output data as obtained from other components of the Ratip package. Each of these tasks are realized by one or several subprocedures which have access to the corresponding modules of the main components. While the main menu defines seven groups of subtasks for data manipulations and computations, a particular task is selected from one of these group menus. This allows to enlarge the program later if technical support for further tasks will become necessary. For each selected task, an interactive dialog about the required input and output data as well as a few additional information are printed during the execution of the program.Reasons for the new version: The requirement for enlarging the previous version of the Utilities [S. Fritzsche, Comput. Phys. Comm. 141 (2001) 163] arose from the recent application of the Ratip package for large-scale radiative and Auger computations. A number of new subtasks now refer to the handling of Auger amplitudes and their proper combination in order to facilitate the interpretation of complex spectra. A few further tasks, such as the direct access to the one-electron matrix elements for some given set of orbital functions, have been found useful also in the analysis of data.Summary of revisions: extraction and handling of atomic data within the framework of Ratip. With the revised version, we now ‘add’ another 13 tasks which refer to the manipulation of data files, the generation and interpretation of Auger spectra, the computation of various one- and two-electron matrix elements as well as the evaluation of momentum densities and grid parameters. Owing to the rather large number of subtasks, the main menu has been divided into seven groups from which the individual tasks can be selected very similarly as before.Typical running time: The program responds promptly for most of the tasks. The responding time for some tasks, such as the generation of a relativistic momentum density, strongly depends on the size of the corresponding data files and the number of grid points.Unusual features of the program: A total of 29 different tasks are supported by the program. Starting from the main menu, the user is guided interactively through the program by a dialog and a few additional explanations. For each task, a short summary about its function is displayed before the program prompts for all the required input data.     

An integrated tool for loop calculations: aITALC

aITALC, a new tool for automating loop calculations in high energy physics, is described. The package creates Fortran code for two-fermion scattering processes automatically, starting from the generation and analysis of the Feynman graphs. We describe the modules of the tool, the intercommunication between them and illustrate its use with three examples.

Program summary

Title of the program:aITALC version 1.2.1 (9 August 2005)Catalogue identifier:ADWOProgram summary URL:http://cpc.cs.qub.ac.uk/summaries/ADWOProgram obtainable from:CPC Program Library, Queen's University of Belfast, N. IrelandComputer:PC i386Operating system:GNU/Linux, tested on different distributions SuSE 8.2 to 9.3, Red Hat 7.2, Debian 3.0, Ubuntu 5.04. Also on SolarisProgramming language used:GNU Make, Diana, Form, Fortran77Additional programs/libraries used:Diana 2.35 (Qgraf 2.0), Form 3.1, LoopTools 2.1 (FF)Memory required to execute with typical data:Up to about 10 MBNo. of processors used:1No. of lines in distributed program, including test data, etc.:40 926No. of bytes in distributed program, including test data, etc.:371 424Distribution format:tar gzip fileHigh-speed storage required:from 1.5 to 30 MB, depending on modules present and unfolding of examplesNature of the physical problem:Calculation of differential cross sections for e⁺e⁻ annihilation in one-loop approximation.Method of solution:Generation and perturbative analysis of Feynman diagrams with later evaluation of matrix elements and form factors.Restriction of the complexity of the problem:The limit of application is, for the moment, the 2→2 particle reactions in the electro-weak standard model.Typical running time:Few minutes, being highly depending on the complexity of the process and the Fortran compiler.     

Pomwig: Herwig for diffractive interactions

We have modified the Herwig event generator to incorporate diffractive interactions. All standard Herwig hard subprocesses are available.     

Helac-Phegas: A generator for all parton level processes

The updated version of the Helac-Phegas¹ event generator is presented. The matrix elements are calculated through Dyson-Schwinger recursive equations using color connection representation. Phase-space generation is based on a multichannel approach, including optimization. Helac-Phegas generates parton level events with all necessary information, in the most recent Les Houches Accord format, for the study of any process within the Standard Model in hadron and lepton colliders.

New version program summary

Program title: HELAC-PHEGASCatalogue identifier: ADMS_v2_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADMS_v2_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.: 35 986No. of bytes in distributed program, including test data, etc.: 380 214Distribution format: tar.gzProgramming language: FortranComputer: AllOperating system: LinuxClassification: 11.1, 11.2External routines: Optionally Les Houches Accord (LHA) PDF Interface library (http://projects.hepforge.org/lhapdf/)Catalogue identifier of previous version: ADMS_v1_0Journal reference of previous version: Comput. Phys. Comm. 132 (2000) 306Does the new version supersede the previous version?: Yes, partlyNature of problem: One of the most striking features of final states in current and future colliders is the large number of events with several jets. Being able to predict their features is essential. To achieve this, the calculations need to describe as accurately as possible the full matrix elements for the underlying hard processes. Even at leading order, perturbation theory based on Feynman graphs runs into computational problems, since the number of graphs contributing to the amplitude grows as n!.Solution method: Recursive algorithms based on Dyson-Schwinger equations have been developed recently in order to overcome the computational obstacles. The calculation of the amplitude, using Dyson-Schwinger recursive equations, results in a computational cost growing asymptotically as 3n, where n is the number of particles involved in the process. Off-shell subamplitudes are introduced, for which a recursion relation has been obtained allowing to express an n-particle amplitude in terms of subamplitudes, with 1-, 2-, …  up to (n−1) particles. The color connection representation is used in order to treat amplitudes involving colored particles. In the present version HELAC-PHEGAS can be used to efficiently obtain helicity amplitudes, total cross sections, parton-level event samples in LHA format, for arbitrary multiparticle processes in the Standard Model in leptonic, and pp collisions.Reasons for new version: Substantial improvements, major functionality upgrade.Summary of revisions: Color connection representation, efficient integration over PDF via the PARNI algorithm, interface to LHAPDF, parton level events generated in the most recent LHA format, k_⊥ reweighting for Parton Shower matching, numerical predictions for amplitudes for arbitrary processes for phase-space points provided by the user, new user interface and the possibility to run over computer clusters.Running time: Depending on the process studied. Usually from seconds to hours.References:

[1]

A. Kanaki, C.G. Papadopoulos, Comput. Phys. Comm. 132 (2000) 306.

[2]

C.G. Papadopoulos, Comput. Phys. Comm. 137 (2001) 247.

     

-XSummer- Transcendental functions and symbolic summation in Form

Harmonic sums and their generalizations are extremely useful in the evaluation of higher-order perturbative corrections in quantum field theory. Of particular interest have been the so-called nested sums, where the harmonic sums and their generalizations appear as building blocks, originating for example, from the expansion of generalized hypergeometric functions around integer values of the parameters. In this paper we discuss the implementation of several algorithms to solve these sums by algebraic means, using the computer algebra system Form.

Program summary

Title of program:XSummerCatalogue identifier:ADXQ_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADXQ_v1_0Program obtainable from:CPC Program Library, Queen's University of Belfast, N. IrelandLicense:GNU Public License and Form LicenseComputers:allOperating system:allProgram language:FormMemory required to execute:Depending on the complexity of the problem, recommended at least 64 MB RAMNo. of lines in distributed program, including test data, etc.:9854No. of bytes in distributed program, including test data, etc.:126 551Distribution format:tar.gzOther programs called:noneExternal files needed:noneNature of the physical problem:Systematic expansion of higher transcendental functions in a small parameter. The expansions arise in the calculation of loop integrals in perturbative quantum field theory.Method of solution:Algebraic manipulations of nested sums.Restrictions on complexity of the problem:Usually limited only by the available disk space.Typical running time:Dependent on the complexity of the problem.     

Qprop: A Schrödinger-solver for intense laser-atom interaction

The Qprop package is presented. Qprop has been developed to study laser-atom interaction in the nonperturbative regime where nonlinear phenomena such as above-threshold ionization, high order harmonic generation, and dynamic stabilization are known to occur. In the nonrelativistic regime and within the single active electron approximation, these phenomena can be studied with Qprop in the most rigorous way by solving the time-dependent Schrödinger equation in three spatial dimensions. Because Qprop is optimized for the study of quantum systems that are spherically symmetric in their initial, unperturbed configuration, all wavefunctions are expanded in spherical harmonics. Time-propagation of the wavefunctions is performed using a split-operator approach. Photoelectron spectra are calculated employing a window-operator technique. Besides the solution of the time-dependent Schrödinger equation in single active electron approximation, Qprop allows to study many-electron systems via the solution of the time-dependent Kohn-Sham equations.

Program summary

Program title:QPROPCatalogue number:ADXBProgram summary URL:http://cpc.cs.qub.ac.uk/summaries/ADXBProgram obtainable from:CPC Program Library, Queen's University of Belfast, N. IrelandComputer on which program has been tested:PC Pentium IV, AthlonOperating system:LinuxProgram language used:C++Memory required to execute with typical data:Memory requirements depend on the number of propagated orbitals and on the size of the orbitals. For instance, time-propagation of a hydrogenic wavefunction in the perturbative regime requires about 64 KB RAM (4 radial orbitals with 1000 grid points). Propagation in the strongly nonperturbative regime providing energy spectra up to high energies may need 60 radial orbitals, each with 30000 grid points, i.e. about 30 MB. Examples are given in the article.No. of bits in a word:Real and complex valued numbers of double precision are usedNo. of lines in distributed program, including test data, etc.:69 995No. of bytes in distributed program, including test data, etc.: 2 927 567Peripheral used:Disk for input-output, terminal for interaction with the userCPU time required to execute test data:Execution time depends on the size of the propagated orbitals and the number of time-stepsDistribution format:tar.gzNature of the physical problem:Atoms put into the strong field of modern lasers display a wealth of novel phenomena that are not accessible to conventional perturbation theory where the external field is considered small as compared to inneratomic forces. Hence, the full ab initio solution of the time-dependent Schrödinger equation is desirable but in full dimensionality only feasible for no more than two (active) electrons. If many-electron effects come into play or effective ground state potentials are needed, (time-dependent) density functional theory may be employed. Qprop aims at providing tools for (i) the time-propagation of the wavefunction according to the time-dependent Schrödinger equation, (ii) the time-propagation of Kohn-Sham orbitals according to the time-dependent Kohn-Sham equations, and (iii) the energy-analysis of the final one-electron wavefunction (or the Kohn-Sham orbitals).Method of solution:An expansion of the wavefunction in spherical harmonics leads to a coupled set of equations for the radial wavefunctions. These radial wavefunctions are propagated using a split-operator technique and the Crank-Nicolson approximation for the short-time propagator. The initial ground state is obtained via imaginary time-propagation for spherically symmetric (but otherwise arbitrary) effective potentials. Excited states can be obtained through the combination of imaginary time-propagation and orthogonalization. For the Kohn-Sham scheme a multipole expansion of the effective potential is employed. Wavefunctions can be analyzed using the window-operator technique, facilitating the calculation of electron spectra, either angular-resolved or integratedRestrictions onto the complexity of the problem:The coupling of the atom to the external field is treated in dipole approximation. The time-dependent Schrödinger solver is restricted to the treatment of a single active electron. As concerns the time-dependent density functional mode of Qprop, the Hartree-potential (accounting for the classical electron-electron repulsion) is expanded up to the quadrupole. Only the monopole term of the Krieger-Li-Iafrate exchange potential is currently implemented. As in any nontrivial optimization problem, convergence to the optimal many-electron state (i.e. the ground state) is not automatically guaranteedExternal routines/libraries used:The program uses the well established libraries blas, lapack, and f2c     

Maple procedures for the coupling of angular momenta. An up-date of the Racah module

An up-date of the Racah module is presented, adopted to Maple 11 and 12, which supports both, algebraic manipulations of expressions from Racah's algebra as well as numerical computations of many functions and symbols from the theory of angular momentum. The functions that are known to the program include the Wigner rotation matrices and n-j symbols, Clebsch-Gordan and Gaunt coefficients, spherical harmonics of various kinds as well as several others.

Program summary

Program title:RacahCatalogue identifier: ADFV_v10_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADFV_v10_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.: 30 436No. of bytes in distributed program, including test data, etc.: 544 866Distribution format: tar.gzProgramming language: Maple 11 and 12Computer: All computers with a license for the computer algebra package Maple [1]Operating system: Suse Linux 10.2+ and Ubuntu 8.10Classification: 4.1, 5Catalogue identifier of previous version: ADFV_v9_0Journal reference of previous version: Comput. Phys. Comm. 174 (2006) 616Does the new version supersede the previous version?: YesNature of problem: The theories of angular momentum and spherical tensor operators, sometimes known also as Racah's algebra, provide a powerful calculus for studying spin networks and (quantum) many-particle systems. For an efficient use of these theories, however, one requires not only a reliable handling of a large number of algebraic transformations and rules but, more often than not, also a fast access to their standard quantities, such as the Wigner n-j symbols, Clebsch-Gordan coefficients, spherical harmonics of various kinds, the rotation matrices, and many others.Solution method: A set of Maple procedures has been developed and maintained during the last decade which supports both, algebraic manipulations as well as fast computations of the standard expressions and symbols from the theory of angular momentum [2,3]. These procedures are based on a sizeable set of group-theoretical (and often rather sophisticated) relations which has been discussed and proven in the literature; see the monograph by Varshalovich et al. [4] for a comprehensive compilation. In particular the algebraic manipulation of complex (Racah) expressions may result in considerable simplifications, thus reducing the ‘numerical costs’, and often help obtain further insight into the behaviour of physical systems.Reasons for new version: A revision of the Racah module became necessary for mainly three reasons: (i) Since the last extension of the Racah procedures [5], which was developed within the framework of Maple 8, several updates of Maple were distributed by the vendors (currently Maple 13) and required a number of adaptations to the source code; (ii) the increasing size and program structure of the Racah module made it advisible to separate the (procedures for the treatment of the) atomic shell model from the manipulation and computation of Racah expressions. Therefore, the computation of angular coefficients for different coupling schemes, (grand) coefficients of fractional parentage as well as the matrix elements (of various irreducible tensors from the shell model) is to be maintained from now on independently within the Jucys module; (iii) a number of bugs and inconsistencies have been reported to us and corrected in the present version.Summary of revisions: In more detail, the following changes have been made:

1.

Since recent versions of Maple now support the automatic type checking of all incoming arguments and the definition of user-defined types; we have adapted most of the code to take advantage of these features, and especially those commands that are accessible by the user.

2.

In the computation of the Wigner n-j symbols and Clebsch-Gordan coefficients, we now return a ‘0’ in all cases in which the triangular rules are not fulfilled, for example, if δ(a,b,c)=0 for or . This change in the program saves the user making these tests on the quantum numbers explicitly everytime (in the summation over more complex expressions) that such a symbol or coefficient is invoked. The program still terminates with an error message if the (half-integer and integer) angular momentum quantum numbers appear in an inproper combination.

3.

While a recursive generation of the Wigner 3-j and 6-j symbols [6] may reduce the costs of some computations (and has thus been utilized in the past), it also makes the program rather sophisticated, especially if an algebraic evaluation or computations with a high number of Digits need to be supported by the same generic commands. The following procedures are therefore no longer supported by the Racah module:Racah_compute_w3j_jrange(), Racah_compute_w3j_mrange(),Racah_compute_w3j_recursive(), Racah_compute_w6j_range(), andRacah_compute_w6j_recursive().On most PCs, a sequential computation of all requested symbols is carried out within the same time basically.

4.

Because the module Jucys has grown to a size of about 35,000 lines of code and data, it appears helpful and necessary to maintain it independently. The procedures from the Jucys modules were designed to facilitate the computation of matrix elements of the unit tensors, the coefficients of fractional parentage (of various types) as well as transformation matrices between different coupling schemes [7] and are, thus, independent of the Racah module (although they typically require that the Racah code is available). The Jucys module is no longer distributed together with the present code.

5.

Apart from the Wigner n-j symbols (see above), some minor bugs have been reported and corrected in Racah_expand() and Racah_set().

6.

To facilitate the test of the installation and as a first tutorial on the module, we now provide the Maple worksheet Racah-tests-2009-maple12.mw in the Racah2009 root directory. This worksheet contains the examples and test cases from the previous versions. For the test of the installation, it is recommended that a ‘copy’ of this worksheet is saved and compared to the results from the re-run. It can be used also as a helpful source to define new examples in interactive work with the Racah module.

The Racah module is distributed in a tar file ADFV_v10_0.tar.gz from which the RACAH2009 root directory is (re-)generated by the command tar -zxvf ADFV_v10_0.tar.gz. This directory contains the source code libraries (tested for Maple 11 and 12), a Read.me for the installation of the program, the worksheet Racah-tests-2009-maple12.mw as well as the document Racah-commands-2009.pdf. This .pdf document serves as a Short Reference Manual and provides the definition of all the data structures of the Racah program together with an alphabetic list of all user relevant (and exported) commands. Although emphasis was placed on preserving the compatibility of the program with earlier releases of Maple, this cannot always be guaranteed due to changes in the Maple syntax. The Racah2009 root also contains an example of a .mapleinit file that can be modified and incorporated into the user's home directory to make the Racah module accessible like any other module of Maple. As mentioned above, the worksheet Racah-tests-2009-maple12.mw, help test the installation and may serve as a first tutorial.Restrictions: The (Racah) program is based on the concept of Racah expressions [cf. Fig. 1 in Ref. [4]] which, in principle, may contain any number of Wigner n-j symbols (n?9), Clebsch-Gordan coefficients, spherical harmonics and/or rotation matrices. In practise, of course, the required time and the success of an evaluation procedure depends on the complexity of the expressions and on the storage available, sometimes also on Maple's internal garbage treatment. In some cases, it is advisable to attempt first a simplification of the magnetic quantum numbers for a given expression before the summation over further 6-j and 9-j symbols should be taken into account. For all other quantities (that are compiled in Ref. [8], Tables 1 and 2, and explained in more detail in the Short Reference Manual, Racah-commands-2009.pdf), we currently just facilitate fast numerical computations by exploiting, as far as possible, Maple's hardware floating-point model. The program also supports simplifications on the Wigner rotation matrices. In integrals over the rotation matrices, products of up to three Wigner D-functions or reduced matrices (with the same angular arguments) are recognized; for the integration over a solid angle, however, the domain of integration must be specified explicitly for the Euler angles α and γ in order to force Maple to generate a constant of integration. In the course of the evaluation of Racah expressions, it is, in practice, often difficult to check internally whether all substructures of an expression are defined properly. Therefore, the user must ensure that all angular momenta (if given explicitly) must finally evaluate to integer and half-integer values and that they satisfy proper coupling conditions.Unusual features: The Racah program is designed for interactive use and for providing a quick and algebraic evaluation of (complex) expressions from Racah's algebra. In the evaluation, it exploits a large set of sum rules which are known from Racah's algebra and which may include (multiple) summations over dummy indices; see Varshalovich et al. [5] for a more detailed account of the theory. One strength of the program is that it recognizes automatically the symmetries of the symbols and functions, and that it applies also (some of) the graphical rules due to Yutsis and coworkers [9]. As before, the result of the evaluation process will be provided as Racah expressions, if a further simplification could be achieved, and may hence be used for further derivations and calculations within the given framework. In dealing with recoupling coefficients, these coefficients can be entered simply as a string of angular momenta (variables), separated by commas, and very similar to how they appear in mathematical texts. This is a crucial advantage of the program, compared with previous developments, for which the angular momenta and coupling coefficients had often to be given in a very detailed format. A Short Reference Manual to all procedures of the Racah program is provided by this distribution; it also contains the worksheet Racah-tests-2009-maple12.mw that contains the examples from all previous versions and may help test the installation. This worksheet can serve as a first tutorial to the Racah procedures. In the past, the Racah program has been utilized extensively in a number of applications including angular and polarization studies of heavy ions [10], angular distributions and correlation functions following photon-induced excitation processes [11], entanglement studies [12], in application of point-group symmetries and several others.Running time: The worksheet supplied with the distribution takes about 1 minute to run.References:

[1] Maple is a registered trademark of Waterloo Maple Inc.

[2] S. Fritzsche, Comp. Phys. Commun. 103 (1997) 51.

[3] S. Fritzsche, S. Varga, D. Geschke, B. Fricke, Comp. Phys. Commun. 111 (1998) 167;

T. Ingho, S. Fritzsche, B. Fricke, Comp. Phys. Commun. 139 (2001) 297;

S. Fritzsche, T. Ingho, T. Bastug, M. Tomaselli, Comp. Phys. Commun. 139 (2001) 314.

[4] D.A. Varshalovich, A.N. Moskalev, V.K. Khersonskii, Quantum Theory of Angular Momentum, World Scientific, Singapore a.o., 1988.

[5] J. Pagaran, S. Fritzsche, G. Gaigalas, Comp. Phys. Commun. 174 (2006) 616.

[6] K. Schulten, R.G. Gordon, Comp. Phys. Commun. 11 (1976) 269.

[7] G. Gaigalas, S. Fritzsche, B. Fricke, Comp. Phys. Commun. 135 (2001) 219;

G. Gaigalas, S. Fritzsche, Comp. Phys. Commun. 149 (2002) 39;

G. Gaigalas, O. Scharf, S. Fritzsche, Comp. Phys. Commun. 166 (2005) 141.

[8] S. Fritzsche, T. Ingho, M. Tomaselli, Comp. Phys. Commun. 153 (2003) 424.

[9] A.P. Yutsis, I.B. Levinson, V.V. Vanagas, The Theory of Angular Momentum, Israel Program for Scientific Translation, Jerusalem, 1962.

[10] S. Fritzsche, P. Indelicato, T. Stöhlker, J. Phys. B 38 (2005) S707.

[11] M. Kitajima, M. Okamoto, M. Hoshino, et al., J. Phys. B 35 (2002) 3327;

N.M. Kabachnik, S. Fritzsche, A.N. Grum-Grzhimailo, et al., Phys. Reports 451 (2007) 155;

S. Fritzsche, A.N. Grum-Grzhimailo, E.V. Gryzlova, N.M. Kabachnik, J. Phys. B 41 (2008) 165601;

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[12] T. Radtke, S. Fritzsche, Comp. Phys. Commun. 175 (2006) 145.

     

Range and Roots: Two common patterns for specifying and propagating counting and occurrence constraints

We propose Range and Roots which are two common patterns useful for specifying a wide range of counting and occurrence constraints. We design specialised propagation algorithms for these two patterns. Counting and occurrence constraints specified using these patterns thus directly inherit a propagation algorithm. To illustrate the capabilities of the Range and Roots constraints, we specify a number of global constraints taken from the literature. Preliminary experiments demonstrate that propagating counting and occurrence constraints using these two patterns leads to a small loss in performance when compared to specialised global constraints and is competitive with alternative decompositions using elementary constraints.     

A combinatorial algorithm for max csp

We consider the problem max csp over multi-valued domains with variables ranging over sets of size s_i?s and constraints involving k_j?k variables. We study two algorithms with approximation ratios A and B, respectively, so we obtain a solution with approximation ratio max(A,B).The first algorithm is based on the linear programming algorithm of Serna, Trevisan, and Xhafa [Proc. 15th Annual Symp. on Theoret. Aspects of Comput. Sci., 1998, pp. 488-498] and gives ratio A which is bounded below by s^1−k. For k=2, our bound in terms of the individual set sizes is the minimum over all constraints involving two variables of , where s₁ and s₂ are the set sizes for the two variables.We then give a simple combinatorial algorithm which has approximation ratio B, with B>A/e. The bound is greater than s^1−k/e in general, and greater than s^1−k(1−(s−1)/2(k−1)) for s?k−1, thus close to the s^1−k linear programming bound for large k. For k=2, the bound is if s=2, 1/2(s−1) if s?3, and in general greater than the minimum of 1/4s₁+1/4s₂ over constraints with set sizes s₁ and s₂, thus within a factor of two of the linear programming bound.For the case of k=2 and s=2 we prove an integrality gap of . This shows that our analysis is tight for any method that uses the linear programming upper bound.     

Quickstep: Fast and accurate density functional calculations using a mixed Gaussian and plane waves approach

We present the Gaussian and plane waves (GPW) method and its implementation in Quickstep which is part of the freely available program package CP2K. The GPW method allows for accurate density functional calculations in gas and condensed phases and can be effectively used for molecular dynamics simulations. We show how derivatives of the GPW energy functional, namely ionic forces and the Kohn-Sham matrix, can be computed in a consistent way. The computational cost of computing the total energy and the Kohn-Sham matrix is scaling linearly with the system size, even for condensed phase systems of just a few tens of atoms. The efficiency of the method allows for the use of large Gaussian basis sets for systems up to 3000 atoms, and we illustrate the accuracy of the method for various basis sets in gas and condensed phases. Agreement with basis set free calculations for single molecules and plane wave based calculations in the condensed phase is excellent. Wave function optimisation with the orbital transformation technique leads to good parallel performance, and outperforms traditional diagonalisation methods. Energy conserving Born-Oppenheimer dynamics can be performed, and a highly efficient scheme is obtained using an extrapolation of the density matrix. We illustrate these findings with calculations using commodity PCs as well as supercomputers.     

Vbfnlo: A parton level Monte Carlo for processes with electroweak bosons

Vbfnlo is a fully flexible parton level Monte Carlo program for the simulation of vector boson fusion, double and triple vector boson production in hadronic collisions at next-to-leading order in the strong coupling constant. Vbfnlo includes Higgs and vector boson decays with full spin correlations and all off-shell effects. In addition, Vbfnlo implements CP-even and CP-odd Higgs boson via gluon fusion, associated with two jets, at the leading-order one-loop level with the full top- and bottom-quark mass dependence in a generic two-Higgs-doublet model.A variety of effects arising from beyond the Standard Model physics are implemented for selected processes. This includes anomalous couplings of Higgs and vector bosons and a Warped Higgsless extra dimension model. The program offers the possibility to generate Les Houches Accord event files for all processes available at leading order.

Program summary

Program title:VbfnloCatalogue identifier: AEDO_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEDO_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: GPL version 2No. of lines in distributed program, including test data, etc.: 339 218No. of bytes in distributed program, including test data, etc.: 2 620 847Distribution format: tar.gzProgramming language: Fortran, parts in C++Computer: AllOperating system: Linux, should also work on other systemsClassification: 11.1, 11.2External routines: Optionally Les Houches Accord PDF Interface library and the GNU Scientific libraryNature of problem: To resolve the large scale dependence inherent in leading order calculations and to quantify the cross section error induced by uncertainties in the determination of parton distribution functions, it is necessary to include NLO corrections. Moreover, whenever stringent cuts are required on decay products and/or identified jets the question arises whether the scale dependence and a k-factor, defined as the ratio of NLO to LO cross section, determined for the inclusive production cross sections are valid for the search region one is interested in.Solution method: The problem is best addressed by implementing the one-loop QCD corrections in a fully flexible NLO parton-level Monte Carlo program, where arbitrary cuts can be specified as well as various scale choices. In addition, any currently available parton distribution function set can be used through the LHAPDF library.Running time: Depending on the process studied. Usually from minutes to hours.     

ODMixed: A tool to obtain optimal designs for heterogeneous longitudinal studies with dropout

ODMixed is a computer program to obtain optimal designs for linear mixed models of longitudinal studies. These designs account for heterogeneous correlated errors and for data with dropout. Designs are compared by using relative efficiencies, e.g., between a D-optimal design for homogeneous data and another for heterogeneous data or between a D-optimal design for complete data against another that optimizes designs when data is missing at random. Two examples are worked out to illustrate how researchers could use this computer program to profit of optimal design theory at the planning stage of longitudinal studies.     

Jahn—A program for representing atomic and nuclear states within an isospin basis

A computer program is presented to deal with atomic and nuclear state functions within an isospin-coupled basis. Apart from the classification of the isospin bases states, the program Jahn supports the computation of the corresponding coefficients of fractional parentage as well as of the transformation matrices going from a LS-coupled to an isospin-coupled basis. In the future, these features may facilitate the treatment of atomic systems in order to obtain a deeper insight into the coupling of open-shell atoms and ions. The Jahn program has been designed for interactive work and is distributed as a Maple module.

Program summary

Title of program:JahnCatalogue identifier:ADXA_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADXA_v1_0Program obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandLicensing provisions:NoneComputers for which the program is designed: All computers with a valid license of the computer algebra package Maple which is a registered trademark of Waterloo Maple Inc.Installations: University of Kassel (Germany)Operating systems under which the program has been tested: Linux 8.1+Program language used:Maple, Release 8 and 9Memory required to execute with typical data: 30 MBNumber of lines in distributed program, including test data, etc.: 38 158Number of bytes in distributed program, including test data, etc.: 743 689Distribution format: tar.gzNature of the physical problem: The accurate computation of atomic (nuclear) properties and level structures requires a good understanding and implementation of the atomic (nuclear) shell model and, hence, a fast and reliable access to its classification, the coefficients of fractional parentage and the coefficients of fractional grandparentage. For open-shell atoms and ions, moreover, a reliable classification of the level structure often requires the knowledge of some transformation matrices in order to find the main components of the wave functions as well as their proper spectroscopic notation. In particular, the transformation from a LS-coupled to an isospin-coupled basis is important for atoms and ions with the two open shells n₁lN₁n₂lN₂.Method of solution: The concept of the isospin formalism is used and explained in [V. Šimonis, PhD Thesis, Institute of Physics, Vilnius, 1982 (in Russian); Z. Rudzikas, J. Kaniauskas, Quasispin and Isospin in the Theory of Atom, Mokslas, Vilnius, 1984 (in Russian); J.M. Kaniauskas, V.?. Šimonis, Z.B. Rudzikas, J. Phys. B: At. Mol. Phys. 20 (1987) 3267]. The coefficients of fractional parentage (CFP) in the isospin basis, the coefficients of fractional grandparentage (CFGP) in the isospin basis and the transformation matrices from a LS-coupled to an isospin-coupled basis are provided for s-, p-, d-shells. These matrices are utilized to transform symmetry-adapted configuration state functions (CSF) as obtained from the coupling of two open shells n₁lN₁n₂lN₂. Moreover, a simple notation is introduced to handle such symmetry functions interactively.Restrictions onto the complexity of the problem: The classification of the n₁lN₁n₂lN₂ electron configurations provides support for the subshell angular momentum l=0,…,2 and for the occupation numbers N₁ and N₂, where N₁ and N₂ must be in the range N₁=0,…,(2l+1) and N₂=0,…,(2l+1), respectively. The program provides the CFP and CFGP for isospin-coupled subshell states for the orbital angular momenta l=0,1 and occupation numbers N?2(2l+1) and for l = 2 with N?4, respectively. It also evaluates the transformation matrices for l=0,1 and occupation numbers N₁, N₂ and N in the range N₁=0,…,2l; N₂=1,2; N=N₁+N₂?2(2l+1) and for l=2 and occupation numbers N₁, N₂ and N in the range N₁=0,…,3; N₂=1,2; N=N₁+N₂?4, respectively. The transformation of an atomic state function (ASF) or configuration state function (CSF) from an LS-coupled to an isospin-coupled basis can be obtained for these orbital momenta and occupation numbers.Unusual features of the program: The program is designed as an interactive environment for the (symbolic) manipulation and computation of expressions from theory of atomic and nuclear shell model. Here we provide the user with a simple access to the coefficients of fractional parentage as well as to the transformation matrices . A complete transformation of LS-coupled CSF or ASF into an isospin-coupled basis can be carried out just by typing a few lines at Maple's prompt. These coefficients and transformation matrices enable the user to make a more detailed analysis of matrix elements of the operators of physical quantities within the isospin basis. The (main) commands of the Jahn program are described in detail in Appendices A and B.Typical running time: The program replies promptly on most requests. Even large tabulations of CFP or transformation matrices can be obtained within a few seconds.