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Manuscript Title: A new version of the general program to calculate atomic continuum processes using the R-matrix method.
Authors: K.A. Berrington, P.G. Burke, M. Le Dourneuf, W.D. Robb, K.T. Taylor, V.K. Lan
Program title: A NEW VERSION OF RMATRX STG3
Catalogue identifier: AAHH_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 14(1978)367
Programming language: Fortran.
Computer: IBM 360/195.
Operating system: OS/360 MVT-HASP.
RAM: 654K words
Word size: 8
Peripherals: magnetic tape, disc.
Keywords: Atomic physics, Polarizability, Householder method, Cross sections, Phase shifts, Long-range potentials, Electron atom, Electron ion, R-matrix, Eigenvalues, Buttle correction, K-matrix, Asymptotic solutions, Scattering, Photoionization, Hamiltonian matrix, Eigenvectors, De volelaere's method, T-matrix, Wbk, Photon.
Classification: 2.4, 2.5.

Subprograms used:
Cat Id Title Reference
AAHF_v1_0 A NEW VERSION OF RMATRX STG1 CPC 14(1978)367
AAHG_v1_0 A NEW VERSION OF RMATRX STG2 CPC 14(1978)367

Other versions:
Cat Id Title Reference
AAHC_v1_0 RMATRX STG3 CPC 8(1974)150
AANV_v1_0 RMATRX STG3R CPC 25(1982)347
ADCP_v1_0 RMATRX1 CPC 92(1995)290

Revision history:
Type Tit le Reference
adaptation 0001 R-MATRIX POLARIZABILITIES See below

Nature of problem:
This program reads the hamiltonian matrix elements, the asymptotic potential coefficients and the dipole length and velocity matrix elements stored on a magnetic tape or disc file by A NEW VERSION of RMATRX STG2. It then diagonalizes the hamiltonian matrix and calculates the R-matrix and its Buttle correction. Then either the electron-atom or -ion cross section, the photoionization cross section and beta asymmetry parameter or the frequency dependent polarizability is calculated, for a range of incident energies or frequencies. In a photoionization or polarizability calculation, the initial state is treated in exactly the same way as the final states.

Solution method:
The Householder method and the bisection method are used to diagonalize the hamiltonian matrix, and the Buttle correction to the R-matrix is calculated by solving a differential equation using the Volgelaere's method. In the case of electron scattering and photoionization, the coupled differential equations are solved in the asymptotic region using either an asymptotic series expansion or a WBK solution. The K-matrix and T-matrix are determined from the R-matrix by matrix algebra.

Restrictions:
The maximum size of the hamiltonian matrix that can be treated is 200, the maximum number of channels is 12 and the maximum number of energies which can be dealt with in one run is 50. All of these can be increased by recompling with larger dimensions.

Running time:
For most practical runs, the time taken to solve the coupled differential equations in the asymptotic region is usually the dominating factor. The test run took 3 s for electron scattering 6 s for photoionization and 6 s for polarizability on the IBM 360/195.

ADAPTATION SUMMARY
Manuscript Title: R-matrix dynamic dipole polarizabilities.
Authors: P. Shorer
Program title: 0001 R-MATRIX POLARIZABILITIES
Catalogue identifier: AAHH_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 22(1981)467
Programming language: Fortran.
Classification: 2.4, 2.5.

Subprograms used:
Cat Id Title Reference
AAHF_v1_0 A NEW VERSION OF RMATRX STG1 CPC 14(1978)367
AAHG_v1_0 A NEW VERSION OF RMATRX STG2 CPC 14(1978)367
AAHH_v1_0 A NEW VERSION OF RMATRX STG3 CPC 14(1978)367

Nature of problem:
The lowest order interaction of electromagnetic radiation with an atom is directly related to the frequency dependent multipole polarizability. A knowledge of the dynamic polarizability of the system is therefore important in determining level shifts, refractive indices, harmonic coefficients, the Van der Waals Csigma coefficient and similar quantities relating to the response of an atom to a perturbing field. The dynamic dipole polarizability can be written in several forms, length and velocity being two of the most common.

Solution method:
Using the method of Dalgarno and lewis the summations over intermediate states are first replaced by differential equations. These differential equations are then solved using straightforward atomic R-matrix methods. The method is readily implemented by making the observation that the non-homogeneous term in each of the equations vanishes for radial distances greater than the R-matrix radius.

Restrictions:
Same as for standard RMATRX.

Running time:
Neon test case using data as for standard RMATRX STG3- approx. 40 photon energies per 20 s, without the Buttle correction.