Angular coefficients for symmetry-adapted configuration states in \(jj\)-coupling. (English) Zbl 1523.81208
Summary: In atomic structure and collision theory, the efficient spin-angular integration is known to be crucial and often decides, how accurate the properties and behavior of atoms can be predicted numerically. Various methods have been developed in the past to keep the computation (and implementation) of the spin-angular integration feasible for complex shell structures, including open \(d\)- and \(f\)-shell elements. To support such computations, we here provide a new implementation of the angular coefficients for \(jj\)-coupled and symmetry-adapted configuration states that is entirely built upon the quasi-spin formalism. The module SpinAngular is based on Julia, a new programming language for scientific computing, and supports a simple access to all (completely) reduced tensors, coefficients of fractional parentage for subshells with \(j \leq 9/2\) as well as the re-coupling coefficients from this formalism. Moreover, this module has been worked out for multiple purposes, including 1) the accurate calculation of atomic properties, 2) further studies on spin-angular integration theory, 3) the development of new or existing computer programs as well as 4) the manipulation of reduced matrix elements from this theory. The present implementation will therefore help advance the algebraic evaluation of many-electron (transition) amplitudes and to apply the theory to newly emerging research areas.
MSC:
| 81V45 | Atomic physics |
| 81U05 | \(2\)-body potential quantum scattering theory |
| 81R25 | Spinor and twistor methods applied to problems in quantum theory |
| 26B15 | Integration of real functions of several variables: length, area, volume |
| 14N20 | Configurations and arrangements of linear subspaces |
| 62H20 | Measures of association (correlation, canonical correlation, etc.) |
| 35P15 | Estimates of eigenvalues in context of PDEs |
| 81-08 | Computational methods for problems pertaining to quantum theory |
Keywords:
spin-angular integration in atomic theory; atomic structure calculations; configuration interaction; correlations; Dirac theory; energy levelsReferences:
| [1] | Fano, U., Phys. Rev. A, 67, Article 140 pp. (1965) |
| [2] | Cowan, R. D., The Theory of Atomic Structure and Spectra (1981), University of California Press: University of California Press Berkeley |
| [3] | Grant, I. P., (Wilson, S., Relativistic Atomic Structure Calculations. Relativistic Atomic Structure Calculations, Methods in Computational Chemistry, vol. 2 (1988), Plenum: Plenum New York), 1 |
| [4] | Gaigalas, G.; Rudzikas, Z.; Froese Fischer, C., J. Phys. B, At. Mol. Opt. Phys., 30, 3747 (1997) |
| [5] | Racah, G., Phys. Rev., 63, 367 (1943) |
| [6] | Racah, G., Group Theory and Spectroscopy, Springer Tracts in Modern Physics, vol. 37, 28 (1965), Springer: Springer Berlin, Heidelberg, New York · Zbl 0134.43703 |
| [7] | Racah, G., Phys. Rev., 62, 438 (1942) |
| [8] | Judd, B. R., Operator Techniques in Atomic Spectroscopy (1998), Princeton Univ. Press: Princeton Univ. Press Princeton, NJ |
| [9] | Sobelman, I. I., Atomic Spectra and Radiative Transitions (1996), Springer |
| [10] | Burke, P. G.; Burke, V. M.; Dunseath, K. M., J. Phys. B, At. Mol. Opt. Phys., 27, 5341 (1994) |
| [11] | Gaigalas, G., Lithuanian J. Phys., 39, 79 (1999) |
| [12] | Grant, I. P., Relativistic Quantum Theory of Atoms and Molecules: Theory and Computation (2007), Springer |
| [13] | Froese Fischer, C., J. Phys. B, At. Mol. Opt. Phys., 49, Article 182004 pp. (2016) |
| [14] | Jönsson, P., Comput. Phys. Commun., 184, 2197 (2013) · Zbl 1344.81171 |
| [15] | Froese Fischer, C., Comput. Phys. Commun., 237, 184 (2019) |
| [16] | Froese Fischer, C., Comput. Phys. Commun., 176, 559 (2007) |
| [17] | Fritzsche, S., J. Electron Spectrosc. Relat. Phenom., 114-116, 1155 (2001) |
| [18] | Fritzsche, S., Comput. Phys. Commun., 183, 1525 (2012) |
| [19] | Kučas, S.; Momkauskaitė, A.; Karazija, R., Astrophys. J., 810, 26 (2015) |
| [20] | Kučas, S., J. Phys. B, At. Mol. Opt. Phys., 52, Article 225001 pp. (2019) |
| [21] | Schippers, S., J. Phys. B, At. Mol. Opt. Phys., 48, Article 144003 pp. (2015) |
| [22] | Schippers, S., Phys. Rev. A, 94, Article 041401 pp. (2016) |
| [23] | Fritzsche, S., Comput. Phys. Commun., 240, 1 (2019) |
| [24] | S. Fritzsche, Jac: manual, compendium & theoretical background, 2018, unpublished. |
| [25] | Tanaka, M.; Hotokezaka, K., Astrophys. J., 775, 113 (2013) |
| [26] | Palaudoux, J., Phys. Rev. A, 82, Article 043419 pp. (2010) |
| [27] | Jonauskas, V.; Kučas, S.; Karazija, R., Phys. Rev. A, 84, Article 053415 pp. (2011) |
| [28] | Schippers, S., Astrophys. J., 849, 5 (2017) |
| [29] | Paufler, W.; Böning, B.; Fritzsche, S., Phys. Rev. A, 98, Article 011401 pp. (2018) |
| [30] | Böning, B.; Fritzsche, S., Phys. Rev. A, 102, Article 053108 pp. (2020) |
| [31] | Merkelis, G., Phys. Scr., 51, 233 (1995) |
| [32] | Rudzikas, Z., Theoretical Atomic Spectroscopy (1997), Cambridge University Press |
| [33] | Gaigalas, G.; Rudzikas, Z., J. Phys. B, At. Mol. Opt. Phys., 29, 3303 (1996) |
| [34] | Gaigalas, G.; Fritzsche, S.; Rudzikas, Z., At. Data Nucl. Data Tables, 76, 235 (2000) |
| [35] | Sewtz, M., Phys. Rev. Lett., 90, Article 163002 pp. (2003) |
| [36] | Radžiūtė, L., Phys. Rev. A, 93, Article 062508 pp. (2016) |
| [37] | The pure spin-angular coefficients of one- or two-particle operator are obtained if the corresponding interaction strength are set to one, \( X^{1 p} = X^{2 p} = 1\). |
| [38] | Jucys, A. P.; Bandzaitis, A. A., Theory of Angular Momentum in Quantum Mechanics (1977), Mintis: Mintis Vilnius, (in Russian) · Zbl 0163.21603 |
| [39] | Gaigalas, G.; Fritzsche, S.; Fricke, B., Comput. Phys. Commun., 135, 219 (2001) · Zbl 1017.81503 |
| [40] | Gaigalas, G.; Scharf, O.; Fritzsche, S., Comput. Phys. Commun., 166, 141 (2005) |
| [41] | Gaigalas, G.; Fritzsche, S., Comput. Phys. Commun., 134, 86 (2001) · Zbl 0970.81099 |
| [42] | Gaigalas, G.; Fritzsche, S.; Grant, I. P., Comput. Phys. Commun., 139, 263 (2001) · Zbl 0986.65122 |
| [43] | Gaigalas, G.; Fritzsche, S., Comput. Phys. Commun., 148, 349 (2002) |
| [44] | Bezanson, J., Proc. ACM Program. Lang., 2, 120 (2018) |
| [45] | Balbaert, I.; Salceanu, A., Julia 1.0 Programming Complete Reference Guide: Discover Julia, a High-Performance Language for Technical Computing (2019), Packt Publishing Ltd: Packt Publishing Ltd Birmingham |
| [46] | Fritzsche, S.; Fricke, B.; Sepp, W.-D., Phys. Rev. A, 45, 1465 (1992) |
| [47] | Schippers, S., Astrophys. J., 908, 52 (2021) |
| [48] | Julia comes with a full-featured interactive and command-line REPL, (read-eval-print loop) that is built into the executable of the language. |
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