Skip to content
BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access November 24, 2013

A rate equation method for the sequential double ionisation, including autoionising state excitation, of a noble gas

Damien Middleton, Katravulapally Tejaswi and Lampros Nikolopoulos
From the journal Open Physics


A set of rate equations have been tested against a more robust set of Time-Dependent Density Matrix (TDDM) equations [D. P. W. Middleton, L. A. A. Nikolopoulos, J. Mod. Opti. 59, 1650 (2012)] by using them to determine the populations of ion species and autoionising states (AIS) in noble gas atoms when interacting with a strong external field. Two field shapes were tested here — sinusoidal and square — and a variety of pulse characteristics were examined, i.e. intensity, duration and photon energy, for the neon atomic system. It was found that the rate equations were sufficiently accurate only when the external field is way off-resonant with the AIS. Moreover, analytical solutions of the rate equations in the square pulse case agree with the numerical solutions for a time-dependent pulse containing many cycles. An attempt to model a stochastic field was also made and it was found that the use of such a field diminished and broadened the ion yield ratio due to the presence of an added bandwidth.

[1] W. Ackermann et al., Nat. Photonics 1, 336 (2007) in Google Scholar

[2] V. Richardson et al., J. Phys. B: At. Mol. Phys. 45, 085601 (2012) in Google Scholar

[3] L. Young et al., Nature (London) 466, 56 (2010) in Google Scholar PubMed

[4] L. A. A. Nikolopoulos, P. Lambropoulos, J. Phys. B: At. Mol. Phys. 40, 1347 (2007) in Google Scholar

[5] M. Meyer et al., Phys. Rev. A 74, 011401 (2006) in Google Scholar

[6] D. P. W. Middleton, L. A. A. Nikolopoulos, J. Mod. Opti. 59, 1650 (2012) in Google Scholar

[7] L. A. A. Nikolopoulos, T. J. Kelly, J. T. Costello, Phys. Rev. A 84, 063419 (2011) in Google Scholar

[8] B.-N. Dai, P. Lambropoulos, Phys. Rev. A 34, 3954 (1986) in Google Scholar PubMed

[9] P. Lambropoulos, P. Zoller, Phys. Rev. A 24, 379 (1981) in Google Scholar

[10] K. Blum, Density matrix theory and its applications (Plenum Press, 1981) in Google Scholar

[11] M. Martins, M. Wellhöfer, A. A. Sorokin, M. Richter, K. Tiedtke, W. Wurth, Phys. Rev. A 80, 023411 (2009) in Google Scholar

[12] U. Fano, Phys. Rev. 124, 1866 (1961) in Google Scholar

[13] S. Stenholm, Foundations of Laser Spectroscopy (John Wiley and Sons, 1984) Search in Google Scholar

[14] R. Bellman, R. S. Roth, Laplace Transforms (Singapore, World Scientific, 1984) in Google Scholar

[15] P. Agostini, A. T. Georges, S. E. Wheatley, P. Lambropoulos, M. D. Levenson, J. Phys. B: At. Mol. Phys. 11, 1733 (1978) in Google Scholar

[16] A. M. Covington et al., Phys. Rev. A 66, 062710 (2002) in Google Scholar

Published Online: 2013-11-24
Published in Print: 2013-9-1

© 2013 Versita Warsaw

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Scroll Up Arrow