Photoionisation and the Born approximation

Cordes, J. G.; Calkin, M. G.

doi:10.1088/0022-3700/13/21/006

Cited by 12 publications

(10 citation statements)

References 9 publications

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“…Moreover, the two latter forms become asymptotically identical at high electron energies (i.e. in the small wavelength region), in agreement with [12]. Nevertheless, at low electron energies, there is an increasing discrepancy with respect to the TDSE results, showing the need to better take into account the two-centre nature of the binding potential in describing the continuum electron (see [17]).…”

Section: Numerical Results and Conclusionsupporting

confidence: 66%

“…In [12] it was shown that the velocity and acceleration forms within the plane-wave approximation for the continuum electron have the correct asymptotic limit at high electron energies. In contrast, the plane-wave length form has not the correct limit unless the plane wave describing the continuum electron is corrected to first order in the binding potential.…”

Section: Introductionmentioning

confidence: 99%

“…In contrast, the plane-wave length form has not the correct limit unless the plane wave describing the continuum electron is corrected to first order in the binding potential. Moreover, the discussion in [12] assumed that exact bound states are used. When not, as is often the case (e.g.…”

Section: Introductionmentioning

confidence: 99%

“…When not, as is often the case (e.g. when using the linear combination of atomic orbitals (LCAO) for the ground states of molecules), the same paper [12] states that 'the velocity and the acceleration forms may differ, one being proportional to the derivative and the other to the value of the wave function at the origin'.…”

Section: Introductionmentioning

confidence: 99%

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Assessing different forms of the strong-field approximation for harmonic generation in molecules

Chirilă

Lein

2007

Journal of Modern Optics

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We analyse three different formulations of the strong-field approximation for high-harmonic generation in diatomic molecules, based on length, velocity and acceleration form for the recombination amplitude. We compare the predictions for the two-centre interference with those from the time-dependent Schro¨dinger equation. We find that the velocity form gives the closest agreement with the exact results while being the simplest from a computational point of view.

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Section: Numerical Results and Conclusionsupporting

confidence: 66%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Assessing different forms of the strong-field approximation for harmonic generation in molecules

Chirilă

Lein

2007

Journal of Modern Optics

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“…Our opinion is that, contrary to the author s belief, this last calculation reduces to that in the length gauge. As a consequence, one reaches the situation noticed before by Bell and Kingston [2] and analyzed later by Cordes and Calkin [3].…”

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confidence: 73%

Comment on ‘‘X-ray absorption by atoms under intense laser fields’’

Cionga

Florescu

1994

Phys. Rev. A

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In connection with a paper by Kalman [Phys. Rev. A 39, 2428(1989], we present an independent analysis of the behavior of the matrix element of r and p, relevant for the ground-state photoelectric cross section in hydrogen, evaluated in the Born approximation. This analysis, performed in momentum space, proves once again that, in the plane-wave approximation, the result obtained in momentum gauge is the correct one in the lowest order in az (a being the fine-structure constant, Z the atomic number}. PACS number(s): 32.80.Wr, 78.70.Dm, 32.80.Fb do' g dQ '0 2srrl(1+vi ) exp(2~rl ), d 0 1exp( -2m. rl } where g =Zfi/a~, =arctan[2gi( I rl ) ], -(2) (3) with p the ejected electron asymptotic momentum, ao the Bohr radius, A Planck's reduced constant, and In a recent paper [1] Kalman presents a discrepancy between two calculations for the photoionization cross section of the ground state of hydrogen, evaluated in the plane-wave approximation for the final electron. The author's claim is that his Eq. (19) is the correct answer, and not his Eq. (9). In this Comment, we argue that the last quoted equation [identical with Eq. (4) below] is the correct one in the lowest approximation in aZ (a the Sne-structure constant, Z the atomic number}. The calculation presented in Sec. II of Ref. [1], and named "the traditional treatment, " corresponds to a lowest-order Born approximation calculation in momentum gauge. In Sec. III of Ref. [1], the author takes an approach called "gauge invariant, " uses once again the Born approximation, and, during the calculation, makes an approximation which leads to his Eq. (19), i.e. , to a cross section four times larger than the first calculation. Our opinion is that, contrary to the author s belief, this last calculation reduces to that in the length gauge. As a consequence, one reaches the situation noticed before by Bell and Kingston [2] and analyzed later by Cordes and Calkin [3]. In our Comment, after describing briefly the well established situation, we give an independent analysis of the contribution of the first terms in the Born series to the EC-shell photoelectric cross section. We conclude with other remarks on Kalman's calculation. The exact expression of the E-she11 differential photoelectric cross section in the nonrelativistic dipole approximation [3,4] is dHg [« '0 is pi' (p 2+$2)4 (4) do dQ I d cr dQ i@i SPY~Ct) = 2 tr alia) i G i with F-= (pis PiO), (8} 6-: {pis riO) . The use of the same initial and final stationary states in both gauges is justified [6] because the electron-radiation interaction is supposed to vanish in the initia1 and final states (for time t +ao and t~-co, respectively}. The energy-conservation relation, Eq. (5},is used in the proof of the coincidence of the results obtained in the two gauges. It is worth mentioning that Forney, Quattropani, and Bassani [7] have justiiied the correctness of the use of the same set of unperturbed eigenfunctions for all orders m, is the electron mass and A, =Zfi/ao. The polarization vector of the photon is denoted by s and its ...

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