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1
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0000161497
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See, for instance, the following reviews and references therein: C. A. Berturlani and G. Baur, Phys. Rep. 163, 299 (1988);
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(1988)
Phys. Rep.
, vol.163
, pp. 299
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-
Berturlani, C.A.1
Baur, G.2
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4
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84956242908
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See, for instance, K. Momberger, A. Belkacem and A. H. Sørensen, Europhys. Lett. 32, 401 (1995) and Phys. Rev. A 53, 1605 (1996).
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(1995)
Europhys. Lett.
, vol.32
, pp. 401
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-
Momberger, K.1
Belkacem, A.2
Sørensen, A.H.3
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5
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0000584758
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A. Aste, K. Hencken, D. Trautmann and G. Baur, Phys. Rev. A 50, 3980 (1994).
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(1994)
Phys. Rev. A
, vol.50
, pp. 3980
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Aste, A.1
Hencken, K.2
Trautmann, D.3
Baur, G.4
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14
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0040068774
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we might arrive at the very same result by using, not the integral representation for the confluent hypergeometric function, but the series expansion. This would lead to the same result, with the hypergeometric function expressed by the Gauss series. The present approach is more general, however, since it is immediately valid in the case (Formula presented), where the Gauss series fails to converge. This makes no difference at all for the calculations considered in the present work, but for calculations involving the photoelectric effect the Gauss series would be inapplicable. Indeed, the only reason for introducing the Kummer transformation in Eq. (44) was that this step gives the expressions a form that enables us to use the Gauss series.
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As Sørensen and Belkacem, Phys. Rev. A 49, 81 (1994), we might arrive at the very same result by using, not the integral representation for the confluent hypergeometric function, but the series expansion. This would lead to the same result, with the hypergeometric function expressed by the Gauss series. The present approach is more general, however, since it is immediately valid in the case (Formula presented), where the Gauss series fails to converge. This makes no difference at all for the calculations considered in the present work, but for calculations involving the photoelectric effect the Gauss series would be inapplicable. Indeed, the only reason for introducing the Kummer transformation in Eq. (44) was that this step gives the expressions a form that enables us to use the Gauss series.
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(1994)
Phys. Rev. A
, vol.49
, pp. 81
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SørensenBelkacem, A.1
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18
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30244490177
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The original formula published by Hall, Rev. Mod. Phys. 8, 358 (1936)
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A. I. Milstein and V. M. Strakhovenko, [JETP 76, 775 (1993)]. The original formula published by Hall, Rev. Mod. Phys. 8, 358 (1936).
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(1993)
JETP
, vol.76
, pp. 775
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Milstein, A.I.1
Strakhovenko, V.M.2
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26
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85037178120
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Kgl. Dan. Vidsk. Selsk. Mat. Fys. Medd. XIII, No. 4 (1935).
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E. J. Williams, Kgl. Dan. Vidsk. Selsk. Mat. Fys. Medd. XIII, No. 4 (1935).
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Williams, E.J.1
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28
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0001175464
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This implies an evaluation of matrix elements between initial and final states of the operator exp(iχ), where χ is the time integral of the perturbing potential. However, it should be realized that two approximations are applied to reach this result. The calculation is performed in the interaction representation. First, in an expansion involving commutators of the interaction potential at different times, only the lowest-order nonvanishing term is retained. Second, in the remaining term the usual Schrödinger representation is used for the potential rather than the interaction representation. While the first approximation is valid due to the rapid variation of the electromagnetic field of the relativistic projectile, the second is highly questionable. Essentially, the second approximation corresponds to neglect of a phase factor which varies over distances of order v/((Formula presented)+E) and this length is certainly not large compared to the extent of the bound state.
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and J. Eichler, Phys. Rev. A 15, 1856 (1977). This implies an evaluation of matrix elements between initial and final states of the operator exp(iχ), where χ is the time integral of the perturbing potential. However, it should be realized that two approximations are applied to reach this result. The calculation is performed in the interaction representation. First, in an expansion involving commutators of the interaction potential at different times, only the lowest-order nonvanishing term is retained. Second, in the remaining term the usual Schrödinger representation is used for the potential rather than the interaction representation. While the first approximation is valid due to the rapid variation of the electromagnetic field of the relativistic projectile, the second is highly questionable. Essentially, the second approximation corresponds to neglect of a phase factor which varies over distances of order v/((Formula presented)+E) and this length is certainly not large compared to the extent of the bound state.
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(1977)
Phys. Rev. A
, vol.15
, pp. 1856
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Eichler, J.1
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