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14
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84926835701
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and in Multiphoton Processes, edited by S. J. Smith and P. L. Knight (Cambridge University Press, Cambridge, England, 1988), p. 35.
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26
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0000645548
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a sophisticated theory of multiphoton ionization in the high-frequency, high-intensity limit has been developed by
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(1987)
Phys. Lett. A
, vol.123
, pp. 469
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Pont, M.1
Gavrila, M.2
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33
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84926791975
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and in Multiphoton Processes, edited by S. J. Smith and P. L. Knight, eds. (Cambridge University Press, Cambridge, England, 1988), p. 350.
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34
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0000162869
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(private communication). Electron loss from a helium atom has also been calculated (in the Hartree-Fock approximation).
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(1987)
Phys. Rev. A
, vol.35
, pp. 445
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Kulander, K.1
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47
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84926835700
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One may always transform to an inertial frame in which a free electron is (on the average) at rest. In that frame we have, in the velocity gauge, p vec =0 and therefore V(v)( τ )=0.
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49
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84926835698
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See, e.g., C. Cohen-Tannoudji, B. Diu, and F. Laloe, Quantum Mechanics (Hermann-Wiley, Paris, 1977), Vol. 1, p. 315.
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50
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84926813925
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Note that associated with each eigenvector | ψi( τ ) > are a denumerably infinite number of physically indistinguishable eigenvectors which differ from | ψi( τ ) > in that the index n of the harmonic components | ψin> is shifted by an integer l; the quasienergy eigenvalue curlepi transforms to curlepi+l hbar omega under the change n -> n-l, and in the weak-field limit it is the harmonic component | ψil> which approaches | φi> . See S.-I. Chu, Ref. 10.
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52
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84926857539
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Though phrased somewhat differently, this idea is contained in Chap. 8 of M. L. Goldberger and K. M. Watson, Collision Theory (Krieger, New York, 1975).
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65
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84926847878
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The use of the trial wave vector | φf(v)(t) > was first suggested in the context of multiphoton ionization by, Phys. Rev. A 18, 538 (1978) and more recently by, ibid.
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(1988)
, vol.37
, pp. 1050
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Jain, M.1
Tzoar, N.2
Basile, S.3
Trombetta, F.4
Ferrante, G.5
Burlon, R.6
Leone, C.7
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75
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84926813924
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We note that in the length gauge the truncated set of coupled equations corresponding to Eq. (4.35) does not admit regular decaying solutions, except in the weak-field limit, because Vback13 +-(l) diverges for r- inf and so tunneling is always possible, and the effective width in the energy is nonzero.
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76
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0000541215
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The orthogonality of Floquet eigenvectors was discussed by, though without regard to the fact that an eigenvector is normalizable only when its harmonic expansion is truncated. The appearance of the weight factor exp[i(N0i-N0j) τ ] in our orthogonality statement is a reminder of this fact.
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(1973)
Phys. Rev. A
, vol.7
, pp. 2203
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Sambe, H.1
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77
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84926835697
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Regarded as an operator in the space of functions that are periodic in tau with period 2pi the time derivative is Hermitian. See Sambe, Ref. 33.
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83
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11744270606
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Application of the Sturmian expansion to multiphoton absorption by hydrogen above the ionization threshold
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(1986)
Physical Review A
, vol.34
, pp. 5119
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Shake- shaft, R.1
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87
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84926813923
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This analysis is similar to the usual discussion of a Landau-Zener crossing of molecular energy curves in a slow atomic collision. See N. F. Mott and H. S. W. Massey, The Theory of Atomic Collisions, 3rd ed. (Oxford, New York, 1965), p. 353; B. H. Bransden, Atomic Collision Theory, 2nd ed. (Benjamin-Cummings, Reading, 1983), pp. 392–400.
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88
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84926835696
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Of course, these rates might eventually increase again as the intensity increases to a sufficiently high value, though even then the yields might not increase if substantial depletion occurs.
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89
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84926813922
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Recall that, by assumption, the ionization widths are smaller than the laser bandwidth, and are therefore smaller than the energy gap if the laser bandwidth is.
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90
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84926813921
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For both wavelengths we have N0i=3. Only spherical harmonics with orbital angular momentum quantum number <= 1, and harmonic components | ψin(v)> with -1 <= n <= 2 and | ψjn(v)> with -3 <= n <= 0, were included.
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92
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0038566991
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As an alternative to solving the inhomogeneous equations for the harmonic components, we have recently demonstrated that a finite ionization amplitude can be constructed from the solution to the homogeneous equations (3.7) by analytic continuation through a computationally practical technique.
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(1988)
Phys. Rev. A
, vol.38
, pp. 1098
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Potvliege, R.M.1
Shakeshaft, R.2
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93
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84926857538
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If there is no bound level which is optically coupled (by one photon) to the initial level we take Δ Ei to be the distance of the initial energy level from the continuum threshold. If there is a near m-photon resonance, with m > 1, we should raise the coupling energy to the power m in the definition of βi, and replace hbar Δ Ωi by the product of m factors Δ Ei-n hbar omega with n=1,2 ,..., m.
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95
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84926835695
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One could discretize the continuum by putting the system in a box whose linear dimensions are large but finite, equal to L, say. However, the coupling between any two of these discrete levels vanishes as L -> inf because of the normalization factor L-3/2. Consequently, transitions occur only between groups of levels, separated in energy by hbar omega (or an integral multiple thereof). Degeneracy effects are smoothed out, so that the coupling in the continuum varies smoothly with omega, and the detuning is simply omega.
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96
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84926791974
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We ignore factors of 2, pi, etc., in defining the parameters. Incidentally, recall that the speed vi which enters βi(v) is the characteristic mean speed; were we to take instead the amplitude of the instantaneous speed, that is, eF0/ μ omega, we would obtain βi(v)=P/ hbar ω = βi(l).
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