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1
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84926792358
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(a) A review of work on atoms in external fields is given by C. W. Clark, K. T. Lu, and A. F. Starace, in Progress in Atomic Spectroscopy, edited by H. J. Beyer and H. Kleinpoppen (Plenum, New York, 1984), Part C, pp. 247–320;
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4
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84926792357
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Many earlier references are cited therein.
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12
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84926836255
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See also Ref. 1(b).
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20
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84926814333
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The wave-packet picture discussed in this paper is most appropriate if a pulsed laser excites the electron to a wave-packet state which is sufficiently compact to give distinct recurrences. In the experiments discussed here, the pulse times are much longer than recurrence times. The physical picture described in the present paper is more consistent with this fact. We consider the steady excitation of electrons into states near the ionization threshold, steady flow of outgoing waves from the vicinity of the nucleus, and steady flow of returning electrons along closed orbits. Interference between the steadily-flowing outgoing and returning waves leads to the oscillations in the spectrum.
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27
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The historical development of Hamilton's analogy between wave motion and particle motion is presented by T. L. Hankins, Sir William Rowan Hamilton (Johns Hopkins University Press, Baltimore, 1980).
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28
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84926836252
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The correspondence principle is expressed in modern mathematical language by V. P. Maslov and M. V. Fedoriuk, Semiclassical Approximation in Quantum Mechanics (Reidel, Boston, 1981).
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37
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3943081675
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discussed the Garton-Tomkins oscillations in terms of motion on a potential-energy ridge. While these ideas are very stimulating, more recent experiments show that observed oscillations are correlated with closed orbits, most of which have no relationship to the potential-energy ridge.
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(1980)
Phys. Rev. A
, vol.22
, pp. 2660
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Fano, U.1
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41
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84926792355
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in Chaotic Behavior of Deterministic Systems, edited by, G. Ioos, et al., North-Holland, Amsterdam
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(1983)
Les Houches Session XXXVI
, pp. 171-272
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52
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There is a subtlety here. Equation (2.4) is presumed to be valid in the limit hbar -> 0 for those paths that travel from q vec prime to q vec within a finite time T. However, in a bounded system, an infinite number of distinct trajectories travel from q vec prime to q vec, and there is no upper limit on the travel time. To obtain a spectrum to arbitrary resolution from closed orbits, we would have to apply Eq. (2.4) for fixed ħ in the limit T -> inf. We do not know whether the formula is applicable in that limit.
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53
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84926836045
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Obviously, a wave is correlated not with any single closed orbit by itself, but rather with the family or pencil of orbits surrounding the closed orbit.
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55
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The importance number approximately measures the classical density of returning trajectories. (This is like estimating local magnetic field strength by counting field lines entering a surface.) The number is useful because it is found immediately from the trajectory integration; evaluation of the classical density takes more work.
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56
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84926792353
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See AIP document No. PAPS PLRAA-38-1896-3 for 3 pages of Table II. Order by PAPS number and journal reference from American Institute of Physics, Auxiliary Publication Service, 335 East 45th Street, New York, NY 10017. The prices are $1.50 for microfiche and $5 for photocopies. Airmail additional. Make checks payable to the American Institute of Physics.
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84926857886
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There are two differences between the present theoretical result and that reported in Ref. 8(a). (i) We now include amplitudes for orbits A prime and A prime prime, which we did not include previously. (ii) The previously reported amplitudes were a factor of 2 too large; we had incorrectly arrived at a factor 223/4 instead of 219/4 in Eq. (3.7a).
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