Bibliography

*

Present address: Department of Mathematics and Sciences, Wayne State College, 1111 Main Street, Wayne, NE 68787.

1

R. H. Pratt, R. Y. Yin, and X. Liang, Phys. Rev. A 35, 1450 (1987).

2

Note that in [1] it is stated that the evenness or oddness of the number of zeros in the bound-free matrix element was determined. In fact, as with our work here, it is actually the evenness or oddness of the number of zero crossings that is determined. That is, it is also possible in principle to have additional zeros which are extrema of the matrix element, not corresponding to energies of a sign change.

3

R. Y. Yin, O. V. Gabriel, and R. H. Pratt, Phys. Rev. A 36, 1207 (1987).

4

R. R. Johnston, J. Qual. Spec. and Rad. Trans. 7, 815 (1967).

5

J. J. Sakurai, in Modern Quantum Mechanics, edited by S. F. Tuan (Addison-Wesley, New York, 1985).

6

R. G. Newton, Scattering Theory of Waves and Particles (McGraw-Hill Book Company, New York, 1966).

7

M. A. Dillon and M. Inokuti, J. Chem. Phys. 74, 6271 (1981).

8

M. A. Dillon and M. Inokuti, J. Chem. Phys. 82, 4415 (1985).

9

E. C. Titchmarsh, The theory of functions, 2nd ed. (Oxford university press, London, 1939).

10

E. N. Lassetre, J. Chem. Phys. 43, 4479 (1965).

11

It is possible to be more precise here. One can retain higher terms in the asymptotic expansion of the wavefunction at large distances and show that matrix elements corresponding to those terms diverge more slowly than 1/k² in the soft photon limit.

12

S. D. Oh and R. H. Pratt, ``New results for bound and continuum transition matrix elements'', 1996, accepted for publication in Comments At. Mol. Phys.

13

J. Holtsmark, Z. Phys. 55, 437 (1929).

14

J. Holtsmark, Z. Phys. 56, 49 (1930).

15

D. Thirumalai and D. G. Truhlar, Phys. Rev. A 25, 3058 (1982).

16

P. J. Davis, in Handbook of Mathematical Functions, 9th ed., edited by M. Abramowitz and I. A. Stegun (Dover Publications, Inc., New York, 1972), pp. 253-293.

17

V. Véniard and B. Piraux, Phys. Rev. A 41, 4019 (1990).

18

S. D. Oh and R. H. Pratt, Phys. Rev. A 34, 2486 (1986).

19

L. I. Schiff, Quantum Mechanics, 3rd ed. (McGraw-Hill Book Company, New York, 1968).

20

M. J. Seaton, C. R. Acad. Sci 240, 1317 (1955).

21

U. Fano and A. R. Rau, Atomic Collisions and Spectra (Academic, New York, 1986).

22

L. Rosenberg, Phys. Rev. A 52, 3824 (1995).

23

H. W. Yang, R. H. Pratt, and X.-M. Tong (unpublished).

24

S. D. Oh and R. H. Pratt, Phys. Rev. A 45, 1583 (1992).

25

R. H. Pratt, Phys. Rev. 120, 1717 (1960).

26

M. Abramowitz, in Handbook of Mathematical Functions, 9th ed., edited by M. Abramowitz and I. A. Stegun (Dover Publications, Inc., New York, 1972), pp. 537-554.

27

L. J. Slater, in Handbook of Mathematical Functions, 9th ed., edited by M. Abramowitz and I. A. Stegun (Dover Publications, Inc., New York, 1972), pp. 503-535.

28

L. D. Landau and E. M. Lifshitz, Quantum Mechanics: Non-relativistic Theory, Vol. 3 of Course of Theoretical Physics (Pergamon Press LTD., London - Paris, 1958).

29

F. Oberhettinger, in Handbook of Mathematical Functions, 9th ed., edited by M. Abramowitz and I. A. Stegun (Dover Publications, Inc., New York, 1972), pp. 555-566.

30

F. E. Low, Phys. Rev. 110, 974 (1958).

31

N. F. Mott and H. S. W. Massey, The Theory of Atomic Collisions (Oxford University Press, Oxford, 1987), Vol. 2.

32

H. Friedrich, Theoretical Atomic Physics (Springer-Verlag, New York, 1990).

33

C. M. Lee, L. Kissel, R. H. Pratt, and H. K. Tseng, Phys. Rev. A 13, 1714 (1976).

34

B. Wallbank and J. K. Holmes, Phys. Rev. A 48, R2515 (1993).

35

A. Weingartshofer, J. K. Holmes, J. Sabbagh, and S. L. Chin, J. Phys. B16, 1805 (1983).

36

B. Wallbank and J. K. Holmes, J. Phys. B27, 1221 (1994).

37

D. D. Reid and J. M. Wadehra, Phys. Rev. A 50, 4859 (1994).

38

B. A. Zon, Sov. Phys. JETP 50, 21 (1979).

39

J. Green, Technical Report No. RDA-TR-4900-007, R & D Associates, Santa Monica, California (unpublished), August 1974.

40

J. Green, Technical Report No. RDA-TR-108600-003, R & D Associates, Santa Monica, California (unpublished), September 1979.

41

M. Ashkin, Phys. Rev. 141, 41 (1965).