The Coulomb Green's function and multiphoton calculations

Journal of Physics B: Atomic, Molecular and Optical Physics

Volumn 31, Issue 17, 1998, Pages 3743-3764

  Maquet, Alfred ^a   Véniard, Valérie ^a   Marian, Tudor A ^b  

^a SORBONNE UNIVERSITÉ   (France)

^b UNIVERSITY OF BUCHAREST   (Romania)

Author keywords

[No Author keywords available]

Indexed keywords

COULOMB GREEN'S FUNCTION; DIRAC EQUATION; MULTIPHOTON TRANSITIONS;

ELECTRON TRANSITIONS; GREEN'S FUNCTION; HYDROGEN; INTEGRAL EQUATIONS; MATRIX ALGEBRA; MULTIPHOTON PROCESSES; PERTURBATION TECHNIQUES;

ATOMIC PHYSICS;

EID: 0032156861     PISSN: 09534075     EISSN: None     Source Type: Journal    
DOI: 10.1088/0953-4075/31/17/004     Document Type: Review

References (182)

1. Appell P and Kampé de Feriet J 1926 Fonctions Hypergéométriques et Hypersphèriques. Polynômes d'Hermite (Paris: Gauthier-Villars)
2. Arnous E, Bastian J and Maquet A 1983 Phys. Rev. A 27 977-95
3. Arnous E, Klarsfeld S and Wane S 1973 Phys. Rev. A 7 1559-68
4. Baker G A Jr and Graves-Morris P 1981 Padé Approximates Part 1: Basic Theory (Reading, MA: Addison-Wesley)
5. Bander M and Itzyckson C 1966 Rev. Mod. Phys. 38 330-45
6. Bebb H B and Gold A 1966 Phys. Rev. 143 1-24
7. Bethe H A 1947 Phys. Rev. 72 339-41
8. Bethe H A, Brown L M and Stehn JR 1950 Phys. Rev. 77 370-4
9. Brown G E, Peierls R E and Woodward J B 1955 Proc. R. Soc. A 227 51-8
10. Buchholz H 1969 The Confluent Hypergeometric Function (Berlin: Springer)
11. Buimistrov V M 1969 Phys. Lett. A 30 136-8
12. Buimistrov V M and Trakhtenberg L I 1976 Sov. Phys.-JETP 42 54-7
13. Byron F W Jr and Joachain C J 1984 J. Phys. B: At. Mol. Phys. 17 L295-301
14. Chen A C and Chen J C Y 1971a J. Phys. B: At. Mol. Phys. 4 L102-5
15. _1971b Phys. Rev. A 4 2226-8
16. Chen J C Y and Chen A C 1972 Adv. At. Mol. Phys. 8 71-129
17. Chu S-I and Reinhardt W P 1977 Phys. Rev. Lett. 39 1195-8
18. Cooper R D, Hoare M R and Rahman M 1977 J. Math. Anal. Appl. 61 262-91
19. Costescu A 1976 Rev. Raum. Phys. 21 3-14
20. Costescu A and Gavrila M 1973 Rev. Roum. Phys. 18 493-521
21. Dalgarno A and Lewis J T 1955 Proc. R. Soc. A 233 70-4
22. Dondera M and Florescu V 1993 Phys. Rev. A 48 4267-71
23. Doolen GD 1975 J. Phys. B: At. Mol. Phys. 8 525-8
24. Dubois A and Maquet A 1989 Phys. Rev. A 40 4288-97
25. Duru J H and Kleinert H 1979 Phys. Lett. B 84 185-8
26. _1982 Fortschr. Phys. 30 401-35
27. Epstein P S 1926 Phys. Rev 28 695-710
28. Fainshtein A G, Manakov N L and Marmo S I 1984 Phys. Lett. A 104 347-50
29. Faisal F H M 1987 Theory of Multiphoton Processes (New York: Plenum)
30. Fifirig M, Cionga A and Florescu V 1997 J. Phys. B: At. Mol. Opt. Phys. 30 2599-608
31. Flank Y and Rachman A 1975 Phys. Lett. A 53 247-8
32. Florescu V 1984 Phys. Rev A 30 2441-8
33. _1986 Phys. Lett. A 115 147-9
34. Florescu V and Cionga A 1985 Z. Phys. A 321 187-200
35. Florescu V and Djamo V 1986 Phys. Lett. A 119 73-8
36. Florescu V and Gavrila M 1976 Phys. Rev. A 14 211-35
37. Florescu V, Halasz A and Marinescu M 1993 Phys. Rev. A 47 394-404
38. Florescu V and Marian T A 1986 Phys. Rev. A 34 4641-6
39. Florescu V, Patrascu S and Stoican O 1987 Phys. Rev. A 36 2155-66
40. Fock V 1935 Z. Phys. 98 145-54
41. Ford W F 1964 Phys. Rev. B 133 1616-21
42. _1966 J. Math. Phys. 7 626-33
43. Fronsdal C 1969 Phys. Rev. 179 1513-7
44. Gavrila M 1967 Phys. Rev. 163 147-55
45. _1969 Lett. Nuovo Cimento 2 180-4
46. _1972a Phys. Rev. A 6 1348-59
47. _1972b Phys. Rev. A 6 1360-7
48. _1974 Rev. Roum. Phys. 19 483-7
49. _1979 Z. Phys. A 293 269-79
50. Gavrila M and Costescu A 1969 Phys. Lett. A 28 614-5
51. _1970 Phys. Rev. A 2 1752-8
52. _1971 Phys. Rev. A 4 1688 (erratum)
53. Gavrila M, Maquet A and Véniard V 1985 Phys. Rev. A 32 2537-40
54. _1985 Phys. Rev. A 33 2826 (erratum)
55. _1990 Phys. Rev. A 42 236-47
56. Gavrila M and Tugulea M N 1975 Rev. Roum. Phys. 20 209-30
57. Gazeau J P 1982 J. Math. Phys. 23 156-64
58. Gazeau J P and Maquet A 1971 C. R. Acad. Sci., Paris 272 1097-9
59. Gontier Y, Rahman N K and Trahin M 1976 Phys. Rev. A 14 2109-25
60. Gontier Y and Trahin M 1968 Phys. Rev. 172 83-7
61. _1971 Phys. Rev. A 4 1896-906
62. Gordon W 1929 Ann. Phys., Lpz. 2 1031-56
63. Gorshkov V G, Mikhailov A J and Sherman S G 1974 Sov. Phys.-JETP 39 995 (1974 JETP 66 2020-7 in Russian)
64. Gorshkov V G, Mikhailov A J and Sherman S G 1974 Sov. Phys.-JETP 39 995 (1974 JETP 66 2020-7 in Russian)
65. Granovskii Ya J 1969 Sov. Phys.-JETP 29 333-6 (1969 JETP 56 605-13 in Russian)
66. Granovskii Ya J 1969 Sov. Phys.-JETP 29 333-6 (1969 JETP 56 605-13 in Russian)
67. Hameka H F 1967 J. Chem. Phys. 47 2728-35
68. _1968 J. Chem. Phys. 48 4810 (erratum)
69. Ho R and Inomata A 1982 Phys. Rev. Lett. 48 231-4
70. Hostler L 1964a J. Math. Phys. 5 591-611
71. _1964b J. Math. Phys. 5 1235-40
72. _1969 Phys. Rev. 178 126-31
73. _1970 J. Math. Phys. 11 2966-70
74. _1983 J. Math. Phys. 24 2366-73
75. _1987 J. Math. Phys. 28 2984-9
76. Hostler L and Pratt RH 1963 Phys. Rev. Lett. 10 469-70
77. Huens E, Piraux B, Bugacov A and Gajda M 1997 Phys. Rev. A 55 2132-43
78. Johnson B R and Hirschfelder J O 1979 J. Math. Phys. 20 2484
79. Karule E 1971 J. Phys. B: At. Mol. Phys. 4 L67-70
80. _1975 Atomnije Processi (Riga: Zinatne) pp 5-24
81. _1978 J. Phys. B: At. Mol. Phys. 11 441-7
82. _1985 J. Phys. B: At. Mol. Phys. 18 2207-18
83. Karule E and Pratt R H 1991 J. Phys. B: At. Mol. Opt. Phys. 24 1585-91
84. Kelsey E J and Macek J 1976 J. Math. Phys. 17 1182-5
85. Klarsfeld S 1969a Lett. Nuovo Cimento 1 682-6
86. _1969b Lett. Nuovo Cimento 2 548-52
87. _1969c Phys. Lett. A 30 382-3
88. _1970 Lett. Nuovo Cimento 3 395-8
89. Klarsfeld S and Maquet A 1973 Phys. Lett. B 43 201-3
90. _1979a Phys. Lett. A 73 100-2
91. _1979b J. Phys. B: At. Mol. Phys. 12 L553-6
92. _1980 Phys. Lett. A 78 40-2
93. Kleinert H 1995 Path Integrals in Quantum Mechanics, Statistics and Polymer Physics 2nd edn (Singapore: World Scientific) ch 13, pp 425-528
94. Korol A V 1997 J. Phys. B: At. Mol. Opt. Phys. 30 413-38
95. Kracke G, Marxer H, Broad J T and Briggs J S 1988 Z. Phys. D 8 103-4
96. Lambropoulos P 1976 Advances in Atomic and Molecular Physics vol 12, ed D R Bates and B Bederson (New York: Academic) pp 87-164
97. Landau L D and Lifshitz E M 1965 Quantum Mechanics. Non-Relativistic Theory 2nd edn (Oxford: Pergamon) see section 77, pp 270-3
98. Laplanche G, Durrieu A, Flank Y, Jaouen M and Rachman A 1976 J. Phys. B: At. Mol. Phys. 9 1263-77
99. Laplanche G and Rachman A 1975 Phys. Lett. A 53 91-3
100. Le Anh Thu, Le Van Hoang, Komarov L J and Romanova T S 1994 J. Phys. B: At. Mol. Opt. Phys. 27 4083-94
101. _1996 J. Phys. B: At. Mol. Opt. Phys. 29 2897-906
102. Lieber M 1968 Phys. Rev. 174 2037-54
103. _1989 Relativistic, Quantum Electrodynamic and Weak Interaction Effect in Atoms (AIP Conf. Proc. 189) ed W Johnson, P Mohr and J Sucher (New York: AIP) pp 445-59
104. Liu J, Kahler D L and Quarles CA 1993 Phys. Rev. A 47 4274
105. Luban M, Nudler B and Freund J 1974 Phys. Lett. A 47 447-8
106. Luban M and Nudler-Blum B 1977 J. Math. Phys. 18 1871-81
107. Manakov N L, Nekipelov A A and Fainshtein A G 1987 Sov. J. Nucl. Phys. 45 677-81 (1987 Yad. Fis. 45 1091-8 in Russian)
108. Manakov N L, Nekipelov A A and Fainshtein A G 1987 Sov. J. Nucl. Phys. 45 677-81 (1987 Yad. Fis. 45 1091-8 in Russian)
109. Manakov N L and Ovsiannikov V D 1977 J. Phys. B: At. Mol. Phys. 10 569-81
110. Manakov N L, Ovsiannikov V D and Rapoport L P 1986 Phys. Rep. 141 319-33
111. Manakov N L and Rapoport L P 1972 Opt. Spectrosc. 33 547-8 (1972 Opt. Spektrosk. 33 998-9 in Russian)
112. Manakov N L and Rapoport L P 1972 Opt. Spectrosc. 33 547-8 (1972 Opt. Spektrosk. 33 998-9 in Russian)
113. Manakov N L, Rapoport L P and Zapryagaev S A 1973 Phys. Lett. A 43 139-40
114. Maquet A 1977 Phys. Rev. A 15 1088-108
115. Maquet A, Chu S-I and Reinhardt W P 1983 Phys. Rev. A 27 2946-70
116. Maquet A, Martin P and Véniard V 1988 Phys. Lett. A 129 26-8
117. Marian T A 1989a Phys. Rev. A 39 3803-15
118. _1989b Phys. Rev. A 39 3816-24
119. _1997a Phys. Rev. A 56 3974-87
120. _1997b Phys. Rev. A 56 3988-4011
121. Martin P C and Glauber R J 1958 Phys. Rev. 109 1307-25
122. Mizuno J 1972 J. Phys. B: At. Mol. Phys. 5 1149-54
123. Morse P M and Feshbach H 1953 Methods of Theoretical Physics Part I (New York: McGraw-Hill)
124. Nutt G L 1968 J. Math. Phys. 9 796-803
125. Nutall J and Stagat RW 1971 Phys. Rev. A 3 1355-8
126. Pan L, Taylor K T and Clark C W 1988 Phys. Rev. Lett. 61 2673-6
127. _1989 Phys. Rev. A 39 4894-7
128. Podolsky B 1928 Proc. Nat. Acad. Sci. 14 253-8
129. Poiner M 1997 Z. Phys. D 39 189-93
130. Potvliege R M 1996 Super Intense Laser-Atom Physics IV (NATO ASI Series 3) vol 13, ed H G Muller and M V Fedorov pp 133-42
131. Potvliege R M and Shakeshaft R 1988a Phys. Rev. A 38 1098-100
132. _1988b Phys. Rev. A 38 4597-621
133. _1989a Phys. Rev. A 39 1545-8
134. _1989b Z. Phys. D 11 93-4
135. _1989c Phys. Rev. A 40 3061-79
136. _1992 Atoms in Intense Laser Fields (Adv. At. Mol. Phys. Suppl. 1) ed M Gavrila pp 373-433
137. Rajagopal A K and Shastry C S 1971 J. Math. Phys. 12 2387-94
138. Rapoport L P and Zon B A 1968 Phys. Lett. A 26 564-5
139. Rapoport L P, Zon B A and Manakov N L 1969 Sov. Phys.-JETP 29 220 (1969 JETP 56 400-1 in Russian)
140. Rapoport L P, Zon B A and Manakov N L 1969 Sov. Phys.-JETP 29 220 (1969 JETP 56 400-1 in Russian)
141. Reinhardt W P 1982 Ann. Rev. Phys. Chem. 33 223-55
142. Rotenberg M 1962 Ann. Phys., NY 19 262-78
143. _1970 Adv. At. Mol. Phys. 6 233-68
144. Schwinger J 1964 J. Math. Phys. 5 1606-8
145. see also _1947 Unpublished Lectures (Cambridge, MA: Harvard University Press)
146. Sherstyuk A J 1971 Opt. Spectrosc. 30 191-2 (1971 Opt. Spektrosk. 30 356-7 in Russian)
147. Sherstyuk A J 1971 Opt. Spectrosc. 30 191-2 (1971 Opt. Spektrosk. 30 356-7 in Russian)
148. Sternheimer R 1951 Phys. Rev 84 244-53
149. Swainson R A and Drake G F W 1991a J. Phys. A: Math. Gen. 24 95-120
150. _1991b J. Phys. A: Math. Gen. 24 1801-24
151. Szegö G 1985 Orthogonal Polynomials 4th edn (Providence, PA: American Mathematical Society)
152. Szmytkowski 1997 J. Phys. B: At. Mol. Opt. Phys. 30 825-61
153. Szymanowski C, Véniard V, Taïeb R and Maquet A 1997a Europhys. Lett. 37 391-6
154. _1997b Phys. Rev. A 56 700-11
155. Taïeb R, Véniard V, Maquet A, Vucic S and Potvliege R M 1991 J. Phys. B: At. Mol. Opt. Phys. 24 3229-40
156. Titchmarsh E C 1958 Eigenfunction Expansion Associated with 2nd Order Differential Equations vol II (Oxford: Oxford University Press)
157. Unsold A 1927 Ann. Phys., Lpz. 82 355-93
158. Van Haeringen H 1980 Charged Particle Interactions. Theory and Formulas (Leyden: Coulomb)
159. Véniard V, Maquet A and Gavrila M 1987 Phys. Rev. A 35 448-51
160. Véniard V and Piraux B 1990 Phys. Rev. A 41 4019-34
161. Vetchinkin S I and Bachrach V L 1972 Int. J. Quantum Chem. 4 143-53
162. Vetchinkin S I and Khristenko SV 1967 Chem. Phys. Lett. 1 437-40
163. Wall H S 1948 Analytic Theory of Continued Fractions (New York: Van Nostrand)
164. Wichmann E H and Kroll N M 1956 Phys. Rev. 101 843-59
165. Yakhontov V and Jungmann K 1996 Z. Phys. D 38 141-52
166. Zapryagaev S A and Manakov N L 1976 Izv. Akad. Nauk. 45 2336
167. _1981 Sov. J. Nucl. Phys. 23 482-6 (1976 Yad. Fis. 23 917-25 in Russian)
168. _1981 Sov. J. Nucl. Phys. 23 482-6 (1976 Yad. Fis. 23 917-25 in Russian)
169. Zernik W 1964a Phys. Rev. A 133 117-22
170. _1964b Phys. Rev. A 135 51-7
171. _1968 Phys. Rev. 176 420-1
172. Zernik W and Klopfenstein R W 1965 J. Math. Phys. 6 262-70
173. Zon B A, Manakov N L and Rapoport L P 1969 Sov. Phys.-JETP 28 480-2 (1968 JETP 55 924-30 in Russian)
174. Zon B A, Manakov N L and Rapoport L P 1969 Sov. Phys.-JETP 28 480-2 (1968 JETP 55 924-30 in Russian)
175. _1970 Sov. Phys.-Dokl. 14 904-5 (1969 Dokl. Akad Nauk. SSSR 188 560-1 in Russian)
176. _1970 Sov. Phys.-Dokl. 14 904-5 (1969 Dokl. Akad Nauk. SSSR 188 560-1 in Russian)
177. _1972a Sov. Phys.-JETP 34 515 (1971 JETP 61 968-75 in Russian)
178. _1972a Sov. Phys.-JETP 34 515 (1971 JETP 61 968-75 in Russian)
179. _1972b Sov. J. Nucl. Phys. 15 282-6 (1972 Yad. Fiz. 15 508-17 in Russian)
180. _1972b Sov. J. Nucl. Phys. 15 282-6 (1972 Yad. Fiz. 15 508-17 in Russian)
181. Zon B A and Rapoport L P 1968 Sov. Phys.-JETP 7 52-5 (1968 JETP 7 70-2 in Russian)
182. Zon B A and Rapoport L P 1968 Sov. Phys.-JETP 7 52-5 (1968 JETP 7 70-2 in Russian)