Effects of Electron-Electron and Electron-Phonon Interactions on the One-Electron States of Solids

Solid State Physics - Advances in Research and Applications

Volumn 23, Issue C, 1970, Pages 1-181

  Hedin, Lars ^a   Lundqvist, Stig ^a  

^a CHALMERS UNIVERSITY OF TECHNOLOGY   (Sweden)

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Indexed keywords

EID: 22144469121     PISSN: 00811947     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S0081-1947(08)60615-3     Document Type: Article

References (284)

1. Clementi, E., IBM J. Res. Develop., 9, 1965, 2.
2. C. Froese, Tech. Rept., Dept. of Math., Univ. of Br. Columbia, Vancouver 8, B.C., March 1966.
3. Can. J. Phys., 46, 1968, 2336.
4. Wigner, E.P., Trans. Faraday Soc., 34, 1938, 678.
5. Slater, J.C., Phys. Rev., 81, 1951, 385.
6. Seitz, F., “The Modern Theory of Solids.”, 1940, McGraw-Hill, New York.
7. Slater, J.C., “Quantum Theory of Atomic Structure,”, II, 1960, McGraw-Hill, New York.
8. Nesbet, R.K., Advan. Chem. Phys., 9, 1965, 321.
9. Hugenholtz, N.M., Physica, 23, 1957, 481.
10. Brueckner, K.A., DeWitt, C., (eds.) “The Many Body Problem”, 1959, Methuen, London, 81.
11. Koopmans, T., Physica, 1, 1934, 104.
12. 9a Sureau, A., Berthier, G., J. Phys. (Paris), 24, 1963, 672.
13. Bagus, P., Phys. Rev., 139, 1965, A619.
14. Lindgren, I., Arkiv Fysik, 31, 1966, 59.
15. Pratt, G.W., Phys. Rev., 102, 1956, 1303.
16. Sachs, L.M., Phys. Rev., 117, 1960, 1504.
17. 13a Goodings, D.A., Phys. Rev., 123, 1961, 1706.
18. Overhauser, A.W., Phys. Rev., 128, 1962, 1437.
19. Rajagopal, A.K., Phys. Rev., 142, 1966, 152.
20. Hamann, D.R., Overhauser, A.W., Phys. Rev., 143, 1966, 183.
21. Fedders, P.A., Martin, P.C., Phys. Rev., 143, 1966, 245.
22. 17a Lomer, W.M., Proc. Phys. Soc., 80, 1962, 489.
23. Löwdin, P.O., Phys. Rev., 97, 1955, 1509.
24. Berggren, K.F., Johansson, B., Int. Journ. Quant. Chem., 2, 1968, 483.
25. Thouless, D.J., “The Quantum Mechanics of Many-Body Systems”, 1961, Academic Press, 88.
26. Lindhard, J., Dan. Math. Phys. Medd., 28, 1954 No. 8.
27. Lundqvist, S., Sjölander, A., Arkiv Fysik, 26, 1964, 17.
28. Pines, D., Solid Stale Phys., 1, 1955, 367.
29. Ehrenreich, H., Cohen, M.H., Phys. Rev., 115, 1959, 786.
30. Hubbard, J., Proc. Roy. Soc., A240, 1957, 539.
31. Gell-Mann, M., Brueckner, K., Phys. Rev., 106, 1957, 364.
32. Hubbard, J., Proc. Roy. Soc., A243, 1957, 336.
33. Singwi, K.S., Tosi, M.P., Land, R.H., Sjölander, A., Phys. Rev., 176, 1968, 589.
34. Hubbard, J., Phys. Letters, 25A, 1967, 709.
35. Van Hove, L., Phys. Rev., 95, 1954, 249.
36. Morse, P.M., Feshbach, H., “Methods of Theoretical Physics,”, 1953, McGraw-Hill, New York, 832 Part I, See e. g.
37. Galitskii, V.M., Migdal, A.B., Sonet Phys. JETP (English Transl.), 7, 1958, 96.
38. Schultz, T.D., “Quantum Field Theory and the Many Body Problem”, 1964, Gordon & Breach, New York For a more complete discussion we refer to e.g. the following textbooks (in order of increasing complexity).
39. Ziman, J.M., “Elements of Advanced Quantum Theory.”, 1969, Cambridge Univ. Press, London.
40. March, N.H., Young, W.H., Sampanthar, S., “The Many Body Problem in Quantum Mechanics.”, 1967, Cambridge Univ. Press, London and New York.
41. Kirzhnits, D.A., “Field Theoretical Methods in Many-Body Systems.”, 1967, Pergamon Press, Oxford.
42. Schrieffer, J.R., “Theory of Superconductivity.”, 1964, Benjamin, New York.
43. Nozières, P., “Theory of Interacting Fermi Systems.”, 1964, Benjamin, New York.
44. Abrikosov, A.A., Gorkov, L.P., Dzyaloshinski, I.E., “Methods of Quantum Field Theory in Statistical Physics”, 1963, Prentice-Hall, Englewood Cliffs, New Jersey.
45. Martin, P.C., Schwinger, J., Phys. Rev., 115, 1959, 1342 The line of approach used here is a simplified zero temperature version of the Martin and Schwinger method, see.
46. Kadanoff, L.P., Baym, G., “Quantum Statistical Mechanics,”, 1962, Benjamin, New York.
47. Hedin, L., Phys. Rev., 139, 1965, A796.
48. 37a Bardeen, J., Phys. Rev., 52, 1937, 688.
49. Fröhlich, H., Proc. Roy. Soc., A215, 1952, 291.
50. Nakajima, S., Buss. Kenkyu, 65, 1953, 116.
51. Bardeen, J., Pines, D., Phys. Rev., 99, 1955, 1140.
52. Ziman, J., Proc. Cambridge Phil. Soc., 51, 1955, 707.
53. Migdal, A.B., Soviet Phys. JETP (English Transl.), 7, 1958, 996.
54. Peierls, R.E., “Quantum Theory of Solids,”, 1955, Oxford Univ. Press, London and New York.
55. Wigner, E., Phys. Rev., 40, 1932, 749.
56. Pitaevskii, L.P., Soviet Phys. JETP (English Transl.), 10, 1960, 1267.
57. Nozières, P., Luttinger, J.M., Phys. Rev., 127, 1962, 1423.
58. Luttinger, J.M., Nozières, P., Phys. Rev., 127, 1962, 1431.
59. 35.
60. Holstein, T., Ann. Phys., 29, 1964, 410.
61. 35.
62. Heine, V., Nozières, P., Wilkins, J.W., Phil. Mag., 13, 1966, 741.
63. Quinn, J.J., Harrison, W.A., Webb, M.B., (eds.) “The Fermi Surface”, 1960, Wiley, New York.
64. Silin, V.P., Soviet Phys. JETP (English Transl.), 8, 1959, 870.
65. Platzman, P.M., Wolff, P.A., Phys. Rev. Letters, 18, 1967, 280.
66. Platzman, P.M., Walsh, W.M. Jr., E-Ni Foo, Phys. Rev., 172, 1968, 689.
67. Mermin, N.D., Cheng, Y.C., Phys. Rev. Letters, 20, 1968, 839.
68. Kohn, W., Phys. Rev., 128, 1961, 1242.
69. Schultz, S., Dunifer, G., Phys. Rev. Letters, 18, 1967, 283.
70. Walsh, W.M. Jr., Platzman, P.M., Phys. Rev. Letters, 15, 1965, 784.
71. Silin, V.P., Soviet Phys. JETP (English Transl.), 7, 1958, 538.
72. Misawa, S., Progr. Theoret. Phys., 30, 1963, 786.
73. 35 p. 94.
74. Bell, J.S., Squires, E.J., Phys. Rev. Letters, 3, 1959, 96.
75. 52.
76. Carr, W.J. Jr., Coldwell-Horsfall, R.A., Fein, A.E., Phys. Rev., 124, 1961, 747.
77. Phillips, J.C., Phys. Rev., 123, 1961, 420.
78. Geldart, D.J.W., Houghton, A., Vosko, S.H., Can. J. Phys., 42, 1964, 1938.
79. Wiser, N., Cohen, M.H., J. Phys., C2, 1969, 193.
80. Ferrell, R.A., Phys. Rev. Letters, 1, 1958, 443.
81. 37 and by.
82. Carr, W.J. Jr., Maradudin, A.A., Phys. Rev., 133, 1964, A371.
83. Nozières, P., Pines, D., Phys. Rev., 111, 1958, 442.
84. Pines, D., “Elementary Excitations in Solids,”, 1963, Benjamin, New York.
85. Clementi, E., J. Chem. Phys., 38, 1963, 2248 39, 175 (1963). If we consider the correlation energy per electron for neutral atoms from He to Ar, we find a rather constant value of 0.075 Ry. Also the correlation energy within one isoelectronic series stays fairly constant over a wide range of electron densities.
86. Ashcroft, N.W., Langreth, D.C., Phys. Rev., 155, 1967, 682.
87. Misawa, S., Phys. Rev., 140, 1965, A1645.
88. Edwards, S.F., Hillel, A.J., J. Phys., C1, 1968, 61.
89. Osaka, Y., J. Phys. Soc. (Japan), 22, 1967, 1513.
90. de Wette, F.W., Phys. Rev., 135, 1964, A287.
91. Van Horn, H.M., Phys. Rev., 157, 1967, 342.
92. a limit.
93. L. Hedin, (to be published).
94. 4 p. 343.
95. Lundqvist, B.I., Physik Kondensierlen Materie, 6, 1967, 206.
96. Luttinger, J.M., Phys. Rev., 121, 1961, 942.
97. Hedin, L., Lundqvist, B.I., Lundqvist, S., Solid State Comm., 5, 1967, 237.
98. Lundqvist, B.I., Physik Kondensierlen Materie, 6, 1967, 193.
99. Lundqvist, B.I., Physik Kondensierten Materie, 7, 1968, 117.
100. Layzer, A.J., Phys. Letters, 13, 1964, 121.
101. Ann. Phys. (N. Y.), 35, 1965, 67.
102. Quinn, J.J., Phys. Rev., 126, 1962, 1453 The curve is drawn after an accurate recalculation by Lundqvist.
103. Daniel, E., Vosko, S.H., Phys. Rev., 120, 1960, 2041.
104. Quinn, J.J., Ferrell, R.A., Plasma Phys. —Acceleralors-Thermonucl. Res. (GB), 2, 1961, 18.
105. Watabe, M., Progr. Theoret. Phys., 29, 1963, 519.
106. Misawa, S., Phys. Letters, 7, 1963, 249.
107. Brouers, F., Deltour, J., Phys. Status Solidi, 11, 1965, K29.
108. Rice, T.M., Ann. Phys. (N. Y.), 31, 1965, 100.
109. Luttinger, J.M., Ward, J.C., Phys. Rev., 118, 1960, 1417.
110. DuBois, D.F., Ann. Phys. (N. Y.), 8, 1959, 24 see p. 54.
111. Brinkman, W.F., Platzmann, P.M., Rice, T.M., Phys. Rev., 174, 1968, 495.
112. Rice, T.M., Phys. Rev., 176, 1968, 858.
113. Silverstein, S.D., Phys. Rev., 128, 1962, 631 130, 1703 (1963).
114. Tosi, M.P., Riv. Nuovo Cimento, 1, 1969, 160.
115. Nozières, P., Pines, D., Nuovo Cimento, 9, 1958, 470.
116. S, in Eq. (26.10). A recent discussion of different effective dielectric functions has been given by, 172, 383 (1968).
117. 116a Langreth, D.C., Phys. Rev., 181, 1969, 753 A recent investigation by, of the large q behavior of the dielectric function supports the H and NP results.
118. Kanazawa, H., Misawa, S., Fujita, E., Progr. Theoret. Phys., 23, 1960, 426.
119. Prange, R.E., Kadanoff, L.P., Phys. Rev., 134, 1964, A566.
120. Prange, R.E., Sachs, A., Phys. Rev., 158, 1967, 672.
121. Grimvall, G., Phys. Kondensierlen Materie, 6, 1967, 15.
122. Grimvall, G., J. Phys. Chem. Solids, 29, 1968, 1221.
123. McMillan, W.L., Rowell, J.M., Parks, R.D., (eds.) “Superconductivity”, 1968, Marcel Dekker, New York.
124. McMillan, W.L., Phys. Rev., 167, 1968, 331.
125. Grimvall, G., Physik Kondensierlen Materie, 9, 1969, 283.
126. Buckingham, M.J., Schafroth, M.R., Proc. Phys. Soc., 67, 1954, 828.
127. Ferrell, R.A., Bull. Am. Phys. Soc., 1, 1956, 217.
128. Quinn, J.J., Harrison, W.A., Webb, M.B., (eds.) “The Fermi Surface”, 1960, Wiley, New York.
129. Nakajima, S., Watabe, M., Progr. Theoret. Phys., 29, 1963, 341.
130. Engelsberg, S., Schrieffer, J.R., Phys. Rev., 131, 1963, 993.
131. Ashcroft, N.W., Wilkins, J.W., Phys. Letters, 14, 1965, 285.
132. Animalu, A.O.E., Bonsignori, F., Bortolani, V., Nuovo Cimento, 42B, 1966, 83.
133. Pytte, E., J. Phys. Chem. Solids, 28, 1967, 93.
134. Janak, J.F., Phys. Letters, 27A, 1968, 105.
135. Trofimenkoff, P.N., Carbotte, J.P., Dynes, R.C., Phys. Letters, 27A, 1968, 394 and others.
136. Sham, L.J., Proc. Roy. Soc., A283, 1965, 33.
137. Krebs, K., Phys. Rev., 138, 1965, A143.
138. Grimvall, G., Phys. Status Solidi, 32, 1969, 383.
139. Eliashberg, G.M., Soviet Phys. JETP (English Transl.), 16, 1963, 780.
140. Krebs, K., Phys. Letters, 6, 1963, 31.
141. Buckingham, M.J., Nature, 168, 1951, 281.
142. Stedman, R., Almqvist, L., Nilason, G., Phys. Rev., 162, 1967, 549.
143. Scher, H., Holstein, T., Phys. Rev., 148, 1966, 598.
144. Wilkins, J.W., Lectures given at NORDITA, 1968, Copenhagen, Denmark.
145. 142a S. Engelsberg, private communication.
146. Herring, C., Rado, G.T., Suhl, H., (eds.) “Magnetism”, IV, 1966, Academic Press, New York see also.
147. Marshall, W., (eds.) “Theory of magnetism in transition metals”, 1967, Academic Press, New York Proc. Int. School of Physics.
148. Pratt, G.W. Jr., Phys. Rev., 118, 1960, 462.
149. Cohen, M.H., Phillips, J.C., Phys. Rev., 124, 1961, 1818.
150. Phillips, J.C., Kleinman, L., Phys. Rev., 128, 1962, 2098.
151. Bassani, F., Robinson, J., Goodman, B., Schrieffer, J.R., Phys. Rev., 127, 1962, 1969.
152. Quinn, J.J., Phys. Rev., 126, 1962, 1453.
153. Pratt, G.W. Jr., Rev. Mod. Phys., 35, 1963, 502.
154. Hedin, L., Arkiv Fysik, 30, 1965, 231.
155. Brinkman, W., Goodman, B., Phys. Rev., 149, 1966, 597.
156. Lundqvist, B.I., Physik Kondensierten Materie, 9, 1969, 236.
157. Nozières, P., Pines, D., Phys. Rev., 109, 1958, 1062.
158. Kramers, H.A., Physica, 13, 1947, 401.
159. Hohenberg, P., Kohn, W., Phys. Rev., 136, 1964, B864.
160. Kohn, W., Sham, L.J., Phys. Rev., 140, 1965, A1133.
161. Sham, L.J., Kohn, W., Phys. Rev., 145, 1966, 561.
162. Adler, S.L., Phys. Rev., 126, 1962, 413.
163. Wiser, N., Phys. Rev., 129, 1963, 62.
164. Hedin, L., Johansson, A., Lundqvist, B.I., Lundqvist, S., Samathiyakanit, V., Arkiv Fysik, 39, 1969, 97.
165. Penn, D.R., Phys. Rev., 128, 1962, 2093.
166. Brandt, W., Reinheimer, J., Can. J. Phys., 46, 1968, 607.
167. Linderberg, J., Arkiv Fysik, 26, 1964, 323.
168. 164a Srinivasan, G., Phys. Rev., 178, 1969, 1244.
169. Dalgarno, A., Advan. Phys., 11, 1962, 281 If we use Hartree-Fock rather than Hartree one-electron functions and energies for the core electrons. See Section 37 and also.
170. Brandt, W., Lundqvist, S., Arkiv Fysik, 28, 1965, 399.
171. Wolff, P.A., Phys. Rev., 126, 1962, 405.
172. The calculation of the optical potential for a surface region is of course more complicated than for a perfect crystal. For recent work on this problem see, e.g., J. W. Gadzuk, Surface Set.11, 465 (1968).
173. 172a L. Hedin and A. Johansson, J. Phys. B (to be published).
174. Ziman, J.M., Advan. Phys., 13, 1964, 89.
175. Moore, C.E., “Atomic Energy Levels”, 1, 1949, Natl. Bur. Std. Circ., Washington, D. C No. 467.
176. Born, M., Heisenberg, W., Z. Physik, 23, 1924, 388.
177. Bethe, H.A., Salpeter, E.E., Flügge, S., (eds.) “Handbuch der Physik”, 35, 1957, Springer, Berlin.
178. 176a Ham, F.S., Solid State Phys., 1, 1955, 127.
179. LaBahn, R.W., Callaway, J., Phys. Rev., 147, 1966, 28.
180. Pu, R.T., Chang, E.S., Phys. Rev., 151, 1966, 31.
181. Kelly, H.P., Phys. Rev., 160, 1967, 44.
182. Thompson, D.G., Proc. Roy. Soc., A294, 1966, 160.
183. Slater, J.C., “Quantum Theory of Molecules and Solids”, 2, 1996, McGraw-Hill, New York See e.g.
184. Schiff, L.I., “Quantum Mechanics”, 1955, McGraw-Hill, New York, 112 See e. g.
185. J.F. Kenney, M. I. T. Solid State and Molecular Theory Group, Quart. Progr. Rept. No. 53, p. 38 (1964).
186. Brooks, H., Nuovo Cimento Suppl., 7, 1958, 165.
187. Callaway, J., “Energy Band Theory.”, 1964, Academic Press, New York.
188. Bienenstock, A., Brooks, H., Phys. Rev., 136, 1964, A784.
189. Gombás, P., Z. Physik, 121, 1943, 523.
190. Lewis, H.W., Phys. Rev., 111, 1958, 1554.
191. Gáspár, R., Acta Phys. Hung., 3, 1954, 263.
192. 3 See also.
193. Gombás, P., Acta Phys. Hung., 4, 1954, 187.
194. Callaway, J., Phys. Rev., 95, 1954, 656.
195. Mitler, H., Phys. Rev., 99, 1955, 1835.
196. 194a Kohn, W., Kubo, R., (eds.) “Many-Body Theory”, 1966, Benjamin, New York.
197. Ma, S.K., Brueckner, K.A., Phys. Rev., 165, 1968, 18.
198. Herring, C., Intern. J. Quant. Chem., 1, 1967, 788.
199. Tong, B.Y., Sham, L.J., Phys. Rev., 144, 1966, 1.
200. Cowan, R.D., Larson, A.C., Liberman, D., Mann, J.B., Waber, J., Phys. Rev., 144, 1966, 5.
201. Connolly, J.W.D., Phys. Rev., 159, 1967, 415.
202. Snow, E.C., Phys. Rev., 171, 1968, 785 172, 708 (1968).
203. Lundqvist, S., Ufford, C.W., Phys. Rev., 139, 1965, A1.
204. Liberman, D.A., Phys. Rev., 171, 1968, 1.
205. L. Hedin, B. I. Lundqvist, and S. Lundqvist (to be published).
206. Parrat, L.G., Rev. Mod. Phys., 31, 1959, 616.
207. Landsberg, P.T., Proc. Phys. Soc., A62, 1949, 806.
208. Ferrell, R.A., Rev. Mod. Phys., 28, 1956, 308.
209. Pirenne, J., Longe, P., Physica, 30, 1964, 277.
210. Hedin, L., Solid State Comm., 5, 1967, 451.
211. Rooke, G.A., Phys. Letters, 3, 1963, 234.
212. Cuthill, J.R., Dobbyn, R.C., McAlister, A.J., Williams, M.L., Phys. Rev., 174, 1968, 515.
213. Brouers, F., Phys. Letters, 11, 1964, 297.
214. Phys. Status Solidi, 11, 1965, K25 22, 213 (1967).
215. Brouers, F., Longe, P., Fabian, D., (eds.) “Soft X-Ray Spectra and the Electronic Structure of Metals and Materials”, 1968, Academic Press, New York.
216. Hedin, L., Fabian, D., (eds.) “Soft X-Ray Spectra and the Electronic Structure of Metals and Materials”, 1968, Academic Press, New York.
217. Glick, A.J., Longe, P., Phys. Rev. Letters, 15, 1965, 589 see also.
218. Longe, P., Glick, A.J., Phys. Rev., 177, 1969, 526.
219. S. M. Bose, Ph.D. Thesis, Univ. of Maryland, 1967.
220. Rystephanick, R.G., Carbotte, J.P., Phys. Rev., 166, 1968, 607.
221. Shuey, R.T., Physik Kondensierlen Malerie., 5, 1966, 192.
222. 214a Friedel, J., Comments Sol. Stat. Phys., 2, 1969, 21.
223. Rooke, G.A., J. Phys. C1:2 (1968), 767–776.
224. Bergersen, B., Brouers, F., J. Phys. C., 2, 1969, 651.
225. Anderson, P.W., Phys. Rev. Letters, 18, 1967, 1049.
226. Mahan, G.D., Phys. Rev., 163, 1967, 612.
227. Roulet, B., Gavoret, J., Nozières, P., Phys. Rev., 178, 1969, 1072.
228. Nozières, P., Gavoret, J., Roulet, B., Phys. Rev., 178, 1969, 1084.
229. Nozières, P., De Dominicis, C.T., Phys. Rev., 178, 1969, 1097.
230. 219a Mizuno, Y., Ishikawa, K., J. Phys. Soc. Japan, 25, 1968, 627.
231. 219a Morita, A., Watabe, M., J. Phys. Soc. Japan, 25, 1968, 1060.
232. 219a D. C. Langreth, Phys. Rev. Comments and Addenda (to be published);.
233. 219a Ausmann, G.A. Jr., Glick, A.J., Techn. Rep., 1969, Univ. of Maryland.
234. Allotey, F.K., Phys. Rev., 157, 1967, 467.
235. 220a Stott, M.J., March, N.H., Fabian, D., (eds.) “Soft X-Ray Band Spectra and the Electronic Structure of Metals and Materials”, 1968, Academic Press, New York.
236. 220b Brust, D., Phys. Rev., 134, 1964, A1337.
237. Dresselhaus, G., Dresselhaus, M.S., Phys. Rev., 160, 1967, 649.
238. Abèlès, F., Fabian, D., (eds.) “Soft X-Ray Spectra and the Electronic Structure of Metals and Materials”, 1968, Academic Press, New York.
239. Siegbahn, K., et al. “ESCA, Atomic, Molecular and Solid State Structure Studied by Means of Electron Spectroscopy”, 1967, Almqvist and Wiksell, Uppsala.
240. Bearden, J.A., Burr, A.F., Rev. Mod. Phys., 39, 1967, 125.
241. Fomichev, V.A., Lukirskii, A.P., Soviet Phys.-Solid State (English Transl.), 8, 1967, 1674.
242. Sagawa, T., et al. J. Phys. Soc. Japan, 21, 1966, 2602.
243. Codling, K., Madden, R.P., Phys. Rev., 167, 1968, 587.
244. Watanabe, H., J. Appl. Phys., 3, 1964, 804.
245. Swanson, N., Powell, C.J., Phys. Rev., 167, 1968, 592.
246. Esposito, R.J., Muldawer, L., Bloomfield, P.E., Phys. Rev., 168, 1968, 744.
247. Spicer, W.E., Phys. Rev., 154, 1967, 385.
248. Hopfield, J.J., Phys. Rev., 139, 1965, A419.
249. Elastic scattering at inelastic thresholds-Application to solids. Proc. Tokyo Summer Inst. Theor. Phys., 1965.
250. Comments Sol. State Phys., 1, 1969, 198.
251. Watabe, M., Yasuhara, H., Phys. Letters, 28A, 1968, 329.
252. Jauch, J.M., Rohrlich, F., “The Theory of Photons and Electrons”, 1958, Addison-Wesley, Reading, Massachusetts, 263 See e. g.
253. O. E. Mogensen, Thesis, Tech. Univ. of Denmark, Lyngby, 1968.
254. Sedov, V.L., Soviet Phys.-Solid State (English Transl.), 9, 1968, 1540.
255. Stewart, A.T., Roellig, L.O., (eds.) “Positron Annihilation”, 1967, Academic Press, New York The experimental setup is discussed in many places, e.g.
256. Donaghy, J.J., Stewart, A.T., Phys. Rev., 164, 1967, 396.
257. Carbotte, J.P., Salvadori, A., Phys. Rev., 162, 1967, 290.
258. Carbotte, J.P., Kahana, S., Phys. Rev., 139, 1965, A213.
259. Weisberg, H.L., Berko, S., Phys. Rev., 154, 1967, 249.
260. B. Bergersen, Ph.D. Thesis, Brandeis Univ., 1964.
261. Kahana, S., Phys. Rev., 117, 1960, 123 129, 1622 (1963).
262. Arponen, J., Jauho, P., Phys. Rev., 167, 1968, 239.
263. Crowell, J., Anderson, V.E., Ritchie, R.H., Phys. Rev., 150, 1966, 243.
264. Zuchelli, A.J., Hickman, T.G., Phys. Rev., 136, 1964, A1728.
265. Kanazawa, H., Ohtsuki, Y., Yanagawa, S., Progr. Theoret. Phys., 33, 1965, 1010.
266. Bergersen, B., Terrell, J.H., Fabian, D., (eds.) “Soft X-Ray Spectra and the Electronic Structure of Metals and Materials”, 1968, Academic Press, New York A third requirement has been discussed by.
267. Carbotte, J.P., Phys. Rev., 155, 1967, 197.
268. Bergersen, B., Phys. Rev., 181, 1969, 499.
269. Majumdar, C.K., Phys. Rev., 140, 1965, A227.
270. Kim, S.M., Stewart, A.T., Carbotte, J.P., Phys. Rev. Letters, 18, 1967, 385.
271. Carbotte, J.P., Arora, H.L., Can. J. Phys., 45, 1967, 387.
272. Stewart, A.T., Shand, J.B., Phys. Rev. Letters, 16, 1966, 261.
273. Proc. Phys. Soc., 88, 1966, 1001.
274. Hamann, D.R., Phys. Rev., 146, 1966, 277.
275. Mikeska, H.J., Phys. Letters, 24A, 1967, 402.
276. Stroud, D., Ehrenreich, H., Phys. Rev., 171, 1968, 399.
277. Lundqvist, B.I., Samathiyakanit, V., Physik Kondensierten Materie, 9, 1969, 231.
278. L. Hedin, B. I. Lundqvist, and V. Samathiyakanit (to be published).
279. Schumacher, R.T., Slichter, C.P., Phys. Rev., 101, 1956, 58.
280. Raether, H., Springer Tracts Mod. Phys., 38, 1965, 84 Springer, Berlin 1965.
281. Kato, T., Kobayashi, T., Namiki, M., Progr. Theor. Phys. Suppl., 15, 1960, 3.
282. Baym, G., Ann. of Physics (N.Y.), 14, 1961, 1 See, e.g.
283. A. Sjölander and R. Johnson, Proc. Intern. Conf. on Inelastic Scattering of Neutrons, Bombay 1964 (IAEA Proceedings series) 1, 61 (1965).
284. Garland, J.W., Phys. Rev., 163, 1967, 460.