Abstract
In an earlier paper we have extended the new Tamm-Dancoff method to the “New Tamm-Dancoff method with intermediate states”. This extension makes it possible to treat the effect of nearby levels in many body systems with Green's functions. In addition to well-known approximations, such as the Hartree-Fock theory and the Hartree-Bogoliubov theory, we obtain a series of new approximations. The “Hartree-Fock theory with intermediate states”, which is the subject of the present investigation, is one of these. By using time reversal invariance we have succeeded in clarifying its structure, and we give the solution procedure. The exchange terms in theN-particle intermediate states can be represented by an additional potentialY, which (as is the case for the generalized density matrixρ) has to be determined selfconsistently. In this way we have overcome the difficulties, that Kerman and Klein met in their “generalized Hartree-Fock approximation”, which has some close similarities with our Hartree-Fock theory with intermediate states. We demonstrate our method for the exactly soluble rotational-vibrational model of Klein et al. Hereby we show how to treat conservation laws and the degeneracy of levels. The Hartree-Fock equations with three intermediate states turn out to give analytical expressions for the energies and the matrix elements. These agree excellently with the exact values in the rotational part of the spectrum.
Similar content being viewed by others
Literatur
Migdal, A.B.: Nuclear theory: the quasiparticle method, p. 35. New York, Amsterdam: W.A. Benjamin, Inc. 1968
Friederich, A., Gerling, W., Bleuler, K.: Z. Naturforsch.30a, 142 (1975)
Gorkov, L. P.: J. Exptl. Theoret. Phys.7, 505 (1958)
Brenig, W., Wagner, H.: Z. Physik173, 484 (1963)
Friederich, A.: Z. Physik223, 152 (1969)
Bleuler, K., Friederich, A., Petry, H.-R., Schütte, D.: In: Quanten und Felder, pp. 267 -277. Braunschweig: Vieweg u. Sohn 1971
Dürr, H. P., Wagner, F.: Nuovo Cimento46, 223 (1966)
Kerman, A.K., Klein, A.: Phys. Rev.132, 1326 (1963)
Kerman, A. K., Klein, A.: Phys. Rev.138B, 1323 (1965)
Klein, A., Calenza, L., Kerman, A. K.: Phys. Rev.140 B, 245 (1965)
Baranger, M.: In: Cargèse lectures in theoretical physics 1962, pp. 61–89, ed. by M. Lévy. New York: W.A.Benjamin, Inc. 1963
Chattopadhyay, P.K., Krejs, F., Klein, A.: Phys. Lett.42B, 315 (1972)
Dasso, C., Krejs, F., Klein, A., Chattopadhyay, P. K.: Nucl. Phys. A210, 429 (1973)
Chattopadhyay, P. K., Klein, A., Krejs, F.: Nucl. Phys. A229, 509 (1974)
Kamlah, A., Meyer, J.: Z. Physik211, 293 (1968)
Fäßler, A., Piastino, A.: Z. Physik220, 88 (1969)
Fäßler, A., Schmid, K.W., Piastino, A.: Nucl. Phys. A174, 26 (1971)
Heisenberg, W.: Einführung in die einheitliche Feldtheorie der Elementarteilchen, pp. 66–80. Stuttgart: Hirzel 1967
Novozhilov, Y. V., Tulub, A. V.: The method of functionals in the quantum theory of fields. New York: Gordon and Breach 1961
Migdal, A.B.: Nucl. Phys. A210, 421 (1973)
Author information
Authors and Affiliations
Additional information
A. Friederich und W. Gerling danken dem Bundesministerium für Forschung und Technologie und der Deutschen Forschungsgemeinschaft für die Finanzierung dieser Arbeit.
Rights and permissions
About this article
Cite this article
Friederich, A., Gerling, W. Die Hartree-Fock-Theorie mit Zwischenzuständen: Klärung ihrer Struktur bei Zeitumkehrinvarianz und Anwendung auf das Kleinsche Rotations-Vibrationsmodell. Z Physik A 277, 47–58 (1976). https://doi.org/10.1007/BF01547501
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01547501