Eur. Phys. J. A 12, 29-40 (2001)

Some considerations on the restoration of Galilei invariance in the nuclear many-body problem

Part I: Mathematical tools, spectral functions and spectroscopic factors of simple bound states

K.W. Schmid

Institut für Theoretische Physik der Universität Tübingen Auf der Morgenstelle 14, D-72076 Tübingen, Germany

karl-wilhelm.schmid@uni-tuebingen.de

(Received: 20 February 2001 / Revised version: 22 May 2001 Communicated by D. Schwalm)

Abstract
The mathematical tools to restore Galilei invariance in the nuclear many-body problem with the help of projection techniques are presented. For simple oscillator configurations recursion relations for the various elementary contractions are derived. The method is then applied to simple configurations for the ground states of ⁴He, ¹⁶O and ⁴⁰Ca as well as to the corresponding one-hole and one-particle states. As a first application the spectral functions and spectroscopic factors for the above-mentioned doubly even nuclei are investigated. It turns out that the conventional picture of an uncorrelated system underestimates the single-particle strengths of the hole states from the last occupied shell while that of the higher excited hole states is overestimated considerably. These results are in complete agreement with those derived by Dieperink and de Forest using different methods. Similar effects are seen for the particle states which have not been studied before. All the calculations presented here are performed analytically and thus can be checked explicitly by the interested reader.

PACS
21.60.-n - Nuclear-structure models and methods.

© Società Italiana di Fisica, Springer-Verlag 2001