Abstract
An ensemble of random particle-hole matrices is studied as a function of the signs of the matrix elements. When all matrix elements have the same sign, a theorem due to Perron ensures the existence of a coherent state: the collective particle-hole state. The example of Gamow-Teller transitions between208Bi(1+) and208Pb(0+) is considered and the strength of the Gamow-Teller giant resonance as well as the fluctuations in the ensemble are studied. When a fractionp of matrix elements are of opposite sign, we find that a giant resonance may still exist providedp is small enough. Its magnitude and position in the spectrum are studied. The method proposed is valid for any particle hole excitation. The two body matrix elements of several interactions are analysed and are shown to fit into a unique valuep=0.2 for the 1 + states.
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Laboratoire associé au C.N.R.S.
The authors are grateful to O. Bohigas for many useful comments during the course of this work. One of us (R.H.) would like to thank Comité des Bourses Joliot-Curie for the award of a fellowship and is grateful to the members of the Division de Physique Théorique Orsay for their kind hospitality.
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Touchard, J., Haq, R.U. & Arvieu, R. An ensemble of random particle-hole matrices with collective eigenstates. Z Physik A 282, 191–201 (1977). https://doi.org/10.1007/BF01408163
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DOI: https://doi.org/10.1007/BF01408163