1.D.2: [ Nuclear Physics A211 (1973) 29--76; (~0 North-Holland Publishing Co., Amsterdam 1.E.1 I Not to be reproduced by photoprint or microfilm without writtenpermission from the publisher COUPLING OF A THREE-PARTICLE (HOLE) VALENCE-SHELL CLUSTER TO QUADRUPOLE VIBRATIONS (ALAGA MODEL): The Z = 50 region: odd Ag and I isotopes; and the Z = 28 region: odd Mn and Ga isotopes v. PAAR The Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark and Institute "Rudjer Bo§kovid", Za#reb, Yugoslavia t Received 22 December 1972 (Revised 2 April 1973) Abstract: The present approach includes two important physical correlations: the interaction be- tween single-particle degrees of freedom and the vibrational field and the Pauli principle for three particles or holes in the valence shell. No new parameters have been introduced. In this way, both the explicit appearance of broken and promoted pairs and the anharmonicities from the neighbouring doubly even nuclei are accounted for. The model is generally characterized b y the coexistence of quasivibrational and quasirotational features. Typical quasirotational ele- ments are the quasiband pattern and the I = j--1 anomaly, while a typical quasivibrational element is the multiplet structure. Both features are naturally introduced by the mechanism of the cluster field coupling. Nuclei with Z = 50=t=3 and Z = 28±3 are qualitatively discussed within the framework of the present approach. A detailed qualitative and quantitative descrip- tion of the properties of low-lying states (energy spectra, electromagnetic properties, transfer reactions) as well as a comparison with experiment are given for lo7. lOgAg ' 127I, 55Mn ' and 69Ga, which are typical and well-known representatives of odd Ag, I, Mn, and Ga nuclei, respectively. 1. Why the three-particle (bole) valence-shell cluster coupled to the quadrupole vibration? Odd-even nuclei in the spherical and transitional region exhibit the presence of low-lying collective modes. E2 transitions and quadrupole moments are appreciably enhanced over single-particle values, and in some cases explicit evidence for the multiplet structure is available. The properties of nuclei with one particle or hole outside of a single-closed shell are fairly well accounted for by coupling one valence-shell particle (hole) to a low- frequency quadrupole mode 39, 40). A simplified extension of this approach to nuclei with 3, 5 .... particles in the valence shell is provided by coupling one quasiparticle to the vibrator 17). In order to obtain the spectrum and wave functions, the following parameters are necessary: single-particle energies, phonon energy, pairing strength, and particle-vibration coupling strength (or the strength Z of the Q-Q force, from which the particle- Permanent address. 29