Abstract
A microscopic description of the interacting boson model is attempted in a basis of multipole pairing vibrations and in the framework of the nuclear field theory. If nothing else, it seems in this way possible to calculate both rotations and vibrations in a common basis.
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References
Cf. e.g. A. Bohr and B. R. Mottelson, Nuclear Structure, Vols. I and II, Benjamin (1969) and (1975).
Cf. e.g. P. F. Bortignon, R. A. Broglia, D. R. Bes, and R. Liotta, Phys. Rep. 30C:305 (1977), and references therein.
P. F. Bortignon, R. A. Broglia, and D. R. Bes, Phys. Lett. 76B:153 (1978).
A. Arima and F. lachello, Phys. Rev. Lett. 40:385 (1978), and references therein.
A. Arima, T. Otsuka, F. lachello, and I. Talmi, Phys. Lett. 66B:205 (1977).
O. Scholten, F. lachello, and A. Arima, Interacting boson model of collective nuclear states III, preprint KVI-126, February 1978 and references therein.
D. R. Bes and R. A. Broglia, Phys. Rev. C3:2349 (1971).
R. A. Broglia, D. R. Bes, and B. Nilsson, Phys. Lett. 50B:213 (1974).
R. A. Broglia and D. R. Bes, Phys. Lett. 69B:129 (1977).
It has been shown8 that Gλ≃27/A MeV, independent of the multipolarity and for fλ(r)=1. It is thus not evident that only the lowest multipolarities are important. However, following ref. 4 we restrict the present discussion to λ=0 and λ=2.
The expansion parameter in the NFT is 1/Ω, Ω being the effective pair-degeneracy of the valence single-particle orbitals. In the case of a j-shell, Ω=j+1/2.
B. Bayman and A. Lande, Nucl. Phys. 77:1 (1966); T. Kishimoto and T. Tamura, A163:100 (1971).
G. Racah, Phys. Rev. 63:367 (1943).
It may be instructive to compare the Pauli correcting factors given in equations (6) and (7) of ref. 15 with those appearing, e.g. in (7). The factor [ 1-(ns-1)/Ω]1/2 corresponds to the first order term in the expansion of [ (2Ω+2-2ns-4nd)/(2Ω+2-4nd)]1/2 in powers of 1/Ω. The term (l-nd/Ω)1/2, which is absent from eq. (7) of ref. 15, is however contained in the reduced matrix element appearing in eq. (6) of the same reference.
A. Arima, T. Otsuka, F. Iachello, and I. Talmi, Phys. Lett. 76B:139 (1978).
R. A. Broglia, V. Paar, and D. R. Bes, Phys. Lett. 37B:257 (1971).
D. R. Bes, R. A. Broglia, and B. Nilsson, Phys. Rep. 16C:1 (1975).
D. R. Bes, G. G. Dussel, and H. Sofia, Am. Journal of Phys. 45:191 (1977).
O. Civitarese, R. A. Broglia, and D. R. Bes, Phys. Lett. 72B:45 (1977).
S. G. Nilsson, Mat. Fys. Medd. Dan. Vid. Selsk. 29:no.16 (1955).
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Bes, D.R., Broglia, R.A. (1979). Nuclear Field Theory Treatment of the Interacting Boson Model. In: Iachello, F. (eds) Interacting Bosons in Nuclear Physics. Ettore Majorana International Science Series. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-3521-4_13
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