The anomalies of the droplet model
Abstract
The droplet model predictions for nuclear density distributions are systematically compared with the results of a self-consistent model with Strutinsky smoothing. The discrepancies between the two predictions for stable nuclei are as large as the discrepancies between the old liquid drop model and the self-consistent one: although the droplet model reproduces quite well the trends of the variations of nuclear radii and neutron skins, it is not able to predict correctly their values. A preliminary discussion is given as to which hypothesis of the droplet model should be modified to generalise it, and two possible variants are suggested.
References (25)
- W.D. Myers et al.
Ann. of Phys.
(1969) - W.D. Myers et al.
Ann. of Phys.
(1974) - W.D. Myers et al.
Nucl. Phys.
(1980) - J. Côté et al.
Nucl. Phys.
(1978) - M. Farine et al.
Nucl. Phys.
(1980) - F. Tondeur
Nucl. Phys.
(1982) - F. Tondeur
Nucl. Phys.
(1978) - F. Tondeur
Nucl. Phys.
(1979) - M. Brack et al.
Phys. Lett.
(1975) - W. Stocker
Nucl. Phys.
(1978)
Phys. Lett.
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Mass predictions in the infinite nuclear matter model
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Finite nuclei to nuclear matter: A leptodermous approach
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Generalized liquid drop model and desaturation effects in nuclei
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Desaturation effects in densities and energies of nuclei
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Thomas-fermi approach to nuclear mass formula. (I). Spherical nuclei
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