The additivity principle of the extreme
shell model stipulates that an average value of a
one-body operator be equal to the sum of the
core contribution and effective contributions of valence (particle or hole) nucleons.
For quadrupole moment and angular momentum operators,
we test this
principle for highly and superdeformed rotational bands in the
nuclei. Calculations are done in the self-consistent
cranked non-relativistic Hartree-Fock
and relativistic Hartree
mean-field approaches.
Results indicate
that the additivity principle is a valid concept that justifies the
use of an extreme single-particle model in an unpaired regime typical
of high angular momenta.

**M. Matev,
A. V. Afanasjev,
J. Dobaczewski,
G. A. Lalazissis,
W. Nazarewicz**

**August 8, 2007**

- Introduction
- Theoretical framework
- Definition of observables
- Additivity of effective s.p. observables
- Determination of effective s.p. observables
- Method of calculations
- Selection of independent-particle configurations

- Results of the additivity analysis
- Effective charge quadrupole moments
- Effective quadrupole moments and
- Effective angular momenta (s.p. alignments)
- Variance and distribution of residuals

- Conclusions
- Acknowledgements
- Bibliography
- About this document ...

Jacek Dobaczewski 2007-08-08