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Depletion of the central density or formation of a hollow structure (Bubble) drew a lot of interest both from the theorists [1-3] as well as from the experimentalists [4,5] due to its conflicting nature vis-a-vis the property of saturation of the nuclear force. One can expect gross deviation from density saturation for finite Fermi systems in which single particle spectrum is discrete instead of a continuum. The formation of shells changes drastically for exotic nuclei having large isospins. As a result new properties of nuclei manifest in this region.
It is generally believed that non-occupation of s-states of exotic nuclei leads to central depression of density. We shall show in this paper that due to correlation between the hole and particle states, nuclei, namely Magnesium-32 near the island of inversion show a bubble like structure. We have used Skyrme-Hartree-Fock method with optimized tensor interaction which has a large influence on the splitting of spin-orbit partners as described in Ref. 6. For all the force parameters [6] we have observed a dip in the central region. The reduction factor is 29.7% for SLy5T. For the r.m.s. charge radius of Mg-32 the calculated value is 3.1891 fm. whereas the experimental value is 3.1863 fm.[7]
References:
[1] X. Campi and D. W. L. Sprung, Phys. Lett. B46, 291 (1973).
[2] M. Bender et al, Phys. Rev. C 60, 034304 (1999).
[3] B. G. Todd-Rutel et al J, Phys. Rev. C69, 021301(R) (2004).
[4] E. Khan et al, Nucl. Phys. A800, 37 (2008).
[5] L. Gaudefroy et al., Phys. Rev. Lett. 97, 092501 (2006).
[6] R. Bhattacharya, Nucl. Phys. A913, 1 (2013)
[7] D.T. Yordanov et al, Phys. Rev, Lett. 108,042504 (2012)
