Treatment of the continuum states in the Woods-Saxon Strutinsky method
S. Takahara1 , Y. R. Shimizu2 , N. Tajima3
1 School of Medicine, Kyorin University
2 Department of Physics, Kyushu University
3 Department of Applied Physics, Fukui University

Contact e-mail: staka@kyorin-u.ac.jp

Strutinsky shell correction methods with finite height potentials have a well known problem [1] in applying to unstable nuclei: The level density around zero energy leads to an artificial
increase. Kruppa et al. [2] have proposed a prescription with which one can get rid of theunwanted contribution of the particle gas to the level density by utilizing the Green function
approach. Namely, a new level density is defined as the difference between two kinds of discretePPM
0level densities: gM () = M
i=1 2δ(−ei )− i=1 2δ(−ei ) , where ei is a single particle level of the0
total Hamiltonian and ei is that of the free Hamiltonian in the same truncated subspace. The
positive energy part of this modified level density does not diverge as the number of basis M isincreased. However, this procedure does not guarantee the fulfillment of the plateau condition
for the smoothed single-particle energy [3].
Recently, it has been shown [4] that the plateau condition can be satisfied by transforming thesingle-particle spectrum in such a way that its average level density coincides with some simple
function. We employ this method, expecting that it works for the Woods-Saxon potential, too.
We have noticed that it is also necessary to modify the BCS gap equation in a similar manneras the Kruppa-Strutinsky method.
With these prescriptions, we have applied the Woods-Saxon Strutinsky method to unstable
nuclei. We met another problem, however, that existing parameter sets of the Woods-Saxon
potential are not suitable for dripline nuclei. We have calculated the driplines for several WoodsSaxon parameter sets and found that all of them have a tendency to retract inward the driplines
compared with those predicted by empirical mass formulae. Therefore, it is necessary to find a
new parameter set applicable not only to near stable nuclei but also to the driplines.
We are also applying the method to investigate the origin of the prolate dominance [5] bychanging the potential parameters. In this case, increasing the diffuseness parameter of potential
tends to unbound the nucleus. So it is necessary to adjust the potential depth as a function ofthe diffuseness. We determine the potential depth so that the Fermi level in the Thomas-Fermi
approximation agrees with that calculated with a mass formula.
In summary, with several modifications, the Strutinsky shell correction method is now capable of treating neutron-rich nuclei because of the proper treatment of the continuum level
density. It becomes possible to perform more accurate and reliable calculations of the nuclear
masses to produce a new mass formula based on the Woods-Saxon Strutinsky method.

1. W. Nazarewicz, T. R. Werner, J. Dobaczewski, Phys. Rev. C50 (1994) 2860.
2. A. T. Kruppa, Phys. Lett. B431 (1998) 237.
3. Vertse et al., Phys. Rev. C61 (2000) 064317.
4. A. G. Magner, K. Arita, S. N. Fedotkin, Prog. Theor. Phys. 115 (2006) 523.
5. N. Tajima, Y. R. Shimizu, N. Suzuki, Phys. Rev. C64 (2001) 037301.