Figures

  

Figure 1: Radial PTG potentials for three values of the parameter $\Lambda$(see Table 8 for the complete set of parameters). The bottom panel shows the potential for L=0, while the middle and top panels correspond to L=4 and the PTG (1) and PTG' (9) potentials, respectively (see text).

  

Figure 2: Schematic representation of different domains of S-matrix poles in the complex momentum and energy planes.

  

Figure 3: Radial PTG wave functions of the 3s_1/2 state calculated analytically for parameters listed in Table 2. The dotted, dashed, and solid lines correspond to resonant, virtual, and bound 3s_1/2 states, respectively. In the inset the same wave functions are shown in the region of attractive potential. Volume element $4\pi r^2$ is included in the definition of wave functions.

  

Figure 4: Localization [Eq. (38)] (a) and phase shift (b) of the s_1/2 continuum PTG states. Circles denote results of numerical calculations performed in the box of 30fm. Solid and dashed lines show the localizations calculated analytically for scattering wave functions normalized in the box of 30fm, and to a constant amplitude of the outgoing wave, respectively. Arrows indicate position of the lowest, very broad, resonance. Parameters of the PTG potential are given in Table 2 (bound 3s_1/2state).

  

Figure 5: Localization [Eq. (38)] of the HFB upper components (dots) of the quasiparticle states, compared with the localization of the s_1/2continuum PTG states (lines).

  

Figure 6: Phase shifts of the HFB upper components (dots) of the quasiparticle states, compared with the phase shifts of the s_1/2continuum PTG states (lines).

  

Figure 7: Canonical wave functions of the 3s_1/2 state, corresponding to the three cases of the HFB calculations listed in Table 4. The dotted, dashed, and solid lines correspond to resonant, virtual, and bound PTG 3s_1/2 states, respectively. In the inset the same wave functions are shown in the logarithmic scale. Volume element $4\pi r^2$ is included in the definition of wave functions.

  

Figure 8: Norms N_n of the s_1/2 lower quasiparticle wave functions $\phi_2 (E_n,\mbox{{\boldmath{$r$ }}}\sigma)$, corresponding to the three cases of the HFB calculations listed in Table 4. Inset shows the same values in the logarithmic scale.

  

Figure 9: Localization of the HFB upper components (dots) of the quasiparticle states compared with the localization of the d_3/2continuum PTG' states (lines). Upper (a) and lower (b) panels differ by the position of the 2d_3/2 resonances with respect to the top of the centrifugal barrier, see text.

  

Figure 10: Norms N_n of the d_3/2 lower quasiparticle wave functions $\phi_2 (E_n,\mbox{{\boldmath{$r$ }}}\sigma)$, corresponding to the two cases of the HFB calculations listed in Table 4. Inset shows the same values in the logarithmic scale.

  

Figure 11: Localizations of the HFB upper components of the d_3/2quasiparticle states (dots) compared with those of the d_3/2continuum PTG' states (lines). The six panels differ by the positions of the lowest d_3/2 resonance with respect to the top of the centrifugal barrier, see text. Arrows indicate values of the canonical energies $\epsilon_{\mbox{\scriptsize {can}}}$ of the 2d_3/2canonical states.

  

Figure 12: Norms N_n of the HFB lower components $\phi_2 (E_n,\mbox{{\boldmath{$r$ }}}\sigma)$of the d_3/2 quasiparticle states. In each panel (similarly as in Fig. 11), arrows indicate values of the canonical energies $\epsilon_{\mbox{\scriptsize {can}}}$ of the 2d_3/2 canonical states, while the corresponding occupation factors $v_{\mbox{\scriptsize {can}}}$ are given explicitly.