Bibliography

1

F. E. Bertrand, Nucl. Phys. A 354 (1981) 129c.

2

F. Dawson and R. J. Furnstahl, Phys. Rev. C 42 (1990) 2009.

3

D. Vretenar, A. Wandelt, and P. Ring, to be published in Phys. Lett. B (2000).

4

Y. K. Gambhir, P. Ring, and A. Thimet, Ann. Phys. NY. 198 (1990) 132.

5

M. L`Huillier and N. Van Giai, Phys. Rev. C 39 (1989) 2022.

6

P. Ring, Progr. Part. Nucl. Phys. 37 (1996) 193.

7

D. Vretenar, H. Berghammer, and P. Ring, Nucl. Phys. A581 (1995) 679.

8

D. Vretenar, N. Paar, P. Ring and G. A. Lalazissis, Phys. Rev. E 60 (1999) 308.

9

G. A. Lalazissis, D. Vretenar, and P. Ring, Nucl. Phys. A4516 (1999) 1.

10

G. A. Lalazissis, D. Vretenar, and P. Ring, Phys. Rev. C 57 (1998) 2294.

11

F. Catara, C. H. Dasso, and A. Vitturi, Nucl. Phys. A602 (1996) 181.

12

Y. Suzuki, K. Ikeda, and H. Sato, Prog. Theor. Phys. 83 (1990) 180.

13

R. Mohan, M. Danos and L. C. Biedenharn, Phys. Rev. C 5 (1971) 1740.

14

D. Vretenar, N. Paar, P. Ring, and G. A. Lalazissis, submitted to Phys. Lett. B (2000).

15

T. Aumann et al., Nucl. Phys. A 649 (1999) 297c.

16

M. Zinser et al., Nucl. Phys. A 619 (1997) 151.

17

T. Nakamura et al., Phys. Lett. B 331 (1994) 296.

18

T. Hartmann, J. Enders, P. Mohr, K. Vogt, S. Volz, and A. Zilges, Phys. Rev. Lett. 85 (2000) 274.

19

J. P. Adams, B. Castel and H. Sagawa, Phys. Rev. C 53 (1996) 1016.

20

J. Chambers, E. Zaremba, J. P. Adams and B. Castel, Phys. Rev. C 50 (1994) R2671.

21

H. Sagawa and T. Suzuki, Phys. Rev. C 59 (1999) 59.

22

Z. W. Bell, L. S. Cardman and P. Axel, Phys. Rev. C 25 (1982) 791.

23

G. Kühner, D. Meuer, S. Müller, A. Richter, E. Spamer, O. Titze and W. Knüpfer, Phys. Lett. B 104 (1981) 189.

24

F. Catara, E. G. Lanza, M. A. Nagarajan and A. Vitturi, Nuc. Phys. A 624 (1997) 449.

25

H. Sagawa, N. Van Giai, N. Takigawa, M. Ishihara and K. Yazaki, Z. Phys. A 351 (1995) 385.

26

H. Sagawa and C. A. Bertulani, Prog. Theor. Phys.(sup.) 124 (1996) 143.

27

S. Ottini-Hustache, et. al., Phys. Rev. C 59 (1999) 3429.

28

Z. Y. Ma, N. Van Giai, A. Wandelt, D. Vretenar and P. Ring, nucl-th/9910054.

29

F. E. Serr, T. S. Dumitrescu, T. Suzuki and C. H. Dasso, Nucl. Phys. A 404 (1983) 359.

Figure Captions

• Fig.1 Isovector dipole strength in $^{208}$Pb for the full RRPA(solid line) and RRPA without contributions from Dirac states (dashed). The dotted, dot-dashed and short-dashed lines correspond to the RRPA with only $\sigma$, $\omega$ and $\rho$ mesons included in the antiparticle-hole couplings, respectively.

• Fig.2 Isovector dipole strength calculated with RRPA for a sequence of oxygen isotopes (Z=8, N=8,14,16,20). Low energy region is noted with dotted line.

• Fig.3 Ratio of the energy weighted moment m$_1$ in the low (E$\leq$10 MeV) and high (E$>$10 MeV) energy region for various nuclei.

• Fig.4 Isovector (dotted line) and isoscalar (thick line) dipole transition densities of low-lying and GDR selected states in $^{22}$O and $^{28}$O. Separated proton and neutron transition densities are displayed by the dashed and dot-dashed lines, respectively. All transition densities are multiplied by r$^2$.

• Fig.5 Dipole strength for isovector mode of oscillations in the $^{40}$Ca, $^{48}$Ca,$^{54}$Ca and $^{60}$Ca nuclei.

• Fig.6 Isovector (dotted line) and isoscalar (thick line) dipole transition densities multiplied by r$^2$ for the low-lying (7.3 MeV) and GDR (15.2 MeV) state in $^{60}$Ca. Proton and neutron transition densities are displayed by the dashed and dot-dashed lines, respectively.

• Fig.7 Isovector dipole strength distributions for $^{48}$Ni, $^{56}$Ni, $^{68}$Ni and $^{78}$Ni nuclei.

• Fig.8 Isovector (IV) and isoscalar (IS) dipole transition densities multiplied by r$^2$ for the low-lying (8.9 MeV) and GDR (16.4 MeV) state in $^{78}$Ni. Proton and neutron transition densities are noted by p and n, respectively.

• Fig.9 Centroid energies( ) of the isovector dipole low-lying ($E\leq10$ MeV) and GDR ($E>10$ MeV) modes, displayed as a function of number of neutrons in Ni isotopes. Energies of the low-lying modes are compared with the hydrodynamical prediction [12] for energy of the pygmy resonances (SIS). GDR modes are compared with the mass dependence law $E=78A^{-1/3}$.

• Fig.10 Isovector dipole strength distributions for $^{100}$Sn, $^{114}$Sn, $^{120}$Sn and $^{132}$Sn nuclei.

• Fig.11 Isovector (IV) and isoscalar (IS) dipole transition densities multiplied by r$^2$ for low-lying 8.9 MeV (a) and GDR 14.8 MeV state (b) in $^{132}$Sn. Proton and neutron transition densities are noted by p and n, respectively. The contributions of the proton-neutron core (Z=50,$N\leq50$)(dashed) and the excess neutrons ($50<N\leq82$)(solid) are displayed for the pygmy (c) and GDR (d) state.

• Fig.12 Velocity distributions in $^{132}$Sn for the RRPA state at 8.6 MeV. The velocity field of the proton-neutron core (Z=50,$N\leq50$)(a) is separated from the contribution of the excess neutrons ($50<N\leq82$)(b).

• Fig.13 The same as in Fig.12, but for the GDR peak at 14.8 MeV in $^{132}$Sn.

• Fig.14: Isovector low-lying ($E\leq10$ MeV) and GDR ($E>10$ MeV) energies as a function of neutron number in Sn isotopes. Energies of the low-lying mode are compared with the hydrodynamical prediction [12] of pygmy resonances (SIS). GDR modes are compared with the mass dependence law $E=78A^{-1/3}$.

• Fig.15 Isovector dipole strength distribution in $^{122}$Zr (a). The neutron(n), proton(p), isovector(IV) and isoscalar(IS) transition densities are displayed for the low-lying state 7.7 MeV (b). Separated transition densities of the excess neutrons $(50<N\leq82)$ vibrating against the core (Z=40, N=50) are shown in the (c) panel.

• Fig.16 Velocity distributions in $^{122}$Zr for the low-lying RRPA state at 7.7 MeV. The velocity field of the proton-neutron core (Z=40,$N\leq50$)(a) is separated from the contribution of the excess neutrons ($50<N\leq82$)(b).

Table: Dominant neutron particle-hole excitations for the main peaks in low energy region of isovector dipole strength for $^{28}$O.

E[MeV]	EWSR[%]	p-h excitation
4.2	0.9	$(92\%\ 1d_{3/2} \to 2p_{3/2})$
4.9	1.4	$(91\%\ 1d_{3/2} \to 2p_{1/2})$
		$(\ 6\%\ 1d_{3/2} \to 2p_{3/2})$
7.3	1.9	$(92\%\ 2s_{1/2} \to 2p_{3/2})$
8.9	6.3	$(71\%\ 1d_{3/2} \to 1f_{5/2})$
		$(16\%\ 1d_{5/2} \to 1f_{7/2})$
		$(\ 3\%\ 1d_{5/2} \to 2p_{3/2})$

Table: Neutron particle-hole excitations in the low energy isovector dipole mode in $^{60}$Ca.

E[MeV]	EWSR[%]	p-h excitation
5.7	1.2	$(93.1\%\ 2p_{1/2} \to 3s_{1/2})$
		$(\ 3.6\%\ 1f_{5/2} \to 2d_{5/2})$
6.8	2.6	$(82.8\%\ 1f_{5/2} \to 2d_{3/2})$
		$(\ 6.1\%\ 1f_{5/2} \to 2d_{5/2})$
		$(\ 3.1\%\ 1f_{7/2} \to 1g_{9/2})$
		$(\ 2.3\%\ 2p_{3/2} \to 2d_{5/2})$
		$(\ 1.1\%\ 2p_{3/2} \to 3s_{1/2})$
7.3	1.6	$(49.3\%\ 2p_{1/2} \to 2d_{3/2})$
		$(41.3\%\ 2p_{3/2} \to 3s_{1/2})$
		$(\ 3.2\%\ 1f_{5/2} \to 2d_{3/2})$
		$(\ 1.5\%\ 2p_{3/2} \to 2d_{5/2})$
7.9	2.0	$(83.8\%\ 2p_{3/2} \to 2d_{5/2})$
		$(\ 5.7\%\ 1f_{5/2} \to 2d_{3/2})$
		$(\ 3.5\%\ 1f_{7/2} \to 1g_{9/2})$
		$(\ 2.4\%\ 1f_{5/2} \to 1g_{7/2})$
9.9	2.1	$(57.7\%\ 1f_{5/2} \to 1g_{7/2})$
		$(22.0\%\ 1f_{7/2} \to 1g_{9/2})$
		$(\ 3.3\%\ 1f_{7/2} \to 2d_{5/2})$

Table: Main neutron particle-hole configurations participating in the low-lying isovector dipole state 9.0 MeV (4.3% EWSR) in $^{68}$Ni (left) and 8.6 MeV state (1.4% EWSR) in $^{132}$Sn(right)

$^{68}$Ni, 9.0 MeV	$^{132}$Sn, 8.6 MeV
$(26.1\%\ 1f_{5/2} \to 2d_{5/2})$	$(28.2\%\ 2d_{3/2} \to 2f_{5/2})$
$(22.9\%\ 2p_{3/2} \to 2d_{5/2})$	$(21.9\%\ 2d_{5/2} \to 2f_{7/2})$
$(11.3\%\ 1f_{7/2} \to 1g_{9/2})$	$(19.7\%\ 2d_{3/2} \to 3p_{1/2})$
$(10.3\%\ 2p_{1/2} \to 2d_{3/2})$	$(10.5\%\ 1h_{11/2} \to 1i_{13/2})$
$(10.0\%\ 1f_{5/2} \to 2d_{3/2})$	$(\ 3.5\%\ 2d_{5/2} \to 3p_{3/2})$
$(\ 8.2\%\ 2p_{3/2} \to 3s_{1/2})$	$(\ 1.9\%\ 1g_{7/2} \to 2f_{5/2})$
$(\ 1.4\%\ 2p_{1/2} \to 3s_{1/2})$	$(\ 1.5\%\ 1g_{7/2} \to 1h_{9/2})$
$(\ 1.0\%\ 1f_{5/2} \to 1g_{7/2})$	$(\ 0.6\%\ 1g_{7/2} \to 2f_{7/2})$
$(\ 0.3\%\ 1s_{5/2} \to 3d_{3/2})$	$(\ 0.6\%\ 2d_{3/2} \to 3p_{3/2})$

Nils Paar, 2001.