1. Continuum QRPA calculation with the Skyrme effective force Niigata University Kazuhito Mizuyama Masayuki Matsuo & Yasuyoshi Serizawa

2. (http://www.rarf.riken.go.jp/RIBF/nuclearchart-e.htm) Mean field theory and Physics of the neutron rich region Shallow fermi level Many valence neutrons Halo, Skin, Soft dipole, Pigmy etc… Continuum QRPA can treat both the continuum and pairing.

3. Continuum QRPA Halo, Skin, Soft dipole, Pigmy etc… Exact HFB green function satisfies correct asymptotic & outgoing boundary conditions Response function M.Matsuo Nucl.Phys.A696(2001)371 Continuum QRPA in coordinate space HFB formalism Continuum QRPA

4. Skyrme HFB + Landau-Migdal approx. cQRPA Continuum QRPA calc. with the velocity dependent terms of the Skyrme interaction. Self consistency is broken. Sum rule is not conserved. To improve these defects, -- Theoretical defects -- Skyrme HFB + Landau-Migdal approx. cQRPA Serizawa, in the previous talk. E. Khan, et.al. PRC66(2002)024309 Continuum QRPA

5. Extension of continuum QRPA with Skyrme force p-h interaction p-p interaction ～ Linear response equation of continuum QRPA ～ These terms come from the singularities of the response function. (cf. K.F.LIU, N.V.GIAI, Phys.Lett.Vol.65,23(1976))

6. Numerical check p-h channel SLy4, (SkM*, SGII, SIII, only for 22 O) p-p interaction V 0 =315[MeV fm -3 ] ρ 0 = 0.32 fm -3 ( Mix pairing (Dobaczewski et al. nucl-th/0203060,0203038)) (E1-dipole) External field R box =15fm l cut =4 E cut =60[MeV] Response function Smoothing constant ε ＝ 1.0[MeV]

7. ～ Residual interaction with velocity dependent terms ～ 22 O tftf The renormalization factor becomes close to 1 in the “full” calculation. Consistent result with M. Yamagami, proceedings of the International Symposium on “FRONTIERS OF COLLECTIVE MOTIONS” (CM2002)@Aizu, Japan 6-9 Nov. 2002. Check(1) Renormalization factor ① ① ② ②

8. E dB(E1)/dE [e 2 fm 2 ] E x [MeV] (cf. K.F.LIU, N.V.GIAI, Phys.Lett.Vol.65,23(1976)) 16 O SLy4 SIII 16 O E1 dipole excitation Check(2) GDR energy position agree with Smoothing constant ε ＝ 1.0[MeV]

9. dB(E1)/dE [e 2 fm 2 /MeV] E x [MeV] M. Yamagami, proceedings of the International Symposium on “FRONTIERS OF COLLECTIVE MOTIONS” (CM2002)@Aizu, Japan 6-9 Nov. 2002. = 1.93 [MeV] 20 O SLy4 20 O E1 dipole excitation Check(3) {1,Δ, ∇ } Landau-Migdal

10. --Summary-- We formulated the continuum QRPA based on the Skyrme energy functional with keeping the velocity dependent terms. We constructed its new numerical code. We checked the renormalization factors for some kinds of parameters of the Skyrme interaction in oxygen isotopes. We also calculated E1 strength functions for oxygen isotopes and compared with other’s work.