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Continuum QRPA calculation with the Skyrme effective force

Continuum QRPA calculation with the Skyrme effective force. Niigata University Kazuhito Mizuyama Masayuki Matsuo & Yasuyoshi Serizawa. Mean field theory and Physics of the neutron rich region. (http://www.rarf.riken.go.jp/RIBF/nuclearchart-e.htm). Halo, Skin, Soft dipole, Pigmy etc….

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Continuum QRPA calculation with the Skyrme effective force

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

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

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

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

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

  6. Response function Numerical check Rbox=15fm lcut=4 Ecut=60[MeV] p-h channel SLy4, (SkM*, SGII, SIII, only for 22O) p-p interaction Smoothing constant ε＝1.0[MeV] V0=315[MeV fm-3] ρ0 = 0.32 fm-3 ( Mix pairing (Dobaczewski et al. nucl-th/0203060,0203038)) External field (E1-dipole)

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

  8. Check(2) 16O E1 dipole excitation Smoothing constant ε＝1.0[MeV] 16O E dB(E1)/dE [e2fm2] SLy4 GDR energy position agree with SIII Ex [MeV] (cf. K.F.LIU, N.V.GIAI, Phys.Lett.Vol.65,23(1976))

  9. Check(3) 20O E1 dipole excitation Landau-Migdal {1,Δ,∇} 20O <Δn>= 1.93 [MeV] dB(E1)/dE [e2fm2/MeV] SLy4 Ex [MeV] M. Yamagami, proceedings of the International Symposium on “FRONTIERS OF COLLECTIVE MOTIONS” (CM2002)@Aizu, Japan 6-9 Nov. 2002.

  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.

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