Excitations in light deformed nuclei investigated by self consistent quasiparticle random phase approximation

Transcription

1 Excitations in light deformed nuclei investigated by self consistent quasiparticle random phase approximation C. Losa, A. Pastore, T. Døssing, E. Vigezzi, R. A. Broglia SISSA, Trieste Trento, December 2011 C. Losa (SISSA) Deformed QRPA Trento, December / 22

2 Outline Phenomenological introduction about vibrational modes in nuclei Theoretical description of collective vibrational modes QRPA theory Details about our work: approach, type of interaction used Results: linear response in 20 O, Mg, 34 Mg Comparison with other approaches Conclusions and perspectives C. Losa (SISSA) Deformed QRPA Trento, December / 22

3 Isoscalar monopole vibrational modes J = 0 C. Losa (SISSA) Deformed QRPA Trento, December / 22

4 Isoscalar monopole vibrational modes J = 0 C. Losa (SISSA) Deformed QRPA Trento, December / 22

5 Isovector dipole vibrational modes J = 1 C. Losa (SISSA) Deformed QRPA Trento, December / 22

6 Isovector dipole vibrational modes J = 1 C. Losa (SISSA) Deformed QRPA Trento, December / 22

7 Isoscalar quadrupole vibrational modes J = 2 C. Losa (SISSA) Deformed QRPA Trento, December / 22

8 Isoscalar quadrupole vibrational modes J = 2 C. Losa (SISSA) Deformed QRPA Trento, December / 22

9 Mean Field Theory H = A i=1 2 2m i + A v(i, j) i<j The description of the many body vibrational systems is given at a first order by a mean field H 0 = A i=1 ) ( 2 2m i + V (i) = H = H 0 + V res H 0 V res = i<j v(i, j) i V (i) C. Losa (SISSA) Deformed QRPA Trento, December / 22

10 Linear Response Theory λ = Q λ 0 Q λ : phonon creation operator RPA Q λ = ph ( ) Xph λ a pa h Yph λ a h a p QRPA Q λ = L<L (X λ LL α L α L Y λ LL α L α L ) 0 HF 0 HFB qp states α K = u K a K v K a K, α K = u K a K v K a K C. Losa (SISSA) Deformed QRPA Trento, December / 22

11 Linear Response Theory λ = Q λ 0 Q λ : phonon creation operator RPA Q λ = ph ( ) Xph λ a pa h Yph λ a h a p QRPA Q λ = L<L (X λ LL α L α L Y λ LL α L α L ) 0 HF 0 HFB qp states α K = u K a K v K a K, α K = u K a K v K a K Spherical symmetry Axial symmetry {Q } are obtained for each block J π {Q } are obtained for each block Ω π J π C. Losa (SISSA) Deformed QRPA Trento, December / 22

12 Approach as Mean Field we consider HF(B) theory as Linear Response we consider (Q)RPA theory we impose Axial Symmetry using Cylindrical Coordinates r, z, φ we work in canonical HO and THO basis wave functions Ca s 1/2 R s1/2 (r) Y 0,0 ψ s1/2 (0,z) / (2π) 1/2 ψ s1/2 THO (0,z) / (2π) 1/2 THO JT HO r ( fm ) f (R) r r R, z z f (R) R r 2 R = b 2 + z2 bz 2 JT J. Terasaki et al. Phys. Rev. C71, 2005 Skyrme (SKM ) force is used both in HFB and QRPA C. Losa (SISSA) Deformed QRPA Trento, December / 22

13 Density Dependent Delta Interaction V pair ( r, r ) = 1 P σ 2 [ V 0 + V ] 1 6 ργ 00 (r) δ ( r r ) R. R. Chasman et al. Phys. Rev. C14, 1976 C. Losa (SISSA) Deformed QRPA Trento, December / 22

14 Density Dependent Delta Interaction V pair ( r, r ) = 1 P σ 2 [ V 0 + V ] 1 6 ργ 00 (r) δ ( r r ) R. R. Chasman et al. Phys. Rev. C14, 1976 The shape of the pairing field (r) depends on the choice of the parameters η, V 1. DDDI - parameters type V 1 γ Surface -37.5V 0 1 Volume 0 1 Mixed V 0 1 J. Dobaczewski et al., EPJ A15, 2002 C. Losa (SISSA) Deformed QRPA Trento, December / 22

15 (Q)RPA equations A B B A X Y = ω λ X Y, λ = Q λ 0 C. Losa (SISSA) Deformed QRPA Trento, December / 22

16 (Q)RPA equations A B B A X Y = ω λ X Y, λ = Q λ 0 Residual Interaction V res V ph KK LL = δ2 E[ρ, κ, κ ] = KK eff eff V Skyrme + V Coul δρ LK δρ LL L K V pp KK LL = δ2 E[ρ, κ, κ ] δκ LK δκ = KK V pair LL eff L K E [ρ, κ, κ ] = E Skyrme [ρ] + E Coul [ρ p ] + E pair [ρ, κ, κ ] C. Losa (SISSA) Deformed QRPA Trento, December / 22

17 Ground state in 20 O and 24 Mg Potential Energy Surfaces Pairing energies C. Losa (SISSA) Deformed QRPA Trento, December / 22

18 Ground state in 26 Mg and 34 Mg Potential Energy Surfaces Pairing energies C. Losa (SISSA) Deformed QRPA Trento, December / 22

19 20 O: without spin orbit and Coulomb interaction in IS 2 + Present work K. Yoshida et al. Phys. Rev. C78, 2008 peaks below 10 MeV: shifted up 200 kev with heights lowered by 20% ISGQR: peak shifted down kev ISGQR: peak heights increase 30%(JT), 15%(HO), 25%(THO) C. Losa (SISSA) Deformed QRPA Trento, December / 22

20 24 Mg: fractions of EWSR in IS 2 + Present work compared to D. H. Youngblood et al. Phys. Rev. C60, 1999 S. Péru et al. Phys. Rev. C77, 2008 D1S SKM HO SKM THO SLY4 HO SLY4 THO Exp ± 0.6 C. Losa (SISSA) Deformed QRPA Trento, December / 22

21 24 26 Mg: strength functions in IV 1 24 Mg 26 Mg S 1 ( e 2 fm 2 /MeV ) HO THO Ω π =0 Ω π =1 IV 1 24 Mg E ( MeV ) S 1 ( e 2 fm 2 /MeV ) HO THO Ω π =0 Ω π =1 IV 1 26 Mg E ( MeV ) C. Losa (SISSA) Deformed QRPA Trento, December / 22

22 34 Mg: strength functions in IS 2 + S. Ebata Canonical basis time dependent Hartree Fock Bogoliubov (Cb TDHFB) approach K. Yoshida QRPA approach in quasi particle basis Present work QRPA approach in THO basis C. Losa (SISSA) Deformed QRPA Trento, December / 22

23 FAM: Finite Amplitude Method T. Nakatsukasa, T. Inakura, and K. Yabana Phys. Rev. C , 2007 P. Avogadro and T. Nakatsukasa Phys. Rev. C , 2011 C. Losa (SISSA) Deformed QRPA Trento, December / 22

24 FAM: Finite Amplitude Method T. Nakatsukasa, T. Inakura, and K. Yabana Phys. Rev. C , 2007 P. Avogadro and T. Nakatsukasa Phys. Rev. C , 2011 QRPA A B B A X Y = ω λ X Y FAM (E µ + E ν )X νµ + δh 20 νµ(ω) (E µ + E ν )Y νµ + δh 20 νµ(ω) = ω λ X νµ Y νµ δh 20 δh (δh, δ ) δh = H(ρ η, κ η ) H(ρ, κ) η ρ η = (V + ηu X )(V + ηu Y ) T κ η = (U + ηv Y )(V + ηu X ) C. Losa (SISSA) Deformed QRPA Trento, December / 22

25 FAM: 24 Mg for 0 + modes M. Stoitsov, M. Kortelainen, T. Nakatsukasa, C. Losa, and W. Nazarewicz Phys. Rev. C (R), 2011 QRPA (Present work) cutoff in ɛ crit = 200 MeV v crit = 10 4 MeV QRPA matrices requiring 16 GB memory FAM requires 0.5 GB memory C. Losa (SISSA) Deformed QRPA Trento, December / 22

26 Conclusions and perspectives software for self consistent HFB+QRPA calculations in canonical HO and THO basis 20 O test of our calculations with those of J. Terasaki comparison with results of K. Yoshida role of self consistency Mg role of intrinsic deformation in the splitting between projections comparison with experimental data and S. Péru 34 Mg agreement with the result of K. Yoshida, S. Ebata comparison with FAM agreement between the IS monopole strength functions future comparisons for higher multipolarities C. Losa (SISSA) Deformed QRPA Trento, December / 22