Introduction: Deformation-induced coupling of E0 and E2 excitations - PowerPoint PPT Presentation

Skyrme-RPA description of isoscalar E0 giant resonance in spherical and deformed nuclei V.O. Nesterenko Joint Institute for Nuclear Research, Dubna, Moscow region, Russia J. Kvasil, A. Repko Institute of Particle and Nuclear Physics, Charles University, Praha , Czech Republic P.-G. Reinhard Institute of Theoretical Physics II, University of Erlangen, Erlangen, Germany W. Kleinig JINR, Dubna. Moscow region, Russia; TU Dresden, Institute of nalysis, Dresden, Germany EMIN 2015, Moscow, 05-07.10.2015

Introduction: Deformation-induced coupling of E0 and E2 excitations splitting of the isoscalar giant monopole resonance (ISGMR) - well known phenomenon, M.N. Harakeh and A. van der Woude, “ Giant Resonances” - many calculations in 80’s within (Oxford: Clarendon, 2001). schematic RPA and other approaches, - should be revisited within modern DFT mean-field self-consistent models K. Yoshida and T. Nakatsukasa, - some recent SC-RPA studies for particular nuclei PRC 88, 034309 (2013). Nd and Sm isotopes 24 Mg Y.K. Gupta, U. Garg, et al, new experiments Phys. Lett. B748, 343 (2015). We propose the systematic Skyrme QRPA study of the deformation- induced ISGMR splitting in a wide mass region:  24 106 116 Mg, Cd , rare-earth, actinide and superheavy nuclei

Deformation-induced coupling of E0 and E2 excitations     0 0 GMR GMR (K=0) B(E0) B(E0) GMR splitting GQR B(E2) B(E2) GMR(K=0) GQR(K=0) coupling K=0 K=1 K=2 - GMR splitting is distinctive if it is larger than the GMR and GQR widths - so far this splitting has been observed only in Nd-Sm isotopes and 238U    0.25 0.35 - light nuclei are especially promising since they can possess a huge deformation  =0.5-0.6 Y.K. Gupta, U. Garg, et al, 24 Mg Phys. Lett. B748, 343 (2015).

V.O.N., J.Kvasil, P.-G.Reinhard, PRC 66, 044307 (2002), Calculation scheme We have the codes: V.O.N., W. Kleinig et al PRC74, 064306 (2006) separable 1D/2D QRPA Self-consistent Skyrme QRPA exact (full) 1D/2D QRPA Repko’2014  E  V mean field  - are obtained as the first and second MF   E  derivatives of the initial Skyrme functional  2 E  V residual interaction   res 2 -both time-even and time-odd densities + Coulomb are taken into account in the residual interaction Strength function           2 2 S E ( 0; ) | | r Y | 0 | ( )   - sum over all RPA states 00   0  1      ( ) with the Lorentz weight    2 2     2 [( ) ]    2 MeV 4 Pairing Large basis: - from 4000 to 10000 2qp states  -force volume pairing, up to 30 – 200 MeV -BCS treatment, - EWSR is exhausted by 95-100% - pp-channel in the residual interaction

W. Kleinig, VON, J. Kvasil, Description of quadrupole deformation in Skyrme DFT: P.-G. Reinhard and P. Vesely, rare-earth, actinide and superheavy regions PRC, 78, 044313 (2008) x - experiment SLy6 theory A open symbols: experiment SV-bas filled symbols: theory VON., V. G. Kartavenko, W. Kleinig, R.V. Jolos, J. Kvasil, and P.-G. Reinhard, arXiv:1504.06492[nucl-th], submitted to PRC.

ISGMR splitting in Nd isotopes experiment Skyrme QRPA: SVbas U. Garg U et al, PPC 29, 93 (1984). sRPA and fRPA give close results for E2(T=0) but somewhat deviate for E0(T=0) The deformation-induced E0-E2 coupling and subsequent splitting of E0(T=0) are clearly seen. Good agreement with the exp. data

J. Kvasil, V.O. Nesterenko, et al J.Phys: Conff.Ser., 580, 012053 (2015) ISGMR splitting in 154Sm  Svbas: K 234 MeV   SkP :  K 202 MeV  sRPA: no E0-E2 coupling sRPA and fRPA: with E0-E2 coupling Experiment: RCNP: M. Itoh et al, PRC68, 064602 (2003). TAMU: D.H. Youngblood et al, PRC69, 034315 (2004). - RCNP data give the splitting while TAMU data not - good agreement of the theory with RCNP data

ISGMR splitting in Cd isotopes   0.2 modest deformation: Skyrme fRPA Experiment : RCNP : D. Patel et al, PLB718, 447 (2012) TAMU: . Y.-W. Lui et al,PRC69, 034611 (2004).   0.2 - theory gives a small splitting deformation is not - no splitting in experiment enough to observe the splitting

ISGMR splitting in 172Yb and 238U Experiment: S. Bradenburg, R.D. Leo, A.G. Drentje, M.N. Harakeh, H. Janszen, A. van der Woude, PRL 49, 1687 (1982).   0.27 perhaps the deformation is already sufficient to observe the splitting

J. Kvasil, V.O. Nesterenko, A. Repko, W ISGMR splitting in superheavy deformed nuclei . Kleinig, P.-G. Reinhard, to be published Skyrme QRPA: SVbas - nothing surprising

24 Mg ISGMR splitting in light deformed nuclei: experiment for   0.605 - very strong prolate deformation strong E0-E2 coupling can be expected   “background - free” ( , ') 386 MeV, RCNP experiment: forward angles Narrow bump at E~16 MeV and broad structure at E~24 MeV -ISGMR splitting is observed in RCNP experiments but not in TAMU ones - Skyrme RPA description: SkM*

J. Kvasil, V.O. Nesterenko, A. Repko, W. Kleinig, Skyrme-QRPA calculations P.-G. Reinhard, to be published   Ref. [11] = PLB’2015 A   2.5 MeV 1/ 3 E 78 MeV  K 234 MeV Svbas:   SkM* : K 217 MeV   SkP :  K 202 MeV  The calculations with SkM*,  SVbas and SkP give qualitatively similar results Two strong arguments in favor of E0-E2 origin of the peak at E~16 MeV: - the peak energy coincides with the energy ISGQR(K=0), - the peak disappears in the spherical limit Generally good description,  worse for SkP , need in complex configurations If TAMU data are indeed worse than RCNP ones? Impact of fragmentation? Light nuclei with a huge quadrupole deformation are especially promising to observe the ISGMR splitting!

Conclusions Systematic analysis of the splitting of ISGMR in light, medium, heavy and superheavy deformed nuclei within the self-consistent Skyrme QRPA model. The calculations have confirmed the results of previous calculations within schematic RPA . Light nuclei with a huge deformation look most promising to observe the splitting. Still essential discrepancies in TAMU and RCNP experimental data. Arrangement of the data is in order. - optimal forward angles to excite both E0 and E2 - looking for nuclei with a minimal fragmentation of E0 strength      - using various reactions: , , ( , ') ( , ' ) 17 17 ( O, O') The splitting of ISGMR depends on: information on the correlation - nuclear incompressibility (GMR) between these two values - isoscalar effective mass (GQR)

Thank you for attention!

Appendix A: Spurious mode connected with the number of particles J.Li, G.Colo, J.Meng In the energy interval E > 8 MeV the influence of the spurious mode is very small