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

• 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

Joint Institute for Nuclear Research, Dubna, Moscow region, Russia 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,
• many calculations in 80’s within

schematic RPA and other approaches,

• should be revisited within modern DFT mean-field self-consistent models
• some recent SC-RPA studies for particular nuclei

new experiments

M.N. Harakeh and A. van der Woude, “Giant Resonances” (Oxford: Clarendon, 2001).

• K. Yoshida and T. Nakatsukasa,

PRC 88, 034309 (2013). Y.K. Gupta, U. Garg, et al,

• 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

Nd and Sm isotopes

24Mg

Deformation-induced coupling of E0 and E2 excitations

B(E2) GQR B(E0)

   

B(E2)

K=1

B(E0) GMR GMR (K=0)

K=0 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
• light nuclei are especially promising since they can possess a huge deformation

GMR splitting

GMR(K=0) GQR(K=0) coupling

 =0.5-0.6

24Mg Y.K. Gupta, U. Garg, et al,

• Phys. Lett. B748, 343 (2015).

0.25 0.35   

Calculation scheme Strength function

2 2 00

( 0; ) | | | 0 | ( ) S E r Y

  

   



    



2 2

1 ( ) 2 [( ) ] 4

 

           

with the Lorentz weight

2 MeV  

• sum over all RPA states

Self-consistent Skyrme QRPA

MF

E V   

2 2 res

E V    

mean field residual interaction

• are obtained as the first and second

derivatives of the initial Skyrme functional

• both time-even and time-odd densities + Coulomb

are taken into account in the residual interaction

 

E   -force volume pairing,

• BCS treatment,
• pp-channel in the residual interaction

Pairing Large basis:

• from 4000 to 10000 2qp states

up to 30 – 200 MeV

• EWSR is exhausted by 95-100%

We have the codes:

separable 1D/2D QRPA exact (full) 1D/2D QRPA

V.O.N., J.Kvasil, P.-G.Reinhard, PRC 66, 044307 (2002), V.O.N., W. Kleinig et al PRC74, 064306 (2006) Repko’2014

Description of quadrupole deformation in Skyrme DFT: rare-earth, actinide and superheavy regions

x - experiment theory

• W. Kleinig, VON, J. Kvasil,

P.-G. Reinhard and P. Vesely, PRC, 78, 044313 (2008)

SLy6

• pen symbols: experiment

filled symbols: theory

SV-bas

VON., V. G. Kartavenko, W. Kleinig, R.V. Jolos,

• J. Kvasil, and P.-G. Reinhard,

arXiv:1504.06492[nucl-th], submitted to PRC.

A

ISGMR splitting in Nd isotopes

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

experiment

• U. Garg U et al, PPC 29, 93 (1984).

Skyrme QRPA: SVbas

ISGMR splitting in 154Sm

234 MeV 202 MeV K K

 

 

Svbas: SkP :



sRPA: no E0-E2 coupling sRPA and fRPA: with E0-E2 coupling

• RCNP data give the splitting while TAMU data not
• good agreement of the theory with RCNP data

Experiment: RCNP:

• M. Itoh et al, PRC68, 064602 (2003).

TAMU:

D.H. Youngblood et al, PRC69, 034315 (2004).

• J. Kvasil, V.O. Nesterenko, et al

J.Phys: Conff.Ser., 580, 012053 (2015)

ISGMR splitting in Cd isotopes modest deformation:

Skyrme fRPA

0.2  

• theory gives a small splitting
• no splitting in experiment

deformation is not enough to observe the splitting 0.2  

Experiment: RCNP :

• D. Patel et al, PLB718, 447 (2012)

TAMU: . Y.-W. Lui et al,PRC69, 034611 (2004).

ISGMR splitting in 172Yb and 238U perhaps the deformation is already sufficient to observe the splitting

0.27  

Experiment:

• S. Bradenburg, R.D. Leo, A.G. Drentje, M.N.

Harakeh, H. Janszen, A. van der Woude, PRL 49, 1687 (1982).

ISGMR splitting in superheavy deformed nuclei

• J. Kvasil, V.O. Nesterenko, A. Repko, W

. Kleinig, P.-G. Reinhard, to be published

• nothing surprising

Skyrme QRPA: SVbas

ISGMR splitting in light deformed nuclei: experiment for 24Mg

• ISGMR splitting is observed in RCNP

experiments but not in TAMU ones

0.605  

• very strong prolate deformation

RCNP experiment: strong E0-E2 coupling can be expected

( , ')  

386 MeV, forward angles “background-free”

• Skyrme RPA description: SkM*

Narrow bump at E~16 MeV and broad structure at E~24 MeV

Skyrme-QRPA calculations

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 The calculations with SkM*, SVbas and SkP give qualitatively similar results

Light nuclei with a huge quadrupole deformation are especially promising to observe the ISGMR splitting!



1/ 3

78 MeV E A 

• J. Kvasil, V.O. Nesterenko, A. Repko, W. Kleinig,

P.-G. Reinhard, to be published

Svbas: SkM* : SkP :



234 MeV 217 MeV 202 MeV K K K

  

  

Generally good description, worse for SkP , need in complex configurations



If TAMU data are indeed worse than RCNP ones? Impact of fragmentation?

• Ref. [11] = PLB’2015

2.5 MeV  

Conclusions

Systematic analysis of the splitting of ISGMR in light, medium, heavy and superheavy deformed nuclei within the self-consistent Skyrme QRPA model.

( , ')  

17 17

( O, O')

( , ' )   

The calculations have confirmed the results of previous calculations within schematic RPA . Light nuclei with a huge deformation look most promising to

• bserve 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: , ,

The splitting of ISGMR depends on:

• nuclear incompressibility (GMR)
• isoscalar effective mass (GQR)

information on the correlation between these two values

Thank you for attention!

Appendix A: Spurious mode connected with the number of particles In the energy interval E > 8 MeV the influence of the spurious mode is very small

J.Li, G.Colo, J.Meng