Collective modes: past, present and future perspectives Muhsin N. Harakeh KVI, Groningen; GANIL, Caen International Symposium on High-resolution Spectroscopy and Tensor interactions (HST15) Osaka, Japan 16-19 November 2015 1 Osaka, Japan; 16-19 November 2015
L =0 L =1 ISGMR ISGDR M. Itoh L =3 L =2 ISGQR ISGOR 2 Osaka, Japan; 16-19 November 2015
Microscopic picture: GRs are coherent (1p-1h) excitations induced by single-particle operators Microscopic structure of ISGMR & ISGDR Transition operators: Constant Overtone 2 ћω excitation Spurious Overtone c.o.m. motion 3 ћω excitation (overtone of c.o.m. motion) 3 Osaka, Japan; 16-19 November 2015
IVGDR t rY 1 D N = 1 E1 (IVGDR) D N = 2 E2 (ISGQR) & D N = 0 E0 (ISGMR) ISGMR ISGQR r 2 Y 0 r 2 Y 2 4 Osaka, Japan; 16-19 November 2015
Equation of state (EOS) of nuclear matter More complex than for infinite neutral liquids Neutrons and protons with different interactions Coulomb interaction of protons 1. Governs the collapse and explosion of giant stars (supernovae) 2. Governs formation of neutron stars (mass, radius, crust) 3. Governs collisions of heavy ions. 4. Important ingredient in the study of nuclear properties. 5 Osaka, Japan; 16-19 November 2015
For the equation of state of symmetric nuclear matter at saturation nuclear density: ( / ) d E A 0 d 0 and one can derive the incompressibility of nuclear matter: 2 ( / ) d E A 2 9 K nm 2 d 0 E/A : binding energy per nucleon ρ : nuclear density J.P. Blaizot, Phys. Rep. 64, 171 (1980) ρ 0 : nuclear density at saturation 6 Osaka, Japan; 16-19 November 2015
Isoscalar Excitation Modes of Nuclei Hydrodynamic models/Giant Resonances Coherent vibrations of nucleonic fluids in a nucleus. Compression modes: ISGMR, ISGDR In Constrained and Scaling Models: K ћ A E ISGMR 2 m r 27 + K 7 A F ћ 25 E ISGDR 2 3 m r F is the Fermi energy and the nucleus incompressibility: K A = r 2 ( d 2 (E/A)/dr 2 ) r =R0 J.P. Blaizot, Phys. Rep. 64 (1980) 171 7 Osaka, Japan; 16-19 November 2015
Giant resonances Macroscopic properties: E x , G , %EWSR Isoscalar giant resonances; compression modes ISGMR, ISGDR Incompressibility, symmetry energy K A = K vol + K surf A 1/3 + K sym (( N Z )/ A ) 2 + K Coul Z 2 A 4/3 8 Osaka, Japan; 16-19 November 2015
ISGQR, ISGMR 10.9 MeV KVI (1977) 208 Pb( , ) at E =120 MeV 13.9 MeV Large instrumental background and nuclear continuum! M. N. Harakeh et al. , Phys. Rev. Lett. 38, 676 (1977) 9 Osaka, Japan; 16-19 November 2015
10 Osaka, Japan; 16-19 November 2015
ISGMR, ISGDR ISGQR, HEOR 100 % EWSR At E x = 14.5 MeV 11 Osaka, Japan; 16-19 November 2015
Grand Raiden@ RCNP ( , ) at E ~ 400 & 200 MeV at RCNP & KVI, respectively BBS@KVI 12 Osaka, Japan; 16-19 November 2015
ISGQR at 10.9 MeV ISGMR at 13.9 MeV 13 Osaka, Japan; 16-19 November 2015
Difference of spectra 0 ′ 3 ° 0 ′ 1.5 ° 1.5 ′ 3 ° Difference 14 Osaka, Japan; 16-19 November 2015
15 Osaka, Japan; 16-19 November 2015
Multipole decomposition analysis (MDA) exp . . calc 2 2 d d ( , ) ( ) ( , ) E a E E . . . . c m L c m d dE d dE L L exp . 2 d ( , ) : Experiment al cross section E . . c m d dE . calc 2 d ( , ) : DWBA cross section (unit cross section) E c . m . d dE L ( ) : EWSR fraction a E L a. ISGR (L<15)+ IVGDR (through Coulomb excitation) b. DWBA formalism; single folding transition potential (| ' |, ( ' )) V r r r + ( , ) ' ( ' , )[ (| ' |, ( ' )) ( ' ) ] U r E d r r E V r r r r 0 0 L L ( ' ) r 0 ( ) ' (| ' |, ( ' )) ( ' ) U r d r V r r r r 0 0 16 Osaka, Japan; 16-19 November 2015
Transition density ISGMR Satchler, Nucl. Phys. A472 (1987) 215 d + ( , ) [ 3 ] ( ) r E r r 0 0 0 dr 2 2 2 0 2 mA r E ISGDR Harakeh & Dieperink, Phys. Rev. C23 (1981) 2329 2 5 d d d d + + + 2 2 1 ( , ) [ 3 10 ( 4 )] ( ) r E r r r r r 1 0 2 3 3 dr dr dr dr R 2 2 6 R 2 1 4 2 2 2 ( 11 ( 25 / 3 ) 10 ) mAE r r r Other modes Bohr-Mottelson (BM) model d ( , ) ( ) r E r 0 L L dr + 2 2 2 2 L ( 2 1 ) 2 L L r 2 2 ( ) c + L L 2 L 1 2 ( 2 ) L mAE r 17 Osaka, Japan; 16-19 November 2015
18 Osaka, Japan; 16-19 November 2015
Uchida et al ., Phys. Lett. B557 (2003) 12 Phys. Rev. C69 (2004) 051301 116 Sn ( , ) spectra at 386 MeV ISGDR ISGDR MDA results for L=0 and L=1 ISGMR ISGMR ISGDR ISGDR ISGMR ISGMR 19 Osaka, Japan; 16-19 November 2015
In HF+RPA calculations, 2 ( / ) d E A 2 9 Nuclear matter K nm 2 d 0 E/A : binding energy per nucleon K A : incompressibility ρ : nuclear density ρ 0 : nuclear density at saturation K A is obtained from excitation 208 Pb energy of ISGMR & ISGDR K A =0.64 K nm - 3.5 J.P. Blaizot, NPA591, 435 (1995) 20 Osaka, Japan; 16-19 November 2015
From GMR data on 208 Pb and 90 Zr, K = 240 10 MeV [ 20 MeV] [See, e.g ., G. Colò et al ., Phys. Rev. C 70 (2004) 024307] This number is consistent with both ISGMR and ISGDR Data and with non-relativistic and relativistic calculations 21 Osaka, Japan; 16-19 November 2015
Isoscalar GMR strength distribution in Sn-isotopes obtained by Multipole Decomposition Analysis of singles spectra obtained in A Sn( , ) measurements at incident energy 400 MeV and angles from 0º to 9º T. Li et al ., Phys. Rev. Lett. 99, 162503 (2007) 22 Osaka, Japan; 16-19 November 2015
K A = K vol + K surf A 1/3 + K sym (( N Z )/ A ) 2 + K coul Z 2 A 4/3 K A ~ K vol (1 + c A -1/3 ) + K t (( N - Z )/ A ) 2 + K Coul Z 2 A -4/3 K A - K Coul Z 2 A -4/3 ~ K vol (1 + c A -1/3 ) + K t (( N - Z )/ A ) 2 ~ Constant + K t (( N - Z )/ A ) 2 We use K Coul - 5.2 MeV (from Sagawa) ( N - Z ) / A 112 Sn – 124 Sn: 0.107 – 0.194 23 Osaka, Japan; 16-19 November 2015
K t 550 100 MeV 24 Osaka, Japan; 16-19 November 2015
555 75 MeV K t D. Patel et al ., Phys. Lett. B 718, 447 (2012) 25 Osaka, Japan; 16-19 November 2015
RPA [ K = 240 MeV]; RRPA FSUGold [ K = 230 MeV]; RMF (DD-ME2) [ K = 240 MeV]; ( QTBA) (T5 Skyrme) [ K = 202 MeV] 26 Osaka, Japan; 16-19 November 2015
RRPA: FSUGold [ K = 230 MeV]; SLy5 [ K = 230 MeV]; NL3 [ K = 271 MeV] 27 Osaka, Japan; 16-19 November 2015
E. Khan, PRC 80, 011307(R) (2009) The Giant Monopole Resonances in Pb isotopes E. Khan, Phys. Rev. C 80, 057302 (2009). K = 230 K = 230 K = 216 Mutually Enhanced Magicity (MEM)? 28 Osaka, Japan; 16-19 November 2015
0 0 spectra 8000 204Pb 206Pb 208Pb 6000 Counts 4000 2000 0 10 20 30 40 E (MeV) x 29 Osaka, Japan; 16-19 November 2015
Conclusions! There has been much progress in understanding ISGMR & ISGDR macroscopic properties Systematics: E x , G , %EWSR K nm 240 MeV K t 500 MeV Sn and Cd nuclei are softer than 208 Pb and 90 Zr. 30 Osaka, Japan; 16-19 November 2015
Challenges with exotic beams • Inverse kinematics E x = 0 MeV E x = 30 MeV 56 Ni(α,α ) 56 Ni* 8 o 6 o 4 o α = Target 2 o E x = 20 MeV 56 Ni = Projectile • Intensity of exotic beams is very low ( 10 4 – 10 5 pps) • To get reasonable yields thick target is needed • Very low energy ( sub MeV) recoil particle will not come out of the thick target 31 Osaka, Japan; 16-19 November 2015
Nuclear structure studies with reactions in inverse kinematics - Possible at FAIR, RIKEN, GANIL, FRIB (beam energies of 50-100 MeV/u are needed!) Approach at GSI-FAIR (EXL): Helium gas-jet target Measure the recoiling alphas ( , ) 4 He target heavy projectile heavy ejectile Inconvenience: recoiling difficulty to detect the low- energy alphas 32 Osaka, Japan; 16-19 November 2015
Storage Ring Experimental storage ring at GSI Luminosity: 10 26 – 10 27 cm -2 s -1 EPJ Web of Conferences 66, 03093 (2014) 33 Osaka, Japan; 16-19 November 2015
Detection system @ FAIR EXL recoil prototype detector has been commissioned 34 Osaka, Japan; 16-19 November 2015
35 Osaka, Japan; 16-19 November 2015
36 Osaka, Japan; 16-19 November 2015
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