COLLECTIVE EXCITATIONS OF ATOMIC NUCLEI Muhsin N. Harakeh - PowerPoint PPT Presentation

COLLECTIVE EXCITATIONS OF ATOMIC NUCLEI Muhsin N. Harakeh KVI-CART, Groningen & GANIL, Caen Collective Motion of Nuclei under Extreme Conditions (COMEX 5) Kraków, Poland 1 14-18 September 2015; Kraków, Poland

ISGDR ?? 2 14-18 September 2015; Kraków, Poland

Microscopic picture: GRs are coherent (1p-1h) excitations induced by single-particle operators.  Excitation energy depends on i ) multipole L ( L ħ ω , since radial operator ∝ r L ; except for ISGMR and ISGDR, 2 ħ ω & 3 ħ ω , respectively), ii ) strength of effective interaction and iii ) collectivity.  Exhaust appreciable % of EWSR  Acquire a width due to coupling to continuum and to underlying 2p-2h configurations. 3 14-18 September 2015; Kraków, Poland

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) 4 14-18 September 2015; Kraków, Poland

Nucleus Many-body system with a finite size Multipole expansion with r, Y lm , τ, σ Vibrations ∆ S=1, ∆ T=1 ∆ S=0, ∆ T=0 ∆ S=0, ∆ T=1 ∆ S=1, ∆ T=1 ∆ S=0, ∆ T=1 L=0: Monopole ISGMR IAS IVGMR GTR IVSGMR τ Y 0 τ r 2 Y 0 τ σ Y 0 τ σ r 2 Y 0 r 2 Y 0 IVSGDR L=1: Dipole IVGDR ISGDR τ rY 1 τσ rY 1 r 3 Y 1 (- 5/3‹r 2 ›rY 1 ) L=2: Quadrupole IVGQR IVSGQR ISGQR τ r 2 Y 2 τσ r 2 Y 2 r 2 Y 2 L=3: Octupole LEOR, HEOR r 3 Y 3 5 14-18 September 2015; Kraków, Poland

IVGDR τ rY 1 ∆ N = 1 E1 (IVGDR) ∆ N = 2 E2 (ISGQR) & ∆ N = 0 E0 (ISGMR) ISGMR ISGQR r 2 Y 0 r 2 Y 2 6 14-18 September 2015; Kraków, Poland

Decay of giant resonances  Width of resonance x Γ, Γ ↑ , Γ ↓ (Γ ↓↑ , Γ ↓↓ ) Γ ↑  Γ ↑ : direct or escape width  Γ ↓ : spreading width Γ ↓ x x Γ ↓↑ : pre- equilibrium, Γ ↓↓ : compound  Decay measurements ⇒ Direct reflection of damping processes Allows detailed comparison with theoretical calculations 7 14-18 September 2015; Kraków, Poland

The collective response of the nucleus Giant Resonances Electric giant resonances Photo-neutron cross sections Isoscalar Isovector 65 Cu Monopole (GMR) Berman and Fultz, Rev. Mod. Phys. 47 (1975) 120 Sn Dipole (GDR) 208 Pb Quadrupole (GQR) 47 8 14-18 September 2015; Kraków, Poland

Measurement of the giant dipole resonance with mono-energetic photons B.L. Berman and S.C. Fultz Rev. Mod. Phys. 47 (1975) 713 Nucleus Centroid Width (MeV) (MeV) 116 Sn 15.68 4.19 117 Sn 15.66 5.02 118 Sn 15.59 4.77 119 Sn 15.53 4.81 120 Sn 15.40 4.89 124 Sn 15.19 4.81 9 14-18 September 2015; Kraków, Poland

a b Quadrupole deformation: β 2 = 0.275 Excitation energies: E 2 /E 1 = 0.911 η + 0.089 Where η = b/a s 1 /s 2 = 1/2 R 10 14-18 September 2015; Kraków, Poland

Grand Raiden@ RCNP ( p , p ′ ) at E p ~ 300 ( α , α′ ) at E α ~ 400 & 200 MeV at RCNP & KVI, respectively BBS@KVI 11 14-18 September 2015; Kraków, Poland

A. Tamii et al ., PRL 107 (2011) 062502 12 14-18 September 2015; Kraków, Poland

Magnetic dipole (M1) Electric dipole (E1) A. Tamii et al ., PRL 107 (2011) 062502 13 14-18 September 2015; Kraków, Poland

Electric dipole (E1) 14 14-18 September 2015; Kraków, Poland

L =0 L =1 ISGMR ISGDR M. Itoh L =3 L =2 ISGQR ISGOR 15 14-18 September 2015; Kraków, Poland

In fluid mechanics, compressibility is a measure of the relative volume change of a fluid as a response to a pressure change. 1 ∂ V β = − −  V ∂ P where P is pressure, V is volume. Incompressibility or bulk modulus ( K ) is a measure of a substance's resistance to uniform compression and can be formally defined: ∂ P K = − V  ∂ V 16 14-18 September 2015; Kraków, Poland

For the equation of state of symmetric nuclear matter at saturation nuclear density:   ( / ) d E A = 0   ρ   d ρ = ρ 0 and one can derive the incompressibility of nuclear matter:   2 ( / ) d E A = ρ 2  9  K nm ρ 2   d ρ = ρ 0 E/A : binding energy per nucleon ρ : nuclear density J.P. Blaizot, Phys. Rep. 64 (1980) 171 ρ 0 : nuclear density at saturation 17 14-18 September 2015; Kraków, Poland

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. 18 14-18 September 2015; Kraków, Poland

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 + ε K 7 A F = ћ 25 E ISGDR 2 3 m r ε 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 19 14-18 September 2015; Kraków, Poland

Giant resonances  Macroscopic properties: E x , Γ , %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 20 14-18 September 2015; Kraków, Poland

21 14-18 September 2015; Kraków, Poland

α′ particle α particle Nucleus, e.g. 208 Pb Inelastic α scattering 22 14-18 September 2015; Kraków, Poland

ISGMR, ISGDR ISGQR, HEOR 100 % EWSR At E x = 14.5 MeV 23 14-18 September 2015; Kraków, Poland

ISGMR L = 0 ISGDR L = 1 24 14-18 September 2015; Kraków, Poland

25 14-18 September 2015; Kraków, Poland

M. N. Harakeh et al. , Phys. Rev. Lett. 38, 676 (1977) ISGQR at 10.9 MeV ISGMR at 13.9 MeV ↑ ↑ 26 14-18 September 2015; Kraków, Poland

Difference of spectra 0° < θ α ′ < 3° 0° < θ α ′ < 1.5° 1.5° < θ α ′ < 3° Difference 27 14-18 September 2015; Kraków, Poland

′ 28 14-18 September 2015; Kraków, Poland

Multipole decomposition analysis (MDA) exp . . calc     σ σ 2 2 d ∑ d     ϑ = ϑ ( , ) ( ) ( , ) E a E E     Ω Ω . . . . c m L c m     d dE d dE L L exp .   σ 2 d   ϑ ( , ) : Experiment al cross section E   Ω . . c m   d dE . calc   σ 2 d   ϑ ( , ) : DWBA cross section (unit cross section) E   Ω . . 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 ∂ − ρ (| ' |, ( ' )) V r r r ∫ δ = δρ − ρ + ρ ( , ) ' ( ' , )[ (| ' |, ( ' )) ( ' ) ] U r E d r r E V r r r r 0 0 ∂ ρ L ( ' ) r 0 ∫ = − ρ ρ ( ) ' (| ' |, ( ' )) ( ' ) U r d r V r r r r 0 0 29 14-18 September 2015; Kraków, Poland

Transition density  ISGMR Satchler, Nucl. Phys. A472 (1987) 215 d δρ = − α + ρ ( , ) [ 3 ] ( ) r E r r 0 0 0 dr π 2  2 α = 2 0 < > 2 mA r E  ISGDR Harakeh & Dieperink, Phys. Rev. C23 (1981) 2329 β 2 5 d d d d δρ = − + − < > + ε + ρ 2 2 1 ( , ) [ 3 10 ( 4 )] ( ) r E r r r r r 1 0 2 3 dr dr dr dr 3 R π 2 2  6 R β = 2 < > − < > − ε < > 1 4 2 2 2 ( 11 ( 25 / 3 ) 10 ) mAE r r r  Other modes Bohr-Mottelson (BM) model d δρ = − δ ρ ( , ) ( ) r E r 0 L L dr − + π < > 2 2 2 2 L ( 2 1 ) 2  L L r δ = β = 2 2 ( ) c + < − > L L 2 1 2 L ( 2 ) L mAE r 30 14-18 September 2015; Kraków, Poland

Uchida et al ., Phys. Lett. B557 (2003) 12 Phys. Rev. C69 (2004) 051301 116 Sn ( α,α′ )spectra at 386 MeV ISGDR ISGDR MDA results for L=0 and L=1 ISGMR ISGMR ISGDR ISGDR ISGMR ISGMR 31 14-18 September 2015; Kraków, Poland

In HF+RPA calculations,   2 ( / ) d E A = ρ 2  9  Nuclear matter K nm ρ 2   d ρ = ρ 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 (1995) 435 32 14-18 September 2015; Kraków, Poland

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 33 14-18 September 2015; Kraków, Poland