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

1 14-18 September 2015; Kraków, Poland

Muhsin N. Harakeh

KVI-CART, Groningen & GANIL, Caen Collective Motion of Nuclei under Extreme Conditions (COMEX 5) Kraków, Poland

COLLECTIVE EXCITATIONS OF ATOMIC NUCLEI

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ISGDR ??

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Microscopic picture: GRs are coherent (1p-1h) excitations induced by single-particle operators.

• Excitation energy depends on

i) multipole L (Lħω, since radial operator ∝ rL; except for ISGMR and ISGDR, 2ħω & 3ħω, 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.

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Microscopic structure of ISGMR & ISGDR

3ћω excitation (overtone of c.o.m. motion) Transition operators:

Overtone Spurious c.o.m. motion Constant Overtone

2ћω excitation

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Nucleus Many-body system with a finite size Vibrations Multipole expansion with r, Ylm , τ, σ

∆S=0, ∆T=0 ∆S=0, ∆T=1 ∆S=0, ∆T=1 ∆S=1, ∆T=1 ∆S=1, ∆T=1

L=0: Monopole L=1: Dipole L=2: Quadrupole L=3: Octupole ISGMR IVGMR IAS GTR IVSGMR LEOR, HEOR

r2Y0 τY0

ISGQR ISGDR

IVGDR

IVSGDR

τ r2Y0 τ σ Y0 τ σ r2Y0 r3Y1 (- 5/3‹r2›rY1) τ rY1 τσ rY1 r2Y2

IVGQR

τ r2Y2 τσ r2Y2 r3Y3

IVSGQR

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∆N = 2 E2 (ISGQR) & ∆N = 0 E0 (ISGMR) ∆N = 1 E1 (IVGDR)

IVGDR

τ rY1

ISGMR

r2Y0

ISGQR

r2Y2

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Decay of giant resonances

• Width of resonance

Γ, Γ↑ , Γ↓ (Γ↓↑ , Γ↓↓) Γ↑

• Γ↑: direct or escape width
• Γ↓ : spreading width Γ↓

Γ↓↑: pre-equilibrium, Γ↓↓: compound

• Decay measurements

⇒ Direct reflection of damping processes Allows detailed comparison with theoretical calculations

x x x

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The collective response of the nucleus Giant Resonances

Isovector Isoscalar Monopole (GMR) Dipole (GDR) Quadrupole (GQR)

Berman and Fultz, Rev. Mod. Phys. 47 (1975) 47

208Pb 120Sn 65Cu

Photo-neutron cross sections Electric giant resonances

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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)

116Sn 15.68

4.19

117Sn 15.66

5.02

118Sn 15.59

4.77

119Sn 15.53

4.81

120Sn 15.40

4.89

124Sn 15.19

4.81

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b a R Quadrupole deformation: β2= 0.275 Excitation energies: E2/E1 = 0.911η + 0.089 Where η = b/a s1/s2 = 1/2

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BBS@KVI Grand Raiden@ RCNP

(p,p′) at Ep~ 300 (α,α′) at Eα~ 400 & 200 MeV at RCNP & KVI, respectively

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• A. Tamii et al., PRL 107 (2011) 062502

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• A. Tamii et al., PRL 107 (2011) 062502

Magnetic dipole (M1) Electric dipole (E1)

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Electric dipole (E1)

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• M. Itoh

L=0 L=1 L=2 L=3 ISGMR ISGDR ISGQR ISGOR

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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

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2 2 2

) / ( 9 ρ ρ ρ ρ =       = d A E d Knm

E/A: binding energy per nucleon ρ : nuclear density ρ0 : nuclear density at saturation For the equation of state of symmetric nuclear matter at saturation nuclear density: and one can derive the incompressibility

• f nuclear matter:

) / ( = =       ρ ρ ρ d A E d

J.P. Blaizot, Phys. Rep. 64 (1980) 171

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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.

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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:

εF is the Fermi energy and the nucleus incompressibility: KA =[r2(d2(E/A)/dr2)]r =R0

J.P. Blaizot, Phys. Rep. 64 (1980) 171

2

27 7 25 3

A F ISGDR

K E m r ε + = ћ

2 ISGMR A

E r K m = ћ

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Giant resonances

• Macroscopic properties: Ex, Γ, %EWSR
• Isoscalar giant resonances; compression

modes ISGMR, ISGDR ⇒ Incompressibility, symmetry energy

KA = Kvol + Ksurf A−1/3 + Ksym((N−Z)/A)2+KCoul Z2A−4/3

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Inelastic α scattering

α particle α′ particle Nucleus, e.g. 208Pb

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ISGMR, ISGDR ISGQR, HEOR 100 % EWSR At Ex= 14.5 MeV

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ISGDR L = 1 ISGMR L = 0

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ISGQR at 10.9 MeV ISGMR at 13.9 MeV

↑ ↑

• M. N. Harakeh et al., Phys. Rev. Lett. 38, 676 (1977)

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0° < θα′ < 3° 0° < θα′ < 1.5° 1.5° < θα′ < 3° Difference Difference of spectra

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′

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Multipole decomposition analysis (MDA)

• a. ISGR (L<15)+ IVGDR (through Coulomb excitation)
• b. DWBA formalism; single folding ⇒ transition potential

fraction EWSR : ) ( section) cross (unit section cross DWBA : . ) , ( section cross al Experiment : . exp ) , ( . ) , ( ) ( . exp ) , (

. . 2 . . 2 . . 2 . . 2

E a calc L E dE d d E dE d d calc L E dE d d E a E dE d d

L m c m c m c L L m c

        Ω         Ω         Ω =         Ω

∑

ϑ σ ϑ σ ϑ σ ϑ σ

) ' ( )) ' ( |, ' (| ' ) ( ] ) ' ( )) ' ( |, ' (| ) ' ( )) ' ( |, ' (| )[ , ' ( ' ) , ( r r r r V r d r U r r r r V r r r r V E r r d E r U

L

ρ ρ ρ ρ ρ ρ δρ δ − = ∂ − ∂ + − =

∫ ∫

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Transition density

• ISGMR Satchler, Nucl. Phys. A472 (1987) 215
• ISGDR Harakeh & Dieperink, Phys. Rev. C23 (1981) 2329
• Other modes Bohr-Mottelson (BM) model

) 10 ) 3 / 25 ( 11 ( 6 ) ( )] 4 ( 3 5 10 3 [ 3 ) , (

2 2 2 4 2 2 2 1 2 2 2 2 1 1

> < − > < − > < = + + > < − + − = r r r R mAE r dr d dr d r dr d r r dr d r R E r ε π β ρ ε β δρ 

E r mA r dr d r E r > < = + − =

2 2 2

2 ) ( ] 3 [ ) , (  π α ρ α δρ

2 1 2 2 2 2 2 2 2

2 ) 2 ( ) 1 2 ( ) ( ) ( ) , ( > < > < + + = = − =

− − L L L L L L

r r mAE L L L c r dr d E r  π β δ ρ δ δρ

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(α,α′)spectra at 386 MeV

MDA results for L=0 and L=1

ISGDR ISGDR ISGDR ISGDR ISGMR ISGMR ISGMR ISGMR

Uchida et al.,

• Phys. Lett. B557 (2003) 12
• Phys. Rev. C69 (2004) 051301

116Sn

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E/A: binding energy per nucleon KA: incompressibility ρ : nuclear density ρ0 : nuclear density at saturation KA is obtained from excitation energy of ISGMR & ISGDR KA =0.64Knm- 3.5 J.P. Blaizot, NPA591 (1995) 435

208Pb

2 2 2

) / ( 9 ρ ρ ρ ρ =       = d A E d Knm

Nuclear matter

In HF+RPA calculations,

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This number is consistent with both ISGMR and ISGDR Data and with non-relativistic and relativistic calculations From GMR data on 208Pb and 90Zr, K∞ = 240 ± 10 MeV [± 20 MeV]

[See, e.g., G. Colò et al., Phys. Rev. C 70 (2004) 024307]

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Isoscalar GMR strength distribution in Sn-isotopes

• btained by Multipole

Decomposition Analysis

• f singles spectra
• btained in ASn(α,α′)

measurements at incident energy 400 MeV and angles from 0º to 9º

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KA ~ Kvol (1 + cA-1/3) + Kτ ((N - Z)/A)2 + KCoul Z2A-4/3 KA - KCoul Z2A-4/3 ~ Kvol (1 + cA-1/3) + Kτ ((N - Z)/A)2 ~ Constant + Kτ ((N - Z)/A)2 KCoul = - 5.2 MeV (from Sagawa) (N - Z)/A

112Sn – 124Sn: 0.107 – 0.194

KA = Kvol + Ksurf A−1/3 + Ksym((N−Z)/A)2+Kcoul Z2A−4/3

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Kτ = − 550 ± 100 MeV

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Colò et al.: Non-relativistic RPA (without pairing) reproduces ISGMR in 208Pb and 90Zr [K∞ = 240 MeV] Piekarewicz: Relativistic RPA (FSUGold model) reproduces g.s. observables and ISGMR in 208Pb,

144Sm and 90Zr [K∞ = 230 MeV]

Vretenar: Relativistic mean field (DD-ME2: density- dependent mean-field effective interaction). [K∞ = 240 MeV]. Tselyaev et al.: Quasi-particle time-blocking approximation (QTBA) (T5 Skyrme interaction) [K∞ = 202 MeV?!]

Softness of Sn and Cd nuclei (compared to 208Pb and 90Zr) is still unresolved.

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Spin-isospin excitations

Neutral (ν,ν′) and charged (νe,e−), (νe ,e+) currents

NC ⇒ Inelastic electron and proton scattering

⇒ M0, M1, M2

CC ⇒ Charge-exchange reactions

Isovector charge-exchange modes ⇒ GTR, IVSGMR, IVSGDR, etc. Importance for nuclear astrophysics, ν-physics, 2β-decay, n-skin thickness, etc. (p,n), (3He,t) {GT−}; (n,p), (d,2He) & (t,3He) {GT+}

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Nucleus Many-body system with a finite size Vibrations Multipole expansion with r, Ylm , τ, σ

∆S=0, ∆T=0 ∆S=0, ∆T=1 ∆S=0, ∆T=1 ∆S=1, ∆T=1 ∆S=1, ∆T=1

L=0: Monopole L=1: Dipole L=2: Quadrupole L=3: Octupole ISGMR IVGMR IAS GTR IVSGMR LEOR, HEOR

r2Y0 τY0

ISGQR ISGDR

IVGDR

IVSGDR

τ r2Y0 τ σ Y0 τ σ r2Y0 τ rY1 τσ rY1 r2Y2

IVGQR

τ r2Y2 τσ r2Y2 r3Y3

IVSGQR (r3 - 5/3‹r2›r)Y1

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Spin-isospin excitations

• Gamow-Teller transitions;

Isospin (∆T=1) Spin (∆S=1) Advantages

• Cross section peaks at

θ° (∆L=0)

• Strong excitation of

GT states at E/A=100-500 MeV/u

∆L=0 ∆S=1 ∆T=1 GTR

p n

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Spin-flip & GT transitions

0+ GS T0 GS GS T0-1 T0+1 T0+1 T0-1 T0 T0+1 GT GT GT GT 1+ 1+ 1+ 1+ 1+ 1+ M1 M1 (N, Z) (N+1, Z-1) (N-1, Z+1) T0+1 T0

∆S=1

GT+ GT− (n,p), (d,2He), (t,3He)… … (3He,t), (p,n) (e,e′), (p,p′) difficult !

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The (3He,t) reaction at 0 degree



Cross sections at E(3He)=450 MeV, q=0 for (3He,t) reactions

• T. N. Taddeucci et al., Nucl. Phys. A469, 125 (1987)
• I. Bergqvist et al., Nucl. Phys. A469, 648 (1987)



Neutrino absorption cross sections F(Z, Ee) is the relativistic Coulomb barrier factor Importance of charge-exchange reactions at intermediate energies

2 2 2 2

( | | ( ) | | ( )) ( )

i f f D D i

k d N J B F N J B GT d k

στ

τ στ

µ µ σ π   = +   Ω   

τ

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45 14-18 September 2015; Kraków, Poland

Determination of GT+ Strength and its Astrophysical Implications

In supernova explosions, electron capture (EC) on fp-shell nuclei plays a dominant role during the last few days of a heavy star with M > 10 M Presupernova stage; deleptonization ⇒ core collapse ⇒ subsequent type IIa Supernova (SN) explosion

H.A. Bethe et al., Nucl. Phys. A324 (1979) 487

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Supernova Simulatie

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Exclusive excitations ∆S=∆T=1: (d,2He)

3S1 deuteron ⇒ 1S0 di-proton (2He) 1S0 dominates if (relative) 2-proton kinetic energy ε < 1 MeV

(n,p)-type probe with exclusive ∆S=1 character (GT+ transitions) But near 0°, tremendous background from d-breakup d

2He

A, Z A, Z-1 p p

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(d,2He) as GT+ probe in fp-shell nuclei

58Ni(d,2He)58Co E = 85 MeV/u 58Ni(n,p)58Co E = 198 MeV

• M. Hagemann et al.,

PLB 579 (2004) 251

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i

• C. Bäumer et al.,

PRC 68, 031303(R) (2003)

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51V(d,2He): Comparison with shell-model calculations

← Experimental result ← Full fp-shell model calculations quenching factor (0.74)2

• G. Martínez-Pinedo,
• K. Langanke

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Outlook

Radioactive ion beams will be available at energies where it will be possible to study ISGMR, ISGDR and GT transitions (RIKEN, NSCL, FAIR, SPIRAL2)

• Determine GT strength in unstable sd & fp shell nuclei
• Measure ISGMR and ISGDR in extended isotope chain
• Unravel the nature of the pygmy dipole resonance
• Use IV(S)GDR as tool to determine n-skin [IV(S)GDR]
• Exotic excitations such as double GT (SHARAQ)

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54 14-18 September 2015; Kraków, Poland

Nuclear structure studies with reactions in inverse kinematics

4He target

heavy projectile heavy ejectile recoiling alphas

(α,α′)

• Possible at FAIR, RIKEN and NSCL

(beam energies of 50-100 MeV/u are needed!) α′ Approach: measure the recoiling alphas Inconvenience: difficulty to detect the low- energy alphas

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EPJ Web of Conferences 66, 03093 (2014)

Experimental storage ring at GSI Luminosity: 1026 – 1027 cm-2s-1

Storage Ring

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Detection system @ FAIR

Use of EXL recoil detector prototype has been successfully tested [Nasser Kalantar talk on Tuesday afternoon]

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Marine Vandebrouck talk on Tuesday afternoon

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Than hank yo you u fo for yo your ur at attentio ion

• Pygmy Dipole Resonance (PDR): Tuesday morning
• IVGMR: Tuesday afternoon (Remco Zegers)
• Anti-analogue GDR and n-skin:

Tuesday afternoon (Attila Krasznahorkay)

• Hot IVGDR: Wednesday morning

Etc.