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Giant resonances in the Skyrme-Hartree-Fock theory P .G. Reinhard Institut fr Theoretische Physik II Universitt Erlangen-Nrnberg COMEX05, Krakow 2015 P .G. Reinhard (Inst.Theor.Physik, Erlangen) Giant resonances in the

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Giant resonances in the Skyrme-Hartree-Fock theory

P .–G. Reinhard

Institut für Theoretische Physik II Universität Erlangen-Nürnberg

COMEX05, Krakow 2015

P .–G. Reinhard (Inst.Theor.Physik, Erlangen) Giant resonances in the Skyrme-Hartree-Fock theory COMEX05, Krakow 2015 1 / 36

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Acknowledgements

Collaborators:

  • W. Nazarewicz, B. Schütrumpf

MSU East Lansing

  • J. Erler, P

. Klüpfel formerly Univ. Erlangen

  • J. Dobaczewski

York (UK), Jyväskyla

  • J. A. Maruhn

Frankfurt P . Stevenson Surrey

  • V. Nesterenko, W. Kleinig

Dubna

  • J. Speth, S. Krewald

Jülich

  • N. Lyutorivich, V. Tselyaev
  • St. Petersburg

Support: BMBF contract 05P12RFFTG, DFG Re-322/12-1

P .–G. Reinhard (Inst.Theor.Physik, Erlangen) Giant resonances in the Skyrme-Hartree-Fock theory COMEX05, Krakow 2015 2 / 36

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Outline

1

Formal framework The Skyrme energy-density functional Observables Optimization of model parameters by least-squares fits

2

Results RPA: convergence and 2ph effects Giant resonances and nuclear matter parameters (NMP) GDR – trends with mass number Isovector dipole strength at low E

3

Conclusions

P .–G. Reinhard (Inst.Theor.Physik, Erlangen) Giant resonances in the Skyrme-Hartree-Fock theory COMEX05, Krakow 2015 3 / 36

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Formal framework

P .–G. Reinhard (Inst.Theor.Physik, Erlangen) Giant resonances in the Skyrme-Hartree-Fock theory COMEX05, Krakow 2015 4 / 36

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The Skyrme energy-density functional (here only time even densities)

Etot =

  • d3r ESkyrme(ρ, τ, J)

✻

1 2B0

ρ2 +

1 2B′

˜ ρ2 +

1 2B3 ρ2+α

+

1 2B′ 3

˜ ρ2ρα + B1 ρτ + B′

1

˜ ρ˜ τ +

1 2B2 (∇ρ)2

+

1 2B′ 2 (∇˜

ρ)2 +

1 2B4

ρ∇J +

1 2B′ 4

˜ ρ∇˜ J isoscalar isovector density ρ(r) =

α v 2 α|ϕα|2

kinetic density τ(r) =

α v 2 α|∇ϕα|2

spin-orbit dens. J(r) = −i

α v 2 αϕ† α∇×σϕα

total & difference ρ = ρn + ρp

  • isoscalar

, ˜ ρ = ρn − ρp

  • isovector

P .–G. Reinhard (Inst.Theor.Physik, Erlangen) Giant resonances in the Skyrme-Hartree-Fock theory COMEX05, Krakow 2015 5 / 36

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The Skyrme energy-density functional (here only time even densities)

Etot = Ekin +

  • d3r ESkyrme(ρ, τ, J) +
  • d3r Epair(χ, ρ) + ECoul − Ecorr✛

correlations from low energy modes: c.m., rotation, vibrat.

✻

Coulomb en.

(exchange = Slater appr.)

✻

  • α

(ϕα|ˆ p2|ϕα) 2mN kinetic energy

✻

  • V pair

p

χ2

p + V pair n

χ2

n

1 − ρ ρpair

  • pairing functional
  • nly surface effects

to define open shell nuclei

✻

1 2B0

ρ2 +

1 2B′

˜ ρ2 +

1 2B3 ρ2+α

+

1 2B′ 3

˜ ρ2ρα + B1 ρτ + B′

1

˜ ρ˜ τ +

1 2B2 (∇ρ)2

+

1 2B′ 2 (∇˜

ρ)2 +

1 2B4

ρ∇J +

1 2B′ 4

˜ ρ∇˜ J isoscalar isovector density ρ(r) =

α v 2 α|ϕα|2

kinetic density τ(r) =

α v 2 α|∇ϕα|2

spin-orbit dens. J(r) = −i

α v 2 αϕ† α∇×σϕα

total & difference ρ = ρn + ρp

  • isoscalar

, ˜ ρ = ρn − ρp

  • isovector

P .–G. Reinhard (Inst.Theor.Physik, Erlangen) Giant resonances in the Skyrme-Hartree-Fock theory COMEX05, Krakow 2015 5 / 36

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The Skyrme energy-density functional (here only time even densities)

Etot = Ekin +

  • d3r ESkyrme(ρ, τ, J) +
  • d3r Epair(χ, ρ) + ECoul − Ecorr✛

correlations from low energy modes: c.m., rotation, vibrat.

✻

Coulomb en.

(exchange = Slater appr.)

✻

  • α

(ϕα|ˆ p2|ϕα) 2mN kinetic energy

✻

  • V pair

p

χ2

p + V pair n

χ2

n

1 − ρ ρpair

  • pairing functional
  • nly surface effects

to define open shell nuclei

✻

1 2B0

ρ2 +

1 2B′

˜ ρ2 +

1 2B3 ρ2+α

+

1 2B′ 3

˜ ρ2ρα + B1 ρτ + B′

1

˜ ρ˜ τ +

1 2B2 (∇ρ)2

+

1 2B′ 2 (∇˜

ρ)2 +

1 2B4

ρ∇J +

1 2B′ 4

˜ ρ∇˜ J isoscalar isovector density ρ(r) =

α v 2 α|ϕα|2

kinetic density τ(r) =

α v 2 α|∇ϕα|2

spin-orbit dens. J(r) = −i

α v 2 αϕ† α∇×σϕα

pair density χ(r) =

α uαvα|ϕα|2

pairing amplit. uα, vα total & difference ρ = ρn + ρp

  • isoscalar

, ˜ ρ = ρn − ρp

  • isovector

free parameters: B0, B′

0, B1, B′ 1, B2, B′ 2, B3, B′ 3, α,

  • ↔ nuclear matter parameters (NMP)

B4, B′

4, V pair p

, V pair

n

, ρpair

P .–G. Reinhard (Inst.Theor.Physik, Erlangen) Giant resonances in the Skyrme-Hartree-Fock theory COMEX05, Krakow 2015 5 / 36

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Observables

P .–G. Reinhard (Inst.Theor.Physik, Erlangen) Giant resonances in the Skyrme-Hartree-Fock theory COMEX05, Krakow 2015 6 / 36

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The nuclear matter parameters (NMP)

given E/A(ρ) = energy per particle in symmetric nuclear matter (ρ = total density) this allows to define basic properties at equilibrium: E/Aeq binding energy per particle at equilibrium point ρeq equilibrium density K = 9ρ2

0∂2 ρ

E A incompressibility (isoscalar static response) m∗ m effective mass (isoscalar dynamic response) J symmetry energy (isovector static response) L = 3ρ0∂ρasym slope of symmetry energy κTRK TRK sum rule enhancement ↔ isovector

m∗

1

m (dynamic response)

asurf surface energy asurf,sym surface symmetry energy these 9 NMP are equivalent to parameters of SHF functional (except l*s & pairing)

P .–G. Reinhard (Inst.Theor.Physik, Erlangen) Giant resonances in the Skyrme-Hartree-Fock theory COMEX05, Krakow 2015 7 / 36

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Ground state properties in the pool of fit data

82 50 28 20 126 82 50 28 20 proton number Z neutron number N full weight reduced weight

large span in mass nmber A sufficient isoscalar information ↔

  • nly weak

isovector ↔ information N−Z direction semi−magic nuclei: spherical

O O ∆

adopted errors from expected correlation effects small correlations smallest correlation effects ↔ "long" chains in nonetheless:

+ _ + _ + _ + _ 1MeV 0.02 fm 0.04 fm 0.04 fm pairing (even−odd stagg.) l*s in doubly magic diffraction radius surface thickness EB r R σ binding energy r.m.s. radius Fit Observables:

P .–G. Reinhard (Inst.Theor.Physik, Erlangen) Giant resonances in the Skyrme-Hartree-Fock theory COMEX05, Krakow 2015 8 / 36

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Further observables

Response properties in 208Pb giant resonances: monopole (GMR), quadrupole (GQR), dipole (GDR) dipole polarizability αD = ∞ dω SD(ω) ω−1 in 208Pb Other: neutron skin rn − rp in 208Pb neutron “equation of state” (EoS) E/Nneut(ρ) binding energy EB for exotic nuclei (super-heavy 120/182; neutron rich 148Sn)

P .–G. Reinhard (Inst.Theor.Physik, Erlangen) Giant resonances in the Skyrme-Hartree-Fock theory COMEX05, Krakow 2015 9 / 36

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Description of excitation spectra ↔ RPA and beyond

RPA: small amplitude limit of time-dependent Hartree-Fock eigenmodes = optimized 1ph excitation operators ˆ C†

N = ν bν ˆ

Aν ˆ Aν ∈

  • ˆ

a†ˆ a, ˆ aˆ a†

  • E <30 MeV

, r L+nYLM, jL(qr)YLM, [ˆ H, r L+nYLM], [ˆ H, jL(qr)YLM]

  • global couplings, high E

RPA equations from variational formulation: δb∗

ν

[ˆ CN, [ˆ H, ˆ C†

N]]

[ˆ CN, ˆ C†

N]

= 0 numerically handled by commutator algebra on the grid

P .–G. Reinhard (Inst.Theor.Physik, Erlangen) Giant resonances in the Skyrme-Hartree-Fock theory COMEX05, Krakow 2015 10 / 36

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Description of excitation spectra ↔ RPA and beyond

RPA: small amplitude limit of time-dependent Hartree-Fock eigenmodes = optimized 1ph excitation operators ˆ C†

N = ν bν ˆ

Aν ˆ Aν ∈

  • ˆ

a†ˆ a, ˆ aˆ a†

  • E <30 MeV

, r L+nYLM, jL(qr)YLM, [ˆ H, r L+nYLM], [ˆ H, jL(qr)YLM]

  • global couplings, high E

RPA equations from variational formulation: δb∗

ν

[ˆ CN, [ˆ H, ˆ C†

N]]

[ˆ CN, ˆ C†

N]

= 0 numerically handled by commutator algebra on the grid +phonons: couple basis states ˆ Aν to few low-lying & strong ˆ C†

S

basis of 1ph & 2ph operators: ˜ C†

˜ N = ν bν ˆ

Aν +

ν,S bν,S ˆ

Aν ˆ C†

S

approximations: residual interaction ˆ Vres from RPA (?: 1ph-1ph used for 1p1p-1ph) exchange terms in ˆ Vres neglected (?: Pauli principle)

P .–G. Reinhard (Inst.Theor.Physik, Erlangen) Giant resonances in the Skyrme-Hartree-Fock theory COMEX05, Krakow 2015 10 / 36

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Optimization of model parameters

P .–G. Reinhard (Inst.Theor.Physik, Erlangen) Giant resonances in the Skyrme-Hartree-Fock theory COMEX05, Krakow 2015 11 / 36

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Optimization of model parameters

model: SHF

parameters: p = (p1...pF) ✲ predicted

  • bservables:

A = ˆ A = A(p) ✲ fit observables: Of = Of(p)

f = 1...Ndata labels fit data

✻

  • exp. fit data: Oexp

f

❄ ✻

χ2(p) =

Ndata

  • f=1
  • Of(p) − Oexp

f

2 ∆O2

f

adopted error ∆Of : χ2(p0) = Ndata−Nparams

✻

least squares error χ2(p)

✛ ❄

feedback to minimize

χ2(p) → χ2(p0)

P .–G. Reinhard (Inst.Theor.Physik, Erlangen) Giant resonances in the Skyrme-Hartree-Fock theory COMEX05, Krakow 2015 12 / 36

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Optimization of model parameters

model: SHF

parameters: p = (p1...pF) ✲ predicted

  • bservables:

A = ˆ A = A(p) ✲ fit observables: Of = Of(p) ✻

  • exp. fit data: Oexp

f

❄ ✻

least squares error χ2(p)

✛ ❄

feedback to minimize

χ2(p) → χ2(p0) error on fit obs.: ∆Of uncertainties: ∆p uncertainties: ∆A mixed variance: ∆2(AB) covariance: cAB = ∆2(AB) ∆A∆B cAB = 1 ↔ highly correlated cAB = 0 ↔ uncorrelated

❅ ❅ ❅ ❅ ❅ ❅ ■

  • ✲

✲

probability for parameters p: W(p) ∝ e−χ2(p)

P .–G. Reinhard (Inst.Theor.Physik, Erlangen) Giant resonances in the Skyrme-Hartree-Fock theory COMEX05, Krakow 2015 12 / 36

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Optimization of model parameters

model: SHF

parameters: p = (p1...pF) ✲ predicted

  • bservables:

A = ˆ A = A(p) ✲ fit observables: Of = Of(p) ✻

  • exp. fit data: Oexp

f

❄ ✻

least squares error χ2(p)

✛ ❄

feedback to minimize

χ2(p) → χ2(p0) error on fit obs.: ∆Of uncertainties: ∆p uncertainties: ∆A mixed variance: ∆2(AB) covariance: cAB = ∆2(AB) ∆A∆B cAB = 1 ↔ highly correlated cAB = 0 ↔ uncorrelated

❅ ❅ ❅ ❅ ❅ ❅ ■

  • ✲

✲

probability for parameters p: W(p) ∝ e−χ2(p) fit to g.s. data only = SV-min , fit to g.s. data + NMP = SV-bas

P .–G. Reinhard (Inst.Theor.Physik, Erlangen) Giant resonances in the Skyrme-Hartree-Fock theory COMEX05, Krakow 2015 12 / 36

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Results

P .–G. Reinhard (Inst.Theor.Physik, Erlangen) Giant resonances in the Skyrme-Hartree-Fock theory COMEX05, Krakow 2015 13 / 36

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RPA: convergence and 2ph effects

P .–G. Reinhard (Inst.Theor.Physik, Erlangen) Giant resonances in the Skyrme-Hartree-Fock theory COMEX05, Krakow 2015 14 / 36

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RPA phase space – example isoscalar quadrupole (L=2,T=0)

4 5 6 7 8 9 10 11 12 13 L=2,T=0 strength energy [MeV]

isoscalar quadrupole

208Pb, SV-bas

exact on grid Emax=300 MeV Emax=30 MeV 4.2 4.3 4.4 4.5 4.6 10.5 11 11.5 12 basis up to Emax ≈ 100 MeV suffices for giant resonances low-lying 2+ states more demanding

P .–G. Reinhard (Inst.Theor.Physik, Erlangen) Giant resonances in the Skyrme-Hartree-Fock theory COMEX05, Krakow 2015 15 / 36

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Giant dipole resonance (GDR) – collisional width 10 12 14 16 18 20 22 photo-abs. strength energy [MeV]

GDR SV-bas

exp. RPA, fine RPA+phonons RPA, E-dep.

RPA, fine: folding 0.2 MeV + escape width ⇒ proper region, unrealistic profile RPA+phonons: perfect peak position, perfect profile ↔ proper smoothing RPA, E-dep.: E-dependend folding width ⇒ acceptable model for collisional width

P .–G. Reinhard (Inst.Theor.Physik, Erlangen) Giant resonances in the Skyrme-Hartree-Fock theory COMEX05, Krakow 2015 16 / 36

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Isoscalar giant resonances (GMR & GQR) – phonon coupling

10 11 12 13 14 15 16 17 energy [MeV]

isoscalar monopole

RPA+phonons RPA exp 4 6 8 10 12 14 energy [MeV]

isoscalar quadrupole

208Pb

SV-bas

width again well reproduced by E-dependent folding phonon coupling ⇒ some downshift of centroid: L=0&2 ↔ ≈ −0.5MeV = ⇒ point not yet settled, remains open (uncertainty 0.5MeV) − → continue with RPA

P .–G. Reinhard (Inst.Theor.Physik, Erlangen) Giant resonances in the Skyrme-Hartree-Fock theory COMEX05, Krakow 2015 17 / 36

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Giant resonances and nuclear matter parameters (NMP)

P .–G. Reinhard (Inst.Theor.Physik, Erlangen) Giant resonances in the Skyrme-Hartree-Fock theory COMEX05, Krakow 2015 18 / 36

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SLIDE 24

GDR – predictions from Skymre forces 8 10 12 14 16 18 20 photo-abs. strength energy [MeV]

GDR

various forces exp. SV-bas SLy6 SkI3

take Skyrme forces with about the same quality for ground states = ⇒ very different predictions for giant resonances, particularly for GDR ← → dynamic response not well determined by ground state data = ⇒ use response properties to tune loosely fixed aspects of the SHF functional

P .–G. Reinhard (Inst.Theor.Physik, Erlangen) Giant resonances in the Skyrme-Hartree-Fock theory COMEX05, Krakow 2015 19 / 36

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Giant resonances and NMP – trend analysis

11 12 13 14 15 220 230 240 GR [MeV], αD [fm2/MeV]

  • incompr. K [MeV]

SV-min GMR GQR GDR αD 0.7 0.8 0.9 1

  • eff. mass m*/m

SV-min 28 30 32 34 symmetry en. J [MeV] SV-min 0.2 0.4 0.6 TRK enhanc. κTRK SV-min

horizontal error bars ↔ uncertainties on NMP from fit to g.s. data only (SV-min) each NMP is particularly sensitive to one response property (in 208Pb): K ↔ GMR – m∗/m ↔ GQR – κTRK ↔ GDR – J ↔ αD = ⇒ tune NMP to basic response properties (GMR, GQR, GDR, αD) = ⇒ fit to g.s. data & with 4 fixed response properties (SV-bas) = ⇒ SV-bas accomodates more properties without sacrifices in quality on g.s. data

P .–G. Reinhard (Inst.Theor.Physik, Erlangen) Giant resonances in the Skyrme-Hartree-Fock theory COMEX05, Krakow 2015 20 / 36

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Giant resonances and NMP – covariance analysis

SV-min

K GMR(208Pb) m*/m GQR(208Pb) κTRK GDR(208Pb) J L d/dρE/Aneut αD(208Pb) n.skin(208Pb) EB(148Sn) EB(120/182) Qα(120/182) K GMR(208Pb) m*/m GQR(208Pb) κTRK GDR(208Pb) J L d/dρE/Aneut αD(208Pb) n.skin(208Pb) EB(148Sn) EB(120/182) Qα(120/182) 0.2 0.4 0.6 0.8 1 correlation

exotic nuclei static isovector dynamic isovector dynamic isoscalar static isoscalar = ⇒ covariances confirm 1:1 correspondence: NMP ↔ giant resonances & αD

P .–G. Reinhard (Inst.Theor.Physik, Erlangen) Giant resonances in the Skyrme-Hartree-Fock theory COMEX05, Krakow 2015 21 / 36

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SLIDE 27

Consequences for extrapolation to neutron matter

5 10 15 20 25 0.05 0.1 0.15 0.2 E/Nneut [MeV] neutron density ρneut [fm-3] SV-min (g.s. data only) SV-bas (g.s. + NMP)

information on response properties reduces uncertainty in extrapolations for neutron equation-of-state particularly important: symmetry energy J

P .–G. Reinhard (Inst.Theor.Physik, Erlangen) Giant resonances in the Skyrme-Hartree-Fock theory COMEX05, Krakow 2015 22 / 36

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Dipole polarizability αD as criterion

SHF DD−PC DD−ME FSU

  • system. varied J

new high quality data for αD: comparison 208Pb ↔ 120Sn ⇒ probe A-dependence of static isovector response generate sets of forces with varied J for SHF and RMF (DD-PC, DD-ME, FSU) ⇒ SHF: fits “allowed” box FSU: excluded by data DD-ME: excluded by data DD-PC: at the edge

P .–G. Reinhard (Inst.Theor.Physik, Erlangen) Giant resonances in the Skyrme-Hartree-Fock theory COMEX05, Krakow 2015 23 / 36

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GDR – problem with light nuclei

P .–G. Reinhard (Inst.Theor.Physik, Erlangen) Giant resonances in the Skyrme-Hartree-Fock theory COMEX05, Krakow 2015 24 / 36

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SLIDE 30

GDR in 16O

10 15 20 25 30 35 photo-abs. strength excitation energy [MeV]

16O

GDR SV-bas RPA exp.

RPA from SHF yields too low GDR energy ↔ general problem for all SHF forces

P .–G. Reinhard (Inst.Theor.Physik, Erlangen) Giant resonances in the Skyrme-Hartree-Fock theory COMEX05, Krakow 2015 25 / 36

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GDR – trends with mass number

26 28 30 32 34 36 38 40 42 0.15 0.2 0.25 0.3 0.35 EGDR *A1/6 [MeV] R-1 [fm-1]

O Pb full RPA

SkM* SLy6 exp. 0.15 0.2 0.25 0.3 0.35 R-1 [fm-1]

O Pb TRK sum rule

SkM* TRK SLy6 TRK exp.

  • exp. = trend of GDR peaks ∝ A−1/6

← → RPA = trend ∝ A−1/3 for all forces = ⇒ principle problem with density dep. of symmetry energy J(ρ) or with κTRK(ρ) ← → more flexible density dependence in SHF functional ? (↔ calibrate to αD(A)?) noteworthy: TRK sum-rule has trend ∝ A−1/6 like experiment ↔ meaning ?

P .–G. Reinhard (Inst.Theor.Physik, Erlangen) Giant resonances in the Skyrme-Hartree-Fock theory COMEX05, Krakow 2015 26 / 36

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SLIDE 32

Isovector dipole strength at low E

P .–G. Reinhard (Inst.Theor.Physik, Erlangen) Giant resonances in the Skyrme-Hartree-Fock theory COMEX05, Krakow 2015 27 / 36

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SLIDE 33

Dipole strength distribution in 208Pb

2 4 6 8 10 6 8 10 12 14 16 dipole strength [arb.units] excitation energy [MeV]

208Pb

SV-bas RPA strength 1 ph strenght/10

collective shift 1ph dipole strength gathers in narrow energy band looks "resonance like" but is composed of several different 1ph states RPA dipole strength collected in resonance peak (and somewhat fragmented to 1ph ...) pygmy strength = "debris" from RPA recoupling reflects to a large extend the original 1ph structure

P .–G. Reinhard (Inst.Theor.Physik, Erlangen) Giant resonances in the Skyrme-Hartree-Fock theory COMEX05, Krakow 2015 28 / 36

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SLIDE 34

Detailed information ← → transition formfactor

transition density: ρ0→N(r) = ΦN|ˆ ρ(r)|Φ0 ← → shows where transition is located transition formfactor: F0→N(q) =

  • d3r eiq·r ρ0→N(r)

← → shows preferred momentum transfer in spherical nuclei sorting with respect to angular momentum L, M: F (LM)

0→N(q) =

  • d3r jL(qr)YLM(Ωr) ρ0→N(r) = ΦN|jL(qr)YLM(Ωr)|Φ0

dipole momentum recovered in the limit q → 0: D(M)

0→N ∝ limq→0 F (1M) 0→N(q)

P .–G. Reinhard (Inst.Theor.Physik, Erlangen) Giant resonances in the Skyrme-Hartree-Fock theory COMEX05, Krakow 2015 29 / 36

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SLIDE 35

Transition formfactor for isoscalar & isovector dipole modes

✲ ✲

low-lying isovector dipoles driven by low-lying isoscalar modes (toroidal, compressional dipole)

P .–G. Reinhard (Inst.Theor.Physik, Erlangen) Giant resonances in the Skyrme-Hartree-Fock theory COMEX05, Krakow 2015 30 / 36

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SLIDE 36

Velocity map of isoscalar toroidal mode at 8.7 MeV

P .–G. Reinhard (Inst.Theor.Physik, Erlangen) Giant resonances in the Skyrme-Hartree-Fock theory COMEX05, Krakow 2015 31 / 36

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SLIDE 37

Conclusions

P .–G. Reinhard (Inst.Theor.Physik, Erlangen) Giant resonances in the Skyrme-Hartree-Fock theory COMEX05, Krakow 2015 32 / 36

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SLIDE 38

Conclusions

Description of excitations (giant resonances etc): RPA: commutator algebra, flexible basis expansion (1ph & local operators) basis up to Emax ≈ 100 MeV for GR, more for low 2+ +phonons: “phonons” = few low-lying RPA states with large strength collisional broadening ↔ can be simulated by E-dep. folding slight down-shift of GMR&GQR ↔ yet open details

P .–G. Reinhard (Inst.Theor.Physik, Erlangen) Giant resonances in the Skyrme-Hartree-Fock theory COMEX05, Krakow 2015 32 / 36

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SLIDE 39

Conclusions

Description of excitations (giant resonances etc): RPA: commutator algebra, flexible basis expansion (1ph & local operators) basis up to Emax ≈ 100 MeV for GR, more for low 2+ +phonons: “phonons” = few low-lying RPA states with large strength collisional broadening ↔ can be simulated by E-dep. folding slight down-shift of GMR&GQR ↔ yet open details Giant resonances ↔ nuclear matter parameters (NMP): trends with NMP & covariances = ⇒ nearly 1:1 correlation: K ↔ GMR – m∗/m ↔ GQR – κTRK ↔ GDR – J ↔ αD fits to g.s. data leaves uncertainty on NMP and giant resonances (& αD) fits leave also leeway ⇒ response properties can be accomodated

P .–G. Reinhard (Inst.Theor.Physik, Erlangen) Giant resonances in the Skyrme-Hartree-Fock theory COMEX05, Krakow 2015 32 / 36

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SLIDE 40

Conclusions

Description of excitations (giant resonances etc): RPA: commutator algebra, flexible basis expansion (1ph & local operators) basis up to Emax ≈ 100 MeV for GR, more for low 2+ +phonons: “phonons” = few low-lying RPA states with large strength collisional broadening ↔ can be simulated by E-dep. folding slight down-shift of GMR&GQR ↔ yet open details Giant resonances ↔ nuclear matter parameters (NMP): trends with NMP & covariances = ⇒ nearly 1:1 correlation: K ↔ GMR – m∗/m ↔ GQR – κTRK ↔ GDR – J ↔ αD fits to g.s. data leaves uncertainty on NMP and giant resonances (& αD) fits leave also leeway ⇒ response properties can be accomodated GDR in light nuclei – problematic trend with mass number A: EGDR(16O) too low for all resonable Skyrme forces

  • exp. trend EGDR ∝ A−1/6

← → RPA trend EGDR ∝ A−1/3

  • more (isovector) density dependence? – complex configurations (phonons)?

P .–G. Reinhard (Inst.Theor.Physik, Erlangen) Giant resonances in the Skyrme-Hartree-Fock theory COMEX05, Krakow 2015 32 / 36

slide-41
SLIDE 41

Conclusions

Description of excitations (giant resonances etc): RPA: commutator algebra, flexible basis expansion (1ph & local operators) basis up to Emax ≈ 100 MeV for GR, more for low 2+ +phonons: “phonons” = few low-lying RPA states with large strength collisional broadening ↔ can be simulated by E-dep. folding slight down-shift of GMR&GQR ↔ yet open details Giant resonances ↔ nuclear matter parameters (NMP): trends with NMP & covariances = ⇒ nearly 1:1 correlation: K ↔ GMR – m∗/m ↔ GQR – κTRK ↔ GDR – J ↔ αD fits to g.s. data leaves uncertainty on NMP and giant resonances (& αD) fits leave also leeway ⇒ response properties can be accomodated GDR in light nuclei – problematic trend with mass number A: EGDR(16O) too low for all resonable Skyrme forces

  • exp. trend EGDR ∝ A−1/6

← → RPA trend EGDR ∝ A−1/3

  • more (isovector) density dependence? – complex configurations (phonons)?

Low-lying isovector dipole modes (“pygmy”, range 7 MeV < E < 10 MeV): energy region where pure 1ph dipole strength was concentrated driven by low-lying isoscalar L=1 modes, transfered momentum q ≈ 0.6/fm mostly isoscalar toroidal models (+ few isovector toroidal strength)

P .–G. Reinhard (Inst.Theor.Physik, Erlangen) Giant resonances in the Skyrme-Hartree-Fock theory COMEX05, Krakow 2015 32 / 36

slide-42
SLIDE 42

P .–G. Reinhard (Inst.Theor.Physik, Erlangen) Giant resonances in the Skyrme-Hartree-Fock theory COMEX05, Krakow 2015 33 / 36