Giant resonances in exotic nuclei & astrophysics

1) Giant resonances: properties & modelisation

2) Giant resonances in exotic nuclei

3) Giant resonances and astrophysics

E. Khan

1) Properties and modelisation

Harmonic vibrations

The least action principle (I)

• A physical state of a system is characterised by an action (J.s) which is minimal

• Variationnal principle : variation of the action S around its minimum is zero

• Numerous applications : mathematics, mecanics, optics, quantum physics, …

Fermat (XVIIeme) Maupertuis (XVIIIeme) Lagrange (XVIIIeme

XIXeme)Feynman (XXeme)

Reformulation of the starting point:

Nuclear Hamiltonian:

Action:

Stationnarity of S (δS=0) for any variation of <Ψ(t)|Schrödinger equation

Energy density functionnalHohenberg-Kohn theorem: existence

The least action principle (II)

The Hohenberg-Kohn (HK) theorem(Chemistry Nobel 98)

• Knowledge of this functional in nuclei ?

• HK states the existence of a functional for a given state, not an universal functionalfor the nuclear chart

• In nuclear physics coefficients in E[ρ] are adjusted on radii, masses, … : takes intoaccount correlations beyond mean field.

• Nuclei: symmetry restoration (broken in self-bound systems)

• Kohn-Sham = method to calculate ρ, knowing E[ρ]

•There exists an energy functionnal E[ρ] which depends on the (local) density. It allows to exactly predict ground state observables (solves the many body problem)

Independent particles

•Application of the least action principle to the many body problem:nuclear physics (~1970)

•Slater determinant

•Justification: nucleus is a quantum liquid (range and intensity of strong interaction)nucleons are “good” independent particles (B. Mottelson ~ 2000)

Time Dependent Hartree-Fock (TDHF)

Variation: ϕi*(t) ϕi

*(t) + δϕi*(t)

A coupled equations : (self-consistent)

mean field:

In practice : - treat VNL quasi-locally : Skyrme, Gogny- interactions fitted on nuclei properties : radii, energies, etc.

correlations beyond HF- LDA from infinite nuclear matter ?

L

TDHF properties

•Self consistent•Minimum of the functionnal : static HF (stationnarity)

• Fusion, fission, compound nucleus, damping, …• Numerically heavy, tunnel effect, interpretation of Ψ ?

HF

•Brueckner-HF : HF calculation with the bare nucleon-nucleon interaction renormalised by the nuclear medium (G matrix).

Poor description of exp masses (B/A ~ 5 MeV, Coester line)

•HF: no suitable phenomenologic interaction able to describe masses and radii (1960)

•Breakthrough:Skyrme HF (Brink,Vautherin (1972))Gogny HF (1975)Relativistic DFT RMF (1990,VL) and RHF (2006)N.B : the 3 above have the best agreement with the data

•Now, in progress:Vlowk= renormalised bare interaction to be used in HF,Bare NnLO potentials : Effective Field Theories (Weinberg, 1990)

Milestones

J. -P. Delaroche, M. Girod, J. Libert, H. Goutte, S. Hilaire, S. Péru, N. Pillet, and G. F. BertschPhys. Rev. C 81, 014303 (2010)

Excited states in the DFT:GCM or RPA ?

•GCM (~5DCH): mixes the HF solutions with various deformation to obtainthe lowest energy states.Adapted for low E and low J states (does not take into account 1p-1h configurations)and for quadrupolar correlations

•RPA: Mixes the 1p-1h configuration on a single HF solution.Adapted for collective states, at low or high E (giant resonances)

RPA: the linear response theory

N.B. 1)

TDHF:

2) Excited states are a superposition of particle-hole excitations.

External oscillating field:ext

ext

First order:ext

HF

Small amplitude perturbations

RPA

Bethe-Salpeter equation

Response function

RPA equation

TDHFext

Π0 ext

Perturbation of the density :ext

Consistent RPA

• Small amplitudes perturbation (RPA) in the DFT framework: residual interaction (beyond mean field)

• 1975 : first calculation with the same EDF for HF and Vres

VRes

•Advantage - EDF is the only parameter

constrain it with excited states

- symmetry restoration - extrapolation for unknownsituation (exotic nuclei)

G.F. Bertsch and S.F. Tsai, Phys. Rept. C18 (1975) 125

•Excitation and pairing •Method known since ~40 years in nuclear physics• Strong peak of activity since year 2000. Why ?

Pairing vibrations, 2n transfer cross sections

N+2,Z

β half-life, GT strength, charge exchange cross section

N+1,Z-1

Study of nuclear transition of the whole nuclear chart (isotopic chain, open shell, drip-line, …)

The Quasiparticle-RPA (QRPA)

E*, S(E*) inelasticcross section

N,Z

30Ne

32Mg

36S34Si 38Ar

Skyrme QRPALow energy states

M. Yamagami and Nguyen Van Giai, Phys. Rev. C 69, 034301 (2004)

Spatial insight

N=14 shell closure

Transition densities

E. Becheva et al, Phys. Rev. Lett. 96, 012501, (2006)

Advantages of the QRPA:

• simplicity, also from the computational point of view;

• relates easily the interaction to the observable

• there is no “core” (that is, no need of effective charges);

• it is possible to study highly excited states.

• Provides densities and transition densities

Disadvantages:

• not all the many-body correlations are taken into account.

• weak predictive power for low energy part of the spectrum

QRPA/shell model

• What happen to giant resonances ? L=0,1,2

• How to measure ?

2) Exotic nuclei

Experimental status of GR in exotic nuclei

• GDR measured in 20O, 132Sn, 28Ne(by Coulomb excitation)

• GMR and GQR measured in 56Ni

Soft GMR

Compression of low-density nuclear matter

Soft GQR

Unexpected shift of the GR

Soft GDR predictions

Neutron skin

Soft mode :Neutron skin+core in phase+collective

Deformation effect on the pygmy mode

D. Peña Arteaga, E. Khan, and P. Ring, Phys. Rev. C 79, 034311 (2009)

The pygmy mode is quenched by the deformation because of the reduction of the n skin

3) Astrophysics

• Neutron stars

•The r process

•e capture in core collapse supernovae

• Ultra high energy cosmic rays

Why Neutron stars ?

• Landau (1932) : compact object held by the gravity• Remnant of a core-collapse supernova

• Densiest « active » object (star) of the Universe :emits radio, visible, X, Gamma rays …

• Pulsars (1968), binaries, magnetars (1011 T)

•May be a site for the r-processthe acceleration of ultra high energy cosmic

rays (1020 eV) GRB, …

The inner crust

Wigner-Seitz cells

~ ρ0 ~ 0.5 ρ0

Supergiant resonances

L=2

71% EWSR

QRPAHFB

1500Zr1800Sn

Impact on the cooling time of the starthrough the specific heat

Astrophysical site ?

1) Core-collapse supernovae

R-process (n,γ) and β decay

drip-line nuclei& free neutrons Neutron star crust

2) Ejection from the neutron star crust

The role of dipole strength in (n,γ) rates

•Statistical model of compound nuclear reaction : Hauser-Feshbach

Photon transmission coefficient sensitive to :

Sn

Tn

(Z,A) + n

(Z,A+1)

Tγ = TE1(E) ρ(E) dE0

Sn+En

Tγ • the E1 strength distribution TE1(E)

• the level density ρ(E)

Why using microscopic calculations ?

Microscopic•Efforts consuming ?•More suited to extrapolatefar from stability : neutron skin•Characterize the n-n interaction on the whole nuclear chart•Test the model validity on a large scale

Lorentzian (Hybrid) Microscopic

Phenomenologic•Fast and simple to use•Extrapolations ?•No feedback about nuclear structure

E1E1

Astrophysical impact

QRPA/Hybrid

Discrepancy pheno/micro

T=1.5 109 K

(n,γ) rates

r-abundance distribution

Electron capture in core collapse supernovae

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•Beta decay and electron capture on A=56 to 120•T ~ 1 MeV

A. Marek, H.Th.JankaPost-bounce evolution of a supernovae

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Gamow-Teller resonance predictions

Finite temperaturecharge exchange RPA

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n states blocking with increasing N

Thermal unblocking

Electron capture cross section

Are Ultra-High Energy Cosmic Raysmade of nuclei ?

The Pierre Augercollaboration

GRB990123

Ultra High energy Cosmic Rays

E=1018-21 eV

AnkleGZK

Redressed spectrum (x E3)

~ E-3

Composition, acceleration & propagation

Comparison with the measured spectrum on Earth (AUGER, …)

• Open question ! • Extra-galactic particles : protons

nuclei (56Fe, …) ?COMPOSITION :

• Open question ! • Gamma Ray Bursts, Active Galaxy Nucleus ?• N(E)~E-β

ACCELERATION :

• Quantitative answers• Interaction with the 2.7 K Cosmic microwave background• Extra-galactic Magnetic fields

PROPAGATION :

Accelerators in the Universe

GRB

RIBF

Propagation of UHECR

2.7 K Cosmic Microwave Background

Photons density

E (MeV)

γ=2.1010

0.1 1 10 100 1000

Lorentz boosted

*10 100

E (MeV)

Photodisintegration cross section

GDR

Photodisintegration rate (~1h-1)

56Fe : 1021 eV

555453

54535251

51504948

50494847

4544

4443

414038

40393736

3634

35

30

26

22

18

15

1413

11 14

9

56

55

545352

51

5049484746

45

4443424140

39

38

3735

36343332

31

302928

27

262524

23

222120

19

181716

15

1312

1110

: PSB path

Z=8

Z=14

Z=18

Z=22

Z=26

Z

N

A

Photodisintegration (II)

Protons & Nuclei : β=2.3

Needs for a galactic CR :Ankle is the galactic/extra-galactic transition

Protons only : β=2.6

Interpretation of the ankle

Conclusions

• Giant resonances are high energy collective modes with large cross section

• Well described by RPA models

• GR are usefull perturbation to investigate nuclear structure (L,T,S)

• Specific modes in exotic nuclei such as the pygmy

• 4 astrophysical applications : cooling of neutron star, r-process nucleosynthesis core-collapse supernovae propagation of ultra-high energy cosmic rays