Nuclear Pygmy Modes as
Doorways to Nucleosynthesis
Horst Lenske
Institut für Theoretische Physik, JLU
GiessenH. Lenske, Hirschegg 2017

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The Richness of Nuclear Spectra…

Pygmy Modes of n-rich heavy nuclei:
PDR, PMR, PQR…
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Pygmy Dipole Strength inn-rich Nuclei:
below particle threshold

Low-Energy GDR Strengthin n-rich Nuclei:
above particle threshold

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Astropyhysical (n,γ) Capture Cross Sections and Nuclear Structuredσ nγ ~ ∑2(+)
qγ B BJ ,c V A χ nA d Ωγ

J ,c• Compund Nuclear Capture: statistical approach at high level density Hauser-Feshbach theory• Direct Capture: population of identifyable nuclear states  microscopic reaction
theory• Investigations by Detailed Balance: (n,γ) ↔ (γ,n)

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Agenda• Pygmy modes: new low-energy modes of nuclear excitation• Theory of low energy modes• Dipole and quadrupole pygmy modes• Pygmy modes, (γ,n) cross sections and nuclear reaction
rates

Our Goals• Microscopic approach to infinite matter and finite nuclei• Ground states and nuclear excitations• Astrophysical investigations
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Nuclear Density Functional Theory

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The Giessen Meson Exchange EDF Approach:()E(ρ, κ) ≈ E(ρ0 , κ0 ) + ∑ ( Tq + U q ( ρ0 ) ) δρq + ∆ q δκq + ∑ f qq ' ( ρ0 )δρq δρq ' + ...
=q p,nq,q ' p,nδρ q ~ ϕk†ϕn ; δκ q ~ ϕk ϕn & h.c.
Single Particle Self-Energy:=Uqδ 1=Vδρq 2∑ Vqq ' (ρ)ρq ' +q'1
δρρ∑ q ' q '' δρ Vq 'q '' ( ρ )2 q 'q ''q

HFB  Gorkov Wave Equation :  2  (+)(−)
 −∇ * ∇ + U q − λq − Eq  ϕ q + ∆ qϕ q = 02mq


2 


 (−)
(+)
−∆ qϕ q +  −∇ * ∇ + U q − λq + Eq  ϕ q = 0


2mq


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GiEDF: Infinite Matter Properties
Symmetric Infinite Matterρ sat = 0.162 [fm −3 ]E ( ρ sat ) / ρ sat = −15.91 [MeV]= 247.05 [MeV]
K ∞ ( ρ sat )Asymmetric Infinite Matter
E sym (ρ sat ) = 33.41 [MeV]Lsym (ρ sat ) = 53.86 [MeV]K sym (ρ sat ) = -188.37 [MeV]
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GiEDF and (npΛeµ) Neutron Stars

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GiEDF and Nuclei:Binding Energy and Skin Thickness
Sn (Z=50)

N. Tsoneva, H.L., PRC (2008)

Data: Krasnahorkay et al.
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Nuclear Excitations

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Strategies for Nuclear Spectroscopy
Multi-configuration Shell Model• Truncation to a few valence shells• Complete np-nh treatment within thevalence space• Systematic expansion in valence shellnumber

Multi-configuration Mean-Field Model• Truncation in ph-number• Limited, but unrestricted configuration
space• Sytematic expansion in np-nh number

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Giessen DFT and Multi-Phonon QRPA (QPM) Theory()E(ρ, κ) ≈ E(ρ0 , κ0 ) + ∑ ( Tq + U q ( ρ0 ) ) δρq + ∆ q δκq + ∑ f qq ' ( ρ0 )δρq δρq ' + ...
=q p,nq,q ' p,nδρ q ~ ϕk†ϕn ; δκ q ~ ϕk ϕn & h.c.

Landau-Migdal Residual Interaction:

δ1
δ2f qq=' Vqq ' (ρ) + 2∑ ρq ''Vq 'q '' ( ρ ) + ∑ ρk 'ρk ''Vk 'k '' ( ρ )δρq
2 k 'k ''δρq δρq 'q ''H. Lenske, Hirschegg 201713

2-Quasiparticle RPA States=
Qα+(α*α +xA−y∑ ph ph ph Aph)ph(Q)RPA Dyson Equation:(Q)RPA Polarization Propagotor: (ω , q )=
Πac0 Γ†a Π (ω , q)Γ c 0

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QRPA Dipole Response Functions

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QRPA-Response 128Sn
Microscopic
DD-QRPAaccumulated, normalized EWSR
S1 (E;Eλ)1
E c Bc (Eλ)∑S1 (Eλ) Ec ≤E

N.Tsoneva, HL,
Phys. Lett. B695 (2011) 174
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Beyond QRPA – including Anharmonicities:
Expansion into up to 6-QP Components•••••

Basis of QRPA phonons:„ph“- and „pp“-type configurations
Pauli-principle, orthogonality…
SPECTRAL FRAGMENTATION
SPECTRAL SHIFTSMulti-Configuration Multi-Quasiparticle Wave Function
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Confronting Theory (GiEDF) with Data (S-DALINAC):
Do we understand nuclear Spectra?

PhysRevC.90.024304(2014)
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Identifying the Skin-Mode:
Dipole Transition Densities in Sn Isotopes

Radius [fm]Mixedtransient
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N.Tsoneva, H. Lenske, PRC 77 (2008) 024321

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Low Energy Dipole Response: Parity Assignment

PRL 104, 072501 (2010)

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The PQR Mode – Quadrupole Oscillations of the Neutron Skin
…predicted in 2011:
Theory…experimentally confirmed in 2015/2016:
124Sn(γ,γ‘)

124Sn(α,α‘)124Sn(17Ο,17Ο‘)

TheoryTransition density

N. Tsoneva, H. Lenske,
PLB 695 (2011)

L.Pellegri, N. Tsoneva et al.,
PRC 92, 014330 (2015)
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M. Spieker, N. Tsoneva et al.,
PLB 752 (2016) 21

Capture Cross Sections

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Astropyhysical (n,γ) Capture Cross Sections and Nuclear Structure

Detailedbalance

Total capture cross section:
Incoherent superposition of electric (E) and magnetic (M) Multipoles

LSJ i J fEqL
BJi J f ( EL) δ S 0 etc.
(q) →q → 0 (2 L + 1)!!
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Cross Section measurements of the 86Kr(γ,n) Reaction
 Probing the s-Process Branch Point at 85Kr

R. Schwengner, N. Tsoneva et al., PhysRevC.87. 024306 (2013)
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GiEDF Multiphonon (QPM) Approach to Capture Cross Sections

N.Tsoneva et al., PhysRevC.91.044318 (2015)
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Collection of Observables recording the Charge Asymmetry
Skin Thickness

Symmetry Energy

Density Dependence of the Symmetry Energy

Nuclear Dipole Polarizability and Photoabsorption

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Summary and Outlook• New low-energy modes: PDR, PMR. PQR…
• GiEDF: extended DFT approach to nuclear spectra• Nuclear ground states by HFB theory• Multi-phonon approach to nuclear excitations• Subthreshold pygmy modes and capture cross sections• Correlations: PDR ↔ skin thickness ↔ polarizability ↔ slope L ↔ …?
• Predictions of s- and r-process nucleosynthesis rates
In collaboration with:
N. Tsoneva, S. Goriely, J. Piekarewicz, R. Schwengner, M. Spieker, A. Tonchev…
Supported by DFG, BMBF, GSI, HIC for FAIR
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