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Institut für Theoretische Physik, Universität Giessen
LOW-ENERGY MULTIPOLE EXCITATIONS AND NUCLEOSYNTHESIS
Nadia Tsoneva
INTERNATIONAL SCHOOL OF NUCLEAR PHYSICS36th Course
Nuclei in the Laboratory and in the CosmosErice-Sicily: September 16-24, 2014
R. Schwengner, F. Donau, S. Frauendorf, E. Grosse
Triangle Universities Nuclear Laboratory, Durham, USAW. Tornow, A.P. Tonchev, G. Rusev et al.
Monash Centre for Astrophysics (MoCA), Australia
M. Lugaro
P. von Neumann-Cosel , N. Pietralla, A. Richter, D. Savran
S. Goriely
Institute of Astronomy and Astrophysics (IAA) Université libre de Bruxelles, Belgium
A. Zilges, V. Derya, M. Spieker et al.
Horst Lenske
N.Tsoneva, ERICE14
Nucleosynthesis of Heavier Elements Heavier elements ( Z> 26-28) can be assembled within stars
by neutron capture processes.
Two main neutron capture processes s- process – slow neutron capture, low neutron densities
~108/cm3
life time ~ 1 – 10 years
r – process - rapid neutron captures
~1020/cm3
…other processes
Fusion in stars
s-process
?
r-process
p-process
N.Tsoneva, ERICE14
Characteristic Response of an Atomic Nucleus to EM Radiation
Scissors modeTwo-phononexcitation
Pygmy-quadrupoleresonance
Pygmy-dipoleresonance
Spin-flip M1
Giant M1resonance
Giant Dipole Resonance
E1 (GDR)
21+
31-
E (MeV)
Theoretical prediction of Pygmy Quadrupole Resonance: N. Tsoneva, H. Lenske, Phys. Lett. B 695 (2011) 174.
N.Tsoneva, ERICE14
The Theoretical ModelN. Tsoneva, H. Lenske, Ch. Stoyanov, Phys. Lett. B 586 (2004) 213N. Tsoneva, H. Lenske, Phys. Rev. C 77 (2008) 024321
MF resHH H
MF sp pairH H H ph ph ppres M SM MH H H H
Nuclear Ground State
Single-Particle StatesPhenomenological density functional approach based on a fully microscopic self-consistent Skyrme Hartree-Fock-Bogoljubov (HFB) theory
Pairing and Quasiparticle States
Excited statesdeformations, vibrations, rotations
HMph - multipole interaction in the
particle-hole channel;HSM
ph - spin-multipole interaction in the particle-hole channel;HM
pp - multipole interaction in the particle-particle channel
Quasiparticle-Phonon Model: V. G. Soloviev: Theory of Atomic Nuclei: Quasiparticles and Phonons (Bristol, 1992)
( ' ) ( ) ( , ') ( , ) ( ', ')V r r R r r Y Y
( , ') ( ) ( ')
0
1
R r r R r R r
isoscalar interaction
isovector interactionN.Tsoneva, ERICE14
Phenomenological Density Functional Approach for Nuclear Ground States
P. Hohenberg, W. Kohn, Phys. Rev. 136 (1964) B864; W. Kohn, L. J. Sham, Phys. Rev. 140 (1965) A 1133.
3
,
1( ) ( ) ,
2pair
q q q qq p n
B A d r U E k
N. Tsoneva, H. Lenske, PRC 77 (2008) 024321
The total binding energy B(A) is expressed as an integral over an energy-density functional
q, q, kq – number, kinetic and pairing density
( )( ) / ( ) ( ) ( )rq q q qB A U U
effective potential
neutron skin thickness
2 3 21( )q q
q
r d rr rA
Z=50
N.Tsoneva, ERICE14
The thickness of the neutron skin scaled with the difference of the Fermi levels of the protons and neutrons F corrected for the Coulomb barrier.
S2p, S2n – two proton (neutron) separation energies,EC – the height of the Coulomb barrier at the nuclear radius (CCF=Coulomb Corrected Fermi energy)
a measure of how loosely the neutrons are bound compared to the protons.
Neutrons Protons
Fn
Fp
Even-Even Neutron-Rich Nucleus
F
E
0r
Vc(r)~Ze2/rEc
E
0
104Sn
108Sn
124Sn
116Sn
132Sn
N.Tsoneva, ERICE14
N. Tsoneva, H. Lenske, Phys. Rev. C 77 (2008) 024321 R. Schwengner et al., Phys. Rev. C 78 (2008) 064314
Calculations of Ground State Densities in Z=50, N=50,82 Nuclei
2 22
1( ) (2 1) ( )
4 q q q
q
q r v j R rr
Radius [fm]
N.Tsoneva, ERICE14
Theory of Nuclear Excitations
The QPM basis is built of phonons:
The phonons are not ‘pure‘ bosons: Pauli principle
QRPA equations are solved:
, i i iH Q E Q
1 2 1 2
1 2
1 2 1 2
1( , ) ( 1) ( , )
2i i
i j j j jj j
Q A j j A j j
' ' ' ' ' ',i i iiQ Q fermionic corrections ~
1 1 2 2
1 2
2 2 1 1
1 2
1 2 1 1 2 2
1 2 1 1 2 2
( , )
( , )
j m j mm m
j m j mm m
A j j j m j m
A j j j m j m
1 1 2 2j m j m
i labels the number of the QRPA state
Quasiparticle-Phonon Model: V. G. Soloviev: Theory of Atomic Nuclei: Quasiparticles and Phonons (Bristol, 1992)
N.Tsoneva, ERICE14
Anharmonicities in Nuclear Wave Function
M. Grinberg, Ch. Stoyanov, Nucl. Phys. A. 573 (1994) 231
For even-even nucleus the QPM wave functions are a mixture of one-, two- and three-phonon components
one-phonon part two-phonon part
three-phonon part
N.Tsoneva, ERICE14
U. Kneissl, N. Pietralla, and A. Zilges, J. Phys. G: Nucl.Part.Phys. 32, R217 (2006)
Two-Phonon Quadrupole-Octupole 1- states
stable and unstable Sn nuclei
Excitation probability of the 21
+ state from the ground state Excitation probability
of the 31- state from the
ground state
Excitation probability of the 11
- state from the ground state
E1 transition probability of the 31
- state to the 21+
state
N. Tsoneva, H. Lenske, Ch. Stoyanov, Phys. Lett. B 586 (2004) 213
N.Tsoneva, ERICE14
Pygmy Dipole Resonance in Sn Isotopes
PDR
GDR
PDR
GDR
PDR
GDR
N. Tsoneva, H. Lenske, PRC 77 (2008) 024321
Radius [fm]
Transition densities are related to nuclear transition strengths
N>Z N=Z
N.Tsoneva, ERICE14
Neutron number increasing
Neutron skin increasing
A connection between PDR
strengths and neutron skins
N. Tsoneva, H. Lenske, PRC 77 (2008) 024321
Pygmy Dipole Resonance and the Dynamics of Nuclear Skin
Similar observations found also in N=50, 82
isotones !
N.Tsoneva, CGS15
Multiphonon Calculations of E1 Transitions in 112,120Sn
N/Z(112Sn)= 1.24N/Z(120Sn)= 1.4
GDR (E*>8MeV) (1ph)PDR (1ph+2ph+3ph)
PDR
PDR
submitted to PRC
N.Tsoneva, ERICE14
Dynamics of Neutron Skin Oscillations in N=50 Isotonesexp: R. Schwengner et al., First systematic photon-scattering experiments in N=50 nuclei: using bremsstrahlung produced with electron beams at the linear accelerator ELBE, Rossendorf and quasi-monoenergetic – rays at HIS facility, Duke university.
N.Tsoneva, ERICE14
R. Raut,…,N.Tsoneva et al., Phys. Rev. Lett. 111, 112501 (2013).
Total cross section of 85Krg (n,)86Kr reaction
A way to investigate 85Kr branching point and the s-process: 85Kr ( ~ 10.57 Y) ground state is a branching point and thus a bridge for the production of 86Kr at low neutron densities.
N.Tsoneva, ERICE14
QRPA, QPM calculations by N. TsonevaTALYS calculations by S. Goriely
TALYS calculations by S. Goriely
Population of 86Kr in n-capture reactions related to s- and r-processes of the nucleosynthesis
s-process r-process
N.Tsoneva, ERICE14
N. Tsoneva, H. Lenske, Phys. Lett. B 695 (2011) 174
Theoretical Prediction of Pygmy Quadrupole Resonance
ISGQR
ISGQR
ISGQR
ISGQR
ISGQR
ISGQRPQR
PQR
PQR
PQR – pygmy quadrupole resonanceISGQR – isoscalar giant quadrupole resonanceIVGQR – isovector giant quadrupole resonance
PQR
PQR
PQR
ISGQR
ISGQR
ISGQR
IVGQR
IVGQR
IVGQR
I=0
I=0
I=0
I=1
I=0
I=1
I=1
PQR strength increases with the neutron number: B(E2) ~ 1/ nb
2
N.Tsoneva, ERICE14
M. Spieker, J. Endres, A. Zilges, Universität zu Köln QPM calculations in comparison with data
5exp. 2 4
2
52 4
2
( 2) 489
( 2) 341
MeV
MeV
MeVQPM
MeV
B E e fm
B E e fm
(,‘)
N.Tsoneva, CGS15
Parity Measurements with Polarized Photon Beams of Low-energy Dipole Excitations at HIS, Duke University
A. Tonchev…N. Tsoneva, et al., Phys. Rev. Lett. 104, 072501 (2010)
138Ba (M1)/(E1) ~ 3%
First systematic spin and parity measurements in comparison
with QPM calculations:
• 138Ba verified for the first time that the pygmy dipole resonance is predominantly electric dipole in nature.
• The fine structure of the M1 spin-flip mode is explained.
• Separation of the PDR to isoscalar and isovector. Interplay between the GDR and the PDR at higher energies.
N.Tsoneva, CGS15
Fine Structure of the Giant M1 Resonance in 90Zr
G. Rusev, N. Tsoneva, F. Dönau, S. Frauendorf, R. Schwengner, A. P. Tonchev, A. S. Adekola, S. L. Hammond, J. H. Kelley, E. Kwan, H. Lenske, W. Tornow, and A. Wagner, Phys. Rev. Lett. 110, 022503 (2013).
•Explaining the fragmentation pattern and the dynamics of the ‘quenching’.
• Multi-particle multi-hole effects increase strongly the orbital part of the magnetic moment.
• Prediction of M1 strength at and above the neutron threshold.
B(M1)Exp. = 4.5 (6) N2 B(M1)QPM. = 4.6 N
2
Ec.m.Exp. = 9.0 MeV Ec.m.
QPM = 9.1 MeV
Precision data on M1 strength distributions are of fundamental importance
gseff=0.8 gs
bare
Spin and Parity Determination at HIS, Duke University, USA
N.Tsoneva, ERICE14
• A theoretical method based on Density Functional Theory and Quasiparticle-Phonon Model is developed.
Presently, this is the only existing method allowing for sufficiently large configuration space such that a unified description of low-energy single-particle, multiple-phonon states and the giant resonances is feasible.
• Different applications of the method are presented: - systematic studies of low energy dipole strengths reveal new mode of
nuclear excitation - Pygmy Dipole Resonance as a unique mode of excitation correlated with the size of the neutron skin.
- theoretical prediction of a higher order multipole pygmy resonance – Pygmy Quadrupole Resonance.
- description of the fragmentation pattern of E1, E2 and M1 strengths
- nuclear structure input for astrophysics
Conclusions
N.Tsoneva, ERICE14
First Systematic Studies of the PDR in N=50 Isotones
R. Schwengner,…, N.Tsoneva et al, Phys. Rev. C 87, 024306 (2013)
Experiment: bremsstrahlung produced with electron beams at the linear accelerator ELBE and quasi-
monoenergetic – rays at HIS facility at Duke university.
N.Tsoneva, LANZHOU14
Cross-Section measurements of the 86Kr(,n) Reaction to Probe the S-Process Branching at 85Kr
R. Schwengner… N. Tsoneva et al., Phys. Rev. C 87, 024306 (2013);R. Raut…N. Tsoneva et al., Phys. Rev. Lett. 111, 112501 (2013).
Lorentz strength function
(,‘) data 86Kr
86Kr
QRPA
N.Tsoneva, LANZHOU14
QRPA CALCULATIONS OF PQR STATES IN SN ISOTOPESN. Tsoneva and H. Lenske, Phys. Lett. B 695 (2011) 174
B(M1; 2i+ 21
+) ~ 10-2N2
Pygmy Quadrupole Resonance is a genuine mode
B(E2) ~ 1/ nb
2
g9/2 - a proton Fermi level;
pb= -12.88 MeV in 134Sn ; p
b=-7.20 MeV in 104Sn
B(E2) increases with the neutron number N
N.Tsoneva, CGS15