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