Threebody forces in neutron rich isotopes in
oxygen and fluorine
Gustav R. Jansen1,2
[email protected]
1 University
2 Oak
of Tennessee, Knoxville
Ridge National Laboratory
November 2. 2012
Collaborators
• Gaute Hagen (ORNL, UTK)
• Morten Hjorth-Jensen (UiO, MSU)
• Thomas Papenbrock (ORNL, UTK)
• Ruprecht Machleidt (UI)
Outline
• Nuclei as open quantum systems.
• Interaction and coupled-cluster theory
• Role of continuum and three-nucleon forces in neutron-rich
oxygen isotopes.
• Threebody forces in neutron-rich flurorine isotopes.
Open Quantum Systems
Three-nucleon forces as in-medium corrections to
nucleon-nucleon forces
Curse of dimensionality
4
1052
10
Slater determinant basis
Be
16
O
40
Ca
48
1044
10
He
10
40
1036
1032
1028
1024
1020
1016
1012
108
104
100
0
50
100
Number of single particle states
150
200
The coupled-cluster method
Excited states using EOM-CC
Eigenvalues of H̄ = e −T̂ Ĥe T̂ − hΦ0 |Ĥ|Φ0 i
H̄R̂
c
= ω R̂
Properties of H̄.
• Non-symmetric (non-hermetian) operator.
• For CCSD and a twobody hamiltonian - six-body operator.
• The matrix representation is very sparse.
• Generally too large to store and diagonalize exactly.
Efficient implementation of H̄R̂
is key.
C
Excited states using EOM-CC
Eigenvalues of H̄ = e −T̂ Ĥe T̂ − hΦ0 |Ĥ|Φ0 i
H̄R̂
c
= ω R̂
Properties of H̄.
• Non-symmetric (non-hermetian) operator.
• For CCSD and a twobody hamiltonian - six-body operator.
• The matrix representation is very sparse.
• Generally too large to store and diagonalize exactly.
Efficient implementation of H̄R̂
is key.
C
Excited states using EOM-CC
Eigenvalues of H̄ = e −T̂ Ĥe T̂ − hΦ0 |Ĥ|Φ0 i
H̄R̂
c
= ω R̂
Properties of H̄.
• Non-symmetric (non-hermetian) operator.
• For CCSD and a twobody hamiltonian - six-body operator.
• The matrix representation is very sparse.
• Generally too large to store and diagonalize exactly.
Efficient implementation of H̄R̂
is key.
C
Is
28
O a bound nucleus?
Resonances in neutron-rich
24
O
The effects of a single proton
• Adding a proton changes
the dripline by 6 neutrons.
• Not all fluorine isotopes
towards the dripline are
bound
• Interplay between
proton-neutron
interactions,
neutron-neutron
interactions, threebody
interactions and
continuum degrees of
freedom.
26
F – probing the proton-neutron interaction
• Simple structure –
24
O plus πd5/2 and νd3/2 .
• First approximation – J π = 1+ − 4+ .
• Weakly bound – Sn ≈ 0.8 MeV.
The effects of a single proton
• Adding a proton changes
the dripline by 6 neutrons.
• Not all fluorine isotopes
towards the dripline are
bound
• Interplay between
proton-neutron
interactions,
neutron-neutron
interactions, threebody
interactions and
continuum degrees of
freedom.
26
F – probing the proton-neutron interaction
• Simple structure –
24
O plus πd5/2 and νd3/2 .
• First approximation – J π = 1+ − 4+ .
• Weakly bound – Sn ≈ 0.8 MeV.
Oxygen isotopes from chiral interaction
Oxygen isotopes from chiral interaction
Negative parity states in O25
Threebody forces in
26
F – Preliminary
Technical details
• Chiral interaction at
N3 LO.
• Identical threebody force
as established in the
oxygen chain
• 17 major harmonic
oscillator shells with a
Gamow-Hartree-Fock
basis for νs1/2 and νd3/2
• CCSD with triples
corrections (Λ-CCSD(T))
for 24 O, with
2PA-EOMCC.
• 26 Ffree = B(25 O) +
B(25 F) − B(24 O)
Threebody forces are crucial for correct levelspacing.
Threebody forces in
26
F – Preliminary
Technical details
• Chiral interaction at
N3 LO.
• Identical threebody force
as established in the
oxygen chain
• 17 major harmonic
oscillator shells with a
Gamow-Hartree-Fock
basis for νs1/2 and νd3/2
• CCSD with triples
corrections (Λ-CCSD(T))
for 24 O, with
2PA-EOMCC.
• 26 Ffree = B(25 O) +
B(25 F) − B(24 O)
Threebody forces are crucial for correct levelspacing.
Summary
• Interactions from chiral EFT probed in nuclei.
• Calculations for oxygen and fluorine isotopes with effects of
3NF and continuum give a significant improvement in binding
energy and spectra.
• Predict spin and parity of newly observed resonance peak in
O24.
• Low 3/2− and 1/2− resonances in O25.
• Threebody forces responsible for level ordering in F26.