Rios (PDF)
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Green’s functions for dense matter
& mean-field connections
Arnau Rios Huguet
Lecturer in Nuclear Theory
Department of Physics
University of Surrey
IPN workshop 3rd October 2017
Complications
NN interaction is not unique
...but phase-shift equivalent!
δ [deg]
90
1
60
S0
30
0
δ [deg]
180
S. Aoki, et al. Comput. Sci. Dis. 1 015009 (2008)
Nij
CDBonn
Av18
N3LO
Nij93
120
60
3
S1
0
0
50
100
150
200
250
E [MeV]
2
Complications
NN interaction is not unique
...but phase-shift equivalent!
δ [deg]
90
1
60
S0
30
0
δ [deg]
180
S. Aoki, et al. Comput. Sci. Dis. 1 015009 (2008)
Nij
CDBonn
Av18
N3LO
Nij93
120
60
3
S1
0
0
50
100
150
200
250
E [MeV]
•Non-uniqueness of nucleon forces ✘
2
Complications
NN interaction is not unique
Strong short-range correlations
Carlson et al., Phys. Rev. C 68 025802 (2003)
S. Aoki, et al. Comput. Sci. Dis. 1 015009 (2008)
•Non-uniqueness of nucleon forces ✘
•Short-range core needs many-body treatment ✘
2
Complications
NN interaction is not unique
S. Aoki, et al. Comput. Sci. Dis. 1 015009 (2008)
Saturation point of nuclear matter
Li, Lombardo, Schulze et al. PRC 74 047304 (2006)
•Non-uniqueness of nucleon forces ✘
•Short-range core needs many-body treatment ✘
•Three-body forces needed for saturation ✘
2
NN forces from EFTs of QCD
ci
Chiral perturbation theory
π
ci
O
ˆ
Q
⇤
˙
•π and N as dof
•Systematic expansion
•2N at N3LO - LECs from πN, NN
•3N at N2LO - 2 more LECs
•(Often further renormalized)
⇤ „ 1 GeV
ci
Weinberg, Phys. Lett. B 251 288 (1990), NPB 363 3 (1991)
Entem & Machleidt, PRC 68, 041001(R) (2003)
Tews, Schwenk et al., PRL 110, 032504 (2013)
Epelbaum, Frebs & Meissner, PRL 115, 122301 (2015) 3
NN forces from EFTs of QCD
ci
Chiral perturbation theory
π
ci
O
ˆ
Q
⇤
˙
•π and N as dof
•Systematic expansion
•2N at N3LO - LECs from πN, NN
•3N at N2LO - 2 more LECs
•(Often further renormalized)
⇤ „ 1 GeV
ci
Weinberg, Phys. Lett. B 251 288 (1990), NPB 363 3 (1991)
Entem & Machleidt, PRC 68, 041001(R) (2003)
Tews, Schwenk et al., PRL 110, 032504 (2013)
Epelbaum, Frebs & Meissner, PRL 115, 122301 (2015) 3
SCGF Ladder approximation
In-medium interaction
Ladder self-energy
•Self-consistent resummation
•Energy and momentum integral
•@Finite T (Matsubara)
pp & hh Pauli blocking
Dyson equation
T-matrix at T=5 MeV
−5
−10
−15
−20
+
Re T(Ω ; P,q=0) [MeV fm3]
0
−25
−30
600
400
Spectral function
One-body properties
Momentum distribution
Thermodynamics & EoS
Transport
200
P [MeV]
0
−200
−100
0
100
200
Ω−2µ [MeV]
Ramos, Polls & Dickhoff, NPA 503 1 (1989)
Alm et al., PRC 53 2181 (1996)
Dewulf et al., PRL 90 152501 (2003)
Frick & Muther, PRC 68 034310 (2003)
Rios, PhD Thesis, U. Barcelona (2007)
Soma & Bozek, PRC 78 054003 (2008)
Rios & Soma PRL 108 012501 (2012)
4
Ladder approximation with 3BF
Effective interactions
Two-body interaction
1
2
In-medium T-matrix
=
+
In-medium T-matrix
GII
Self-energy
=
+
Self-energy
1
Dyson equation
12
Carbone et al., PRC 88 054326 (2013)
A. Carbone, PhD Thesis 5
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