Three-nucleon forces:
From neutron-rich nuclei to matter in astrophysics
Achim Schwenk

ARIS 2014 – Tokyo, Japan
June 3, 2014

Main message
3N forces and neutron-rich nuclei

3N forces and neutron stars
based on same strong interactions
A=1057(PSR J0348+0432)

Chiral effective field theory for nuclear forces see also talk by Ulf Meißner
Separation of scales: low momenta
NN

3N

4N

breakdown scale ~500 MeV

include long-range pion physics
few short-range couplings,
fit to experiment once
systematic: can work to desired
accuracy and obtain error estimatesconsistent electroweak interactions
and matching to lattice QCD

Weinberg, van Kolck, Kaplan, Savage, Wise, Bernard, Epelbaum, Kaiser, Machleidt, Meissner,…

Chiral effective field theory and many-body forces
Separation of scales: low momenta
NN

3N

4N

breakdown scale ~500 MeV

consistent NN-3N-4N interactions
3N,4N: 2 new couplings to N3LO
+ no new couplings for neutrons

ci from πN and NN Meissner et al. (2007)
derived in (2002)

cD, cE fit to light nuclei only(2011)(2006)

Weinberg, van Kolck, Kaplan, Savage, Wise, Bernard, Epelbaum, Kaiser, Machleidt, Meissner,…

The oxygen anomaly Otsuka, Suzuki, Holt, AS, Akaishi, PRL (2010)

F	O	
without 3N forces, NN interactions too attractive
3N forces crucial for location of neutron dripline

New ab initio methods extend reach
impact of 3N forces confirmed in large-space calculations:
Coupled Cluster theory with phenomenological 3N Hagen et al., PRL (2012)
In-Medium Similarity RG based on chiral NN+3N Hergert et al., PRL (2013)
Green’s function methods based on chiral NN+3N Cipollone et al., PRL (2013)

3N forces and proton-rich nuclei Holt, Menendez, AS, PRL (2013)
first results with 3N forces for ground and excited states of N=8, 20

3N forcesprediction for 20Mg agrees with newstate observed at GSI Mukha, private comm.

Ab initio calculations going open shell: SM interactions
In-Medium Similarity RG
to derive valence-shell interactions
Tsukiyama, Bogner, AS, PRL (2011), PRC (2012)
Bogner, Hergert, Holt, AS et al., 1402.1407

Ab initio calculations going open shell: SM interactions
In-Medium Similarity RG
to derive valence-shell interactions
Tsukiyama, Bogner, AS, PRL (2011), PRC (2012)
Bogner, Hergert, Holt, AS et al., 1402.1407

Coupled Cluster calculations
for effective interactions
Jansen et al., arXiv:1402.2563

Towards theoretical uncertainties see talk by Javier Menéndez
based on NN+3N interactions
that predict nuclear matter saturation within uncertainties
Preliminary

new 51,52Ca TITAN measurements
52Ca is 1.74 MeV more boundcompared to atomic mass evaluation
Gallant et al., PRL (2012)

behavior of 2n separation energy S2nagrees with NN+3N predictions

18S2n (MeV)

161412AME2003
TITAN
NN+3N (MBPT)
NN+3N (emp)10(3)∆n (MeV)

83282930

3132

TITAN+AME2003

210282930

31

Neutron Number N32

Frontier of ab initio calculations at A~50

53,54Ca masses measured at

ISOLTRAP using new
MR-TOF mass spectrometersee talk by Susanne Kreim

establish prominent N=32
shell closure in calcium
excellent agreement withtheoretical NN+3N prediction

Frontier of ab initio calculations at A~50

53,54Ca masses measured at

ISOLTRAP using new
MR-TOF mass spectrometersee talk by Susanne Kreim

interesting continuum effects
for very neutron-rich Ca
see Forssen et al., Physica Scripta (2013)

overall good agreement withdensity functional predictions
but DF’s do not reproduce
shell closures
cf. N=50, 82, 126 “arches”
Bender et al. (2005)

3N forces and magic numbers
Hagen et al., PRL (2012)

Holt et al., JPG (2012, 2013)

2+ energy measured at RIBF
suggests magic number N=34
Steppenbeck et al., Nature (2013)
see talk by David SteppenbackAb initio calculations going open shell: around Ca
Gorkov Green’s function methods based on chiral NN+3N
Somà, Cipollone, Barbieri, Navratil, Duguet, PRC (2014)
see talk by Carlo Barbieri

multi-reference IM-SRG
Hergert et al., PRL (2013)

shell model based on NN+3N
Holt, Menéndez, Simonis, AS, arXiv:1405.7602
55

5Ca-

1/2
7/2
-

3/2
9/2

Energy (MeV)

4-

5/2

3-

2-

7/2
3/2
1/2

3/29/23/25/2-

3/2
3/2
5/2
9/2
7/25/2
3/2

7/2
5/2

1-

3/2

--

0-

5/2

(5/2 )

1/2
5/2

-

5/2

-

1/2

NN+3N
pfg9/2Expt.

GXPF1A

KB3G

Chiral EFT for electroweak currents
NN3N4N

one-body currents at Q0 and Q2+ two-body currents at Q3

same couplings in forces and currents!

Chiral EFT currents and electroweak interactions
predicts consistent 1- and 2-body currents
GFMC calcs of magnetic moments in light nuclei Pastore et al., PRC (2012)
2-body currents (meson-exchange currents) are key!

Main message
3N forces and neutron-rich nuclei

3N forces and neutron stars
based on same strong interactions
A=1057(PSR J0348+0432)

Chiral effective field theory and many-body forces
Separation of scales: low momentaNN3N4N

breakdown scale ~500 MeV

consistent NN-3N-4N interactions
3N,4N: 2 new couplings to N3LO
+ no new couplings for neutrons

ci from πN and NN Meissner et al. (2007)
cD, cE fit to light nuclei only

Weinberg, van Kolck, Kaplan, Savage, Wise, Bernard, Epelbaum, Kaiser, Machleidt, Meissner,…

Complete N3LO calculation of neutron matterfirst complete N3LO result Tews, Krüger, Hebeler, AS, PRL (2013)
includes uncertainties from NN, 3N (dominates), 4N

Quantum Monte Carlo for neutron matter Gezerlis, Tews, et al., PRL (2013)
and arXiv:1406.0454
based on new local chiral EFT potentials,
order-by-order convergence up to saturation density

Quantum Monte Carlo for neutron matter Gezerlis, Tews, et al., PRL (2013)
and arXiv:1406.0454
based on new local chiral EFT potentials,
order-by-order convergence up to saturation density

excellent agreement withperturbative calculations
for low cutoffs (~400 MeV)

Quantum Monte Carlo for neutron matter Gezerlis, Tews, et al., PRL (2013)
and arXiv:1406.0454
based on new local chiral EFT potentials,
order-by-order convergence up to saturation density

excellent agreement with
perturbative calculations
for low cutoffs (~400 MeV)
light nuclei based on GFMC
Lynn et al., in prep.
4He

nuclear lattice simulations
see talk by Ulf Meißner

Discovery of the heaviest neutron star

Nature (2010)

direct measurement of
neutron star mass fromincrease in signal travel
time near companion
J1614-2230
most edge-on binary
pulsar known (89.17°)+ massive white dwarf
companion (0.5 Msun)
heaviest neutron starwith 1.97±0.04 Msun

Discovery of the heaviest neutron star Science (2013)

Impact on neutron stars Hebeler, Lattimer, Pethick, AS, PRL (2010), ApJ (2013)
Equation of state/pressure for neutron-star matter (includes small Ye,p)crust EOS

log 10 P [dyne / cm 2 ]37
36

crust EOS (BPS)
neutron star matterwith c i uncertainties

35

32crust

134
33
32
31
13.0

13.5

14.0

log 10311223[g / cm ]pressure below nuclear densities agrees with standard crust equation ofstate only after 3N forces are included
extend uncertainty band to higher densities using piecewise polytropes
allow for soft regions

Impact on neutron stars Hebeler, Lattimer, Pethick, AS, PRL (2010), ApJ (2013)
constrain high-density EOS by causality, require to support 2 Msun starlog 10 P [dyne / cm 2 ]

3635

WFF1
WFF2
WFF3
AP4AP3MS1
MS3
GM3ENG
PAL
GS1
GS2

PCL2
SQM1
SQM2
SQM3
PS

34

33
14.2

14.4

14.6

log 1014.8

15.0

15.2

3

[g / cm ]low-density pressure sets scale, chiral EFT interactions provide strong
constraints, ruling out many model equations of state

15.4

Impact on neutron stars Hebeler, Lattimer, Pethick, AS, PRL (2010), ApJ (2013)
constrain high-density EOS by causality, require to support 2 Msun star
this work
RG evolved

3Mass [M . ]°2.5

itysaluca

2

1.5
10.5
08

10

1214Radius [km]16

low-density pressure sets scale, chiral EFT interactions provide strong
constraints, ruling out many model equations of statepredicts neutron star radius: 9.7-13.9 km for M=1.4 Msun (±18% !)Impact on neutron stars Hebeler, Lattimer, Pethick, AS, PRL (2010), ApJ (2013)
constrain high-density EOS by causality, require to support 2 Msun starcentral densities
for 1.4 Msun star: 1.8-4.4 ρ0
not very high momenta!

Neutron-star mergers and gravitational waves
explore sensitivity to neutron-rich matter in neutron-star merger
predictions for gravitational-wave signal, including NP uncertainties
Bauswein, Janka, PRL (2012)
Bauswein, Janka, Hebeler, AS, PRD (2012)predict range ofgw frequencies

Calculations of asymmetric matter Drischler, Soma, AS, PRD (2014)
Esym comparison with extraction from isobaric analogue states (IAS)
3N forces fit to 3H, 4He properties only
50
this work
Akmal et al. (1998)
BHF, AV18+UIX
Danielewicz & Lee (2013) IAS
Danielewicz & Lee (2013) IAS + skins

Esym [MeV]

4030

20

10000.05

0.1-3n [fm ]

0.15

0.2

Symmetry energy and pressure of neutron matter
neutron matter band predicts
symmetry energy Sv andits density derivative L
comparison to experimental
and observational constraints
Lattimer, Lim, ApJ (2012), EPJA (2014)

neutron matter constraints
H: Hebeler et al. (2010)
G: Gandolfi et al. (2011)provide tight constraints!
combined with Skyrme EDFs
predicts neutron skin
208Pb: 0.182(10) fm
48Ca: 0.173(5) fm
Brown, AS, PRC (2014)

Summary and perspectives
3N forces are an exciting frontier for nuclei and astrophysics
ab initio calculations are going open shell: O to Ca/Ni/Sn regionneed to quantify uncertainties, dominated by uncertainties in 3N forces
see talk by Javier Menéndez

nuclear structure with N3LO 3N forces breakthrough: 3N matrix elements by Kai Hebeler+ N3LO 4N perturbatively
impact of chiral EFT two-body currents (meson-exchange currents)
on electroweak transitions, provide new tests
provide ab initio constraints to powerful density functional theory
see talks by Jacek Dobaczewski and Witek Nazarewicz