r. machleidt, university of idaho

R. Machleidt, University of Idaho

Recent advances in the theory of nuclear forces and its relevance for the microscopic approach to

dense matter

OutlineOutline

• IntroductionIntroduction

• Historical perspective – Historical perspective –

The many-body problem and the nuclear The many-body problem and the nuclear force problem: two very different histories force problem: two very different histories

• The link between nuclear forces and QCD: The link between nuclear forces and QCD: chiral effective field theory (EFT)chiral effective field theory (EFT)

• EFT based nuclear forces and resultsEFT based nuclear forces and results

• The limitations of chiral EFT and the lasting The limitations of chiral EFT and the lasting significance of meson theorysignificance of meson theory

• ConclusionsConclusions

R. MachleidtR. Machleidt

Theory of Nuclear Forces ... Theory of Nuclear Forces ... IWND09, Shanghai, 8-24- IWND09, Shanghai, 8-24-

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Explain the properties of nuclear matter and finite nuclei

in terms of the basic forces between the constituents.

One of the most fundamental goals of

theoretical nuclear physics:



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This microscopic approach tonuclear structure and reactions,

a.k.a. the ab initio approach, has two ingredients

•Many-body theory/methodsMany-body theory/methods

•““Bare” nuclear forcesBare” nuclear forces

But note: The history of each ingredient is very different.



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Some many-body history



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“Brueck

ner Theory”

≈1955




Coupled Cluster T

heory

≈1958



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• The fundamental basis for today’s many-body methods was provided already 50 years ago.

• “The nuclear force” 50 years ago: Gammel-Thaler potential

Only since ≈ A.D. 2000 quantitative nuclear forces derived on fundamental grounds have been developed.



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The The CRUXCRUX of NN potential of NN potential development up to about 2000development up to about 2000

• There are many There are many quantitativequantitative NN potentials which are, NN potentials which are, however, however, not fundamentalnot fundamental (the latest are the “high- (the latest are the “high-precision potentials” developed in the 1990s).precision potentials” developed in the 1990s).

• FundamentalFundamental approaches were either not approaches were either not fundamental or fundamental or not quantitativenot quantitative..

• In short:In short: The more quantitative, the less The more quantitative, the less

fundamental.fundamental. The more fundamental, the less The more fundamental, the less

quantitative.quantitative.



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Therefore, we need …Therefore, we need …

• a a fundamental fundamental approach that approach that produces a produces a quantitativequantitative description of the nuclear description of the nuclear force.force.

• A fundamental approach must A fundamental approach must necessarily be based upon necessarily be based upon QCDQCD..

The chiral effective field theory The chiral effective field theory approach to nuclear forcesapproach to nuclear forces

• Clear connection to QCD: via Clear connection to QCD: via symmetriessymmetries

• Degrees of freedom relevant to (low-Degrees of freedom relevant to (low-energy) nuclear physics: pions and energy) nuclear physics: pions and nucleonsnucleons

• Systematic expansion: Q/ΛSystematic expansion: Q/Λ

• Controlled error, predictive power.Controlled error, predictive power.

• Explains the empirically known Explains the empirically known hierarchy of nuclear forceshierarchy of nuclear forces



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2N forces 3N forces 4N forces

Leading Order

Next-to-Next-to Leading Order

Next-to-Next-to-Next-to Leading Order

Next-to Leading Order

The Hierarchy of Nuclear

Forces



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Forces


Forces

2N forces

Leading Order






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Phase shifts up to 300 MeVRed Line: N3LO Potential by Entem & Machleidt, PRC 68, 041001 (2003).Green dashed line: NNLO Potential, and blue dotted line: NLO Potential by Epelbaum et al., Eur. Phys. J. A19, 401 (2004).




N3LO Potential by Entem & Machleidt, PRC 68, 041001 (2003).NNLO and NLO Potentials by Epelbaum et al., Eur. Phys. J. A19, 401 (2004).



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Forces


Forces

2N forces

Leading Order




4N forces




4NF at N3LO (leading order)

(2) (1) (0)

Note that only vertices from

, and are involved,

no new parameters,

weak.

First rough estimate:

0.1 MeV to binding.

N NN

L L L

Essentially negligible,as to be expected.

Interim summaryInterim summary

• 2NF o.k.2NF o.k.

• 4NF (negligibly) small …4NF (negligibly) small …



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3NF


Forces


Forces

2N forces 3N forces

Leading Order




The focus:The 3NF

4N forces



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Three-nucleon forces at N2LOThree-nucleon forces at N2LO

TPE-3NF

OPE-3NF

Contact-3NF

No new parameters!

One new parameter, D.

One new parameter, E.

Strategy: Adjust D and E to two few-nucleon observables, e.g., the triton and alpha-particle binding energies. Then

predict properties of other light nuclei.




Results from applications of chiral Results from applications of chiral nuclear forcesnuclear forces

• Nuclear matter in the Brueckner pair Nuclear matter in the Brueckner pair approximation approximation

• Ground state of finite nuclei with A≤48 Ground state of finite nuclei with A≤48 using Coupled Cluster theoryusing Coupled Cluster theory

• Spectra of light nuclei using the no-core Spectra of light nuclei using the no-core shell modelshell model



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Nuclear matter [from Bogner et al. (2009)]




Chiral NN potential at N3LO underbinds by ~1MeV/nucleon. (Size extensivity at its best.)

Nucleus E / A [MeV]

4He 1.08 (0.73FY)

16O 1.25

40Ca 0.84

48Ca 1.27

48Ni 1.21




Calculating the properties of light nuclei usingCalculating the properties of light nuclei usingchiral 2N and 3N forces chiral 2N and 3N forces

2N (N3LO) +3N (N2LO)

forces

“No-Core Shell Model “ Calculations by P. Navratil et al.,

LLNL

2N (N3LO) force only



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How does the chiral EFT approachTo nuclear forces compare

To the conventional approach(Meson Theory)?

OPE




ChPT Conventional meson theory

TPE

Short range

“Contacts”ω



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What are contact terms?

Contact terms take care of the short range contributions.

Consider the contribution from the exchange of a heavy meson

+ + + …



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OPE




ChPT Conventional meson theory

TPE

Short range

σρ

“Contacts”ω



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Question: When everything is so equivalent to conventional meson theory,

why not just use conventional meson theory?

Answer: In ChPT, there is an organizational scheme (“power

counting”) that allows to estimate the size of the various contributions and the error. This

applies also to contributions from many-body forces.

In conventional meson theory, we don’t have this.



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However, there is a “However”!



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Phase shifts up to 300 MeVRed Line: N3LO Potential by Entem & Machleidt, PRC 68, 041001 (2003).Green dashed line: NNLO Potential, and blue dotted line: NLO Potential by Epelbaum et al., Eur. Phys. J. A19, 401 (2004).



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red = Idaho N3LO, green = Juelich N3LO,

black = CD-Bonn



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pp TOTAL CROSS pp TOTAL CROSS SECTIONSSECTIONS

LOW

INTER-MEDIATE

HIGH

ChPT

Mesonland

pQCD



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INTERMEDIATE ENERGIESINTERMEDIATE ENERGIESabove about 0.4 MeVabove about 0.4 MeV

• Too high for ChPTToo high for ChPT

• Too low for perturbative QCD (pQCD)Too low for perturbative QCD (pQCD)

• Lattice QCD Lattice QCD … … not very practicalnot very practical

• But there is a well-established model But there is a well-established model ––

the relativistic meson modelthe relativistic meson model



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Conclusions



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• After 70 years of struggle, we have now a After 70 years of struggle, we have now a proper theory of nuclear forces that is based proper theory of nuclear forces that is based

upon the fundamental theory of strong upon the fundamental theory of strong interactions, QCD. It is interactions, QCD. It is chiral effectivechiral effective field field

theorytheory in which the pion plays a fundamental in which the pion plays a fundamental role. role. Thus, the original Yukawa idea of just ONE Thus, the original Yukawa idea of just ONE

MESON which makes the nuclear force is re-MESON which makes the nuclear force is re-instatedinstated,, but with some refinements (chiral but with some refinements (chiral symmetry). symmetry). The circle of history is closing.The circle of history is closing.

• Based upon chiral perturbation theory (ChPT), Based upon chiral perturbation theory (ChPT), quantitative NN potentials have been quantitative NN potentials have been

successfully developed and are available for successfully developed and are available for nuclear structure applications.nuclear structure applications.

• In ChPT, two- and many-body forces are In ChPT, two- and many-body forces are generated on an equal footing. Many-body generated on an equal footing. Many-body

forces are predicted to be much smaller than forces are predicted to be much smaller than two-body forces, consistent with experience.two-body forces, consistent with experience.

• The theory is fundamental AND quantitative!The theory is fundamental AND quantitative!

• A new era of microscopic nuclear structure has A new era of microscopic nuclear structure has started.started.

However ..However ..

• Chiral EFT is a Chiral EFT is a LOW-ENERGY LOW-ENERGY theory, theory, restricted to momenta below ≈ 400 restricted to momenta below ≈ 400 MeV/cMeV/c

• O.k. for normal nuclear densities.O.k. for normal nuclear densities.

• Too low for dense matter.Too low for dense matter.

• At intermediate energies “meson At intermediate energies “meson theory” remains the only valid model.theory” remains the only valid model.



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r. machleidt, university of idaho

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