Low Energy Nuclear Theory, Exercises of Nuclear Physics

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Low Energy Nuclear Theory

KD Launey

LA Light Source

Louisiana State University

Low Energy Nuclear Theory

KD Launey

LA Light Source

Louisiana State University

LA Light Source @ LSU

Fantastic 4

… nuclei… elements… stars…

q u a r k s & g l u o n s

U N I V E R S E

Condensed

Matter

Nuclear

p r o t o n s n e u t r o n s

From Nucleons to Stars

… nuclei… elements… stars…

q u a r k s & g l u o n s

U N I V E R S E

Condensed

Matter

Nuclear

p r o t o n s n e u t r o n s

1. How did visible matter come into being and how does it evolve?

2.How does subatomic matter organize itself and what phenomena emerge?

3.Are the fundamental interactions that are basic to the structure of

matter fully understood?

4. What are the origins of heavy elements?

The Big Science Questions

… nuclei… elements… stars…

q u a r k s & g l u o n s

U N I V E R S E

Condensed

Matter

Nuclear

p r o t o n s n e u t r o n s

FRIB (Facility for Rare Isotope Beams)

Ab initio Theory Density Functional Theory

Astrophysics: the origin of the elements

NIF (National Ignition Facility) at Lawrence Livermore National Lab T2K; DUNE

Advanced

LIGO

Neutrino physics;

fundamental symmetries

Nuclei: fuel of the Cosmos and ideal labs!

Applied energy Neutrino Detectors

(^12) C, 16 O, 40 Ar

Neutrinoless ββ decay

FRIB (Facility for Rare Isotope Beams)

Advanced

LIGO

… nuclei… elements… stars…

q u a r k s & g l u o n s

U N I V E R S E

Condensed

Matter

Nuclear

p r o t o n s n e u t r o n s

Ab initio Theory Density Functional Theory

Astrophysics: the origin of the elements

NIF (National Ignition Facility) at Lawrence Livermore National Lab T2K; DUNE

Neutrino physics;

fundamental symmetries

Why Ab initio?

Applied energy Neutrino Detectors

(^12) C, 16 O, 40 Ar

Neutrinoless ββ decay

✓Explains ✓Predicts

Measured masses

Mass difference, MeV

Rb

D. Lunney, CSNSM (2004)

Unstable nuclei: need reliable

prediction (mass models diverge)

Nucleus – relevant scales

baryon chemical potential =

measure of net baryon density

baryon = made of 3 quarks

(protons, neutrons, …)

mesons = made of quark-antiquark

(pions, …)

hadrons

Nucleus – relevant scales

Mass of nucleon

(proton or neutron)

~1 GeV = 10 3 MeV

Separation energy

per particle

6-8 MeV

Nucleus – relevant scales

Mass of nucleon

(proton or neutron)

~1 GeV = 10 3 MeV

Separation energy

per particle

6-8 MeV

dof= nucleons + mesons

Mass of pion

~140 MeV

low-energy

nuclear physics

Radioactive beam facilities

(FRIB)

Intermediate energy

High energy

a few GeV

GeV/TeV

Size ~0.8 fm

Nucleus – relevant scales

Mass of nucleon

(proton or neutron)

~1 GeV = 10 3 MeV

Separation energy

per particle

6-8 MeV

dof= nucleons + mesons

Mass of pion

~140 MeV

Intermediate energy

High energy

a few GeV

GeV/TeV

Size ~0.8 fm

Many

surprises:

nuclear sizes!

Various dof

² Collective

² Clusters

² Halo

Modeling the nucleus … The challenges

Interaction

between particles

States

NN, 3N, ...

E.g., 6 particles in 200 states:

8x10 10 ways !!!

E.g., 2 particles in 4 states

|1100> |0011>

|1010> |0101>

|1001> |0110>

Model space

available to nucleus

All possible ways:

20 particles in 80 states

HUGE!

Reproduces NN scattering

(these are free nucleons,

not in nuclear medium;

I will refer to this force

as “bare”)

In addition, there might

be 3N, 4N, …

Modeling the nucleus … The ingredients

Specified by

basis,

model space (size & resolution)

Many-body Approach

Nuclear properties:

structure & reactions

Nuclear force

L (^) eff

1/Λeff

“size”

“resolution”

Resolving high-

momentum

physics

Important for

wave function tail,

large shapes/clusters,

asymptotics, etc.

Two-body problem

v A=2: pp (

2 He), pn ( 2 H), nn (?)

v Non-relativistic quantum mechanics: H = T rel + V( r,r’ )

r Center of mass (CM)

Relative (intrinsic)

Position:

Momentum:

T =

2M M/2 (^) Reduced mass

Global motion of a free nucleus is described by a

plane wave with momentum P

(irrelevant to the intrinsic nuclear dynamics)

Entem & Machleidt

v Realistic interactions:

NN reproduce phase shifts to high precision

Chiral Potentials

Quark/gluon dynamics

(Quantum

chromodynamics, QCD)

Degrees of freedom Symmetry

High energy What is most important for a

theory? The symmetries and

not the degrees of freedom

The usual (Lorentz

covariance, parity, etc.)+

L = − (^) Chiral symmetry

1

4

G ∝ν

a Ga

∝ν

• q (^) L i γ∝ D

∝ q (^) L + q (^) R i γ∝ D

∝ q (^) R − q M q

Nucleon/pion dynamics

(Effective field theory)

Low energy