effective theory of shallow nuclei n.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
Effective Theory of Shallow Nuclei PowerPoint Presentation
Download Presentation
Effective Theory of Shallow Nuclei

Loading in 2 Seconds...

play fullscreen
1 / 20

Effective Theory of Shallow Nuclei - PowerPoint PPT Presentation


  • 73 Views
  • Uploaded on

Effective Theory of Shallow Nuclei. U. van Kolck. University of Arizona. Supported in part by US DOE. Background by S. Hossenfelder. Outline. Introduction Effective (Field) Theories Few-nucleon systems Halo nuclei Outlook . c. N.B. On wiki page:.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Effective Theory of Shallow Nuclei' - massimo


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
effective theory of shallow nuclei
Effective TheoryofShallow Nuclei

U. van Kolck

University of Arizona

Supported in part by US DOE

v. Kolck, Shallow Nuclei

Background by S. Hossenfelder

outline
Outline
  • Introduction
  • Effective (Field) Theories
  • Few-nucleon systems
  • Halo nuclei
  • Outlook

c

N.B. On wiki page:

  • suggested reading
  • homework!

v. Kolck, Shallow Nuclei

slide3

MPI-Heidelberg

Nuclear Chart

see

Bertulani’s

lecture

What are the nucleosynthesis reaction rates?

What are the limits of nuclear existence?

v. Kolck, Shallow Nuclei

slide4

Nuclear scales

perturbative QCD

~1 GeV

see

Schwenk’s

lecture

Chiral EFT

Typical

nuclei

~10 MeV

~150 MeV

Contact and Halo/cluster EFTs

Shallow

nuclei

~1 MeV

~30 MeV

TODAY

v. Kolck, Shallow Nuclei

slide5

In classical mechanics:

bound-state size

range of force

e.g.

square well

reduced mass

But…

not always true in

quantum mechanics!

v. Kolck, Shallow Nuclei

slide6

(center-of-mass frame)

In quantum mechanics:

elastic scattering

(for simplicity)

(N.B.: )

(conservation of energy)

: given by certain probability amplitude – the “scattering amplitude”

angular

momentum

Legendre

polynomial

partial-wave

amplitude

Two important properties:

  • Poles
  • Low-energy expansion

bound states

effective

range

shape

parameter

resonances

(before any singularity)

v. Kolck, Shallow Nuclei

“Effective-Range Expansion”

scattering

length

b.s.:

slide7

square well, S-wave

e.g.

when

generic

fine-tuning

etc.

new scale emerges

v. Kolck, Shallow Nuclei

slide8

In the quantum world,

one can have a b.s. with

size much larger than

the range of the force

provided there is

fine-tuning

v. Kolck, Shallow Nuclei

slide9

Feshbach resonance

Chiral EFT:

(incomplete) NLO

Beane, Bedaque, Savage + v.K. ’02

cf. Beane + Savage. ’03

Fukugita et al. ‘95

Lattice QCD:

quenched

cf. Beane, et al. ‘06

Regal + Jin ‘03

unitarity limit

NN triplet

scattering

length

Large deuteron size because

v. Kolck, Shallow Nuclei

slide10

c

EFT : the basic idea

more generally:

same argument for any

short-range potential

same

same wf tail

similar observables

systematic

improvement:

in the limit,

v. Kolck, Shallow Nuclei

just like multipole expansion

slide11

Effective Hamiltonian

fitted to

2-body data

3-body data

etc.

3-body interaction

no calculation

in physics

(except for TOE,

if it exists)

is ever exact

“Whatever

can happen

will happen”

Wikipedia

quantum field theory

v. Kolck, Shallow Nuclei

slide12

Chen, Rupak + Savage ’99

fitted

LO EFT

NNLO

EFT

predicted

NLO EFT

Nijmegen

PSA

LO EFT

fitted

NLO EFT

Nijmegen

PSA

predicted

NNLO

EFT

v. Kolck, Shallow Nuclei

slide13

Rupak ’01

fitted

NNNNLO EFT

v. Kolck, Shallow Nuclei

slide14

Bedaque, Hammer + v.K. ’99 ’00

Hammer + Mehen ’01

Bedaque et al. ’03

Bedaque + v.K. ’97

Bedaque, Hammer + v.K. ’98

no 3-body force up to NNNNLO

3-body force already at LO

fitted

predicted

v.Oers + Seagrave ‘67

NNLO

EFT

Dilg et al. ‘71

v.Oers + Seagrave ‘67

NLO EFT

Kievsky et al. ‘96

LO EFT

LO EFT

fitted nothing

predicted

Dilg et al. ‘71

v. Kolck, Shallow Nuclei

QED-like precision!

slide15

Light nuclei

Stetcu, Barrett +v.K., ‘06

LO EFT

fitted to d, t, a ground-state binding energies

Harmonic-oscillator basis

fits

works within ~10% !

see

Rotureau’s

lecture

works within ~30%

v. Kolck, Shallow Nuclei

slide16

new scale leads to proliferation of shallow states (near driplines):

loosely bound nucleons around tightly bound cores

Halo/Cluster states

separation

energy

core excitation

energy

core

p

n

n

p

p

p

n

n

p

n

“ ”

e.g.

resonance at

bound state at

resonance at

v. Kolck, Shallow Nuclei

resonance at

slide17

Bertulani, Hammer + v.K. ’02

fitted

fitted

LO

NLO

NLO EFT

LO EFT

Arndt et al. ’73

NLO EFT

fitted

scatt length only

NNNLO

EFT

v. Kolck, Shallow Nuclei

slide18

Higa, Hammer + v.K. ‘08

see Higa’s lecture

Extra

fitting parameters

Bohr radius

none

fitted with

and

More

fine-tuning!!!

fine-tuning of

1 in 10

fine-tuning of

1 in 1000!

v. Kolck, Shallow Nuclei

slide19

What next

Bertulani, Higa + v.K., in progress

  • Coulomb interaction in higher waves:

e.g.

  • three-body states:

e.g. 1)

2)

  • reactions:

e.g.

c.f.

Kong + Ravndal ’99

Rotureau,

in progress

c.f.

Bedaque, Hammer + v.K. ’99

Higa + Rupak, in progress

c.f.

Rupak ’01

v. Kolck, Shallow Nuclei

slide20

SM

Forecast

QCD

lattice

Extrapolates to

realistically small

Chiral

EFT

Faddeev* eqs, …

Extrapolate

to larger

and larger

Contact

EFT

NCSM, …

Halo/cluster

EFT

Low-energy

reactions

v. Kolck, Shallow Nuclei