FIDIPRO- data to proceed to the drip lines EFES … · Nucleon correlations Using nuclear reaction and structure data to proceed to the drip lines ... data including high-momentum

Nucleon correlations

Using nuclear reaction and structure data to proceed to the drip lines

• Scientific question I

• Green‘s function method / framework

• DOM: data ⇒ self-energy / propagator data-driven extrapolations ⇒ drip line

• Outlook

• Scientific question II (some other time)

• Dynamic pion exchange

• (p,2p) in inverse kinematics ⇔ (e,e’p)

Arctic FIDIPRO-

EFES Workshop 4-21-09

Wim DickhoffBob Charity

Jon MuellerBec Shane

Lee SobotkaMark BurnettJonathan MorrisSeth WaldeckerWashington University in St. LouisCarlo Barbieri, RIKENDimitri Van Neck, U GhentArnau Rios, MSU/SurreyArtur Polls, U Barcelona...


Scientific Question I• How do the properties of protons and neutrons change as a

function of nucleon asymmetry?Properties: elastic p and n cross sections, bound single-particle properties, including removal energy, spectroscopic factors, strength distribution, one-body density matrix, E/A due to VNN.

Program• Employ framework of Green’s function method to link presently

available data to be cast in the form of the complex potentials (including their asymmetry dependence) that govern the behavior of nucleons in a large energy window: εF±200 MeV (or more) thereby linking (some) nuclear reactions with nuclear structure.

• Prediction of data for nuclei further along towards the dripline follows, allowing further improvements, etc.


Description of the nuclear many-body problemIngredients: Nucleons interacting by “realistic interactions” Nonrelativistic many-body problemMethod: Green’s functions (Propagators) amplitudes instead of wave functions (efficient) keep track of all nucleons, including the high-momentum onesBook: Dimitri Van Neck & W.D. 2nd ed. 2008 Why: Physical insight and useful for all many-body systems Link between experiment and theory clear Can include all energy scales

Also available as a framework to analyze and interpret experimental data

Review: W.H.D. & C. Barbieri, Prog. Part. Nucl. Phys. 52, 377 (2004)


Available applications:• Start from VNN (realistic) in infinite matter Rios et al.

– short-range correlations = SRC (ladders)

– fully self-consistent in nuclear and isospin asymmetric matter at finite temperature

• Start from VNN (realistic) in finite nuclei or Vee in atoms and molecules Barbieri et al.

– SRC ⇒ G-matrix (as effective interaction in model space)

– LRC : Faddeev-RPA (pp/hh and ph phonons)

– In progress: contribution of high-momenta to ground state and self-consistent Pauli principle (self-consistent model space)

• Start from DATA = Dispersive Optical Model St. Louis group

– Fit of complex potentials (self-energy) including nucleon asymmetry dependence ⇒predict more exotic systems

• Under construction: quasi-particle density functional theory StL-Ghent

(Effective)centralforce

Repulsivecore:500-600MeV

Attractivepocket:about30MeV

Bothofthesearesmallerthanweexpect.Thisisansweredbythequarkmassdependence.

The following diagram is contained.

This leads to the one pion exchangeat the large spatial separation.

N.Ishii, S.Aoki, T.Hatsuda, Phys.Rev.Lett.99,022001(’07).

Ishii talk at 3rd LACM-EFES-JUSTIPEN WorkshopOak Ridge 2009

Quarkmassdependenceofthecentralforce:(1) mπ=380MeV: Nconf=2034 [28 exceptional configurations have been removed](2) mπ=529MeV: Nconf=2000(3) mπ=731MeV: Nconf=1000

1S0

Strongquarkmassdependenceisfound.

Inthelightquarkmassregion,

therepulsivecoregrowsrapidly.

attractivepocketisenhancedmildly.

ThelatticeQCDcalculationatlightquarkmassregionisquiteimportant.

Ishii talk at 3rd LACM-EFES-JUSTIPEN WorkshopOak Ridge 2009


Correlations for nuclei with N very different from Z?⇒ Radioactive beam facilities

• Short-Range Correlation ~ the same between pp, np, and nn

• Tensor force disappears for n when N >> Z but the opposite for p in matter (volume effect)

• Role of the surface?

Some pointers: from theory and experiment

Nuclei are TWO-component Fermi liquids


Self-Consistent-Green’s-Function calculation for isospin-polarized nuclear matterincluding SRC ⇒ momentum distribution ⇒ n(k=0)

0.16 fm-3

T=10 MeVneutrons

protons

asymmetry = (N-Z)/A

Frick, Rios et al.PRC71,014313(2005)

CDBonnArV18Reid

n(k=

0)

SRCcan be handled!

{

small uncertainty


Temperature vs. correlations Rios, Polls, WD

arXiv:0904.2183


Fixed by phase shifts?!

arXiv:0904.2183


Gade et al. Phys Rev C77, 044396 (2008)

⇒ Spectroscopic factors become very small; way too small?

RS ≠ not spectroscopic factor

Reduction w.r.t. shell model

neutrons more correlated with increasing proton numberand accompanying increasing separation energy & vice versa


Faddeev-RPA ⇒ Barbieri, WD 2009

Trend similar but magnitude ...

arXiv:0901.1920


History for atoms


F-RPA application to Neon atomC. Barbieri, D. Van Neck, and WD, Phys. Rev. A76, 052503 (2007)

Spectroscopic factors in brackets

*

* Consistent with results from Heidelberg group

One of the developers of the no-core shell model:“F-RPA/Green’s function method maybe the only way to do heavy nuclei”


Periodic table: Ne ionization energy

HF: 23.12 eV

Σ(2): 20.32 eVF-RPA: 21.73 eVExp: 21.57 eV


Green’s functions as a framework:DOM = Dispersive Optical Model

Vehicle for data-driven extrapolations / predictions to the dripline

Green’s function formulation ⇒ “Mahaux analysis” Goal: extract “propagator”/”self-energy” from data

C. Mahaux and R. Sartor, Adv. Nucl. Phys. 20, 1 (1991)


FRAMEWORK FOR EXTRAPOLATIONS BASED ON EXPERIMENTAL DATA

Combined analysis of protons/neutrons in 40Ca and 48CaCharity, Sobotka, & WD, Phys. Rev. Lett. 97, 162503 (2006)Charity, Mueller, Sobotka, & WD, Phys. Rev. C76, 044314 (2007).

Goal: Extract asymmetry dependence ⇒ δ/β = (N - Z)/A ⇒ Predict proton properties at large asymmetry ⇒ 60Ca ⇒ Predict(?) neutron properties … the dripline based on data!

Large energy window (> 200 MeV)

Recent extension of DOM


Dyson Equation and “experiment”Equivalent to …

�

− 2∇2

2mΨn

N−1 a r m Ψ0N + d

r ∫

m '∑ 'Σ'* ( r m, r 'm';En

−) ΨnN−1 a r 'm' Ψ0

N = En− Ψn

N−1 a r m Ψ0N

Self-energy: non-local, energy-dependent potentialWith energy dependence: spectroscopic factors < 1 ⇒ as observed in (e,e’p) �

En− = E0

N − EnN−1

Schrödinger-like equation with:

�

S = ΨnN−1 aαqh

Ψ0N 2

= 1

1−∂Σ'* αqh ,αqh;E( )

∂EEn

−

αqh solution of DE at En-

DE yields

�

ΨnN−1 a r m Ψ0

N =ψnN−1 r m( )

Ψ0N a r m Ψk

N +1 =ψkN +1 r m( )

ΨEc,N−1 a r m Ψ0

N = χcN−1 r m;E( )

Ψ0N a r m ΨE

c,N +1 = χcN +1 r m;E( )

Bound states in N-1 Bound states in N+1 Scattering states in N-1

Elastic scattering in N+1

Elastic scattering wave function for (p,p) or (n,n)


Dispersion relations (nuclear matter or nuclei)

Imaginary part both above and below εF

Above εF:required by elastic nucleon scattering data

Below εF:required by e.g. (e,e’p) and (p,2p) data

Consequences:Fermi sea is depletedand there is occupation of“particle-like” states (high-momenta e.g.)


Fit and predictions of n & p elastic scattering cross sections

Above εF


Mougey et al., Nucl. Phys. A335, 35 (1980) 16O(e,e’p)

Energy

Moment

um

∝ Cross section


40Ca spectral functionRecent theoretical development: nonlocal self-energy below the Fermi energyVan Neck, Charity, Sobotka,WD 2009

Old (p,2p) data from Liverpool

Below εF


HIMAC data: Kobayashi et al. Nucl. Phys. A805, 431c (2008)


What about neutrons?• Almost no elastic scattering data on 48Ca until

recently!• Most pressing information• Also very relevant for future applications of

transfer reactions involving deuterons

Protons:Surface absorption increaseswith increasing asymmetry


Extrapolation in δNaïve: p/n ⇒ D1 ⇒ ± (N-Z)/A

Cannot be extrapolated for n

Less naïve:

D2⇒ p ⇒ +(N-Z)/A

D2⇒ n ⇒ 0Emphasizes coupling to GT resonanceConsistent with n+AMo data

Need n+48Ca elastic scattering data!!!Performed recently at TUNL (Sobotka & Charity)

D1D2


WashU exp: Sobotka, Shane, Mueller, Charity at TUNL


Prelim

inary$$$


Total neutron cross section 48Ca vs. 40Ca

Prelim

inary

WashU exp: Sobotka, Shane, Mueller, Charity at LANL


Preliminary fit including n data

Correlations at large asymmetry

Fragmentation of strength E. Quint, Ph.D.thesis NIKHEF, 1988

Spectroscopic factor S(2s1/2) =0.65I. Sick & P de Witt Huberts,

Comm. Nucl. Part. Phys.,20, 177 (1991)

Intermediatefragmentation

Strong fragmentation of deeply-bound strength ⇒ self-energy has significant imaginary part!

Towards a “global” DOM

208Pb

DOM spectroscopic factors

Correlations at large asymmetry

M. van Batenburg & L. Lapikás from 208Pb (e,e´p) 207Tl NIKHEF in preparation

Up to 100 MeV missing energy and270 MeV/c missing momentum

Covers the whole mean-field domainfor the FIRST time!!

Occupation of deeply-bound proton levels from EXPERIMENT

Confirms predictions for depletion

SRCLRC

n(0) ⇒ 0.85 Reid 0.87 Argonne V18 0.89 CDBonn

Nuclear matter


Project DOM-DRIP How to do it:Experiment

✦ Elastic scattering n+48Ca, total neutron cross sections (& other N ≠ Z nuclei)

✦ Elastic scattering of radioactive beams off p

✦ Heavy-on knock-out reactions (DOM + ...)

✦ (p,2p & pn) inverse kinematics (DOM + NN T-matrix) to match (e,e’p)

✦ Transfer reactions (DOM + Johnson, Tostevin, Nunes approach)

Extend DOM (⇒ more nuclei)

๏ Nonlocality (Van Neck)

๏ Isospin (Waldecker)

๏ Include charge density data

๏ Include (e,e’p) data including high-momentum JLab results

๏ Include higher energy elastic scattering data ⇒ relativity (Piekarewicz)

Theory

✴ Calculate self-energy microscopically; include tensor force explicitly (Barbieri)

✴ Input for quasiparticle DFT (Burnett, Van Neck)


ConclusionProject DOM-DRIP

• suggests many new experiments (some in the pipeline)

• allows data-driven extrapolation to the drip line

• many reactions can be included in DOM framework including (n,γ)

• room for lots of theoretical input

• room for lots of improvements and collaborations

Documents

FIDIPRO- data to proceed to the drip lines EFES … · Nucleon correlations Using nuclear reaction and structure data to proceed to the drip lines ... data including high-momentum