Jenny Lee RIKEN , Nishina Center

Jenny LeeRIKEN , Nishina Center

Studies of Nucleon Correlations using Direct Reactions

Isospin Dependence of Nucleon Correlations (knockout and transfer reactions)

Neutron-Proton Correlations (knockout, transfer, quasi-free scattering reactions)

Di-neutron Correlations (breakup reaction ?)

BCS to BEC Transitions ? (knockout and transfer reaction ??)


Isospin Dependence of Nucleon Correlations

BCS to BEC Transitions ?

34,46Ar(p,d) at 70 AMeV

14O knockout on C & p a 65 AMeV

30Ne, 36Mg knockout on C at 250 AMeV

Quasi-free scattering, proton beam at 2.8 GeV

Neutron-Proton Correlations

np-transfer on sd-shell nuclei

np-knockout on 12C at 200 AMeV

Di-neutron Correlations

6He breakup on C & p at 70 AMeV

Support from Theorists


Isospin Dependence of Nucleon CorrelationsMSU/ NSCL 09084 (planned in 2014):

Comparison of the Neutron Spectroscopic Factors from Transfer and Knockout Reactions at E/A=70 MeV

RIKEN (performed in Dec 2010):

Spectroscopic information towards “Island of Inversion” using knockout reaction with in-beam gamma technique

RCNP E390 (planned in 2013):

Understanding Nucleon Stripping Reaction Mechanisms from Exotic Nuclei at Intermediate Energy

RIKEN NP1112-SAMURAI06 (submitted deferred):Steps to Clarify the Isospin Dependence of Nucleon Correlations

Nucleon Correlations

Truncated shell model space + effective interactions

Few active orbitals High Occupancy

Inert Core Inert Core

Greater distribution of nucleons to higher energy configuration

Reduction in Occupancy

Short-range, tensor & collective correlations

In reality

Removing nucleon from occupied orbital Cross sections (probability) depend on the single-particle occupancy & overlap of many-body wave functions

Probing the nuclear wave function

Spectroscopic Factor (SF)

How much ? What is the Isospin Dependence of nucleon correlations?

How good the effective interaction in Shell Model can describe the correlations ?

SM description is accurate

Some correlations missing in the interactions ?

Cross Sections Reaction ModelSpectroscopic Factors (expt)

Quantify Occupancy Correlation Effects

(e,e’p) reactions

(e,e’p) – Stable nuclei (near closed shell)

• Constant ~30-40% of SF reduction compared to theory

• Correlations missing in shell-model interactionsL. Lapikas, Nucl. Phys. A553, 297c (1993)

How about Transfer Reactions ?

Transfer Reactions -- long history ( >50 years) abundant data, but Problems in SF(expt) !

Experimental SF from Transfer Reactions

ADWA (consistent set) Johnson-Soper (JS)

Adiabatic Approximation takes care of d-break-up effects

Use global p and n optical potential with standardized parameters (CH89)

Include finite range & non-locality corrections

n-potential : Woods-Saxon shape ro=1.25 & ao=0.65 fm; depth adjusted to reproduce experimental binding energy

TWOFNR, M. Igarashi et al., X.D. Liu et al., Phys Rev. C 69 (2004) 064313

J. Lee et al., Phys. Rev. C75 (2007) 064320

Well-known problem- optical model potentials - parameters - reaction models

SF=1.01± 0.06SF(SM) = 1.00

Consistent SFs for 41Ca

Reliable Framework Systematic Studies

Survey of Spectroscopic Factor (Transfer Reactions)

Benchmark 20 % agreement to theory Ground-state

SF(e

xpt)

Extend to 88 nuclei (ground-state) :

Found 225 relevant papers

Re-analyzed (unified model) > 430 data sets

Extracted 88 SF(expt)

SF(theory)

Extend Survey to excited states :

Re-analyzed >2,000 data ( >300 papers )

Extracted 565 SF(expt)

SF(e

xpt)

SF(theory)

Z=8-16Do we understand all the correlations ?

J. Lee, M. B. Tsang et al., Phys. Rev. C79, 054611 (2009)

M.B. Tsang, J. Lee et al., Phys. Rev. Lett 95, 222501 (2005)M.B. Tsang, J. Lee et al., Phys. Rev. Lett 102, 062501 (2009)J. Lee, M. B. Tsang et al., Phys. Rev. C75, 064320 (2007)

Microscopic Input in Reaction Model

JLM potential & Hartree-Fock (SK20)

CH89 + ro=1.25 fm with minimum assumption consistent SF(expt) with Shell Model

ro=1.25 fm HF rms radius

Global CH89 JLM + HF densities

Constant ~30% reduction in SFs

Suppression of SFs in Transfer Reactions

J. Lee et al., Phys. Rev. C 73 , 044608 (2006)

J. Lee et al., Phys. Rev. C 73 , 044608 (2006)

Suppression of SFs in Transfer Reactions

Constant ~30% reduction in SFs

• Transfer reactions do not yield absolute SF ; Systematic approach relative SF can be obtained reliably over a wide range of nuclei

• Nuclear structure purpose Relative normalized SFs

Different sets of consistent parameters different normalizations

p-rich

n-rich

CH89

JLM+HF

ΔS=Sn-Sp


ΔS=Sn-Sp

Neutron-rich

(e,e p’) Rs = 0.6-0.7

34,36,46Ar + p→d + 33,35,45Ar

Inverse kinematics at 33MeV/A

S800

Target ChamberJ. Lee et al., Phys. Rev. Lett 104, 112701 (2010)

Weak Isospin Dependence of nucleon correlations

Transfer Reactions:

Proton-rich

Nucleon Knockout with Fast Beams on 9Be / 12C Target

A. Gade et al., Phys. Rev. C 77, 044306 (2008) and reference therein

One-nucleon knockout -- away from stability

• Rs strongly depends on separation energy

• More correlation effect - strongly bound valence nucleon

Rs = σ(expt)/σ (ES+SM)

ΔS=Sn-Sp

Projectile (fast beam)

Target

Core

9Be or 12C

High incident energy Reaction only affects a nucleon at surface

Reaction Theory: Eikonal & Sudden ApproximationsJ. Tostevin et al., J. Phys. G, Part. Phys. 25, 735 (1999)

Knockout reactions: Yes & Strong

Transfer reactions: Weak

Q: Isospin Dependence ?

Systematic difference between two probes !

Incompatibility Incomplete understanding in underlying reaction mechanism

Red

uctio

n Fa

ctor

Isospin Dependence of Shell Occupancies?

J. Lee et al., Phys. Rev. Lett 104, 112701 (2010)

A. Gade et al., Phys. Rev. C 77, 044306 (2008) & reference therein

p(34,36,46Ar,d) at 33 A MeV

MSU/ NSCL 09084 (planned in 2014):


S800

Focal Plane

Beam from A1900

Target Chamber

NSCL 09084: 34,46Ar(p,d) 33,45Ar at 70 AMeV

Same incident energy as knockout reaction Direct comparison

Same SF from transfer at higher energy ? (reliability and applicability of model)

70 AMeV Very few reliable transfer reaction measurements exist

Establishing transfer reactions can be used as spectroscopic tools at reasonably high energy due to the beam intensity and quality (eg at RIKEN, energy degraded beam)

Knockout reactions: Yes & Strong

Transfer reactions: Weak

Q: Isospin Dependence ?

Systematic difference between two probes !

Incompatibility Incomplete understanding in underlying reaction mechanism

Red

uctio

n Fa

ctor

Isospin Dependence of Shell Occupancies?

J. Lee et al., Phys. Rev. Lett 104, 112701 (2010)

A. Gade et al., Phys. Rev. C 77, 044306 (2008) & reference therein

p(34,36,46Ar,d) at 33 A MeV

Knockout Reaction ?Transfer Reaction Future NSCL 09084: 34,46Ar(p,d) at 70 MeV/A - same energy as knockout reactions for direct comparison

Is Strong Dependence Theoretically Explaned ?

Dispersive Optical Model (DOM)(elastic-scattering & bound-level data for 40-49Ca)

R.J. Charity et al., Phys. Rev. C 76 , 044314 (2007)

C. Barbieri & W. H. Dickhoff, arXiv:0901.1920v1

Self-consistent Green’s Functions + FRPA

Weak dependence

Knockout reactions: Strong Dependence

Weak dependence

Applicability of Eikonal Model (inert-core approximation) for nucleon removal from deeply bound states ?

Direct KO

Knockout Reaction Mechanism

NSCL, MSU - 14O knockout at 60 AMeVF. Flavigny, A. Obertelli et al., Phys. Rev. Lett 108, 252501 (2012)

Multiple scattering/ Evaporation

Core excitation

14O(d,t)

Rs=sexp/stheo

Weakly-bound Deeply-bound

ΔS=Sn-Sp (MeV)

C. Louchart, A. Obertelli et al., Phys. Rev. C 83, 011601 (R) (2011)

Intranuclear Cascade Model (INC)

GANIL E569S – SPIRAL d(14O,t) 13O at 18 A MeV F. Flavigny, A. Obertelli et al. paper in preparation

INC: Significant core-excitation process depletes the one-neutron removal channel

(d,t) transfer

14O(d,t)

ΔS=Sn-Sp (MeV)

Knockout Reaction Mechanism

NSCL, MSU - 14O knockout at 60 AMeVF. Flavigny, A. Obertelli et al., Phys. Rev. Lett 108, 252501 (2012)

GANIL E569S – SPIRAL d(14O,t) 13O at 18 A MeV F. Flavigny, A. Obertelli et al. paper in preparation

14O(d,t)

ΔS=Sn-Sp (MeV)

kinematical cut

low energy tail

Low energy tail : Inelastic interaction between core and target ?

FSI between the neutron and the target ?

(d,t) transfer

Complete Sets of Data Detailed Investigation of Nucleon Stripping Mechanisms at Intermediate-energy

Weakly-bound Deeply-bound

with detection of knocked-out nucleons in one-nucleon removal

Measuring core-excitation channels Justify over-prediction due to

inert-core assumption

12N: 1n-knockout + 1p decay 11C: 1n-knockout + 2p decay

Data: 12C( 14O, 13N), 12C( 14O, 13O), 12C( 14O, 12N+p), 12C( 14O, 11C+2p) @ 65 A MeV

with detection of forward-moving protons tagging decayed protons (core-excitation)

Goal (i) : Investigate the origin of discrepancies between Spectroscopic Factors extracted from Transfer and Knockout

Nucleon removal

14O (Z=8) - p-shell spherical nucleus, in reach of ab-initio Calc. Reliable structure input examine different reaction models

RCNP E390: Exclusive Measurement I

Planned in Fall 2013 at RCNP

“Proton” target – structure-less probe

Goal (ii) : Study the dynamics of proton-induced deeply-bound nucleon-removal

Fully Exclusive Measurements with Detection of Knocked-out nucleons and Forward-moving proton

Data: 1H( 14O, 13N), 1H( 14O, 13O), 1H( 14O, 12N+p), 1H( 14O, 11C+2p) @ 65 A MeV

Simpler reaction mechanism Sensitive to larger part of wave function

Fully-exclusive Data needed at inter-mediate energy better understanding & tight control of reaction mechanism benchmark technique for structure studies deeply-bounded nucleon -- determine origin of discrepancy in SF studies

Y. Kondo et al, Phys. Rev. C 79, 014602 (2009)

A. Ozawa et al, Phys. Rev. C 84, 064315 (2011)

Semi-inclusive Data for loosely-bound neutron in 18C, 19C , 20C (40 A MeV & 81 A MeV)

RCNP E390: Exclusive Measurement II

Planned in Fall 2013 at RCNP

12C target :14O 13O + n neutron energy/angular distribution14O 13N + p proton energy/angular distribution14O 12N + n + p evaporation channels 14O 11C + n + 2p evaporation channels

CH2 target:14O(p,pn)13O energy/angular distribution14O(p,2p)13N energy/angular distribution14O(p,pn+p)12N evaporation channels14O(p,pn+2p)11C evaporation channels14O(p,d)13O transfer -- angular distribution14O(p,p)14O elastic scattering -- angular distribution

14°Proton / Neutron

Heavy Residuesγ

Target

RCNP E390


Exclusive Knockout data of 14O on C & proton targets at ~ 250 A MeV

Target

Neutron ( up to 10° )

Proton, Heavy Residues

Proton/ Neutron

Compete Data Set for Detailed Study of Reaction Mechanism

Proton Detector was not ready Proposal Deferred

With RCNP E390 at 60 AMeV necessary for 250AMeV data ?

SAMURAI


Isospin Dependence of Nucleon CorrelationsMSU/ NSCL 09084 (planned in 2014):




RCNP E390 (planned in 2013):

Understanding Nucleon Stripping Reaction Mechanisms from Exotic Nuclei at Intermediate Energy


Energy Level SchemeIndicate the presence of pf-shell intrude

configurations

Single-neutron Removal

Cross Sections Quantify the intrusion of pf-shell configurations

-1n

-1n

31Na 32Na 33Na

34Mg

32Ne31Ne30Ne

32Mg 33Mg

29Ne28Ne27Ne26Ne25Ne

-1n

N=20

35Mg 36Mg

Island of Inversio

n

Nuclear Structure in the “Island of Inversion”

1p3/2

1p1/2

1d5/2

2s1/2

1d3/2

1f7/2

1s1/

2

2

8

20 Magic number

n l j

(36Mg,25Mg + g)

(30Ne, 29Ne + g)

Systematic study towards and across the island of inversion: establish the role of intruder configurations evaluate the current shell models

1p3/2

BigRIPS (Beam PID) ZeroDegree (fragment PID & momentum measurement)

DALI2(γ-ray detection)



Beams: 30Ne, 36Mg @ ~ 250 A MeV

Target: Carbon

RCNP E365 (completed in Jan 2012):

Systematic studies of neutron-proton pairing in sd-shell nuclei using (p,3He) and (3He,p) transfer reactions


Probing Neutron-Proton Correlations

RIKEN NP1206-SAMURAI10 (April 18-19, 2013):

Study of Neutron-Proton Correlation & 3N-Force in N=Z nuclei Proposal:Study of Short-range Correlation in nuclei with high energy proton beam

Idea: np-knockout using proton target at ~ 400 AMeV ?

In nuclei: 4 types of Pairs

Neutron-Proton Pair Correlations

Isovector (T=1) np-pairing Well defined from the Isospin Symmetry

Isoscalar (T=0) np-pairing A lot of uncertainties !!

Isoscalar (T=0, S=1) np pair (deuteron-like) new phase of nuclear matter

Isovector (T=1, S=0) nn, pp, np pair np should be similar to nn & pp

Theoretical & experimental efforts since 60’s Contradicting opinions & results !

○ Nature of T=0 pair in nuclear medium ?○ Mutual Strength & Interplay of T=0 and T=1 np, nn, pp pairs ? ○ Does T=0 pairing give rise to collective modes ?

Long-standing open fundamental questions:

R. Subedi et al.,Science 320 (2008) 1476.

Strong NN tensor force (short-range correlations)

12C(e,e’pN) @ 4.627 GeV

n p >

factor of 18

n n

J.M. Kidd et al., PRC 37, 2613 (1988).

-2p

-2n

-np

12C + 12C X + anything @ 250 MeV/u (inclusive)

factor of ~ 8

12C

12C – Interesting Physics Found & Hidden

12C(p,3He) , 12C(p,t) @ 40 MeV

σnp / σ nn ~2.4

What is the behavior of np-correlations as a function of the relative momentum of the pair ?

For 12C, 4p & 4n on p3/2 shell No correlation: factor of 2.67 (pair counting)

M. Yasue et al., J. Phys. Soc. Jap. 42, 367 (1977).

Neutron-Proton Removal Reactions

Tensor Interaction – different relative significance to Central at different region

• Transfer: ~ 1-2• HI-induced Knockout : ~8

12C: ratio of np/nn cross section

• (e,e’pn): ~18

Different Reaction Mechanisms Sensitive to Different range of 2N Correlations

Various types of Reaction Mechanisms Complete Picture of np-tensor Correlations ?

np

pp

R. Schiavilla et al., Phys. Rev. Lett. 98, 132501 (2007)

M. Alvioli et al., Phys. Rev. Lett. 100, 162503 (2008)

Probing Neutron-Proton CorrelationsRCNP E365 (completed in Jan 2012):


Proposal:

Study of Short-range Correlation in nuclei with high energy proton beam

RIKEN NP1206-SAMURAI10 (April 18, 2013):

Study of Neutron-Proton Correlation & 3N-Force in N=Z nuclei

longer-range

short-range

Two-nucleon Transfer Reactions

Two-nucleon transfer reactions like (t,p) or (p,t) specific tool to probe T=1 pair correlations

Similarity between pairing field and 2-body transfer operator

R.A. Broglia et al., Adv. Nucl. Phys. 6, 287 (1973)

Ground-state composed of BCS pairs, two-nucleon transfer cross sections enhanced

S.J. Freeman et al. PRC 75 051301(R) (2007)

Spectra from (p,t) reactions

76Ge & 76,78Se(p,t) strength: predominately to the ground states simple BCS paired states

Neutron-Proton pairing using np transfer ?

Two-nucleon Transfer Reactions

Interacting Boson Model (IBM-4)

Reactions(p, 3He), (3He,p) DT=0,1(d,a), (a,d) DT=0(a, 6Li), (6Li,a) DT=0

T=0 (T=1) pairing:enhanced transfer probabilities 0+ → 1+ (0+ → 0+) levels

Measure the np transfer cross section to T=1 and T=0 states

Absolute σ(T=1) and σ(T=0) – character and strength of the correlationsσ(T=1) /σ(T=0) – interplay of T=1 and T=0 pairing modes

T=0 stronger

T=1 stronger

Ratio of cross section (T=1/ T=0) - reducing systematic effects of absolute normalization

Shiro Yoshida, NP 33, 685 (1962)

Systematics of T=0 & T=1 np-pairing in sd-shell

Closed-shell nuclei 16O, 40Ca NOT follow single-particle estimate ?

Doubtful increase of > a factor of 10 from 24Mg to 28Si ?

No intuitive understanding – 20Ne, 24Mg follow single-particle prediction ?

Inconsistencies in the trends (sd-shell):

N=Z nuclei in sd-shell

(3He,p)

from A. Macchiavelli (LBNL)

Goals: Insight & quantitative knowledge of T=0 and T=1 np-pairing mechanism

Systematic measurements spanning sd-shell nuclei under SAME condition

Consistent absolute (dσ/dΩ) + at 0º Reliable systematics

– Interplay of T=0 and T=1 np pairing– Individual T=0 & T=1 collectivity

Joint analysis (3He,p) & (p,3He)

complete understanding – addition & removal transfer reactions for np-pairing

Systematic framework -- studies of np pairing in heavier N=Z nuclei (RI Beams)

24Mg(3He,p), 32S(3He,p) @ 25 MeV

24Mg(p,3He), 28Si(p,3He) & 40Ca(p,3He) @ 65 MeV

Five reactions proposed:

Two MWDCs -- positionOne plastic scintillator -- E, TOF for PID

65 MeV proton / 25 MeV 3He beams from injector AVF cyclotron (bypass Ring-Cyclotron)

Plastic scintillators (front of FP)

Grand Raiden

3H beam at 25 MeV24Mg(3He,p), 32S(3He,p)

Proton beam at 65 MeV24Mg(p,3He),28Si(p,3He),40Ca(p,3He)

RCNP E365 (Completed in Jan 2012):Systematic studies of neutron-proton pairing in sd-shell nuclei using (p,3He) and (3He,p) transfer reactions

Grand Raiden recoil particle

LAS elastic scattering reaction(beam normalization & target thickness measurement)

LAS

Revisiting (p,3He) and (3He,p) reactions in the sd shell RCNP Experiment – E365

24Mg (3He,p) at 25MeV

Theoretical analysis of structure by Alex Brown (MSU) and full two-step transfer reactions by Ian Thompson (LLNL)

Completed in Jan, 2012

Online Analysis

Online Analysis

Data Analysis On-going






longer-range

Target

Projectile (fast beam)

9Be/ 12C

Two-Nucleon Knockout Model

E.C. Simpson and J. Tostevin et al., PRL 102, 132502 (2009)

J. Tostevin, B.A. Brown, PRC 74, 064604 (2006)

Theoretical Cross sections:Reaction: Eikonal & Sudden approximationStructure: 2N Overlap from Shell Model

2n or 2p knockout (T=1)

A. Gade et al., Phys. Rev. C 74 , 021302(R) (2006)D. Bazin et al., Phys. Rev. Lett. 91, 012501 (2003)

K. Yoneda et al., Phys. Rev. C 74 , 021303(R) (2006)

Framework to quantitatively assess descriptions of 2n & 2p T=1 correlations

P. Fallon et al., PRC 81, 041302(R) (2010)

- 2n knockout from 34Ar, 30S, 26Si

2N knockout cross sections 　　　　　　　　　　 carry information of 2N correlations

12C – Interesting Physics Found & Hidden

T=0 np-spatial correlations in the wave functions are insufficient

First Calculations : np removal from 12C (with Shell Model Calc. from B.A. Brown)

Advanced Model np removal with T=0

-2p

-2n

-np

p-shell

E.C. Simpson and J.A. Tostevin, PRC 83, 014605 (2011).

WBP

PJT interaction

T = 0 cross-sections – sensitive to different effective interactions !

10BShell model

np-Correlations & 3-body Force

TOSM (tensor-optimized shell model) T. Myo (Osaka Tech)

■ Conventional Shell model

Ο NCSM (NN+3N)

∆ NCSM (NN, w/o3N)

Significant Increase in the T=0 Cross Sections !

T=0 cross section Sensitive to 3N-force !

Final-State-Exclusive Data needed to pin-point the physics !

No-core Shell Model (NCSM) (realistic 2-body and 3-body forces ) P. Navratil (TRIUMF)

Conventional Shell Model B.A. Brown (MSU)

Structure Model

Eikonal-Theory Reaction Model σ(theo)

theo

. σ -n

p (m

b)

np-removal of 12C on 12C target

10B

E. C. Simpson, P. Navrátil, R. Roth, and J. A. TostevinPhys. Rev. C 86, 054609

DALI2

Target

RIBF: First final-state exclusive measurement of np-pair removal in 12C (April 18, 2013)

12C 10B (-np), 10C (-2n), 10Be (-2p) @ 200 A MeV

SAMURAI at RIBF Systematic & Quantitative knowledge of np-Correlations & 3N-force toward exotic N=Z nuclei

Benchmark: New Powerful Tool of Direct np-removal reaction

First detailed study of diffractive mechanism in 2N removal reaction

First insight into internal structure of correlated pairs (FSI considered)

First quantitative study of np-correlation & 3-body force

γ-residues-neutron MeasurementSAMURAI

LAS (3.2 Tm)

GR (5.66 Tm)

Proton detectorsNeutron detectors

SAMURAI

Reaction Mechanism / Cross Sections ?

np-knockout using proton target (or proton beam) at ~ 400 AMeV ?

More direct information about np-correlations !

SAMURAI large acceptance 1N and 2N removal channel can be measured simultaneously




Proposal

Study of Short-range Correlation in nuclei with high energy proton beam



longer-range

short-range

Short Range Correlations in Nuclei

1.f

Nucleons

2N-SRC

1.7f

o = 0.16 GeV/fm3

~1 fm

1.7 fm

A~1057

SRC ~RN

LRC ~RA

Cold-Dense Nuclear Matter (from deuteron to neutron-stars).

What SRC in nuclei can tell us about:

High – Momentum Component of the Nuclear Wave Function.

The Strong Short-Range Force Between Nucleons.tensor force, repulsive core, 3N forces

Nucleon structure modification in the medium ?EMC and SRC

http://upload.wikimedia.org/wikipedia/commons/e/ed/Neutron_star_cross_section.jpg




MISSING :

Spectroscopicfactors

for (e, e’p)reactions

show only60-70%of the

expectedsingle-particle

strength.L. Lapikas, Nucl. Phys. A553, 297c (1993)

Correlations Between Nucleons SRC and LRC

Benhar et al., Phys. Lett. B 177 (1986) 135.

Indication for SRC

Spec

trosc

opic

Fac

tor

12C – Interesting Physics found & hidden

12C(e,e’pN) @ Jefferson Lab. (US)

n p >~ 18 times

n n

How about using proton beam ? 12C(p,ppN) A variety of incident energies

Proton Beams on “radioactive target”

Proton Target & Radioactive Beam Larger Reaction Cross Sections

GSI ->FAIR (2018 ?)

CSR, Lanzhou

Under Discussion …

Facility with GeV proton beams

Proton beam with: GeVEK 8.2max cGeV /6.3

IMP

pf

p

p

p1

p0

p2

From p0, p1, and p2 we can deduce, event-by-event whatpf and the binding energy of each knocked-out proton is.

Targetnucleus

p pn

pn

We can then comparepn with pf and seeif they are roughly “back to back.”

Kinematics -- High-energy Proton Beams

~1 fm

= h/p = hc/pc = 2 0.197 GeV-fm/(2.8 GeV) 0.44 fm.

They have Small deBroglie wavelength:

SRC ~RN

BeamVeto box

20o60o

2 meter 6 meter

32.5o

2 planes of GEM or W.ch. ~1m apart

Array : 3 layers of 10x10x200 cm3 scintillators



Total 450 scintillating counters

γ

Mean-field SRC

Brookhaven National Laboratory (BNL)

High Statistics & Resolution (p,ppN) data ! No more (p,ppn) Expt at BNL

Parasitic measurement No (nn or pp) data

Only 18 coincidence event !

Rates

Triple coincidence 12C(p,2pn)

Triple coincidence 12C(p,pnn)

np pairs

nn pairs

100 events/hour

1 events/hour

In 15 days (100% beam availability) 35,000 events

In 15 days (100% beam availability) 350 events

(For a 109 protons/sec beam)

High Statistics & resolutions Physics

Physics I : Mapping transition from mean field to SRC

EVA / BNL: Only 18 12C(p,2p+n) events with pn>kF

CSR Lanzhou: Expecting 35,000 12C(p,2p+n) events with pn>kF

cMeVpmiss /15

With 100ps TOF resolution:

Sharp Transition !Mean-field SRC

Physics II. SRC Isospin Structure and the Tensor Force

Asymmetric nuclei N>Z:

np-SRC dominance Equal number of protons and neutrons above kF

The probability for a proton to be with momentum above kF

is higher than for a neutron

12C27Al

56Fe197Au

Theory prediction

Physics III: Pair-momentum Dependence of Tensor Force

At the CSR we propose to study the nucleon relative momentum range below 400 MeV/c, were the np/pp ratio is expected to be smaller.

At 400-600 MeV/c

3He

Sargsian, Abrahamyan, Strikman, Frankfurt PR C71 044615 (2005).

Physics VI: SRC C.M. and Relative Momenta Distributions:

EVA / BNL: Only 18 12C(p,2p+n) events with pn>kF

CSR Lanzhou: Expecting 35,000 12C(p,2p+n) events with pn>kF

350 12C(p,np+n) events with pn>kF

Can compare nn-SRC to np-SRC

Physics V: Reaction Mechanism

Hard processes

high energy and large momentum-transfer

~1 fm

How low in t, u, Q2 … can we still use the advantages of hard scattering ?

Important practical question:

• Simple Measurement Direct and Clear Probe to SRC• Experimental Program: 12C (40Ca, 48Ca, 208Pb, deuteron)

Experimental study of Short Range Correlation (SRC)

High-momentum components of nuclear wave function Tensor NN interaction, repulsive core & 3N forces Cold-dense nuclear matter (neutron stars)

New Physics of (p,ppN) @ 2.8 GeV , IMP LanzhouI. Transition from Mean-field to Short-range Correlations

II. SRC Isospin Structure and Tensor Force

III. Pair relative-momentum dependence of Tensor Force

IV. SRC COM and Relative Momentum Distribution

V. Reaction Mechanism

R.B. Wiringa et al., PRC 78, 021001 R (2008)W. Horiuchi et al., PRC 84, 061304 (2011)W. Horiuchi et al., arXiv 1202.0368v1 (2012)

W. Horiuchi et al., PRC 76, 024311 (2007)R. Schiavilla et al., Phys. Rev. Lett. 98, 132501 (2007)

np

ppM. Vanhalst et al., PRC 84, 031302 R (2011)

H. Feldeier,W. Horiuchi et al., PRC 84, 054003 (2011)

Universality of Tensor Correlations ?

Correlations at ranges “longer” than “short-range” makes nuclei unique ?

Few hundred MeV/nucleon energy (eg.RIBF) Less selective in reaction mechanism Spatial (or “momentum”) Correlations



Neutron-Proton Correlations (knockout and transfer reactions)

Di-neutron Correlations (breakup reaction)

BCS to BEC Transitions ? (transfer reaction ?)

Di-neutron CorrelationsY. Oganessian et al., Phys. Rev. Lett. 82, 4996 (1999)

di-neutron

Cigar-like

6He W. Horiuchi et al., Phys. Rev. C. 76, 024311 (2007)

A. Chatterjee et al., Phys. Rev. Lett. 101, 032701 (2008)

Y. Oganessian et al., Phys. Rev. Lett. 82, 4996 (1999)

Two-neutron exchange dashed: di-neutrondotted: cigar-like

6He + 65Cu Elab=22.6 MeV

T. Nakamura et al., Phys. Rev. Lett. 96, 252502 (2006)

Neutron Correlations in 11Li

Strong two-nucleon correlation

Coulomb breakup – not good probe

Y. Kikuchi et al., PRC 81, 044308 (2010)

Dominant effect of final-state interaction

How about Nuclear Breakup reactions ?



Neutron-Proton Correlations (knockout, transfer, quasi-free scattering reactions)

Di-neutron Correlations (breakup reaction ?)

BCS to BEC Transitions ? (knockout and transfer reaction ??)

• How Pair Correlation in exotic nuclei is different from stable nuclei ?• Strong density dependence (normal density low nucleon density)?

Sn isotopes(Z=50)

n

n

nn

More neutron-rich

………100Sn N=Z

102Sn

adding neutronsneutron cloud

134Sn

Neutron skin Low density distribution

Di-neutron Correlation: BCS BEC towards n-rich ?

Cooper pair exhibits a strong spatial dineutron correlation over a wide range of neutron densities ρ/ρ0 ≈ 10-4 –0.5

Crossover behavior between the weak coupling BCS type and the Bose-Einstein condensation of bound neutron pairs (ρ/ρ0 ≈ 10-4 – 10-1 domain of BCS-BEC crosssover).

M. Matsuo, PRC 73, 044309 (2006)

Neutron-pairing in Sn Isotopes

H. Shimoyama, M. Matsuo, paper in preparation (0+ systematics)M. Matsuo, H. Shimoyama, PRC 82, 024318 (2010). (2+ systematics) How to see & interpret these nn-pairing

structure in Transfer Reaction ?

Skyrme HFB + QRPA approach Probability for Cooper pair to be correlated at short distances r < few fm is significantly enhanced at R > Rsurf

How to probe the features ?

Pair Transition density – Skyrme HFB + QRPA approach

M. Matsuo et al., PRC 82, 024318 (2010)

Structure Calc.Pair Transfer Strength from QRPA Form Factor

One-step transfer + QRPA Form Factor

TWOFNR, M. Igarashi et al.,

Instruction: Y. Aoki (Tsukuba), Calc: D.Y. Pang, JL

gs-gs

Reaction Calc: 02+ & 21

+ (in progress)

(p,t) Reaction Calc.

Neutron-pairing in Sn Isotopes

Di-neutron Correlation: BCS BEC towards n-rich ?

What is the appropriate observables ?Cross sections / Angular correlations / Momentum correlations / or ?

Observables free from final-state-interactions

What is the appropriate reaction mechanism ?

What is the appropriate energy ?

Kinematics chosen to suppress the effect of final-state-interactions

Energy chosen for Kinematics & for model framework & experimental feasibility



BCS to BEC Transitions ?

34,46Ar(p,d) at 70 AMeV

14O knockout on C & p a 65 AMeV

30Ne, 36Mg knockout on C at 250 AMeV

Quasi-free scattering, proton beam at 2.8 GeV

Neutron-Proton Correlations

np-transfer on sd-shell nuclei

np-knockout on 12C at 200 AMeV

Di-neutron Correlations

6He breakup on C & p at 70 AMeV

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Documents

Jenny Lee RIKEN , Nishina Center