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 ??)
Jenny Lee
RIKEN , Nishina Center
Studies of Nucleon Correlations
using Direct Reactions
Neutron-Proton
Correlations
Isospin Dependence of
Nucleon Correlations
30Ne, 36Mg
34,46Ar(p,d)
at 70 AMeV
knockout
on C at 250 AMeV np-transfer on
sd-shell nuclei
14O knockout on
C & p a 65 AMeV
np-knockout
Support from
Theorists
Di-neutron Correlations
6He
breakup on C
& p at 70 AMeV
BCS to BEC
Transitions ?
on 12C at
200 AMeV
Quasi-free
scattering,
proton beam
at 2.8 GeV
Isospin Dependence of Nucleon Correlations
MSU/ NSCL 09084 (planned in 2014):
Comparison of the Neutron Spectroscopic Factors from
Transfer and Knockout Reactions at E/A=70 MeV
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
RIKEN (performed in Dec 2010):
Spectroscopic information towards “Island of Inversion”
using knockout reaction withJenny
in-beam
Lee gamma technique
RIKEN , Nishina Center
Nucleon Correlations
Truncated shell model space
+ effective interactions
Greater
distribution of
nucleons to
higher energy
configuration
In reality
Short-range,
tensor &
collective
correlations
Few active
orbitals
High
Occupancy
Inert Core
Reduction in
Occupancy
Inert Core
Probing the nuclear wave function
Removing nucleon from occupied orbital
 Cross sections (probability) depend on the single-particle occupancy &
overlap of many-body wave functions
Spectroscopic Factor (SF)
Cross Sections
Reaction Model
Spectroscopic Factors (expt)
How good the effective interaction in
Shell Model can describe the correlations ?
Quantify Occupancy Correlation Effects
SM description is
accurate
How much ? What is the Isospin
Dependence of nucleon correlations?
Some correlations
missing in the
interactions ?
(e,e’p) – Stable nuclei (near closed shell)
• Constant ~30-40% of SF reduction compared to theory
• Correlations missing in shell-model interactions
L. Lapikas, Nucl. Phys. A553, 297c (1993)
(e,e’p) reactions
How about Transfer Reactions ?
Transfer Reactions -- long history ( >50 years)
 abundant data, but Problems in SF(expt) !
Experimental SF from Transfer Reactions
Well-known problem
- optical model potentials
- parameters
- reaction models
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 & nonlocality 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
Consistent SFs for 41Ca
Reliable Framework
 Systematic Studies
SF=1.01± 0.06
SF(SM) = 1.00
Survey of Spectroscopic Factor (Transfer Reactions)
Extend to 88 nuclei (ground-state) :
SF(expt)
Found 225 relevant papers
Re-analyzed (unified model) > 430 data sets
 Extracted 88 SF(expt)
Ground-state
Benchmark  20 % agreement to theory
SF(theory)
Re-analyzed >2,000 data ( >300 papers )
 Extracted 565 SF(expt)
SF(expt)
Extend Survey to excited states :
Z=8-16
Do we understand all the correlations ?
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)
J. Lee, M. B. Tsang et al., Phys. Rev. C79, 054611 (2009)
SF(theory)
Suppression of SFs in Transfer Reactions
CH89 + ro=1.25 fm with minimum assumption
 consistent SF(expt) with Shell Model
Microscopic Input in Reaction Model
 JLM potential & Hartree-Fock (SK20)
ro=1.25 fm  HF rms radius
Global CH89  JLM + HF densities
Constant ~30% reduction in SFs
J. Lee et al., Phys. Rev. C 73 , 044608 (2006)
Suppression of SFs in Transfer Reactions
n-rich
p-rich
CH89
JLM+HF
ΔS=Sn-Sp
Constant ~30% reduction in SFs
Different sets of consistent parameters
 different normalizations
J. Lee et al., Phys. Rev. C 73 , 044608 (2006)
• 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
Isospin Dependence of Nucleon Correlations
ΔS=Sn-Sp
34,36,46Ar
+ p→d + 33,35,45Ar
Inverse kinematics at 33MeV/A
(e,e p’) Rs = 0.6-0.7
S800
Neutron-rich
Proton-rich
Transfer Reactions:
Weak Isospin Dependence of
nucleon correlations
J. Lee et al., Phys. Rev. Lett 104, 112701 (2010)
Target
Chamber
Nucleon Knockout with Fast Beams on 9Be / 12C Target
Target
9Be
or 12C
High incident energy  Reaction only
affects a nucleon at surface
Reaction Theory:
Eikonal & Sudden Approximations
Core
J. Tostevin et al., J. Phys. G, Part. Phys. 25, 735 (1999)
Projectile (fast beam)
Rs = σ(expt)/σ (ES+SM)
One-nucleon knockout -- away from stability
• Rs strongly depends on separation energy
• More correlation effect - strongly bound
valence nucleon
A. Gade et al., Phys. Rev. C 77, 044306 (2008)
and reference therein
ΔS=Sn-Sp
Isospin Dependence of Shell Occupancies?
Reduction Factor
Q: Isospin Dependence ?
Knockout reactions: Yes & Strong
A. Gade et al., Phys. Rev. C 77, 044306 (2008) & reference therein
Transfer reactions: Weak
p(34,36,46Ar,d) at 33 A MeV
J. Lee et al., Phys. Rev. Lett 104, 112701 (2010)
Systematic difference
between two probes !
Incompatibility  Incomplete understanding in underlying reaction mechanism
MSU/ NSCL 09084 (planned in 2014):
Comparison of the Neutron Spectroscopic Factors from
Transfer and Knockout Reactions at E/A=70 MeV
Focal Plane
34,46Ar(p,d) 33,45Ar
NSCL 09084:
at 70 AMeV
Target
Chamber
S800
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)
Isospin Dependence of Shell Occupancies?
Reduction Factor
Q: Isospin Dependence ?
Knockout reactions: Yes & Strong
A. Gade et al., Phys. Rev. C 77, 044306 (2008) & reference therein
Transfer reactions: Weak
p(34,36,46Ar,d) at 33 A MeV
J. Lee et al., Phys. Rev. Lett 104, 112701 (2010)
Systematic difference
between two probes !
Incompatibility  Incomplete understanding in underlying reaction mechanism
Transfer Reaction
 Future NSCL 09084: 34,46Ar(p,d) at 70 MeV/A
- same energy as knockout reactions for direct comparison
Knockout Reaction ?
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)
Weak dependence
Self-consistent Green’s Functions + FRPA
C. Barbieri & W. H. Dickhoff, arXiv:0901.1920v1
Knockout reactions: Strong Dependence
Applicability of Eikonal Model
(inert-core approximation) for
nucleon removal from deeply bound
states ?
Weak dependence
Knockout Reaction Mechanism
Deeply-bound
Weakly-bound
Rs=sexp/stheo
Direct KO
(d,t)
transfer
Multiple scattering/
Evaporation
Core excitation
Intranuclear Cascade Model (INC)
C. Louchart, A. Obertelli et al., Phys. Rev. C 83, 011601 (R) (2011)
14O(d,t)
ΔS=Sn-Sp (MeV)
NSCL, MSU - 14O knockout at 60 AMeV
F. Flavigny, A. Obertelli et al., Phys. Rev. Lett 108, 252501 (2012) INC:
GANIL E569S – SPIRAL d(14O,t) 13O at 18 A MeV
F. Flavigny, A. Obertelli et al. paper in preparation
Significant core-excitation process
depletes the one-neutron removal channel
Knockout Reaction Mechanism
Deeply-bound
Weakly-bound
kinematical
cut
(d,t)
transfer
low energy tail
14O(d,t)
Low energy tail :
ΔS=Sn-Sp (MeV)
NSCL, MSU - 14O knockout at 60 AMeV

Inelastic interaction between core and target ?

FSI between the neutron and the target ?
F. 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
Complete Sets of Data  Detailed
Investigation of Nucleon Stripping
Mechanisms at Intermediate-energy
RCNP E390: Exclusive Measurement I
14O
(Z=8) - p-shell spherical nucleus, in reach of ab-initio Calc.
Reliable structure input  examine different reaction models
Goal (i) : Investigate the origin of discrepancies between
Spectroscopic Factors extracted from Transfer and Knockout
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)
with detection of knocked-out nucleons in one-nucleon removal
Planned in Fall 2013 at RCNP
RCNP E390: Exclusive Measurement II
“Proton” target – structure-less probe
 Simpler reaction mechanism
 Sensitive to larger part of wave function
Semi-inclusive Data for looselybound neutron in 18C, 19C , 20C
(40 A MeV & 81 A MeV)
Y. Kondo et al, Phys. Rev. C 79, 014602 (2009)
A. Ozawa et al, Phys. Rev. C 84, 064315 (2011)
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
Goal (ii) : Study the dynamics of proton-induced deeply-bound nucleon-removal
Data: 1H( 14O, 13N), 1H( 14O, 13O), 1H( 14O, 12N+p), 1H( 14O, 11C+2p) @ 65 A MeV
Fully Exclusive Measurements with Detection of Knocked-out nucleons
and Forward-moving proton
Planned in Fall 2013 at RCNP
12C
target :
 13O + n
14O  13N + p
14O  12N + n + p
14O  11C + n + 2p
14O
neutron energy/angular distribution
proton energy/angular distribution
evaporation channels
evaporation channels
CH2 target:
14O(p,pn)13O
energy/angular distribution
energy/angular distribution
evaporation channels
evaporation channels
transfer -- angular distribution
elastic scattering -- angular distribution
14O(p,2p)13N
14O(p,pn+p)12N
14O(p,pn+2p)11C
14O(p,d)13O
14O(p,p)14O
RCNP E390
Proton / Neutron
Target
14°
γ
Heavy Residues
RIKEN NP1112-SAMURAI06 (submitted  deferred):
Steps to Clarify the Isospin Dependence of Nucleon Correlations
Exclusive Knockout data of 14O on C & proton targets at ~ 250 A MeV
Proton/ Neutron
Neutron ( up to 10° )
Compete Data Set for Detailed
Study of Reaction Mechanism
Proton Detector was not
ready  Proposal Deferred
Target
With RCNP E390 at 60 AMeV
 necessary for 250AMeV data ?
Proton, Heavy Residues
SAMURAI
Isospin Dependence of Nucleon Correlations
MSU/ NSCL 09084 (planned in 2014):
Comparison of the Neutron Spectroscopic Factors from
Transfer and Knockout Reactions at E/A=70 MeV
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
RIKEN (performed in Dec 2010):
Spectroscopic information towards “Island of Inversion”
using knockout reaction with in-beam gamma technique
Jenny Lee
RIKEN , Nishina Center
Nuclear Structure in the “Island of Inversion”
-1n
Single-neutron Removal
-1n
-1n
Island of
Inversion
1p3/2
1f7/2
32Mg 33Mg 34Mg 35Mg 36Mg
1d3/2
31Na 32Na 33Na
2s1/2
1d5/2
25Ne 26Ne 27Ne 28Ne 29Ne 30Ne 31Ne 32Ne
N=20
Energy Level Scheme
Indicate the presence of pf-shell intrude configurations
Cross Sections
 Quantify the intrusion of pf-shell configurations
20
Magic
number
8
1p1/2
1p3/2
nlj
1s1/2
2
Systematic study towards and across the island of inversion: (36Mg,25Mg + g)
 establish the role of intruder configurations
(30Ne, 29Ne + g)
 evaluate the current shell models
RIKEN (performed in Dec 2010):
Spectroscopic information towards “Island of Inversion”
using knockout reaction with in-beam gamma technique
Beams: 30Ne, 36Mg @ ~ 250 A MeV
DALI2
(γ-ray
detection)
Target:
Carbon
BigRIPS (Beam PID)
ZeroDegree (fragment PID &
momentum measurement)
Probing Neutron-Proton Correlations
RCNP E365 (completed in Jan 2012):
Systematic studies of neutron-proton pairing in sd-shell
nuclei using (p,3He) and (3He,p) transfer reactions
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
Jenny at
Lee~ 400 AMeV ?
RIKEN , Nishina Center
Neutron-Proton Pair Correlations
In nuclei: 4 types of Pairs
Isovector (T=1, S=0) nn, pp, np pair
np should be similar to nn & pp
Isoscalar (T=0, S=1) np pair (deuteron-like)
 new phase of nuclear matter
Theoretical & experimental efforts
since 60’s  Contradicting opinions
& results !
Isovector (T=1) np-pairing
Well defined from the
Isospin Symmetry
Isoscalar (T=0) np-pairing
A lot of uncertainties !!
Long-standing open fundamental questions:
○ 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 ?
12C
12C(e,e’pN)
– Interesting Physics Found & Hidden
@ 4.627 GeV
factor of 18
n p
>
n n
+ 12C  X + anything
@ 250 MeV/u (inclusive)
12C
12C
Strong NN tensor force
(short-range correlations)
R. Subedi et al.,Science 320 (2008) 1476.
J.M. Kidd et al.,
PRC 37, 2613 (1988).
12C(p,3He)
, 12C(p,t) @ 40 MeV
σnp / σ nn ~2.4
M. Yasue et al., J. Phys. Soc. Jap. 42, 367 (1977).
For 12C, 4p & 4n on p3/2 shell
No correlation: factor of 2.67 (pair counting)
What is the behavior of np-correlations as a
function of the relative momentum of the pair ?
factor of ~ 8
-2p
-np
-2n
Neutron-Proton Removal Reactions
R. Schiavilla et al., Phys. Rev.
Lett. 98, 132501 (2007)
np
M. Alvioli et al., Phys. Rev.
Lett. 100, 162503 (2008)
pp
Tensor Interaction – different relative
significance to Central at different region
12C:
ratio of np/nn cross section
• Transfer: ~ 1-2
• HI-induced Knockout : ~8
Different Reaction Mechanisms
 Sensitive to Different range of 2N Correlations
• (e,e’pn): ~18
Various types of Reaction Mechanisms  Complete Picture of np-tensor Correlations ?
Probing Neutron-Proton Correlations
RCNP E365 (completed in Jan 2012):
longer-range
Systematic studies of neutron-proton pairing
in sd-shell nuclei using (p,3He) and (3He,p)
transfer reactions
RIKEN NP1206-SAMURAI10 (April 18, 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
short-range
Two-nucleon Transfer Reactions
Similarity between pairing field and 2-body transfer operator
Two-nucleon transfer reactions like (t,p) or (p,t) 
specific tool to probe T=1 pair correlations
Spectra from (p,t) reactions
Ground-state composed of BCS pairs, twonucleon transfer cross sections enhanced
R.A. Broglia et al., Adv. Nucl. Phys. 6, 287 (1973)
76Ge
& 76,78Se(p,t) strength: predominately to
the ground states  simple BCS paired states
Neutron-Proton pairing using np transfer ?
S.J. Freeman et al. PRC 75 051301(R) (2007)
Two-nucleon Transfer Reactions
T=0 (T=1) pairing:
enhanced transfer probabilities
0+ → 1+ (0+ → 0+) levels
Interacting Boson Model (IBM-4)
T=0 stronger
T=1 stronger
Reactions
(p, 3He), (3He,p) DT=0,1
(d,a), (a,d)
DT=0
(a, 6Li), (6Li,a) DT=0
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 correlations
σ(T=1) /σ(T=0) – interplay of T=1 and T=0 pairing modes
Systematics of T=0 & T=1 np-pairing in sd-shell
N=Z nuclei in sd-shell
Ratio of cross section (T=1/ T=0)
- reducing systematic effects of
absolute normalization
from A. Macchiavelli (LBNL)
(3He,p)
Shiro Yoshida, NP 33, 685 (1962)
Inconsistencies in the trends (sd-shell):
 Closed-shell nuclei 16O, 40Ca NOT follow single-particle estimate ?
 No intuitive understanding – 20Ne, 24Mg follow single-particle prediction ?
 Doubtful increase of > a factor of 10 from 24Mg to 28Si ?
Goals: Insight & quantitative knowledge of T=0 and T=1
np-pairing mechanism
Five reactions proposed:
24Mg(3He,p), 32S(3He,p)
@ 25 MeV
24Mg(p,3He), 28Si(p,3He)
& 40Ca(p,3He) @ 65 MeV
 Systematic measurements spanning
sd-shell nuclei under SAME condition
 Joint analysis (3He,p) & (p,3He)
 complete understanding – addition &
removal transfer reactions for np-pairing
 Consistent absolute (dσ/dΩ) + at 0º
 Reliable systematics
– Interplay of T=0 and T=1 np pairing
– Individual T=0 & T=1 collectivity
Systematic framework -- studies of np pairing in heavier N=Z nuclei (RI Beams)
RCNP E365 (Completed in Jan 2012):
Systematic studies of neutron-proton pairing in sd-shell
nuclei using (p,3He) and (3He,p) transfer reactions
3H
LAS
beam at 25 MeV
24Mg(3He,p), 32S(3He,p)
Proton beam at 65 MeV
24Mg(p,3He),28Si(p,3He),40Ca(p,3He)
Grand Raiden
Plastic
scintillators
(front of FP)
Grand Raiden  recoil particle
Two MWDCs -- position
LAS  elastic scattering reaction
One plastic scintillator
-- E, TOF for PID
(beam normalization & target thickness
measurement)
65 MeV proton / 25 MeV 3He beams from
injector AVF cyclotron (bypass Ring-Cyclotron)
Revisiting (p,3He) and (3He,p) reactions in the sd shell
RCNP Experiment – E365
24Mg (3He,p)
Completed in Jan, 2012
at 25MeV
Online Analysis
Cross Sec on (ub /sr)
Ex=1.05 (T=0) Distribu on
1.E+03
1.E+02
Online Analysis
1.E+01
0
4
8
12
16
20
24
28
32
36
lab - theta (deg)
Data Analysis On-going
40
Theoretical analysis of structure by Alex Brown (MSU) and
full two-step transfer reactions by Ian Thompson (LLNL)
Probing Neutron-Proton Correlations
RCNP E365 (completed in Jan 2012):
Systematic studies of neutron-proton pairing
in sd-shell nuclei using (p,3He) and (3He,p)
transfer reactions
RIKEN NP1206-SAMURAI10 (April 18, 2013):
Study of Neutron-Proton Correlation & 3N-Force
in N=Z nuclei
longer-range
Two-Nucleon Knockout Model
Target
9Be/ 12C
Theoretical Cross sections:
Reaction: Eikonal & Sudden approximation
Structure: 2N Overlap from Shell Model
J. Tostevin, B.A. Brown, PRC 74, 064604 (2006)
E.C. Simpson and J. Tostevin et al., PRL 102, 132502 (2009)
Projectile (fast beam)
- 2n knockout from 34Ar, 30S, 26Si
2n or 2p knockout (T=1)
K. Yoneda et al., Phys. Rev. C 74 , 021303(R) (2006)
D. Bazin et al., Phys. Rev. Lett. 91, 012501 (2003)
A. Gade et al., Phys. Rev. C 74 , 021302(R) (2006)
P. Fallon et al., PRC 81, 041302(R) (2010)
2N knockout cross sections
 carry information of 2N correlations
Framework to quantitatively assess
descriptions of 2n & 2p T=1 correlations
12C
– Interesting Physics Found & Hidden
Advanced Model np removal with T=0
First Calculations : np removal from 12C (with Shell Model Calc. from B.A. Brown)
E.C. Simpson and J.A. Tostevin, PRC 83, 014605 (2011).
-2n
Shell model
10B
PJT interaction
-2p
WBP
-np
p-shell
T=0 np-spatial correlations in the
wave functions are insufficient
T = 0 cross-sections – sensitive to
different effective interactions !
np-Correlations & 3-body Force
Structure
Model
Eikonal-Theory
Reaction Model
np-removal of 12C on 12C target
Significant Increase in the T=0
Cross Sections !
T=0 cross section Sensitive to 3N-force !
theo. σ-np (mb)
 Conventional Shell Model
B.A. Brown (MSU)
 No-core Shell Model (NCSM)
(realistic 2-body and 3-body forces )
P. Navratil (TRIUMF)
σ(theo)
Ο
NCSM (NN+3N)
∆ NCSM
(NN, w/o3N)
10B
■ Conventional
Shell model
E. C. Simpson, P. Navrátil, R. Roth, and J. A. Tostevin
Phys. Rev. C 86, 054609
 TOSM (tensor-optimized shell model) T. Myo (Osaka Tech)
Final-State-Exclusive Data needed to pin-point the physics !
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
DALI2
γ-residues-neutron Measurement

First quantitative study of npcorrelation & 3-body force
 First detailed study of diffractive
mechanism in 2N removal reaction
Target
 First insight into internal structure
of correlated pairs (FSI considered)
Benchmark: New Powerful Tool of Direct np-removal reaction
SAMURAI at RIBF  Systematic & Quantitative knowledge of
np-Correlations & 3N-force toward exotic N=Z nuclei
np-knockout using proton target
(or proton beam) at ~ 400 AMeV ?
More direct information about np-correlations !
Reaction Mechanism / Cross Sections ?
GR (5.66 Tm)
LAS (3.2 Tm)
Neutron detectors
SAMURAI
Proton
detectors
SAMURAI  large acceptance  1N and 2N removal
channel can be measured simultaneously
Probing Neutron-Proton Correlations
RCNP E365 (completed in Jan 2012):
longer-range
Systematic studies of neutron-proton pairing
in sd-shell nuclei using (p,3He) and (3He,p)
transfer reactions
RIKEN NP1206-SAMURAI10 (April 18, 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
short-range
Short Range Correlations in Nuclei
2N-SRC
SRC ~RN
~1 fm
LRC ~RA
1.f
1.7f
A~1057
o = 0.16 GeV/fm3
1.7 fm
Nucleons
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
Cold-Dense Nuclear Matter (from deuteron to neutron-stars).
Nucleon structure modification in the medium ?
EMC and SRC
Spectroscopic
factors
for (e, e’p)
reactions
show only
60-70%
of the
expected
single-particle
strength.
Spectroscopic Factor
Indication for SRC
L. Lapikas, Nucl. Phys. A553, 297c (1993)
Benhar et al., Phys. Lett. B 177 (1986) 135.
MISSING :
Correlations Between Nucleons
SRC and LRC
12C
– Interesting Physics found & hidden
~ 18 times
n p
12C(e,e’pN)
@ Jefferson Lab. (US)
>
n n
How about using proton beam ?
12C(p,ppN)
A variety of incident energies
Larger Reaction Cross Sections
Proton Target & Radioactive Beam
Proton Beams on “radioactive target”
Facility with GeV proton beams
CSR, Lanzhou
Under Discussion …
GSI ->FAIR (2018 ?)
IMP
Proton beam with:
max
EK
 2 . 8 GeV
 3 . 6 GeV / c
Kinematics -- High-energy Proton Beams
They have Small deBroglie wavelength:
 = h/p = hc/pc = 2  0.197 GeV-fm/(2.8 GeV)  0.44 fm.
p
~1 fm

p1
SRC ~RN


pf
p
n
p0
p

pn



From p0, p1, and p2 we can
deduce, event-by-event what

pf and the binding energy of
each knocked-out proton is.
Target
nucleus

p2
p
We can
then compare


pn with pf and see
if they are roughly “back to back.”
2 planes of GEM or W.ch. ~1m apart
Array : 3 layers of 10x10x200
cm3 scintillators
Veto box
32.5o
Beam
60o
2 meter
20o
Array : 3 layers of 10x10x200
cm3 scintillators
Total 450 scintillating counters
6 meter
Array : 3 layers of
10x10x100 cm3
scintillators
γ
Brookhaven National Laboratory (BNL)
Only 18 coincidence event !
Parasitic measurement
No (nn or pp) data
No more (p,ppn) Expt at BNL
High Statistics & Resolution (p,ppN) data !
Mean-field
SRC
Rates (For a 109 protons/sec beam)
Triple coincidence
12C(p,2pn)
np pairs
100 events/hour
In 15 days (100% beam availability) 35,000 events
Triple coincidence
12C(p,pnn)
nn pairs
1 events/hour
In 15 days (100% beam availability) 350 events
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
With 100ps TOF
resolution:
D p miss  15 MeV / c
Mean-field
SRC
Sharp Transition !
Physics II. SRC Isospin Structure and the Tensor Force
Asymmetric nuclei N>Z:
np-SRC dominance
The probability for a proton to
be with momentum above kF
is higher than for a neutron
Theory prediction
12C
27Al
Equal number of protons
and neutrons above kF
56Fe
197Au
Physics III: Pair-momentum Dependence of Tensor Force
3He
At 400-600 MeV/c
Sargsian, Abrahamyan,
Strikman, Frankfurt PR
C71 044615 (2005).
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.
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
Important practical question:
How low in t, u, Q2 … can we still use the
advantages of hard scattering ?
~1 fm
Experimental study of Short Range Correlation (SRC)
New Physics of (p,ppN) @ 2.8 GeV , IMP Lanzhou
I.
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
 High-momentum components of nuclear wave function
 Tensor NN interaction, repulsive core & 3N forces
 Cold-dense nuclear matter (neutron stars)
• Simple Measurement  Direct and Clear Probe to SRC
• Experimental Program: 12C (40Ca, 48Ca, 208Pb, deuteron)
Universality of Tensor Correlations ?
np
R. Schiavilla et al., Phys. Rev. Lett. 98, 132501 (2007)
W. Horiuchi et al., PRC 76, 024311 (2007)
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)
pp
M. Vanhalst et al., PRC
84, 031302 R (2011)
Correlations at ranges “longer” than
“short-range” makes nuclei unique ?
H. Feldeier,W. Horiuchi et al., PRC 84, 054003 (2011)
Few hundred MeV/nucleon energy (eg.RIBF)
 Less selective in reaction mechanism
 Spatial (or “momentum”) Correlations
Studies of Nucleon Correlations
using Direct Reactions

Isospin Dependence of Nucleon Correlations
(knockout and transfer reactions)

Neutron-Proton Correlations
(knockout and transfer reactions)

Di-neutron Correlations
(breakup reaction)

BCS to BEC Transitions ?
(transfer reaction ?)
Di-neutron Correlations
6He
Y. Oganessian et al., Phys. Rev. Lett. 82, 4996 (1999)
W. Horiuchi et al., Phys. Rev. C.
76, 024311 (2007)
di-neutron
Cigar-like
Y. Oganessian et al., Phys. Rev. Lett. 82, 4996 (1999)
6He
+ 65Cu Elab=22.6 MeV
A. Chatterjee et al., Phys. Rev. Lett.
101, 032701 (2008)
Two-neutron exchange
dashed: di-neutron
dotted: cigar-like
Neutron Correlations in 11Li
T. Nakamura et al., Phys. Rev. Lett. 96, 252502 (2006)
Strong two-nucleon correlation
Coulomb breakup – not good probe
Dominant effect of final-state interaction
Y. Kikuchi et al., PRC 81, 044308 (2010)
How about Nuclear Breakup reactions ?
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 ??)
Di-neutron Correlation: BCS  BEC towards n-rich ?
neutron cloud
n
Sn isotopes
(Z=50)
n
100Sn
adding neutrons
………
102Sn
N=Z
n
n
134Sn
More neutron-rich
Neutron skin  Low density distribution
• How Pair Correlation in exotic nuclei is different from stable nuclei ?
• Strong density dependence (normal density  low nucleon density)?
Cooper pair exhibits a strong spatial dineutron
correlation over a wide range of neutron
densities ρ/ρ0 ≈ 10-4 –0.5
M. Matsuo, PRC 73, 044309 (2006)
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).
Neutron-pairing in Sn Isotopes
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 ?
M. Matsuo, H. Shimoyama, PRC 82, 024318 (2010). (2+ systematics)
H. Shimoyama, M. Matsuo, paper in preparation (0+ systematics)
How to see & interpret these nn-pairing
structure in Transfer Reaction ?
Neutron-pairing in Sn Isotopes
Pair Transition density – Skyrme HFB + QRPA approach
M. Matsuo et al., PRC 82, 024318 (2010)
One-step transfer + QRPA Form Factor
TWOFNR, M. Igarashi et al.,
Instruction: Y. Aoki (Tsukuba), Calc: D.Y. Pang, JL
(p,t) Reaction Calc.
Structure Calc.
Pair Transfer Strength from
QRPA Form Factor
gs-gs
Reaction Calc: 02+ & 21+ (in progress)
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 ?
Kinematics chosen to suppress the effect of final-state-interactions
What is the appropriate energy ?
Energy chosen for Kinematics & for model framework &
experimental feasibility
Studies of Nucleon Correlations
using Direct Reactions
Neutron-Proton
Correlations
Isospin Dependence of
Nucleon Correlations
30Ne, 36Mg
34,46Ar(p,d)
at 70 AMeV
knockout
on C at 250 AMeV np-transfer on
sd-shell nuclei
14O knockout on
C & p a 65 AMeV
np-knockout
Support from
Theorists
Di-neutron Correlations
6He
breakup on C
& p at 70 AMeV
BCS to BEC
Transitions ?
on 12C at
200 AMeV
Quasi-free
scattering,
proton beam
at 2.8 GeV