Jenny Lee RIKEN , 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 ??)
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). - PowerPoint PPT Presentation
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Jenny LeeRIKEN , Nishina Center
Studies of Nucleon Correlations using Direct Reactions
Isospin Dependence of Nucleon Correlations (knockout and 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
Different sets of consistent parameters different normalizations
p-rich
n-rich
CH89
JLM+HF
ΔS=Sn-Sp
Isospin Dependence of Nucleon Correlations
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):
Comparison of the Neutron Spectroscopic Factors from Transfer and Knockout Reactions at E/A=70 MeV
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
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
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
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
Jenny LeeRIKEN , Nishina Center
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
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
○ 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):
Systematic studies of neutron-proton pairing in sd-shell nuclei using (p,3He) and (3He,p) transfer reactions
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
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
Studies of Nucleon Correlations using Direct Reactions