Betty Tsang

ECT workshop: Reactions and Nucleon Properties in Rare Isotopes

April 6-10, 2010, Trento, Italy

Spectroscopic Factors of Ar isotopes from transfer and knock-out reactions

Survey: Extractions of Neutron Spectroscopic Factors using

systematic approach from Transfer Reactions

Experiment: 34,46Ar(p,d) Transfer Reactions in Inverse Kinematics

Comparisons to knockout results

Asymmetry Dependence of Neutron Correlations

Questions about spectroscopic factor measurements

Is there a clear understanding of the uncertainties (both data and theory)?

Are there disagreements in the structure obtained using different reaction probes?

How would one get absolute SFs from transfer or is this not possible?

Are there specific experiments or theoretical developments that would move us

forward?

Spectroscopic Factor from experiments

Knockout reaction

Exotic nuclei

Very low beam intensity (~ 102 pps)

• High energy (>50MeV/A)

x So far only hole-state

(e,e’p)

Theory description is clear

(plane-wave impulse approximation)

x Only stable nuclei, only proton SF

e-

p

Three main experimental techniques SF(expt)

Transfer reaction

Stable & exotic nuclei

Particle- & hole-state

High & low energy

Long history (>50 years)

x Beam intensity (>104 pps)(d,p)

SF’s Reduction and Asymmetry Dependence

One-nucleon knockout -- away from

stability

• Measured SF relative to LB-SM

strongly depends on the asymmetry

• More reduction experienced by strongly

bound valence nucleonA. Gade et al, PC 77, 044306 (2008)

30-40%

ΔS = Sn-Sp for n-SF

ΔS = Sp-Sn for p-SF

How about Transfer Reactions ?

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

(e,e’p) -- nuclei near closed shell

• Constant ~30-50% of SF reduction

compared to IPM

J. Lee et al., PRC73, 044608 (2006)

Experimental SFs from transfer reactions

Spectroscopic factor (SF)

• reflects the properties of valence neutron

•independent of incident energy

Need systematic approach

consistent SFs

Past SF analysis are

(mis)guided by shell-model !

Example: 1f 7/2 n SF in 41Ca = 40Ca+n

SF(SM)=1.0

J. Lee et al., PRC75, 064320 (2007)

B-1

B

Theo

EXP

EXP d

dSF

d

d

Johnson- Soper Adiabatic

Distorted Wave (AWD)to take

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.

Systematic methods for consistent spectroscopic factors

TWOFNR from Jeff Tostevin (University of Surrey)

Compute with TWOFNR code

J. Lee et al., PRC75, 064320 (2007)

Johnson & Soper, PRC1,976(1970)

Quality Control of extracted SFs

J. Lee et al, Phys. Rev. C75 (2007) 064320B(p,d)A : SF+ ; A(d,p)B : SF-

Ground-state to ground-state transition

SF+= SF- (Detailed balance)

18 nuclei have both SF+ and SF-

80 g.s. SFs for Li to Cr (~ 430 (p,d) and (d,p) angular distributions)

Associated uncertainty

• Standard deviations

•

-- SF+ = SF- Systematic method works

-- 20% uncertainty for each measurement

Comparisons of (e,e’p) and (p,d)&(d,p) transfer reactions

Pure single-particle state

Beyond IPM

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

(e,e’p) -- nuclei near closed shell

• Constant ~30-40% of SF

reduction compared to IPM

J. Lee et al., PRC75, 064320 (2007)

Magic number

N=2

Independent Particle Model (IPM)

mean field created by

nucleons from core

i

ii rUm

pH

2

2

N=20

N=8

n, l j

Comparisons to IPM

Pure single-particle state

IPM needs refinement ?

M.B. Tsang and J. Lee et al., PRL 95, 222501 (2005)

Large Basis Shell Model (LB-SM)

IPMSMLB SFSF

Residual interactions

H p i2

2mU ri

i

VNN r i r j i j

U ri i

How good the interaction in LB-SM can

describe the nucleus ?

LB-SM description is accurate

Some correlations missing in the interactions ?

correlated motions

of valence nucleons

Correlations between nucleons

Mixing of particle-hole configuration near

the fermi surface

Weakening of single-particle strengths

Mean field

1s, N=0

1d, 2s N=2

1f, 2p N=3

1p N=1

core

Survey of Neutron Spectroscopic Factors and

Asymmetry Dependence of Neutron Correlations

M.B. Tsang and J. Lee et al., PRL 95, 222501 (2005)

• Most extracted SFs less than IPM-plus-pairing predictions• Absence of nucleon-nucleon correlations

Ground-state Spectroscopic Factors of Z=3-24IPM + Maximal pairing

LB-SM code : Oxbash, Alex Brown (MSU)

LB-SM predictions

(Residual interactions)

20% agreement

Ni isotopes -

Ground states

Ground state

Predictive power of transfer reaction cross sections

Excited states

USDA/USDBExcited states

GXPF1A

~SF(LB-SM)

from good

interactions in

Hilbert spaces

CH89

approach

in ADWA

model

M.B. Tsang and J. Lee et al., PRL 95, 222501 (2005)

Suppression of Spectroscopic Factors in Transfer Reactions

J. Lee, J.A

. Tostev

inet al., P

RC

73 , 0

44608 (2

006)

Global CH89 + ro=1.25 fm with minimum

assumption consistent SF with LB-SM

Predictive power for experimental x-sections

& Astrophysics rates!

JLM optical potential + bound n-

radii constrained with HF geometry

Overall ~30% reduction in SFs

~SF(LB-SM) from

good interactions in

Hilbert spaces

CH89 approach

in ADWA model

Jeff Tostevin

ro=1.25 fm HF rms radius

Global CH89 microscopic

nucleon-nucleon JLM + HF

densities

p-richn-rich

Neutron transfer reactions for neutron rich and proton rich Ar isotopes

p(34Ar,d)33Ar

p(46Ar,d)45Ar

Inverse kinematics at 33MeV/u

NSCL Expt05133 (Oct 19-30, 2007)

Thesis (2010) Jenny Lee

34Ar

46Ar

L-matching—desirable but not necessary

L ≈ Q · R = |Kin-Kout| · R Condition is well-matched

transferred momentum is bound

by the condition to ~ ±1

nucleon-transfer probability

to that particular state would be

relative large

contributions from other

reaction channels are negligible

simple one-step DWBA

description to the data is valid

A-1

A

J. Lee , NSCL Thesis (2010)

Primary Devices(CH2)n Target

34,36,46Ar Beam

34,36,46Ar + p→d + 33,35,45Ar

Φ To S800Spectrograph

33,35,45Ar P,E,Φ

2. S800 Spectrograph

3. Micro-Channel Plates

MCP's

θ

deuteron

1. High Resolution Array

Inverse kinematics at 33MeV/A

Complete kinematics measurement

First transfer reaction experiment using HiRA with S800 + MCP at NSCL

Goal: neutron spectroscopic factors

Asymmetry dependence of neutron correlations – Transfer Reactions

Observables: deuteron differential cross sections

Experimental Setup

S800

Focal Plane

Target Chamber

16 HiRA telescopes – efficiency ~40%

High Resolution Array (HiRA)

d

p

t

p

d

t

1.5mm Si

65μm SiCsI(Tl)

1024 pixels (2mm x2mm)0.16° at 35 cm setup

Energy resolution: DE ~50 keV; EF ~ 70keV

The observed resolutions are reproduced by GEANT4 simulations (finite beam spot, energy + angular straggling , detector resolutions)

Experimental results – Kinematics & Q-value

p(36Ar,d)35Ar

g.s. 470 keV FWHM

p(36Ar,d)35Ar

θlab (deg)

p(46Ar,d)45Ar

g.s. 410 keV

FWHM

(θlab<19° )

p(46Ar,d)45Ar

θlab (deg)

g.s. 500 keV FWHM

p(34Ar,d)33Ar

p(34Ar,d)33Ar

θlab (deg)

p(34Ar,d)33Ar

p(34Ar,d)33Ar

g.s. 500 keV FWHM

(A+pB+d+Q)

J. Lee et al., PRL104, 112701 (2010).

J. Lee et al., PRL104, 112701 (2010).

Transfer SF’s depend

less strongly on the

neutron-proton

asymmetry than do

those measured in

knockout reactions.

Summary III: Asymmetry dependence of neutron correlations

J. Lee et al., PRL104, 112701 (2010).

ADWASMLBExp )d

d(SF)

d

d(

Results indicate that

Important for astrophysical applications

Systematics can be used to test SM

interactions & spin assignments

confirmations.

Ground states

MB

. Tsan

g et al., P

RL

95, 2

22501 (2

005)

J. Lee, et al., P

RC

75

, 06

43

20 (2

00

7)

J.Lee, et al., . R

ev. C7

9, 0

54

611(2

00

9)

sd shell

M.B

. Tsan

g, et al., P

RL

. 102, 0

62501 (2

009).

fp shell

M.B

. Tsan

g, et al., P

RL

. 102, 0

62501 (2

009).

Summary I: Predictive power of transfer reaction cross-sections

Summary II: SF’s depends on choice of OMP and bound state geometry

cc

J. Lee, J.A

. Tostev

inet al., P

RC

73 , 0

44608 (2

006)

J. Lee et al., NSCL Thesis (2010)

Are there specific experiments or theoretical developments that would

move us forward?

p(34Ar,d) 33Ar & p(46Ar,d) 45Ar at 33MeV/A

Charity:

Application of the DOM to

(p,d) and (d,p) reactions.

HiRA

Perform 34Ar(p,d) at

E/A=70 MeV; 32Ar?

Theory development: Ron Johnston & others

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

HiRA group:Andy Rogers, Vladimir Henzl, Daniela Henzlova, Daniel Coupland;

Micha Kilburn, Alisher Sanetullaev, Mike Youngs, Sun Zhiyu (孙志宇)

Betty Tsang (曾敏兒); Bill Lynch (連致標)

HiRA Collaborators:

Lee Sobotka, Bob Charity, Jon Elson (WU in St. Louis)

Sylvie Hudan (Indiana University)

Mike Famiano (Western Michigan University)

Dan Shapira (ORNL)

Jolie Cizewski, Bill Peters, Patrick O'Malley (Rutgers University)

Kate Jones, Kyle Schmitt, Andy Chae (University of Tennesee)

Hoi Kit Cheung (張凱傑 ) (Chinese University of Hong Kong)

Theory & SF survey Collaborators:

Alex Brown, Angelo Signoracci, Hang Liu (刘航), Scott Warrant (NSCL)

Jeff Tostevin (University of Surrey)

Mihai Horoi (Central Michigan University)

Ming-chung Chu(朱明中), Shi Chun Su(蘇士俊), Jiayan Dai(戴家琰)

(Chinese University of Hong Kong)

Acknowledgements Jenny Lee (李曉菁)