Spectroscopic factors and Asymptotic normalization coefficients Oak Ridge, Oct 2006 F.M. Nunes NSCL,...

Spectroscopic factors and Asymptotic normalization

coefficients

Oak Ridge, Oct 2006

F.M. Nunes

NSCL, Michigan State UniversityNSCL, Michigan State University

in collaboration with D. Pang and A.M. Mukhamedzhanov

Publications

Oak Ridge, Oct 2006

Search for spectroscopic

AND transfer reactionin PHYS journals

How to measure spectroscopic factors?

Oak Ridge, Oct 2006

Transfer reactions using light beams (d,p), (3He,d) or using heavy ions (12C,13C) or

(16O,17O)

Knockout using radioactive beams (Knockout using radioactive beams (1212C,C,1111B)B)

Knockout using stable beams (e,e’p)

For stable nuclei

For radioactive beamsFor radioactive beams

Transfer reactions using exotic Transfer reactions using exotic beams (inverse kinematics)beams (inverse kinematics)

Larger Larger combination of combination of initial and final initial and final statesstates

Standard approach to transfer

Oak Ridge, Oct 2006

dppd

BAAB

I

I

Overlap functions

Spectroscopic factor

d

dS

d

dDWj

j

)(exp

exp

Experimental xs related to DWBA xs

BpAd

ipdABf IVIM DWBA transition matrix element

ABABj IINS

Validity of DWBA Optical pot (Uopt-in & Uopt-out )

Single particle parameters for IAB(r)

SF versus ANC

Oak Ridge, Oct 2006

)()( rihiCrI lljRr

ABN

Many Body

)()( rihibr lnljRr

nljN

Single Particle

)()( rArI nljnljAB approximation

2

22

nljb

CAS ljnlj

Bnlj

BpAd

SF versus ANC: definitions

Oak Ridge, Oct 2006

)()( rihiCrI lljRr

ABN

0

2 )(r

ABAB

lj rIdrS

r (fm)

extracting SF or ANCs?

Oak Ridge, Oct 2006

)M)(M

()M)((MM outin

outin b

bAbbbA

2222 )M)(M

()M)(M

( outin

outin

b

bC

b

bSb

Goncharov et al.,Sov. J. Nucl. Phys. 35 (1982) 383

indABf IVIM DWBA transition matrix element

Mukhamedzhanov et al., PRC72 (2005) 017602

2

expexp

CR

2bR

DWDW

exp)( RbRDW pinning down the single particle ANC

extracting SF or ANCs?

Oak Ridge, Oct 2006

)M)(M

()M)((MM outin

outin b

bAbbbA

2222 )M)(M

()M)(M

( outin

outin

b

bC

b

bSb

Goncharov et al.,Sov. J. Nucl. Phys. 35 (1982) 383

indABf IVIM DWBA transition matrix element

Mukhamedzhanov et al., PRC72 (2005) 017602

If Min is negligible then one cannot extract SF unambiguouslyone can only extract ANC

Typically Mout is large so if ANC is unknownlarge error in SF

The question:

Oak Ridge, Oct 2006

Are the analyses of transfers to extract SF consistent with independent ANC measurements?

14C(d,p)15C @14 MeV

16O(d,p)17O @ 15 MeV

40Ca(d,p)41Ca @ 11 MeV

Requirements:• data for elastic+transfer at an energy above the barrier• data from which to extract ANC independently

Three test cases:

Q=-1.0 MeV

Q=+1.9 MeV

Q=+6.1 MeV

BE=1.2 MeV

BE=4.1 MeV

BE=8.4 MeV

Independent ANC

Oak Ridge, Oct 2006

Sub-Coulomb heavy ion transfer reactions can be used to extract ANCs

Pb(17O, 16O)Pb @ 67 MeV

C2(exp)

=0.67(05) fm-1Franey et al., NPA324 (1979) 193.

16O(17O, 16O)17O @ 22 MeV

C2(exp)

=0.69(03) fm-1Burzynski et al., NPA399 (1983) 230.

Knockout data on 9Be and 12C ~50 MeV/u was used to extract the 15C ANCSauvan et al., PRC 69 (2004) 044603.Maddalena et al., NPA 682 (2001) 332.

C2(exp)

=1.48(18) fm-1

Only 40Ca(d,p)[email protected] MeV to extract ANC

C2(exp)

=8.36(42) fm-1

Kocher et al., NPA172 (1971) 652.

Global optical potentials

Oak Ridge, Oct 2006 Uin=Perey&Perey; Uout=CH89

16O(d,p)17O @ 15 MeV


C2(exp)

=0.67(5) fm-1

C2(exp)

=8.36(42) fm-1

r0=1.2 fmC2=0.75 fm-1

r0=1.2 fmC2=5.0 fm-1

Values consistent with SF=1Values consistent with SF=1

Procedure: keep a=0.65, vary r0 to obtain a range of ANCs



16O(d,p)17O @ 15 MeV


r0=1.5 fmC2=0.81 fm-1

r0=1.35 fmC2=5.1 fm-1

C2(exp)

=0.67(5) fm-1

C2(exp)

=8.36(42) fm-1

Values consistent with SF=0.7Values consistent with SF=0.7



14C(d,p)15C @14 MeV

r0=1.7 fmC2=2.66 fm-1

C2(exp)

=1.48(18) fm-1

Value consistent with SF=1Value consistent with SF=1

r0=1.2 fmC2=2.54 fm-1

SF=1.27

Standard s.p. parametersStandard s.p. parameters

Fitting elastic

Oak Ridge, Oct 2006

r0=1.1 fmC2=0.62 fm-1

C2(exp)

=0.67(5) fm-1

r0=1.1 fmC2=2.7 fm-1

C2(exp)

=8.36(42) fm-1

r0=1.65 fmC2=2.65 fm-1

C2(exp)

=1.48(18) fm-1


14C(d,p)15C @14 MeV 16O(d,p)17O @ 15 MeV 40Ca(d,p)41Ca @ 11 MeV

peripherality

Oak Ridge, Oct 2006

R

r


fit to elastic+transfer

Oak Ridge, Oct 2006

deuteron breakup

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Uin=Johnson and Soper

r0=1.2 fmC2=0.77 fm-1

C2(exp)

=0.67(5) fm-1

r0=1.15 fmC2=4.2 fm-1

C2(exp)

=8.36(42) fm-1

r0=1.5 fmC2=2.38 fm-1

C2(exp)

=1.48(18) fm-1



increase ~ 3%reduction ~ 10% reduction ~ 15%

Target excitation

Oak Ridge, Oct 2006

CRC results14C(d,p)15C 16O(d,p)17O 40Ca(d,p)41Ca

reduction ~ 20% increase ~ 20%weak

CCBA results

weak reduction ~20% reduction ~50%

summary

Oak Ridge, Oct 2006

1) Global pot

SF=1.0(1) SF=0.7(1) SF=0.7(1)

summary

Oak Ridge, Oct 2006

1) Global pot2) Fit to elastic

SF=1.0(1) SF=0.7(1) SF=0.7(1)

summary

Oak Ridge, Oct 2006

SF=1.0(1) SF=0.7(1) SF=0.7(1)

1) Global pot2) Fit to elastic3) Deuteron breakup

summary

Oak Ridge, Oct 2006

SF=1.0(1) SF=0.7(1) SF=0.7(1)

1) Global pot2) Fit to elastic3) Deuteron breakup4) Couplings

summary

Oak Ridge, Oct 2006

SF=1.0(1) SF=0.7(1) SF=0.7(1)

1) Global pot2) Fit to elastic3) Deuteron breakup4) Couplings5) Overall estimate

conclusions

Oak Ridge, Oct 2006

• Transfer reactions, even well above the Coulomb barrier, have a very large contribution from large distances

Important to pin down ANC independently

• ANC measurements for good test cases (closed shell nuclei)to provide a handle on reaction theory limitations

ANC for 41Ca

• Solving the cases for stable nuclei is the first step to tackle exotic nuclei!

Sub-Coulomb heavy ion transfer or breakup

The end

Oak Ridge, Oct 2006

Spectroscopic factors and Asymptotic normalization coefficients Oak Ridge, Oct 2006 F.M. Nunes NSCL,...

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