spectroscopic factors and asymptotic normalization coefficients oak ridge, oct 2006 f.m. nunes nscl,...
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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
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
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
40Ca(d,p)41Ca @ 11 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
Global optical potentials
Oak Ridge, Oct 2006 Uin=Perey&Perey; Uout=CH89
16O(d,p)17O @ 15 MeV
40Ca(d,p)41Ca @ 11 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
Global optical potentials
Oak Ridge, Oct 2006 Uin=Perey&Perey; Uout=CH89
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
Values consistent with SF=1Values consistent with SF=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
14C(d,p)15C @14 MeV 16O(d,p)17O @ 15 MeV 40Ca(d,p)41Ca @ 11 MeV
deuteron breakup
Oak Ridge, Oct 2006
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
14C(d,p)15C @14 MeV 16O(d,p)17O @ 15 MeV 40Ca(d,p)41Ca @ 11 MeV
Values consistent with SF=1Values consistent with SF=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
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