# Presentation: 929351

## Spectroscopic factors and Asymptotic normalization coefficients

- Oak Ridge, Oct 2006

- F.M. Nunes

- NSCL, Michigan State University

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

## Publications

- Oak Ridge, Oct 2006

- Search for
- spectroscopic
- AND
-  transfer reaction
- in 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 (12C,11B)

- Knockout using stable beams (e,e’p)

- For stable nuclei

- For radioactive beams

- Transfer reactions using exotic beams (inverse kinematics)

## Standard approach to transfer

- Oak Ridge, Oct 2006

- Overlap functions

- Spectroscopic factor

- Experimental xs related to DWBA xs

- DWBA transition matrix element

-  Validity of DWBA
-  Optical pot (Uopt-in & Uopt-out )
** **Single particle parameters for IAB(r)

## SF versus ANC

- Oak Ridge, Oct 2006

**Single Particle**

## SF versus ANC: definitions

- Oak Ridge, Oct 2006

- r (fm)

## extracting SF or ANCs?

- Oak Ridge, Oct 2006

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

- DWBA transition matrix element

- Mukhamedzhanov et al., PRC72 (2005) 017602

## extracting SF or ANCs?

- Oak Ridge, Oct 2006

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

- DWBA transition matrix element

- Mukhamedzhanov et al., PRC72 (2005) 017602

- If **M****in**** is negligible** then one cannot extract SF unambiguously
- 					**one can only extract ANC**

- Typically** M****out**** is large** so if ANC is unknown
- 			**large error in SF**

## The question:

- Oak Ridge, Oct 2006

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

## Independent ANC

- Oak Ridge, Oct 2006

## Global optical potentials

- Oak Ridge, Oct 2006

- Uin=Perey&Perey; Uout=CH89

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

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

- 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 fm
- C2=0.81 fm-1

- r0=1.35 fm
- C2=5.1 fm-1

- C2(exp) =0.67(5) fm-1

- C2(exp) =8.36(42) fm-1

- Values 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 fm
- C2=2.66 fm-1

- C2(exp) =1.48(18) fm-1

- Value consistent with SF=1

## Fitting elastic

- Oak Ridge, Oct 2006

- r0=1.1 fm
- C2=0.62 fm-1

- C2(exp) =0.67(5) fm-1

- r0=1.1 fm
- C2=2.7 fm-1

- C2(exp) =8.36(42) fm-1

- r0=1.65 fm
- C2=2.65 fm-1

- C2(exp) =1.48(18) fm-1

- Values 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

## fit to elastic+transfer

- Oak Ridge, Oct 2006

## deuteron breakup

- Oak Ridge, Oct 2006

- Uin=Johnson and Soper

- r0=1.2 fm
- C2=0.77 fm-1

- C2(exp) =0.67(5) fm-1

- r0=1.15 fm
- C2=4.2 fm-1

- C2(exp) =8.36(42) fm-1

- r0=1.5 fm
- C2=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=1

- increase ~ 3%

- reduction ~ 10%

- reduction ~ 15%

## Target excitation

- Oak Ridge, Oct 2006

- CRC results

- 14C(d,p)15C

- 16O(d,p)17O

- 40Ca(d,p)41Ca

- reduction ~ 20%

- increase ~ 20%

- weak

## 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

- Global pot
- 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)

- Global pot
- Fit to elastic
- Deuteron breakup

## summary

- Oak Ridge, Oct 2006

- SF=1.0(1)

- SF=0.7(1)

- SF=0.7(1)

- Global pot
- Fit to elastic
- Deuteron breakup
- Couplings

## summary

- Oak Ridge, Oct 2006

- SF=1.0(1)

- SF=0.7(1)

- SF=0.7(1)

- Global pot
- Fit to elastic
- Deuteron breakup
- Couplings
- 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 ****41****Ca**

-  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