The National Superconducting Cyclotron Laboratory @ Michigan State University

1. Survey of the neutron spectroscopic factors from Li to Cr Betty Tsang, 2/24-26/2005 INFN Workshop on Reactions and Structure with Exotic Nuclei Spectroscopic Factors: Measure the orbital configuration of the valence nucleons. Magic number N=20 N=10 N=2 The National Superconducting Cyclotron Laboratory @Michigan State University

2. Transfer Reactions Measurements of Absolute Spectroscopic Factors

3. Rise and Fall of transfer reactions? Opportunity to do an overview of the field(especially for outsider) # of papers Decade

4. Spectroscopic Factors from literatures Example: 1p1/2 neutron SF in 13C = 12C+n • Published spectroscopic factors show large fluctuations from analysis to analysis • Consequence of using different optical model potentials and parameters for the DWBA reaction model.

5. A(d,p)B  B(p,d)A Basic assumptions of DWBA The reaction is dominated by 1-step direct transfer. Elastic Scattering is the main process in the entrance and exit channels. TDWBA = <Apf|V|Bdi>

6. Extraction of Spectroscopic Factor • For each angular distribution: • Fit first peak only (emphasize on maximum and shape) • Require more than 1 data point

7. Surrey’s TWOFNR Use global proton optical potential and standardized parameters Soper-Johnson Adiabatic Approximation to take care of d-break-up effects. n-potential – wood-Saxon shape with depth adjusted to binding energy. ro=1.25 fm & ao=.65. Include finite range & non-locality corrections 12C(d,p)13Cgs

8. The spectroscopic factors deduced in a systematic and consistent way show that we can extract spectroscopic factors within the measurement uncertainties. Systematic extraction of SF’s Liu et al, PRC 69, 064313 (2004) Apply the technique to a large data set

9. Z=3 Li 6, 7, 8 Z=4 Be 9, 10, 11 Z=5 B 10, 11, 12 Z=6 C 12, 13, 14, 15 Z=7 N 14, 15, 16 Z=8 O 16, 17, 18, 19 Z=9 F 19, 20 Z=10 Ne 21, 22, 23 Z=11 Na 24 Z=12 Mg 24, 25, 26, 27 Z=13 Al 27, 28 Z=14 Si 28, 29, 30, 31 Z=15 P 32 Z=16 S 32, 33, 34, 35, 36, 37 Z=17 Cl 35, 36, 37, 38 Z=18 Ar 36, 37, 38, 39, 40 Z=19 K 39, 40, 41, 42 Z=20 Ca 40, 41, 42, 43, 44, 45, 47, 48, 49 Z=21 Sc 45, 46 Z=22 Ti 46, 47, 48, 49, 50, 51 Z=23 V 51 Z=24 Cr 50, 51, 52, 53, 55 We studied 79 nuclei by digitizing ~ 430 angular distributions from literaturefor (p,d) & (d,p) reactions on target from Z=3-24.

10. Digitization of ~430 angular distributions from literaturefor (p,d) & (d,p) reactions on target from Z=3-24 • No adjustment of input parameters to calculations • Quality control: • Compare to Endt’s “Best” values when available. • Compare SF’s derived from (p,d) and (d,p) reactions separately to estimate the uncertainties in our method.

11. Comparison with Endt’s results Endt in 1977 compiled SF’s of the s-d shell nuclei from (p,d), (d,p) – 50% uncertainty (p,d), (d,p), (d,t), (3He, a) – 25% uncertainty There are some scattering of the values but there is a strong correlation between present analysis and Endt values

12. A+pB+d S+ B+dA+p S- Equivalent processes S+ = S- Digitization of ~430 angular distributions from literaturefor (p,d) & (d,p) reactions on target from Z=3-24 Data come from many groups over 40 years. -- Require quality control How to assess the uncertainties of the procedure? Self Consistency Checks Sn79 nuclei from Li to Cr (p,d) : S+47 nuclei (d,p) : S-55 nuclei (p,d) & (d,p) 18 nuclei

13. Comparison of (p,d) and (d,p) reactions By requiring the chi-square per degree of freedom is 1, we obtain nominal uncertainty of 20% for each measurement.

14. Direct Nuclear Reaction Theories by Austern; pg 291 l=7/2, S=1, 2, 0.75, 4, 0.5, 6, 0.25, 8 ACa = 40Ca +(A-40)n  Assume 40Ca is a good inert core. Textbook Example: Spectroscopic factors of Ca isotopes

15. IPM (Austern, pg 291) For n odd For n even 40-48Ca isotopes have good single particle states with spherical cores SF for 49Ca is lower than IPM and shell model predictions.

16. Comparison with Austern’s IP Model Most experimental SF values are less than predictions. There are no constant quenching even for close shell nuclei. Discrepancies may be explained by including interaction between nucleons and core

17. Compare with Modern Shell Model(Oxbash) Good agreement with most isotopes Outliners: deformed nuclei and isotopes with small SF’s (Ne)

18. Measurements of Spectroscopic Factors Transfer Reactions

19. (e,e’p) – sensitive to interior of the wave-functions 40Ca Spectroscopic factor 12C 16O

20. Speculations: SF(p/d) – SF(e,e’p) -- short range correlation effects! (e,e’p) – sensitive to interior of the wave-functions (d,p), (p,d) – sensitive to surface of the wave-functions Shell model -- long range correlation effects 40Ca Spectroscopic factor 12C 16O

21. Summary • We have extracted ground state neutron spectroscopic factors for 79 (Z=3-24) nuclei • 40Ca to 48Ca isotopes follow the simple IPM predictions • Good valence nucleons around spherical cores • No quenching for gs n-orbital for the closed shell nuclei of 40Ca? • Are we measuring absolutely SF’s? • Most SF’s fall short of IPM predictions but agree with modern day shell model calculations – long range correlation. • Is difference between SF’s from (e,e’p) and transfer reactions the short range correlations? • Thanks to Hiu Ching Lee