Ann-Cecilie Larsen Workshop on Level Density and Gamma Strength in Continuum Oslo, May 21-24, 2007

1. Experimental level densities and -ray strength functions in the f7/2 nuclei 44,45Sc and 50,51V Ann-Cecilie Larsen Workshop on Level Density and Gamma Strength in Continuum Oslo, May 21-24, 2007 DEPARTMENT OF PHYSICS UNIVERSITY OF OSLO

2. Overview • Motivation - why study Sc and V? • Some experimental details • The Oslo method • Level densities • Gamma-ray strength functions • Summary

3. Motivation • Nuclei with A~40-50 • Shell effects, Z=20, N=28 shell gap • Upbend structure in strength functions? (previously seen in 56,57Fe, 93-98Mo)

4. Where are we? (I) 44,45Sc,  44Sc,  45Sc,  f5/2 f5/2 f5/2 p3/2 p3/2 p3/2 f7/2 f7/2 f7/2 d3/2 d3/2 d3/2

5. 50,51V,  50V,  51V,  f5/2 f5/2 f5/2 p3/2 p3/2 p3/2 f7/2 f7/2 f7/2 d3/2 d3/2 d3/2 Where are we? (II)

6. Experimental details (I) 3He beam, 30 MeV on 51V and 38 MeV on 45Sc. Reactions: Inelastic scattering(3He,3He’) Pick-up (3He,)

7. Experimental details (II) • Particle- coincidences NaI(Tl) Si E-E telescope  3He 45o Target nucleus

8. The Oslo method • Unfold all  spectra † • Apply the first-generation method †† • Ansatz: first-gen. matrix  (E-E)T(E) ††† † : M. Guttormsen et al., NIM A374 (1996) 371 †† : M. Guttormsen et al., NIM A255 (1987) 518 ††† : A. Schiller et al., NIM A447 (2000) 498

9. Normalizing the first-generation matrix Emin = 3.3 MeV E (MeV) 0 50V 4 8 0 4 8 E (MeV) Emax = 9.2 MeV E,min = 1.7 MeV

10. Extraction of level density and -ray transmission coefficient The primary -ray matrix P(E, E) is factorized according to Theoretical approach:

11. E E Input matrix P(E, E), 50V The resulting Pth(E, E), 50V E E Iteration method Minimize

12. Quality of the iteration procedure 50V 44Sc

13. Normalizing the level density • Low E: known, discrete levels • At Bn (or Bp): data from neutron (proton) resonance experiments

14. Uncertainties in normalization • Calculation of (Un/p), spin cutoff parameter 1) 2) 3)

15. Spin distributions, 44Sc A. Gilbert and A.G.W. Cameron, Can. J. Phys. 43, 1446 (1965) T. von Egidy and D. Bucurescu, Phys. Rev. C 72, 044311 (2005), Phys. Rev. C 73, 049901(E) (2006) S. Goriely, HF+BCS Demetriou and Goriely, Nucl. Phys. A695 (2001) 95 1) 2) 3)

16. Level densities of 44,45Sc Preliminary

17. Level densities of 50,51V Constant-temperature model

18. Model to calculate the level density • Combining all possible proton and neutron configurations • Nilsson energy scheme • BCS quasiparticles Single q.p energy: Total energy due to q.p. excitations:

19. Nilsson levels, 45Sc • Model parameters: • = 0.066 • = 0.32 [D.C.S. White et al., Nucl. Phys. A 260, 189 (1976)] • = 0.23 [In agreement with P. Bednarczyk et al., Phys. Lett. B 393, 285 (1997)]

20. Calculated level densities, 44,45Sc

21. Average number of broken pairs

22. Parity asymmetry Defining the parity asymmetry as [U. Agvaanluvsan, G.E. Mitchell, J.F. Shriner Jr., Phys. Rev. C 67, 064608 (2003)] ~0.02 for (J=1/2, J=3/2)

23. The -ray transmission coefficient Assuming dominance of dipole radiation (E1 and M1)

24. Normalizing the -ray strength functions of 44,45Sc Data from J. Kopecky and M. Uhl: fE1 = 1.61(59)·10-8 MeV-3 fM1 = 1.17(59)·10-8 MeV-3

25. Comparing with other data and theory 45Sc(,n)44Sc 46Ti(,p)45Sc

26. The -ray strength functions of 50,51V Kadmenskij, Markushev and Furman: Lorentzian, spin-flip:

27. Summary • Extraction of  and T from first-generation  spectra • Level densities of 44,45Sc and 50,51V • New model to calculate , Nqp,  • Gamma-ray strength functions of 44,45Sc and 50,51V

28. Collaborators • Oslo: M. Guttormsen, S. Messelt, F. Ingebretsen, J. Rekstad, S. Siem and N.U.H. Syed • Åbo Akademi, Finland: T. Lönnroth • NSCL/MSU, USA: A. Schiller • Ohio University, USA: A. Voinov Thank you!