Experimental level densities and -ray strength functions in

the f7/2 nuclei 44,45Sc and 50,51V

Ann-Cecilie LarsenWorkshop on Level Density

and Gamma Strength in Continuum

Oslo, May 21-24, 2007

DEPARTMENT OF PHYSICSUNIVERSITY OF OSLO

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

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)

Where are we? (I)

44,45Sc, 44Sc, 45Sc,

d3/2

f7/2

p3/2

f5/2

d3/2

f7/2

p3/2

f5/2

d3/2

f7/2

p3/2

f5/2

Where are we? (II)

50,51V,

d3/2

f7/2

p3/2

f5/2

50V,

d3/2

f7/2

p3/2

f5/2

51V,

d3/2

f7/2

p3/2

f5/2

Experimental details (I)

3He beam, 30 MeV on 51Vand 38 MeV on 45Sc.Reactions:

Inelastic scattering (3He,3He’)Pick-up (3He,)

Experimental details (II)• Particle- coincidences

45o

NaI(Tl)

Si E-E telescope

3He

Target nucleus

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

Normalizing the first-generation matrix

E (MeV)

0

4

8

40 8

E (MeV)

50V

E,min = 1.7 MeV

Emin = 3.3 MeV

Emax = 9.2 MeV

Extraction of level density and -ray transmission coefficient

The primary -ray matrix P(E, E)is factorized according to

Theoretical approach:

Iteration methodMinimize

E

Input matrixP(E, E), 50V

E

The resultingPth(E, E), 50V

E

E

Quality of the iteration procedure

50V 44Sc

Normalizing the level density

• Low E: known, discrete levels

• At Bn (or Bp): data from neutron (proton) resonance experiments

Uncertainties in normalization

• Calculation of (Un/p), spin cutoff parameter

1)

2)

3)

Spin distributions, 44Sc

1) A. Gilbert and A.G.W. Cameron, Can. J. Phys. 43, 1446 (1965)

2) T. von Egidy and D. Bucurescu, Phys. Rev. C 72, 044311 (2005), Phys. Rev. C 73, 049901(E) (2006)

3) S. Goriely, HF+BCSDemetriou and Goriely, Nucl. Phys. A695 (2001) 95

1)

2)

3)

Level densities of 44,45Sc

Level densities of 50,51V

Constant-temperaturemodel

Model to calculate the level density

• Combining all possible proton and neutron configurations

• Nilsson energy scheme• BCS quasiparticlesSingle q.p energy:

Total energy due to q.p. excitations:

Nilsson levels, 45ScModel 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)]

Calculated level densities, 44,45Sc

Average number of broken pairs

Parity asymmetry

Defining the parity asymmetry as

[U. Agvaanluvsan, G.E. Mitchell,J.F. Shriner Jr., Phys. Rev. C 67, 064608 (2003)]

~0.02for (J=1/2, J=3/2)

The -ray transmission coefficient

Assuming dominanceof dipole radiation (E1 and M1)

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

Comparing with other data and theory

45Sc(,n)44Sc

46Ti(,p)45Sc

The -ray strength functions of 50,51V

Kadmenskij, Markushev and Furman:

Lorentzian, spin-flip:

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

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