Shifts in neutron single-particle states outside N=82. S.J.Freeman, B.P.Kay, J.P.Schiffer, J.A.Clark, C.Deibel, A.Heinz, A.Parikh, P.D.Parker, K.E.Rehm and C.Wrede University of Manchester, Argonne National Laboratory and Yale University. Proton states outside Z=50.
S.J.Freeman, B.P.Kay, J.P.Schiffer, J.A.Clark, C.Deibel, A.Heinz, A.Parikh, P.D.Parker, K.E.Rehm and C.Wrede
University of Manchester, Argonne National Laboratory and Yale University
Monopole shifts: neutron h11/2 (νj>) filling in Sn cores with increasing A attractive effect on πg7/2(πj<) repulsive effect on πh11/2(πj>)
Careful measurements of spectroscopic factors in Sn(α,t) reactions indicate lowest states carry majority of h11/2 and g7/2 strength with little variation.Schiffer et al. Phys. Rev. Lett. 92(2004)162501
Main driver of the shifts appears to be the tensor part of the interaction, now beginning to be included in MF calculations.Otsuka et al. Phys. Rev. Lett. 97(2006)162501
HF+Skryme Calculations:Colò et al. Phys Lett. B646(2007)227-231
Increasing neutron excess
No measurements of spectroscopic factors for i13/2 or h9/2 states from reactions well matched for high ℓ transfer done in a careful relative way.Existing (d,p) data suggests significant fragmentation.
Tensor force seems necessary to reproduce ordering, but need to be sure of centroids of i13/2 and h9/2 before an informed comparison can be made.
Spectra at 20 degrees
DWBA using standard optical andbound-state parameters, give goodreproduction of angular distributions
Common normalization for all isotopesand for both L=5 and 6
As might be expected, deduced spectroscopic factors differ significantlyfrom older (d,p) work
Only statistical errors from peak fitting shown here.
Absolute numbers good to ±15%Relative values to ±5%
Particle-core coupling:0+ h9/2 mixes with 2+ f7/20+ i13/2 mixes with 3 f7/2
Proportion of single-particle strength in higher-lying state:(i) for L=5 falls after Ba and is then roughly constant(ii) for L=6 increases with Z
Proportion of single-particle strength in upper states depends on proximity of centroid to the core vibration.
Agreement with more detailed calculationsAna-Maria Oros, Doctoral Thesis, University of Köln, Germany 1996
“Skyrme + tensor” calculations suggest sequential filling g7/2, d5/2 and h11/2 by protons leading to systematic monopole shifts in calculated neutron i13/2-h9/2 energy difference.
Experimental proton occupancy from transfer reactions:
Difference in centroid energies not well reproduced by “Skyrme+tensor” calculations; centroids qualitatively consistent with g7/2 and d5/2filling at the same rate, with g7/2 interaction dominating.
Wildenthal, Newman and Auble, Phys. Rev. C3 (1971) 1199