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 Careful measurements of spectroscopic factors in Sn(α,t) reactions indicate lowest states carry majority of h 11/2 and g 7/2 strength with little variation. Schiffer et al. Phys. Rev. Lett. 92(2004) Monopole shifts: neutron h 11/2 (νj > ) filling in Sn cores with increasing A attractive effect on πg 7/2 (πj ) 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) Gogny+tensor Gogny

Neutron states outside N=82 No measurements of spectroscopic factors for i 13/2 or h 9/2 states from reactions well matched for high ℓ transfer done in a careful relative way. Existing (d,p) data suggests significant fragmentation. HF+Skryme Calculations: Colò et al. Phys Lett. B646(2007) Tensor force seems necessary to reproduce ordering, but need to be sure of centroids of i 13/2 and h 9/2 before an informed comparison can be made. Increasing neutron excess

Experimental Details N=82(a, 3 He) Reactions: neutron transfer with large Q, favouring high-L transfer 51 MeV alpha particles on 138 Ba, 140 Ce, 142 Nd and 144 Sm from Yale ESTU tandem Ejectile 3 He ions analysed in Yale Split Pole Spectrograph Elastic scattering measured at 20 MeV (Rutherford) to enable extraction of absolute cross section Measurements at 6, 11 and 20°, in addition to 30° for Ce and Ba Spectra at 20 degrees

Angular Distributions Examples of DWBA fits to Nd and Sm Red L=6 Blue L=5 Ba Spectra: “hide and seek” for some peaks due to O/C contaminents To check DWBA and to move contaminants. Spin assignments from previous work

Spectroscopic factors Only statistical errors from peak fitting shown here. Absolute numbers good to ±15% Relative values to ±5% DWBA using standard optical and bound-state parameters, give good reproduction of angular distributions Common normalization for all isotopes and for both L=5 and 6 As might be expected, deduced spectroscopic factors differ significantly from older (d,p) work

Fragmentation Proportion of single-particle strength in upper states depends on proximity of centroid to the core vibration. Agreement with more detailed calculations Ana-Maria Oros, Doctoral Thesis, University of Köln, Germany 1996 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 Particle-core coupling: 0 +  h 9/2 mixes with 2 +  f 7/2 0 +  i 13/2 mixes with 3   f 7/2

Trends in centroid energies Wildenthal, Newman and Auble, Phys. Rev. C3 (1971) 1199 Difference in centroid energies not well reproduced by “Skyrme+tensor” calculations; centroids qualitatively consistent with g 7/2 and d 5/2 filling at the same rate, with g 7/2 interaction dominating. “Skyrme + tensor” calculations suggest sequential filling g 7/2, d 5/2 and h 11/2 by protons leading to systematic monopole shifts in calculated neutron i 13/2 -h 9/2 energy difference. Experimental proton occupancy from transfer reactions:

Conclusions Clear example where good relative spectroscopic factors are needed to disentangle fragmentation effects from trends in single-particle states Shifts in centroids of single-neutron i 13/2 and h 9/2 states are qualitatively consistent with interactions due to proton g 7/2 and d 5/2 orbitals filling at the same rate, in contrast to recent “Skryme+tensor” calculations which appear to predict sequential filling. Reversal in the trends of single-neutron states appears to be seen when proton h 11/2 is expected to start to fill. BUT (i) this is from data not sensitive to the single-particle structure and (ii) is at the point where the coupling to octupole vibrations of the core might be expected to be strongest. Experiments with radioactive beams are important to address trends over a wider range of neutron excess.