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Shifts in neutron single-particle states outside N=82

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.

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Shifts in neutron single-particle states outside N=82

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  1. 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

  2. Proton states outside Z=50 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>) Gogny+tensor Gogny 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

  3. Neutron states outside N=82 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.

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

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

  6. Spectroscopic factors 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%

  7. Fragmentation 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

  8. Trends in centroid energies “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

  9. 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 i13/2 and h9/2 states are qualitatively consistent with interactions due to proton g7/2 and d5/2 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 h11/2 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.

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