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 h11/2 and g7/2 strength with little variation.Schiffer et al. Phys. Rev. Lett. 92(2004)162501

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>)

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

Gogny+tensor

Gogny

Neutron states outside N=82

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.

HF+Skryme Calculations: Colò et al. Phys Lett. B646(2007)227-231

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.

Increasing neutron excess

Experimental Details

N=82(a,3He) Reactions: neutron transfer with large 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

Spectra at 20 degrees

Angular DistributionsExamples of DWBA fits to Nd and SmRed 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 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

Fragmentation

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

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+ h9/2 mixes with 2+ f7/2

0+ i13/2 mixes with 3 f7/2

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 g7/2 and d5/2

filling at the same rate, with g7/2 interaction dominating.

“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:

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.