Trends in Single-Particle Excitations (and their fragmentation) Some object lessons from stable nuclei as we move toward the limits J. P. Schiffer Argonne National Laboratory and University of Chicago
Single-particle states form the backbone of the framework in which we understand nuclear structure. Spectroscopic factors provide the measure of the single-particle content of a state, its overlap with the nucleon+nucleus wave function. The s.p. framework was established in the 1960-s by fitting energies in doubly-magic nuclei with Woods-Saxon potentials and using the potentials to interpolate. Exotic nuclei indicated significant changes in shell structure. We * have undertaken a set of precision measurements of transfer reactions re-explore trends (of high-j states) over ranges of stable semi-magic nuclei. * Argonne Manchester (S.J. Freeman et al.) collaboration.
What does an experimentalist mean by single-particle states? A single state outside a closed shell, of a given ( l, j ) that has a large spectroscopic factor in a nucleon adding reaction -- with no other such state with significant strength. Or, if the strength is fragmented, then the centroid: the spectroscopic-factor-weighted mean energy. Absolute spectroscopic factors have to do with correlations in the many-body system and with reaction theory. Comparing spectroscopic factors in the same vicinity of nuclei is an important tool for understanding nuclear structure. \ 3
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To obtain reliable information on spectroscopic factors, momentum matching is important: qr l. 6
~1970 work on the proton adding reaction 124 Sn( 3 He,d) 125 Sb Our work on 122 Sn(α,t) 123 Sb h 11/2 g 7/2 7
The Sn nuclei have a closed shell of 50 protons and their internal structure (low-lying 2 + and 3 - states) is stable. 8
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g 7/2 h 11/2 ±8.5% rms among fourteen values 10
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Neutron Occupancies in Sn h 11/2 filling in Sn cores with increasing A. REPULSIVE effect with h 11/2 ATTRACTIVE effect with g 7/2 gradient is ~0.12 MeV per nucleon From (d,p) spectroscopic factors Otsuka et al. [PRL95(2005)232502]
. In the N=83 nuclei there are vibrational weakcoupling states of the right spin. Thus the first state of a given j is not an accurate measure of the singleparticle energy. But the rms deviation in summed spectroscopic factors is ±13% for eight transitions. B.P. Kay et al. Phys. Let. 656, 216
The lowest 13/2 + and 9/2 - states actually cross over, but
the centroid energies do not quite cross. Calculations with the tensor interaction are consistent with the data Otsukaxx
Proton Occupancies in N=82 from ( 3 He,d) Protons in N=82 nuclei fill the πg 7/2 (j.< ) and πd 5/2 (j > ) orbits the former dominates. The effect is ATTRACTIVE for υi 13/2, REPULSIVE for υh 9/2 Difference is ~0.18 MeV per nucleon
When 40 Ca(d,p) 41 Ca was first studied, two l=1 transitions were seen. They had roughly the right ratio of cross sections and were assumed to be the spin-orbit doublet, 1p 3/2 and 1p 1/2. But the splitting was smaller than expected!
Later detailed work (first on angular correlations in neutron capture, later by polarization measurements, showed that the second l=1 state was also 3/2 -. The strengths were severely fragmented and the splitting from centroids is close to what was expected!
Similar fragmentation of the lower-spin single-particle excitations is seen in heavier semi-magic nuclei.
Collaborators C.L. Jiang, K.E. Rehm, J.S Argonne National Laboratory, USA S.J. Freeman, B.P. Kay, C.R. Fitzpatrick Schuster Laboratory, University of Manchester, UK J.A. Clark, C.M. Deibel, P.D. Parker, A. Heinz, A. Parikh, C. Wrede WNSL, Yale University, USA 28