COLLABORATORS: S.J. Freeman, B.P. Kay, (three experiments)   S.J. Freeman, B.P. Kay, T. Adachi, J.A. Clark, C.M. Deibel, C.R. Fitzpatrick, H. Fujita, Y. Fujita, P. Grabmayr, S. Gros, K. Hatanaka, A. Heinz, D. Hirata, D. Ishikawa, C.L. Jiang, H. Matsubara, Y. Meada, H. Okamura, A. Parikh, P. Parker, K.E. Rehm, Y. Shimizu, H. Shimoda, K. Suda,Y. Tameshige, A. Tamii, A.C.C. Villari, W. Werner, C. Wrede Argonne U. of Manchester (U.K.) Yale, RCNP Osaka Tübingen GANIL Chicago

Neutrinoless double -decay, when/if observed, would prove that neutrinos are their own anti- particles.. …. But it could also provide unique information on the neutrino mass, if the nuclear matrix element is known reliably. . What can be done experimentally to check the reliability of calculations of the matrix elements?

Values from the Majorana Collaboration web site (2006)

All these calculations grind out the sums over all possible intermediate virtual states. \ But, since the virtual neutrinos are confined to the nucleus, virtual momenta are large (up to >200 MeV/c), and all excitations in the giant resonance regime are accessible: all the p-h strength. (This is unlike the 2 mode). Closure should be a good approximation, and the detailed structure of the intermediate nucleus will not matter (but most existing calculations do not make use of this).

If the intermediate states do not matter, this leaves the initial and final states and the overlap between them:. .for instance, the ground states of 76Ge and 76Se.

What can be done experimentally? The nucleons that are free to change from neutrons to protons are valence nucleons. 1) We can measure the extent of pair correlations (BCS–like) that characterize the 0+ ground states of even-even nuclei. Such correlations can be constant or may vary from nucleus to nucleus (the pairing vibrations of Bohr and Mottleson), and we can track these quantitatively. We can also map out the microscopic distribution of valence nucleons between the orbits at the Fermi surface, broadened out by the BCS correlations, and especially the difference between the distribution between the initial and final states.

Cancellation between nucleon pairs that couple to different total angular momenta with respect to the nucleus, shows a pattern that appears to be a general feature of QRPA and shell-model calculations. Figure from P. Vogel.

Simkovič & Vogel

76Ge(p,t)74Ge at 3o

1. There is no significant fragmentation of the 0+ strength (<1%). 2.The reduced cross sections for 76Ge and 76Se are as nearly identical as we can measure (<5%). The BCS approximation for neutron pairs appears to work well here. S.J. Freeman, et al. Phys. Rev. C105, 0r1301 (2007).

John Schiffer, NDM09, Madison, WI

John Schiffer, NDM09, Madison, WI Extreme caricature of how structural effects could matter ‘Forbidden’ neutron proton g9/2 moves below f5/2 f5/2 moves below p3/2 ‘Normal’ John Schiffer, NDM09, Madison, WI

Neutron transfer measurements also done at Yale: (d,p) and (p,d) (for l = 1) (,3He) & (3He,) (for l = 3 and 4). N.B. momentum matching is important. Targets 76Ge, 76Se, plus 74Ge, 78Se for redundancy. These (d,p) and (p,d) transfer reactions had been measured ~30 years ago.  Our objective was to get accurate cross sections at the angles where the cross sections peak.

Calculated angular distributions for different l–values in neutron transfer.

How about missing some strength? For valence orbits very little seems to be beyond 2 MeV excitation.

Comparison with prior QRPA: Occupancy.

More Important are the Differences J.P. Schiffer et al. Phys. Rev. Lett. 100, 112501 (2008).

Angular Distributions Polarization

The observed differences between proton and neutron occupancies indicate that the occupancy is changing appreciably in all the valence orbits, for both protons and neutrons. In the original QRPA calculations the g9/2 orbit accounted for almost all the change for neutrons and almost none of it for protons. Newer calculations, carried out after the neutron data were published, are in better agreement with the data. B. P. Kay, et al. Phys. Rev. C 79, R021301 (2009).