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COLLABORATORS: (three experiments) S.J. Freeman , B.P. Kay , T. Adach i, 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,

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(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


U. of Manchester (U.K.)


RCNP Osaka





Neutrinoless double -decay, when/if observed,

would prove that neutrinos are their own anti-



But it could also provide unique information on

the neutrino mass, ifthe nuclear matrix element

is known reliably.


What can be done experimentally to check the

reliability of calculations of the matrix elements?


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 valencenucleons.
  • 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.


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).


Extreme caricature of how structural effects could matter


neutron proton

g9/2moves below f5/2 f5/2 moves below p3/2


John Schiffer, NDM09, Madison, WI


Neutron transfer measurements also done at Yale:

(d,p) and (p,d) (forl = 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.


More Important are the Differences

J.P. Schiffer et al. Phys. Rev. Lett. 100, 112501 (2008).






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).