A numerical study of resonance contributions to nuclear sum rules

The strength of beta-decays to the continuum

“…It may be of interest to briefly compare the found resonances with the famous case of the 8 Be ground state. Comparing the Schrödinger equations in the tunneling region for the α + α case and for p+ 10 Be one finds that scaling the radius in the latter case up by the ratio of reduced masses in the two systems and the energies down by the same factor, one obtains exactly the same equation. In other words, the 8 Be ground state corresponds to a proton resonance at 42 keV.…”

“…A more formal treatment of the question of how to formulate the completeness relation including continuum states was given by Berggren and collaborators [7,8]. With a careful definition of the continuum wavefunctions one can derive general sum rules [9,10] where for our specific case the sum over discrete states is replaced by a sum over bound states and an integral over all (real values of the) momenta in the continuum…”

“…If one wishes to assign strength to a specific resonance this can be done, but there is in principle a risk of obtaining non-positive values. The question of when continuum contributions will remain important is treated in [9,10].…”

“…The basic assumption in this discretized continuum direct decay model (DCDD) is that the initial state is an s-wave neutron in the potential given by 10 Be that is assumed to be inert. The final states are continuum wave functions of a proton in an s-wave in the combined Coulomb and nuclear potential from 10 Be.…”

“…The basic assumption in this discretized continuum direct decay model (DCDD) is that the initial state is an s-wave neutron in the potential given by 10 Be that is assumed to be inert. The final states are continuum wave functions of a proton in an s-wave in the combined Coulomb and nuclear potential from 10 Be. The Gamow-Teller operator simply converts the halo neutron into a proton (the spin operator will not change the physics) so the matrix element reduces to the overlap between the two wavefunctions.…”