Charge-exchange reaction cross sections and the Gamow-Teller strength for double β decay

The proportionality between single charge-exchange reaction cross sections in the forward direction as found, for example, from (p,n) and (He-3,t) and from (n,p) and (d,He-2) reactions, and the Gamow-Teller (GT) strength into the same final nuclear states has been studied and/or assumed often in the past. Using the most physically justified theory we have at our disposal and for the specific example of the Ge-76-Se-76 system that may undergo double beta decay, we demonstrate that the proportionality is a relatively good assumption for reactions changing a neutron into a proton, i.e., Ge-76(p,n)As-76. In this channel, the main contribution to the GT strengths comes from the removal of a neutron from an occupied single-particle (SP) state and the placement of a proton into an unoccupied SP state having either the same state quantum numbers or those of the spin-orbit partner. In contrast to this, in the second leg of the double beta decay, a single proton must be taken from an occupied SP state and a neutron placed into an unoccupied one. This second process often is Pauli forbidden in medium-heavy nuclei and can only be effected if the Fermi surface is smeared out. Such is the case for Se-76(n,p)As-76. Our results suggest that one may not always assume a proportionality between the forward-angle cross sections of the charge-exchange reactions and the GT strength in any such medium-heavy nuclei. The discrepancy originates from a pronounced effect of the radial dependence of the nucleon-nucleon (NN) interaction in connection with the Pauli principle on the cross sections in the (n,p) reaction channel. Such a radial dependence is completely absent in the GT transition operator.