Population of the giant pairing vibration

Abstract

Background: The giant pairing vibration (GPV), a correlated two-nucleon mode in the second shell above the Fermi surface, has long been predicted and expected to be strongly populated in two-nucleon transfer cross sections similar to those of the normal pairing vibration. Recent experiments have provided evidence for this mode in $^{14,15}\text{C}$ but, despite sensitive studies, it has not been definitively identified in either Sn or Pb nuclei where pairing correlations are known to play a crucial role.Purpose: Our aim is to test whether features inherent to the mixing of bound and unbound levels might account for this and to study the effect in a simple and intuitively clear approach.Method: We study the mixing of unbound levels in a set of toy models that capture the essential physics of the GPV, along with a more realistic calculation including distorted-wave Born approximation transfer amplitudes.Results: The calculated (relative) cross section to populate a simulated GPV state is effectively low, compared to the case of bound levels with no widthsConclusions: The mixing turns out to be only a minor contributor to the weak population. Rather, the main reason is the melting of the GPV peak due to the width it acquires from the low orbital angular momentum single-particle states playing a dominant role in two-nucleon transfer amplitudes. This effect, in addition to a severe $Q$-value mismatch, may account for the elusive nature of this mode in $(t,p)$ and $(p,t)$ reactions.