A=3 (e,e') $x_B \geq 1$ cross-section ratios and the isospin structure of short-range correlations

Abstract

We study the relation between measured high-$x_B$, high-$Q^2$, Helium-3 to Tritium, $(e,e')$ inclusive-scattering cross-section ratios and the relative abundance of high-momentum neutron-proton ($np$) and proton-proton ($pp$) short-range correlated (SRC) nucleon pairs in three-body ($A=3$) nuclei. Analysis of this data using a simple pair-counting cross-section model suggested a much smaller $np/pp$ ratio than previously measured in heavier nuclei, questioning our understanding of $A=3$ nuclei and, by extension, all other nuclei. Here we examine this finding using spectral-function-based cross-section calculations, with both an \textit{ab initio} $A=3$ spectral function and effective Generalized Contact Formalism (GCF) spectral functions using different nucleon-nucleon interaction models. The \textit{ab initio} calculation agrees with the data, showing good understanding of the structure of $A=3$ nuclei. An 8\% uncertainty on the simple pair-counting model, as implied by the difference between it and the \textit{ab initio} calculation, gives a factor of 5 uncertainty in the extracted $np/pp$ ratio. Thus we see no evidence for the claimed ``unexpected structure in the high-momentum wavefunction for hydrogen-3 and helium-3''.