Meaning of the nuclear wave function

Abstract

Background The intense current experimental interest in studying the structure of the deuteron and using it to enable accurate studies of neutron structure motivate us to examine the four-dimensional space-time nature of the nuclear wave function, and the various approximations used to reduce it to an object that depends only on three spatial variables. Purpose: The aim is to determine if the ability to understand and analyze measured experimental cross sections is compromised by making the reduction from four to three dimensions. Method: Simple, exactly-calculable, covariant models of a bound-state wave state wave function (a scalar boson made of two constituent-scalar bosons) with parameters chosen to represent a deuteron are used to investigate the accuracy of using different approximations to the nuclear wave function to compute the quasi-elastic scattering cross section. Four different versions of the wave function are defined (light-front spectator, light-front, light-front with scaling and non-relativistic) and used to compute the cross sections as a function of how far off the mass-shell (how virtual) is the struck constituent. Results: We show that making an exact calculation of the quasi-elastic scattering cross section involves using the light-front spectator wave function. All of the other approaches fail to reproduce the model exact calculation if the value of Bjorken $x$ differs from unity. The model is extended to consider an essential effect of spin to show that constituent nucleons cannot be treated as being on their mass shell even when taking the matrix element of a `good' current. Conclusions: It is necessary to develop realistic light-front spectator wave functions to meet the needs of current and planned experiments.

17 pages 11 figures

References in corpus (8)

• Chiral effective field theory and nuclear forces
• Evidence for the Strong Dominance of Proton-Neutron Correlations in Nuclei
• Short Range Correlations and the EMC Effect
• Ab initio calculation of the spectrum and structure of ${}^{16}$O
• Correlated Fermion Pairs in Nuclei and Ultracold Atomic Gases
• Electromagnetic Form Factors and Charge Densities From Hadrons to Nuclei
• Modern Studies of the Deuteron: from the Lab Frame to the Light Front
• Neutron spin structure with polarized deuterons and spectator proton tagging at EIC

Cited by in corpus (1)

• Comparison of two Minkowski-space approaches to heavy quarkonia