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 fourdimensional 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 Developing realistic light-front spectator wave functions to meet the needs of current and planned experiments is a worthwhile activity.

Comparison of two Minkowski-space approaches to heavy quarkonia

“…Though it is well-known that establishing a proper connection between Bethe-Salpeter amplitudes or any of its threedimensional reductions, with light-front wave functions is a non-trivial problem, attempts to solve or at least bridge the two approaches have been developed in multiple contexts [10][11][12][13][14][15][16][17][18][19].…”

Theoretical study on production cross sections of exotic actinide nuclei in multinucleon transfer reactions

“…Due to low separation and detection efficiency of the available laboratory equipment at the time, few new heavy isotopes were observed based on multinucleon transfer reactions. However, as it is a promising approach, the multinucleon transfer process has been extensively investigated experimentally [10][11][12][13][14][15][16][17][18][19][20][21] and theoretically in recent years. Recently, five new neutron-deficient isotopes 216 U, 219 Np, 223 Am, 229 Am, and 233 Bk were observed in the transfer reaction 48 Ca + 248 Cm [44].…”