Light-Front Nuclear Physics: Mean Field Theory for Finite Nuclei

Abstract

A light-front treatment for finite nuclei is developed from a relativistic effective Lagrangian (QHD1) involving nucleons, scalar mesons and vector mesons. We show that the necessary variational principle is a constrained one which fixes the expectation value of the total momentum operator $P^{+}$ to be the same as that for $P^{-}$. This is the same as minimizing the sum of the total momentum operators: $P^{-}+P^{+}$. We obtain a new light-front version of the equation that defines the single nucleon modes. The solutions of this equation are approximately a non-trivial phase factor times certain solutions of the usual equal-time Dirac equation. The ground state wave function is treated as a meson-nucleon Fock state, and the meson fields are treated as expectation values of field operators in that ground state. The resulting equations for these expectation values are shown to be closely related to the usual meson field equations. A new numerical technique to solve the self-consistent field equations is introduced and applied to ${}^{16}$O and ${}^{40}$Ca. The computed binding energies are essentially the same as for the usual equal-time theory. The nucleon plus momentum distribution (probability for a nucleon to have a given value of $p^{+}$) is obtained, and peaks for values of $p^{+}$ about seventy percent of the nucleon mass. The mesonic component of the ground state wave function is used to determine the scalar and vector meson momentum distribution functions, with a result that the vector mesons carry about thirty percent of the nuclear plus-momentum. The vector meson momentum distribution becomes more concentrated at $p^{+}=0$ as $A$ increases.

36 pages, 2 figures

References in corpus (3)

• Infinite Nuclear Matter on the Light Front: Nucleon-Nucleon Correlations
• Light Front Theory Of Nuclear Matter
• Light Front Nuclear Physics: Toy Models, Static Sources and Tilted Light Front Coordinates

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• Return of the EMC Effect: Finite Nuclei
• Light-front Ward-Takahashi Identity for Two-Fermion Systems
• Study of the in-medium nucleon electromagnetic form factors using a light-front nucleon wave function combined with the quark-meson coupling model
• Unambiguous Extraction of the Electromagnetic Form Factors for Spin-1 Particles on the Light-Front
• Light Front Nuclear Physics: Toy Models, Static Sources and Tilted Light Front Coordinates
• Quarks and Antiquarks in Nuclei
• Nuclear Physics on the Light Front