标题： 轻锥核物理：有限核的平均场理论 显示英文标题

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

摘要： 从包含核子、标量介子和矢量介子的相对论有效拉格朗日量（QHD1）出发，发展了一种对有限核的轻锥处理方法。 我们表明，必要的变分原理是一个约束原理，它使总动量算符的期望值 $P^+$与 $P^-$的相同。 这等同于最小化总动量算符之和： $P^-+P^+$。 我们得到了定义单个核子模式的新轻锥版本的方程。 该方程的解近似为一个非平凡的相位因子乘以通常等时狄拉克方程的某些解。 基态波函数被当作介子-核子福克态，介子场被当作该基态中场算符的期望值。 这些期望值的相应方程被证明与通常的介子场方程密切相关。 引入了一种新的数值技术来求解自洽场方程，并应用于 $^{16}$O 和 $^{40}$Ca。 计算得到的结合能与通常等时理论的结果基本相同。 获得了核子加动量分布（核子具有给定 $p^+$值的概率），对于 $p^+$值约为核子质量的百分之七十时出现峰值。 基态波函数的介子成分被用来确定标量和矢量介子的动量分布函数，结果表明矢量介子携带约百分之三十的核子加动量。 矢量介子动量分布随着$A$的增加而在$p^+=0$处更加集中。 显示英文摘要

摘要： 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.