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arXiv 1003.0235nucl-th
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关于核物质的量子化相对论平均场论

On the Quantized Relativistic Mean Field Theory for Nuclear Matter

Qi-Ren Zhang, Chun-Yuan Gao

摘要:

本文提出了一种核子-标量介子系统的量子化方法,其中引入了一个任意平均的标量介子场$ϕ$。对于任何给定的$ϕ$值,证明了该方法与通常方法的等价性。利用这一过程,Walecka的RMFT和Chin的RHA中的标量介子场在平均场附近被量子化。它对这些理论的修正被认为是由扰动到二阶。$ϕ$的任意性使我们可以在计算的任何阶段自由地修正它。当我们用Walecka的RMFT方法修正它时,量子修正很大,结果不收敛。当我们用Chin的RHA方法修正它时,量子修正小到可以忽略不计,并且收敛性很好。结果表明,RHA涵盖了核系统量子场论的主要部分,是进一步量子修正的优良零级近似,而Walecka的RMFT则不然。我们建议在整个计算的最后通过最小化核物质的每个核子的总能量或有限核的总能量来固定参数$ϕ$,使量子化相对论平均场论(QRMFT)成为变分方法。

英文摘要:

We propose a quantization procedure for the nucleon-scalar meson system, in which an arbitrary mean scalar meson field $ϕ$ is introduced. The equivalence of this procedure with the usual ones is proven for any given value of $ϕ$. By use of this procedure, the scalar meson field in the Walecka's RMFT and in Chin's RHA are quantized around the mean field. Its corrections on these theories are considered by perturbation up to the second order. The arbitrariness of $ϕ$ makes us free to fix it at any stage in the calculation. When we fix it in the way of Walecka's RMFT, the quantum corrections are big, and the result does not converge. When we fix it in the way of Chin's RHA, the quantum correction is negligibly small, and the convergence is excellent. It shows that RHA covers the leading part of quantum field theory for nuclear systems and is an excellent zeroth order approximation for further quantum corrections, while the Walecka's RMFT does not. We suggest to fix the parameter $ϕ$ at the end of the whole calculation by minimizing the total energy per-nucleon for the nuclear matter or the total energy for the finite nucleus, to make the quantized relativistic mean field theory (QRMFT) a variational method.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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