On the Quantized Relativistic Mean Field Theory for Nuclear Matter

TL;DR

This paper introduces a quantization method for the nucleon-scalar meson system within relativistic mean field theory, demonstrating that the choice of mean scalar field significantly affects quantum correction convergence and proposing a variational approach for optimal parameter fixing.

Contribution

It develops a quantization procedure for the nucleon-scalar meson system and compares its effects within Walecka's RMFT and Chin's RHA, highlighting RHA's effectiveness as a zeroth order approximation.

Findings

Quantum corrections are large and non-convergent in Walecka's RMFT.

Quantum corrections are negligible and converge well in Chin's RHA.

RHA effectively captures leading quantum effects in nuclear systems.

Abstract

We propose a quantization procedure for the nucleon-scalar meson system, in which an arbitrary mean scalar meson field $\phi$ is introduced. The equivalence of this procedure with the usual ones is proven for any given value of $\phi$. 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 $\phi$ 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 $\phi$ 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.