Walecka mean field theory, Help to find its M*

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SUMMARY

The discussion focuses on computing the equation of state (EoS) for the Walecka model of baryon interaction, specifically addressing the equation M* = M - gs² * nb/ms². The user encounters difficulties in solving this equation using the bisection method, particularly in matching the graph of M*/M with established references. The user cites J. D. Walecka as a primary reference and mentions a parameter set developed for both finite nuclei and infinite nuclear matter, which has shown promising results in previous work.

PREREQUISITES
  • Understanding of Walecka mean field theory
  • Proficiency in numerical methods, specifically the bisection method
  • Familiarity with equations of state (EoS) in nuclear physics
  • Knowledge of relativistic mean field theory and Lagrangian density
NEXT STEPS
  • Study the implementation of the bisection method in numerical analysis
  • Explore the derivation and applications of the Walecka model in nuclear physics
  • Research the role of effective mass (M*) in nuclear matter calculations
  • Review recent papers on relativistic mean field parameter sets for insights on model accuracy
USEFUL FOR

Physicists and researchers in nuclear physics, particularly those working on baryon interactions and the Walecka model, as well as students seeking to understand advanced numerical methods in theoretical physics.

Leonardo Machado
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Hello friends.

I'm trying to compute an EoS to walecka model of barion interaction, but I'm having trouble to solve this equation by bisection.

M*=M-gs²*nb/ms²

where nb= (M*)*( kf*Ef- (M*)²* ln (kf+Ef)/M*) , using Ef= sqrt( kf²+(M*)²)

and Cs²= gs² M² / ms² = 267.1

I'm using J. D. Walecka as my reference for obvious reasons, but the graph of M*/M is not matching with the reference.

May any of you can help me to solve this equation by bisection ?
 
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In this direction, I have done lots of work. You can see in arxiv my work related to finite nuclei and infinite nuclear matter, where I have taken biggest lagrangian density and develop a new relativistic mean field parameter set. It has work very well in case of finite nuclei as well as for nuclear matter. You can excess my paper on this link https://arxiv.org/find/nucl-th/1/au:+Kumar_B/0/1/0/all/0/1 .
 

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