Walecka mean field theory, Help to find its M*

In summary, the speaker is seeking help with solving an equation using bisection in order to compute an EoS to Walecka model of barion interaction. The equation involves variables such as M*, gs², nb, and ms². They mention using the reference of J.D. Walecka and exploring different lagrangian density and relativistic mean field parameter sets. They also share a link to their work on finite nuclei and infinite nuclear matter.
  • #1
Leonardo Machado
57
2
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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  • #2
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 .
 

Related to Walecka mean field theory, Help to find its M*

1. What is Walecka mean field theory?

Walecka mean field theory is a theoretical framework used in nuclear physics to describe the behavior of nuclei and nuclear matter. It is based on the idea that the nucleons (protons and neutrons) in a nucleus interact through an effective potential, known as the mean field, rather than directly interacting with each other.

2. How does Walecka mean field theory work?

Walecka mean field theory uses a self-consistent approach, where the mean field is determined by the density and other properties of the nuclear matter. The nucleons move in this mean field and their interactions are described by the exchange of mesons (particles that mediate the strong nuclear force).

3. What are the advantages of using Walecka mean field theory?

Walecka mean field theory provides a simple and computationally efficient way to describe the properties of nuclei and nuclear matter. It also allows for the inclusion of additional effects, such as the presence of a magnetic field or the introduction of exotic particles, into the description of nuclear systems.

4. What is the significance of M* in Walecka mean field theory?

M* (pronounced "M star") represents the effective mass of nucleons in the mean field. This quantity takes into account the effects of the strong nuclear force and the surrounding nucleons on the motion of a nucleon within a nucleus. It is an important parameter in Walecka mean field theory as it affects the properties of nuclei and nuclear matter.

5. How is Walecka mean field theory used in current research?

Walecka mean field theory is still widely used in nuclear physics research, particularly in studies of nuclear structure and reactions. It has also been applied to other areas, such as the study of neutron stars and the properties of dense nuclear matter. Ongoing research continues to refine and improve this theoretical framework.

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