# Parameters in Bohr-Mottelson Collective Hamiltonian

• patric44
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patric44
Homework Statement
how do I find the value of the mass parameter and the width of the potential well present in the Bohr-Mottelson Hamiltonian?
Relevant Equations
-hbar^2/2B
Hi all
I was reading a certain paper that involves solving the Bohr-Mottelson Hamiltonian for a 5dimential square well potential, the B-M Hamiltoian reads:

my question is just how do I calculate the mass parameter "B" for a certain nuclei, and with a 5D infinite potential well how do I get the width of the potential well?
I will appreciate any help, thanks in advance.

can any one suggest a paper or a book that address these points

## What is the Bohr-Mottelson Collective Hamiltonian?

The Bohr-Mottelson Collective Hamiltonian is a theoretical framework used in nuclear physics to describe the collective motion of nucleons within an atomic nucleus. It incorporates both vibrational and rotational degrees of freedom, providing a comprehensive model for understanding nuclear structure and dynamics.

## What are the key parameters in the Bohr-Mottelson Collective Hamiltonian?

The key parameters in the Bohr-Mottelson Collective Hamiltonian include the mass parameters (or moments of inertia) which describe the resistance of the nucleus to deformation, the potential energy surface which defines the shape of the nucleus, and the coupling constants that link the vibrational and rotational motions.

## How are the parameters of the Bohr-Mottelson Collective Hamiltonian determined?

The parameters of the Bohr-Mottelson Collective Hamiltonian are typically determined through a combination of experimental data and theoretical models. Experimental data such as energy levels, transition rates, and moments of inertia are used to fit the parameters, while theoretical models provide guidance on the functional forms and interrelations of these parameters.

## What role do vibrational and rotational degrees of freedom play in the Bohr-Mottelson Collective Hamiltonian?

In the Bohr-Mottelson Collective Hamiltonian, vibrational degrees of freedom describe the oscillations of the nuclear shape around an equilibrium configuration, while rotational degrees of freedom account for the rotation of the deformed nucleus as a whole. The interplay between these degrees of freedom is crucial for accurately modeling the collective behavior of nuclei.

## Why is the Bohr-Mottelson Collective Hamiltonian important in nuclear physics?

The Bohr-Mottelson Collective Hamiltonian is important in nuclear physics because it provides a unified and versatile framework for understanding a wide range of nuclear phenomena. It enables the prediction and interpretation of nuclear spectra, transition probabilities, and other observables, thereby enhancing our understanding of nuclear structure and reactions.

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