Help understanding Nuclear physics concepts

[nikhill]

Hello,

I am a Computer Science student and am working on a nuclear physics code. Actually I am not a physics guy but need to have a very basic understanding of some nuclear physics terms. I am reading a paper on this project and need your help in understanding some concepts.

Some of these terms are: many body interaction, Hamiltonian and large harmonic oscillator(and how are these related), basis states(single particle basis state etc.), wavefunctions, basis functions and how they are useful in matrix vector multiplication, (somehow all these suggest a matrix or a vector I guess).

My task is basically related to matrix multiplication and optimization and speed up of the program by using parallel IO. I know these questions may be a bit too much to explain in layman's terms but whatever help you all can give could be of great help.

Some of the methods mentioned in the paper which I have no clue about are:
1. Expand nuclear wave function in H.O. basis functions
2. Generate Many–Body basis
Slater-Determinant of single particle states
Carbon-12 using 8 H.O. levels: 33 million basis states
3. Construct Many–Body Hamiltonian from 2-body (and 3-body) interactions

I have little knowledge of nuclear physics that I had learned a long time back. Kindly provide some explanations that I can relate to as a computer science student.

Thanks.

 

[eljose79]

Dear Computer Science student,

It's great to see your interest in nuclear physics and the work you are doing on the nuclear physics code. I am a scientist in the field of nuclear physics and would be happy to help you understand the concepts you mentioned.

Firstly, the many body interaction refers to the interactions between multiple nucleons (protons and neutrons) in a nucleus. These interactions are described by the Hamiltonian, which is a mathematical operator that represents the total energy of the system. The Hamiltonian includes terms for the kinetic energy of the nucleons, their potential energy due to the interactions, and other factors. The large harmonic oscillator is a specific model used to describe the nuclear interactions, where the nucleons are treated as oscillating particles in a potential well.

In nuclear physics, we use the concept of basis states or basis functions to describe the possible states of the system. These are essentially different configurations of the nucleons, such as different energy levels or spin orientations. The wavefunctions represent the probability amplitudes for finding the nucleons in these different states. The basis states or functions are useful in matrix-vector multiplication because they can be represented as matrices or vectors, making it easier to perform calculations and simulations.

Now, let's look at the methods mentioned in the paper. The first method involves expanding the nuclear wave function (the probability amplitude of the whole system) in terms of harmonic oscillator basis functions. This helps in simplifying the calculations and allows for a more efficient representation of the wave function.

The second method involves generating a many-body basis by combining single particle states. This is done using a mathematical concept called a Slater determinant, which helps in describing the different configurations of the nucleons in the nucleus. In the case of Carbon-12, there are 6 protons and 6 neutrons, and using 8 harmonic oscillator levels, we get a total of 33 million basis states (6 protons and 6 neutrons in each of the 8 levels).

Finally, the third method involves constructing the many-body Hamiltonian (mathematical operator representing the total energy) using two-body and three-body interactions between nucleons. These interactions are described by nuclear potential models that take into account the properties of the nucleons and their interactions.

I hope this explanation helps you understand the concepts better. As a computer science student, you can think of these concepts in terms of mathematical operations and data structures used in coding. Please feel free to ask any further

 

[denian]

Hello,

I am happy to help you understand these nuclear physics concepts. Nuclear physics is a complex and fascinating field, and understanding these terms will definitely help you in your project.

Firstly, let's start with the concept of many body interaction. This refers to the interactions between multiple particles in a nuclear system. In nuclear physics, we often study systems with many particles, such as atoms or nuclei, and understanding how these particles interact with each other is crucial in understanding the behavior of the system as a whole.

Next, the Hamiltonian is a mathematical operator that represents the total energy of a system. In the context of nuclear physics, the Hamiltonian represents the total energy of all the particles in a nuclear system, taking into account their interactions with each other. The Hamiltonian is a central concept in quantum mechanics, which is the framework used to study nuclear physics.

Now, let's talk about the large harmonic oscillator. This is a mathematical model used to describe the motion of particles in a potential well. In nuclear physics, we often use the large harmonic oscillator model to describe the motion of nucleons (protons and neutrons) in a nucleus. This model is useful because it allows us to simplify the complex interactions between particles in a nucleus.

The basis states, or single particle basis states, refer to the possible states that a single particle can occupy in a system. In nuclear physics, we often use the large harmonic oscillator model to describe these states. Wavefunctions, on the other hand, describe the probability of finding a particle in a particular state. Basis functions are mathematical functions that are used to represent wavefunctions, and they are useful in matrix vector multiplication because they allow us to express complex functions in terms of simpler ones.

Now, let's discuss the methods mentioned in the paper. The first method, expanding the nuclear wave function in H.O. basis functions, involves representing the wave function of a nuclear system in terms of the basis functions of the large harmonic oscillator model. This allows us to simplify the wave function and make calculations easier.

The second method, generating a many-body basis, involves creating a set of basis states for a system with multiple particles. In this case, the authors use the Slater-Determinant of single particle states to represent the basis states for Carbon-12. This results in a large number of basis states (33 million) which can be used to describe the complex interactions between particles in the nucleus.

Finally, the third method involves using the two-body (