Nuclear Shell Model, how to develop a shell-model code
Contents
Slater determinants as basis states, Repetition
Slater determinants as basis states, repetition
Slater determinants as basis states
Slater determinants as basis states
Quick repetition of the occupation representation
Quick repetition of the occupation representation
Quick repetition of the occupation representation
Full Configuration Interaction Theory
Full Configuration Interaction Theory
Full Configuration Interaction Theory
Full Configuration Interaction Theory
Full Configuration Interaction Theory
Full Configuration Interaction Theory
Example of a Hamiltonian matrix
Example of a Hamiltonian matrix with a Hartree-Fock basis
Shell-model jargon
FCI and the exponential growth
Exponential wall
A non-practical way of solving the eigenvalue problem
A non-practical way of solving the eigenvalue problem
A non-practical way of solving the eigenvalue problem
Rewriting the FCI equation
Rewriting the FCI equation
Rewriting the FCI equation, does not stop here
Rewriting the FCI equation, please stop here
Rewriting the FCI equation, more to add
Rewriting the FCI equation, more to add
Summarizing FCI and bringing in approximative methods
Definition of the correlation energy
FCI equation and the coefficients
Important ingredients to have in codes
A structured approach to solving problems
Additional benefits
Unit Testing
Unit Testing, benefits
Simple example of unit test
Simple example of unit test
"Unit tests":"https://github.com/philsquared/Catch/blob/master/docs/tutorial.md"
Examples
Factorial Example
What did we do (1)?
What did we do (2)?
Unit test summary and testing approach
Coding Recommendations
Summary and recommendations
Building a many-body basis
Building a many-body basis
Building a many-body basis
Building a many-body basis
Building a many-body basis
Building a many-body basis
Building a many-body basis
Building a many-body basis
Building a many-body basis
Building a many-body basis
Building a many-body basis
Building a many-body basis
Shell-model Project
Shell-model project
Shell-model project
Shell-model project
Shell-model project
Shell-model project
Shell-model project
Shell-model project
Shell-model project
Shell-model project
Shell-model project
Shell-model project
Shell-model project
Shell-model project
Shell-model project
Shell-model project
Shell-model project
Example case: pairing Hamiltonian
Example case: pairing Hamiltonian
Example case: pairing Hamiltonian
Example case: pairing Hamiltonian
Example case: pairing Hamiltonian
Example case: pairing Hamiltonian
Example case: pairing Hamiltonian
Example case: pairing Hamiltonian
Example case: pairing Hamiltonian
Building a Hamiltonian matrix
Building a Hamiltonian matrix
Building a Hamiltonian matrix
Building a Hamiltonian matrix, first step
Building a Hamiltonian matrix, second step
Building a Hamiltonian matrix
Building a Hamiltonian matrix
Building a Hamiltonian matrix
Building a Hamiltonian matrix
Building a Hamiltonian matrix
Building a Hamiltonian matrix
Hamiltonian matrix without the bit representation
Hamiltonian matrix without the bit representation, one and two-body operators
Strategies for setting up an algorithm
Computing expectation values and transitions in the shell-model
Computing expectation values and transitions in the shell-model and spectroscopic factors
Operators in second quantization
Operators in second quantization
Operators in second quantization
Operators in second quantization
Operators in second quantization
Operators in second quantization
Operators in second quantization
Operators in second quantization
Operators in second quantization
Bit counting
Eigenvalue problems, basic definitions
Eigenvalue problems, basic definitions
Eigenvalue problems, basic definitions
Abel-Ruffini Impossibility Theorem
Abel-Ruffini Impossibility Theorem
Eigenvalue problems, basic definitions
Eigenvalue problems, basic definitions
Eigenvalue problems, basic definitions
Eigenvalue problems, basic definitions
Discussion of methods for eigenvalues
Eigenvalues methods
Discussion of methods for eigenvalues
Eigenvalues and Lanczos' method
Eigenvalues and Lanczos' method, tridiagonal matrix
Eigenvalues and Lanczos' method, tridiagonal and orthogonal matrices
Eigenvalues and Lanczos' method
Eigenvalues and Lanczos' method, defining the Lanczos' vectors
Eigenvalues and Lanczos' method, basic steps
Building a many-body basis
Example: two \( j=1/2 \) orbits
Index
\( n \)
\( l \)
\( j \)
\( m_j \)
1
0
0
1/2
-1/2
2
0
0
1/2
1/2
3
1
0
1/2
-1/2
4
1
0
1/2
1/2
Note that the order is arbitrary.
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