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https://github.com/0382/cgcoefficient.jl
Compute CG coefficient, Racah coefficient, and Wigner 3j, 6j, 9j Symbols, and give the exact results.
https://github.com/0382/cgcoefficient.jl
clebsch-gordan-coefficients julia math moshinsky wigner-symbols
Last synced: 8 days ago
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Compute CG coefficient, Racah coefficient, and Wigner 3j, 6j, 9j Symbols, and give the exact results.
- Host: GitHub
- URL: https://github.com/0382/cgcoefficient.jl
- Owner: 0382
- License: mit
- Created: 2020-10-18T02:44:58.000Z (about 4 years ago)
- Default Branch: master
- Last Pushed: 2024-12-28T03:38:50.000Z (8 days ago)
- Last Synced: 2024-12-28T04:26:45.222Z (8 days ago)
- Topics: clebsch-gordan-coefficients, julia, math, moshinsky, wigner-symbols
- Language: Julia
- Homepage: https://0382.github.io/CGcoefficient.jl/
- Size: 571 KB
- Stars: 1
- Watchers: 2
- Forks: 1
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
Awesome Lists containing this project
README
# CGcoefficient.jl
[](LICENSE)
[](https://github.com/0382/CGcoefficient.jl/actions/workflows/CI.yml)
[](https://codecov.io/gh/0382/CGcoefficient.jl)
[](https://0382.github.io/CGcoefficient.jl/dev)
[[中文](README_zh.md)]
A package to calculate CG-coefficient, Racah coefficient, Wigner 3j, 6j, 9j symbols and Moshinsky brakets.
One can get the exact result with `SqrtRational` type, which use `BigInt` to avoid overflow. And we also offer float version for numeric calculation, which is about twice faster than [GNU Scientific Library](https://www.gnu.org/software/gsl/).
I also rewrite the float version with c++ for numeric calculation: [WignerSymbol](https://github.com/0382/WignerSymbol).
For more details and the calculation formula, please see the document [](https://0382.github.io/CGcoefficient.jl/dev).
### Install
Just start a Julia REPL, and install it
```julia-repl
julia> ]
pkg> add CGcoefficient
```
### Example
```julia-repl
julia> CG(1,2,3,1,1,2)
√(2//3)
julia> nineJ(1,2,3,4,5,6,3,6,9)
1//1274√(3//5)
julia> f6j(6,6,6,6,6,6)
-0.07142857142857142
```
For more examples please see the document.
### API
This package contains two types of functions:
1. The exact functions return `SqrtRational`, which are designed for demonstration. They use `BigInt` in the internal calculation, and do not cache the binomial table, so they are not efficient.
2. The floating-point functions return `Float64`, which are designed for numeric calculation. They use `Int, Float64` in the internal calculation, and you should pre-call `wigner_init_float` to calculate and cache the binomial table for later calculation. They may give inaccurate result for vary large angular momentum, due to floating-point arithmetic. They are trustworthy for angular momentum number `Jmax <= 60`.
#### Exact functions
Exact function only for demonstration, some of them can be `Real` arguments, like `1, 3//2, 0.5`, but `4//3, 0.6` will throw error.
- `CG(j1, j2, j3, m1, m2, m3)`, CG-coefficient, `Real` arguments.
- `CG0(j1, j2, j3)`, CG-coefficient for `m1 = m2 = m3 = 0`, only integer angular momentum number is meaningful.
- `threeJ(j1, j2, j3, m1, m2, m3)`, Wigner 3j-symbol, `Real` arguments.
- `sixJ(j1, j2, j3, j4, j5, j6)`, Wigner 6j-symbol, `Real` arguments.
- `Racah(j1, j2, j3, j4, j5, j6)`, Racah coefficient, `Real` arguments.
- `nineJ(j1, j2, j3, j4, j5, j6, j7, j8, j9)`, Wigner 9j-symbol, `Real` arguments.
- `norm9J(j2, j3, j4, j5, j5, j6, j7, j8, j9)`, normalized 9j-symbol, `Real` arguments.
- `lsjj(l1, l2, j1, j2, L, S, J)`, LS-coupling to jj-coupling transform coefficient. It actually equals to a normalized 9j-symbol, but easy to use and faster. `j1, j2` can be `Real`.
- `Moshinsky(N, L, n, l, n1, l1, n2, l2, Λ)`, Moshinsky brakets, `Integer` arguments.
#### Float functions
For faster numeric calculation, if the angular momentum number can be half-integer, the argument of the functions is actually double of the number. So that all arguments are integers. The doubled arguments are named starts with `d`.
- `fCG(dj1, dj2, dj3, dm1, dm2, dm3)`, CG-coefficient.
- `fCG0(j1, j2, j3)`, CG-coefficient for `m1 = m2 = m3 = 0`.
- `fCGspin(ds1, ds2, S)`, quicker CG-coefficient for two spin-1/2 coupling.
- `f3j(dj1, dj2, dj3, dm1, dm2, dm3)`, Wigner 3j-symbol.
- `f6j(dj1, dj2, dj3, dj4, dj5, dj6)`, Wigner 6j-symbol.
- `fRacah(dj1, dj2, dj3, dj4, dj5, dj6)`, Racah coefficient.
- `f9j(dj1, dj2, dj3, dj4, dj5, dj6, dj7, dj8, dj9)`, Wigner 9j-symbol.
- `fnorm9j(dj1, dj2, dj3, dj4, dj5, dj6, dj7, dj8, dj9)`, normalized 9j-symbol.
- `flsjj(l1, l2, dj1, dj2, L, S, J)`, LS-coupling to jj-coupling transform coefficient.
- `fMoshinsky(N, L, n, l, n1, l1, n2, l2, Λ)`, Moshinsky brakets.
- `dfunc(dj, dm1, dm2, β)`, Wigner d-function.
### Reference
- [https://github.com/ManyBodyPhysics/CENS](https://github.com/ManyBodyPhysics/CENS)
- D. A. Varshalovich, A. N. Moskalev and V. K. Khersonskii, *Quantum Theory of Angular Momentum*, (World Scientific, 1988).
- Buck et al. Nuc. Phys. A 600 (1996) 387-402.