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Working result for SRC

This commit is contained in:
Nuwan Yapa 2024-10-30 16:40:57 -04:00
parent 7e641d32b3
commit 262ab3d426
3 changed files with 30 additions and 15 deletions
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12
ho_basis.jl
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@ -155,4 +155,14 @@ function get_jacobi_V2_matrix(V_of_r, E_max, Λ, μω_global; atol=10^-6, maxeva
V2 = U' * V_relative * U
return V2
end
end
function get_2p_p1p2_matrix(n1s, l1s, n2s, l2s, Λ, μ1ω1, μ2ω2)
mat = spzeros(Float64, length(n1s), length(n1s))
for idx in CartesianIndices(mat)
(i, j) = Tuple(idx)
val = racahs_reduction_formula(n1s[i], l1s[i], n2s[i], l2s[i], n1s[j], l1s[j], n2s[j], l2s[j], Λ, μ1ω1, μ2ω2)
if !(val ≈ 0); mat[idx] = val; end
end
return mat
end

26
ho_basis_3body.jl
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@ -7,13 +7,11 @@ Va = -2
Ra = 2
E_max = 40
μω_global = 0.5
μω_global = 0.3
# due to Jacobi coordinates
μ1ω1 = μω_global * 1/2
μ2ω2 = μω_global * 2
μ1 = m * 1/2
μ2 = m * 2/3
# due to simple relative coordinates
μω = μω_global * 2
μ = m/2
println("No of threads = ", Threads.nthreads())
@ -26,19 +24,21 @@ end
println("Basis size = ", length(Es))
println("Constructing KE matrices")
@time "T1" T1 = get_sp_T_matrix(n1s, l1s; mask=mask1, μω_gen=μ1ω1, μ=μ1)
@time "T2" T2 = get_sp_T_matrix(n2s, l2s; mask=mask2, μω_gen=μ2ω2, μ=μ2)
@time "T1" T1 = get_sp_T_matrix(n1s, l1s; mask=mask1, μω_gen=μω, μ=μ)
@time "T2" T2 = get_sp_T_matrix(n2s, l2s; mask=mask2, μω_gen=μω, μ=μ)
@time "T_cross" T_cross = get_2p_p1p2_matrix(n1s, l1s, n2s, l2s, Λ, μω, μω) ./ (2*μ)
println("Constructing PE matrices")
V1_elem(l, n1, n2) = Va * V_Gaussian(Ra, l, n1, n2; μω_gen=μ1ω1)
V_elem(l, n1, n2) = Va * V_Gaussian(Ra, l, n1, n2; μω_gen=μω)
V_relative_elem(l, n1, n2) = Va * V_Gaussian(Ra, l, n1, n2; μω_gen=μω_global)
@time "V1" V1 = get_sp_V_matrix(V1_elem, n1s, l1s; mask=mask1)
@time "V relative" V_relative = get_sp_V_matrix(V_relative_elem, n1s, l1s; mask=mask1) + get_sp_V_matrix(V_relative_elem, n2s, l2s; mask=mask2)
@time "V1" V1 = get_sp_V_matrix(V_elem, n1s, l1s; mask=mask1)
@time "V2" V2 = get_sp_V_matrix(V_elem, n2s, l2s; mask=mask2)
@time "V relative" V_relative = get_sp_V_matrix(V_relative_elem, n1s, l1s; mask=mask1)
@time "Moshinsky brackets" U = Moshinsky_transform(Es, n1s, l1s, n2s, l2s, Λ)
@time "V2" V2 = U' * V_relative * U
@time "V12" V12 = U' * V_relative * U
println("Calculating spectrum")
@time "H" H = T1 + T2 + V1 + V2
@time "H" H = T1 + T2 + T_cross + V1 + V2 + V12
@time "Eigenvalues" evals, _ = eigs(H, nev=3, ncv=30, which=:SR, maxiter=5000, tol=1e-5, ritzvec=false, check=1)
display(evals)

7
math.jl
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@ -30,4 +30,9 @@ end
reduced_matrix_element(np, lp, n, l, μω) = (-1)^lp * sqrt(2*lp + 1) * sqrt(2*l + 1) * wigner3j(Float64, lp, 1, l, 0, 0, 0) * integral(np, lp, n, l, μω)
"Matrix element <n1p l1p n2p l2p| p1⋅p2 |n1 l1 n2 l2> (Ref: de-Shalit & Talmi, Eq 15.5)"
racahs_reduction_formula(n1p, l1p, n2p, l2p, n1, l1, n2, l2, Λ, μ1ω1, μ2ω2) = (-1)^(l1 + l2p + Λ) * wigner6j(Float64, l1p, l2p, Λ, l2, l1, 1) * reduced_matrix_element(n1p, l1p, n1, l1, μ1ω1) * reduced_matrix_element(n2p, l2p, n2, l2, μ2ω2)
function racahs_reduction_formula(n1p, l1p, n2p, l2p, n1, l1, n2, l2, Λ, μ1ω1, μ2ω2)
val = wigner6j(Float64, l1p, l2p, Λ, l2, l1, 1)
if val != 0; val *= reduced_matrix_element(n1p, l1p, n1, l1, μ1ω1); end
if val != 0; val *= reduced_matrix_element(n2p, l2p, n2, l2, μ2ω2); end
return (-1)^(l1 + l2p + Λ) * val
end