Working result for SRC

ho_basis.jl

@@ -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

ho_basis_3body.jl

@@ -7,13 +7,11 @@ Va = -2
 Ra = 2
 
 E_max = 40
-μω_global = 0.5
+μω_global = 0.3
 
-# due to Jacobi coordinates
+# due to simple relative coordinates
-μ1ω1 = μω_global * 1/2
+μω = μω_global * 2
-μ2ω2 = μω_global * 2
+μ = m/2
-μ1 = m * 1/2
-μ2 = m * 2/3
 
 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 "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=μ2ω2, μ=μ2)
+@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 "V1" V1 = get_sp_V_matrix(V_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 "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)

math.jl

@@ -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