DOC: split vertex type enum explanation

.cspell/project.txt

@@ -1,3 +1,4 @@
 Mikhasenko
 Misha
+multline
 Semileptonic

docs/description.md

@@ -175,20 +175,29 @@ Vertices define the nodes in the decay graphs, where one particle transits into
 
 - **`type`:** Specifies how the helicity recoupling factor `H_{l1,l2}` is computed.
   Three types are defined: `ls`, `parity`, and `helicity`.
-  These reflect different ways of relating combinations of the helicity indices to a real-valued factor, the recoupling coefficient.
-
-  $$
-  \begin{align}
-  H^\text{helicity}(\lambda_a,\lambda_b|\lambda_a^0,\lambda_b^0) &= \delta_{\lambda_a,\lambda_a^0}\delta_{\lambda_b,\lambda_b^0}\,, \\
-  H^\text{parity}(\lambda_a,\lambda_b|\lambda_a^0,\lambda_b^0, f) &=
-  \delta_{\lambda_a,\lambda_a^0}\delta_{\lambda_b,\lambda_b^0} + f \delta_{\lambda_a,-\lambda_a^0}\delta_{\lambda_b,-\lambda_b^0}\,, \\
-  H^\text{ls}(\lambda_a,\lambda_b|l,s,j_a,j_b,j) &= \sqrt{\frac{2l+1}{2j+1}}
-  \left\langle j_a,\lambda_a; j_b,-\lambda_b|s,\lambda_a-\lambda_b\right\rangle
-  \left\langle l,0; s,\lambda_a-\lambda_b|j,\lambda_a-\lambda_b\right\rangle\,.
-  \end{align}
-  $$
-
-  The `helicity` indicated no recoupling, the factor is $1$ for a pair of selected helicities ($\lambda_a^0$ and $\lambda_b^0$) and zero for other combinations. The `ParityRecoupling` is controlled by the controlled by the `parity factor`, $f$, and gives non-zero value for two combination of the helicity pair, the selected one and the opposite. Finally, the `RecouplingLS` computes the value of the recoupling functions from Clebsch–Gordan coefficients. For spin-half particles, this recoupling is equivalent to `ParityRecoupling`, with $f = (-1)^l$.
+  These reflect different ways of relating combinations of the helicity indices to a real-valued "recoupling coefficient".
+
+  - `helicity` indicates no recoupling: the factor is $1$ for a pair of selected helicities ($\lambda_a^0$ and $\lambda_b^0$) and zero for other combinations.
+
+    $$
+    H^\text{helicity}(\lambda_a,\lambda_b|\lambda_a^0,\lambda_b^0) = \delta_{\lambda_a,\lambda_a^0}\delta_{\lambda_b,\lambda_b^0}
+    $$
+
+  - `parity` is controlled by the controlled by the `parity factor`, $f$, and gives a non-zero value for two combination of the helicity pair.
+    $$
+    H^\text{parity}(\lambda_a,\lambda_b|\lambda_a^0,\lambda_b^0, f) =
+      \delta_{\lambda_a,\lambda_a^0}\delta_{\lambda_b,\lambda_b^0} + f \delta_{\lambda_a,-\lambda_a^0}\delta_{\lambda_b,-\lambda_b^0}
+    $$
+  - `ls` computes the value of the recoupling functions from Clebsch–Gordan coefficients.
+    $$
+    \begin{multline}
+    H^\text{ls}(\lambda_a,\lambda_b|l,s,j_a,j_b,j) = \\
+      \sqrt{\frac{2l+1}{2j+1}}
+      \left\langle j_a,\lambda_a; j_b,-\lambda_b|s,\lambda_a-\lambda_b\right\rangle
+      \left\langle l,0; s,\lambda_a-\lambda_b|j,\lambda_a-\lambda_b\right\rangle
+    \end{multline}
+    $$
+    For spin-half particles, this recoupling is equivalent to the `parity` recoupling, with $f = (-1)^l$.
 
 ### Propagators