Explain notation convention in Gay-Berne formula (espressomd#3839)

Fixes espressomd#3834

doc/sphinx/inter_non-bonded.rst

@@ -719,7 +719,8 @@ parameters can be set via::
 This defines a Gay--Berne potential for prolate and oblate particles
 between particles types ``type1`` and ``type2``. The Gay--Berne potential is an
 anisotropic version of the classic Lennard-Jones potential, with
-orientational dependence of the range :math:`\sigma_0` and the well-depth :math:`\epsilon_0`.
+orientational dependence of the range :math:`\sigma_0` and the well-depth
+:math:`\varepsilon_0`.
 
 Assume two particles with orientations given by the unit vectors
 :math:`\mathbf{\hat{u}}_i` and :math:`\mathbf{\hat{u}}_j` and
@@ -730,7 +731,7 @@ particles is given by
 .. math::
 
    V(\mathbf{r}_{ij}, \mathbf{\hat{u}}_i, \mathbf{\hat{u}}_j) = 4
-     \epsilon(\mathbf{\hat{r}}_{ij}, \mathbf{\hat{u}}_i,
+     \varepsilon(\mathbf{\hat{r}}_{ij}, \mathbf{\hat{u}}_i,
      \mathbf{\hat{u}}_j) \left( \tilde{r}_{ij}^{-12}-\tilde{r}_{ij}^{-6}
      \right),
 
@@ -760,9 +761,9 @@ and
 .. math::
 
    \begin{gathered}
-     \epsilon(\mathbf{\hat{r}}, \mathbf{\hat{u}}_i,
+     \varepsilon(\mathbf{\hat{r}}, \mathbf{\hat{u}}_i,
      \mathbf{\hat{u}}_j) = \\
-     \epsilon_0 \left( 1- \chi^{2}(\mathbf{\hat{u}}_i
+     \varepsilon_0 \left( 1- \chi^{2}(\mathbf{\hat{u}}_i
        \cdot \mathbf{\hat{u}}_j)^{2} \right)^{-\frac {\nu}{2}} \left[1-\frac
        {\chi'}{2} \left( \frac { (\mathbf{\hat{r}} \cdot
            \mathbf{\hat{u}}_i+ \mathbf{\hat{r}} \cdot
@@ -772,6 +773,10 @@ and
            \mathbf{\hat{u}}_j)^{2}} {1-\chi' \, \mathbf{\hat{u}}_i \cdot
            \mathbf{\hat{u}}_j } \right) \right]^{\mu}.\end{gathered}
 
+Note that contrary to the original paper :cite:`gay81a`, here
+:math:`\varepsilon_0` is not raised to the power of :math:`\nu`,
+in agreement with the convention used in the Gay--Berne literature.
+
 The parameters :math:`\chi = \left(k_1^{2} - 1\right)/\left(k_1^{2} + 1\right)`
 and :math:`\chi' = \left(k_2^{1/\mu} -  1\right)/\left(k_2^{1/\mu} + 1\right)`
 are responsible for the degree of anisotropy of the molecular properties. :math:`k_1` is

doc/sphinx/zrefs.bib

@@ -329,6 +329,17 @@ @BOOK{frenkel02b
   edition = {Second},
 }
 
+@Article{gay81a,
+  title = {Modification of the overlap potential to mimic a linear site-site potential},
+  author = {Gay, J. G. and Berne, B. J.},
+  journal = {Journal of Chemical Physics},
+  year = {1981},
+  number = {6},
+  pages = {3316-3319},
+  volume = {74},
+  doi = {10.1063/1.441483},
+}
+
 @article{Gompper1996,
 author = {Gompper, G and Kroll, D M},
 title = {{Random surface discretizations and the renormalization of the bending rigidity}},

src/core/nonbonded_interactions/gay_berne.hpp

@@ -24,6 +24,10 @@
 /** \file
  *  Routines to calculate the Gay-Berne potential between particle pairs.
  *
+ *  Please note that contrary to the original Gay and Berne 1981 paper, here
+ *  the GB prefactor @f$ \varepsilon_0 @f$ is not raised to the power of
+ *  @f$ \nu @f$, in agreement with the convention used in the GB literature.
+ *
  *  Implementation in \ref gay_berne.cpp.
  */