Fermi-Jagla model: Difference between revisions

Revision as of 14:37, 24 January 2014

The Fermi-Jagla model is a smooth variant of the Jagla model. It is given by (Eq. 1 in ^[1]):

\Phi _{12}(r)=\epsilon _{0}\left[\left({\frac {a}{r}}\right)^{n}+{\frac {A_{0}}{1+\exp \left[{\frac {A_{1}}{A_{0}}}{\frac {r}{a-A_{2}}}\right]}}-{\frac {B_{0}}{1+\exp \left[{\frac {B_{1}}{B_{0}}}{\frac {r}{a-B_{2}}}\right]}}\right]

There is a relation between the Fermi function and hyperbolic tangent:

{\frac {1}{e^{x}+1}}={\frac {1}{2}}-{\frac {1}{2}}\tanh {\frac {x}{2}}

Using this relation one can show that Fermi-Jagla model is equivalent to the generalised Fomin potential (which has scientific priority).

@@ Line 3: / Line 3: @@
 :<math>\Phi_{12}(r) = \epsilon_0 \left[ \left( \frac{a}{r} \right)^n + \frac{A_0}{1+\exp \left[ \frac{A_1}{A_0} \frac{r}{a-A_2} \right]} - \frac{B_0}{1+\exp \left[ \frac{B_1}{B_0} \frac{r}{a-B_2} \right]}  \right]</math>
-There is a relation between Fermi function and hyperbolic tangent:
+There is a relation between the Fermi function and hyperbolic tangent:
 :<math>\frac{1}{e^x+1}=\frac{1}{2}-\frac{1}{2}\tanh \frac{x}{2}</math>
-Using this relation one can show that Fermi-Jagla model is equivalent to [[Fomin potential]] introduced earlier.
+Using this relation one can show that Fermi-Jagla model is equivalent to the generalised [[Fomin potential]] (which has scientific priority).
 ==References==
 <references/>