\documentclass{letter}
\usepackage{amsmath,capt-of,ifthen,calc}
\usepackage{graphicx,xr}

%%%%%%%%%% Start TeXmacs macros
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\begin{document}

Qualitative understanding of many-electron atoms

1. centr. field $\Upsilon ( r )$ ``close`` to  $+ \tmop{Ze}$ nucleus


the ratio $R ( r )$
\[ R ( r ) = \frac{\text{$\Upsilon ( r )$}}{V ( r )} = \frac{\text{$\Upsilon (
   r )$}}{- \frac{\tmop{Ze}^2}{r}} \]
is such that  close to nucleus, $R ( r \rightarrow 0 ) \rightarrow 1 -
\frac{5}{16 Z} \approx 1$  while  for large r $R ( r \rightarrow \infty )
\rightarrow \frac{1}{Z}$

\includegraphics[scale=0.6]{ratio_pots.pdf}

%\tmfloat{h}{small}{figure}{}{}


\[ ( 1 s )^2 ( 2 s )^2 ( 2 p )^6 \rightarrow \tmop{Ne} \]
$( 1 s )^2 ( 2 s )^2 ( 2 p )^6 \rightarrow \tmop{Ne}$

$( 1 s )^2 ( 2 s )^2 ( 2 p )^6 ( 3 s )^2 ( 3 p )^6 ( 3 d )^{10} \rightarrow
\tmop{Ni}$   But this does not work

\end{document}