informations from them the following physical quantities are defined and calculated. They are the one-body density

$\rho _{1}(r_{1})=\int \left| \Psi _{L}\right| ^{2}d{\bf r}_{2}d{\bf r}%
_{3}\cdot \cdot \cdot d{\bf r}_{13}$    ,                      (5a)

the two-body density

$\rho _{2}({\bf r}_{1}{\bf ,r}_{2})=\int \left| \Psi _{L}\right| ^{2}d{\bf r}%
_{3}d{\bf r}_{4}\cdot \cdot \cdot d{\bf r}_{13}$    ,                   (5b)

and the three-body density

$\rho _{3}({\bf r}_{1}{\bf ,r}_{2}{\bf ,r}_{3})=\int \left| \Psi _{L}\right|
^{2}d{\bf r}_{4}d{\bf r}_{5}\cdot \cdot \cdot d{\bf r}_{13}$  ,               (5c)

It was found that in many cases the $\rho _{1}(r)$ has an outer peak and an inner peak with a minimum lying in between (at $r=a)$. In this case we can define an outer region ($r$ $\geq a$) and an inner region ($r$ $<$ $a$) .  Accordingly, we can define the average number of particles $N_{out}$ and $N_{in}$ contained in the outer and inner regions, respectively,  as

$N_{out}=N\int_{a}^{\infty }\rho _{1}(r_{1})d{\bf r}_{1}$                    (6a)   $\qquad N_{in}=N\int_{0}^{a}\rho _{1}(r_{1})d{\bf r}_{1}$                     (6b)

For example,  the (88)$_{1}$ state has $a$ =367.8$\stackrel{o}{A}$, $%
N_{out}=$ 9.97 and $N_{in}=$3.03.

Once the border $a$ is defined, we can define the angular momenta $%
l_{out}$ and the moments of inertia $I_{out}$ contributed by the outer region, respectively , as

$l_{out}=N\int_{a}^{\infty }d{\bf r}_{1}\int \Psi _{L}^{\ast }%
\widehat{l_{1}}\Psi _{L}d{\bf r}_{2}\cdot \cdot 