  In this paper we obtain the central limit theorems, moderate deviations and
the laws of the iterated logarithm for the energy \[H_n=\sum_{1\le j<k\le
n}\omega_j\omega_k1_{\{S_j=S_k\}}\] of the polymer $\{S_1,...,S_n\}$ equipped
with random electrical charges $\{\omega_1,...,\omega_n\}$. Our approach is
based on comparison of the moments between $H_n$ and the self-intersection
local time \[Q_n=\sum_{1\le j<k\le n}1_{\{S_j=S_k\}}\] run by the
$d$-dimensional random walk $\{S_k\}$. As partially needed for our main
objective and partially motivated by their independent interest, the central
limit theorems and exponential integrability for $Q_n$ are also investigated in
the case $d\ge3$.
