Derive an expression of average logarithmic energy decrement per collision (). Hence, show that for large mass number, it is independent of energy. Using this formula, plot average logarithmic energy decrement for different nuclides of mass number A.

In reactor physics, the concept of average logarithmic energy decrement per collision (denoted as \( \xi \)) plays a significant role in describing the energy loss of neutrons due to collisions with atoms in the reactor core. It quantifies the average reduction in the neutron's energy after each collision with the medium, such as the fuel or moderator.

### Derivation of Expression for Average Logarithmic Energy Decrement:

The average logarithmic energy decrement per collision is defined as the ratio of the logarithm of the neutron's energy before and after a single collision. Mathematically, it is expressed as:

\[
\xi = \frac{1}{N} \sum_{i} \ln \left( \frac{E_0}{E_i} \right)
\]

where:
- \( N \) is the number of collisions,
- \( E_0 \) is the initial energy of the neutron,
- \( E_i \) is the energy after the \( i \)-th collision.

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