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.

The average logarithmic energy decrement per collision, denoted by \( L(E) \), plays a significant role in reactor physics as it characterizes the energy loss of a neutron in a single collision with a target nucleus. This concept is particularly crucial for understanding the behavior of neutrons in reactors, as it influences the slowing down of neutrons and their thermalization process.

### Derivation of the Average Logarithmic Energy Decrement

The energy of a neutron changes due to a collision with a nucleus in the reactor. The average logarithmic energy decrement is defined as the average change in the logarithm of the neutron's energy per collision. To derive this expression, we first need to consider the energy transfer during a neutron-nucleus collision.

Let \( E \) be the initial energy of the neutron before the collision, and \( E' \) be the energy after the collision. The average logarithmic energy decrement, \( L(E) \), is given by:

\[
L(E) = \langle \ln \left( \frac{E}{E'} \right) \rangle
\]

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