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, often denoted as \( \langle \Delta \ln E \rangle \), refers to the average reduction in energy of a particle per collision, expressed in logarithmic terms. It is particularly relevant for neutrons as they undergo scattering events in a reactor.

To derive the expression for the average logarithmic energy decrement per collision, we start with the basic idea of elastic scattering of neutrons by nuclei. The energy loss of a neutron in a _____ __________ ___ ________ ______.
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