## Elastic Scattering and Neutron Moderators

To be **an effective moderator**, the probability of elastic reaction between neutron and the nucleus must be high. In terms of cross-sections, the elastic scattering cross-section of a moderator’s nucleus must be high. Therefore, a **high elastic scattering cross-section** is important but does not describe the comprehensive capabilities of moderators. To describe the capabilities of a material to slow down neutrons, three new material variables must be defined:

- high cross-section for neutron scattering
- high energy loss per collision
- low cross-section for absorption
- high melting and boiling point
- high thermal conductivity
- high specific heat capacity
- low viscosity
- low activity
- low corrosive
- cheap

## Macroscopic Slowing Down Power – MSDP

We have defined the **probability of elastic scattering reaction and** **the average energy loss** during the reaction. The product of these variables (the logarithmic energy decrement and the macroscopic cross-section for scattering in the material) is **the macroscopic slowing down power (MSDP)**.

**MSDP = ξ . Σ _{s}**

The MSDP describes** the ability of a given material to slow down neutrons** and indicates how rapidly a neutron will slow down in the material. Still, it does not fully reflect the effectiveness of the material as a moderator. In fact, the material with high **MSDP** can slow down neutrons with high efficiency, but it can be a poor moderator because of its high probability of absorbing neutrons. It is typical, for example, for boron, which has a high slowing down power but is **absolutely inappropriate** as a moderator. The complete measure of the effectiveness of a moderator is **the Moderating Ratio (MR)**, where:

**MR = ξ . Σ_{s}**

**/**

**Σ**_{a}