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In the first part of this section a fairly intuitive deduction of the spin-latice relaxation time {EQUATION()}$T_1${EQUATION} is preseted without the claim of exactness followed by the empirical introduction of spin-spin relaxation time {EQUATION()}$T_2${EQUATION}. It is not an aim of this section to provide a deep analysis of the relaxation physics, instead it intends to give a brief insight to the basic idea of these processes with a simple model.
At first, we introduce a quantity that plays important role in magnetic resonance called magnetization. Magnetization is defined by the net magnetic moment per unit volume, that is:
::{EQUATION()}
\label{magnetization_definition}
\mathbf{M} = \frac{1}{V} \sum_i \boldsymbol{\mu_i}
{EQUATION}::
Where {EQUATION()}$i${EQUATION} runs on all the magnetic moments in the volume. In this interpretation the volume V has to be small enough for the magnetization to be a function of space, and big enough to contain a large number of moments. In the following chapters we will usually use magnetization vector to describe the the time evolution of the system, but first we examine the basic concepts of relaxation.