Magnetic form factor

 Magnetic form factor is the Fourier-transformed spatial density function of unpaired electrons, which are responsible for magnetism of matter.  The intensity of a magnetic Bragg peak is proportional to a square of the magnetic form factor. The density function can be described by the spherical Bessel functions. In a low-Q region, <j0(Q)>, which is the integral of the spherical component, is dominant.

 An analytic approximation to the <j0(Q)> integral is given in the web site of ILL. By using the coefficients tabulated in the web site, we can reproduce the |Q| dependence of the form factor. (The higher order integrals, <j2(Q)>, <j4(Q)>, ..., are also listed on the ILL web site.)

Step 2

The approximation for the <j0> integral is given by 

The variable x is not the momentum transfer of neutron, Q, but sinθ/λ. 

Step 3

|Q| is given by 2ki sinθ(=2*2π/λ*sinθ), and therefore the difference between Q and x is the factor of 4π. 

The Q dependence of the <j0> integral for Fe3+ is obtained as below. 

The square of <j0(Q)> integral, which is proportional to the intensity of a magnetic Bragg peak, rapidly decays with increasing Q.