Section 4.4.4.4. Correction for electromagnetic interactions

The effective bound coherent scattering length that describes the interaction of a neutron with an atom includes additional contributions from electromagnetic interactions (Bacon, 1975; Sears, 1986a, 1996). For a neutral atom with atomic number Z, this quantity is of the form where q is the wavevector transfer in the collision, and are constants, and f(q) is the atomic scattering factor (Section 6.1.1 ). The latter quantity is the Fourier transform of the electron number density and is normalized such that f(0) = Z.

The main contribution to is from the nuclear interaction between the neutron and the nucleus but there is also a small electrostatic contribution ( 0.5%) arising from the neutron electric polarizability. The coefficient is called the neutron–electron scattering length and has the value −1.32 (4) × 10⁻³ fm (Koester, Waschkowski & Meier, 1988). This quantity is due mainly to the Foldy interaction with a small additional contribution (∼10%) from the intrinsic charge distribution of the neutron.

The correction of the bound coherent scattering length for electromagnetic interactions requires a knowledge of the atomic scattering factor f(q). Tables 6.1.1.1 and 6.1.1.3 provide accurate values of f(q) obtained from relativistic Hartree–Fock calculations for all the atoms and chemically important ions in the Periodic Table. Alternatively, since the correction is small (∼1%), one can often use the approximate analytical expression (Sears, 1986a, 1996) with . The value γ = 1.90 ± 0.07 Å⁻¹ provides a good fit to the Hartree–Fock results in Table 6.1.1.1 for .