  The magnetization profile and the related magnetic small-angle neutron
scattering cross section of a single spherical nanoparticle with Neel surface
anisotropy is analytically investigated. We employ a Hamiltonian that comprises
the isotropic exchange interaction, an external magnetic field, a uniaxial
magnetocrystalline anisotropy in the core of the particle, and the Neel
anisotropy at the surface. Using a perturbation approach, the determination of
the magnetization profile can be reduced to a Helmholtz equation with Neumann
boundary condition, whose solution is represented by an infinite series in
terms of spherical harmonics and spherical Bessel functions. From the resulting
infinite series expansion, we analytically calculate the Fourier transform,
which is algebraically related to the magnetic small-angle neutron scattering
cross section. The approximate analytical solution is compared to the numerical
solution using the Landau-Lifshitz equation, which accounts for the full
nonlinearity of the problem.
