This is to be read in parallel to the answer by probably_someone.
The de Broglie relation,(as also the Bohr planetary model of the atom), belongs to the time before the quantum mechanical theory was validated, and it is one of the experimental observations that led to the theory.
In the small dimensions of molecules, atoms, nuclei, nucleons and quarks there are no matter waves,as the de Broglie observation implies by modeling the data, with
where p is the momentum,λ the wavelength and h Planck's constant.
In the quantum mechanical framework which is the one validated for particles and nuclei, there is no spread of the mass of the elementary point particle, there is only the probability of finding the particle at a particular (x,y,z,t) . It is the probability that displays a wave nature. The particle appears whole at each (x,y,z,t). The de Broglie relation is an envelope of this mathematical description , in a similar way that the Heisenberg uncertainty principle is an envelope of the mathematics of commutators in the theory of QM.
For quantum mechanical particles composed of elementary particles, like nucleons, the premise that the probability holds the wave nature also applies. In molecules there are the molecular orbitals, probability loci. In nucleons complicated quantum mechanical models exist , and the basic premise is that any measurement at the quantum scale is a probability measurement.
In this light, of probability waves,
E.g. In 280 MeV proton, "direct reactions", the De Broglie wavelength is comparable to nucleon-nucleon distances so proton interacts with a single nucleon not the whole nucleus.
Because the probability of interacting is very large mathematically when the de Broglie wavelength is of the size of the nucleus, when calculating the scattering of a proton of that energy with the nucleus.
At higher energies wavelength becomes fraction of a proton; the interaction occurs in quark scale.
Again, in calculations it is a matter of QM probabilities. Rutherford scattering was first found experimentally, and it was then explained rigorously in quantum mechanics. The higher the energy of the projectile the smaller the wavelength for high probability of scattering. That is why higher and higher energy colliders are required to check for compositness of the present elementary particles .