# Collision of Two Neutrons in the de Broglie–Bohm Approach

Collision of Two Neutrons in the de Broglie–Bohm Approach

Neutron scattering is a spectroscopic method of measuring the motions of magnetic particles. This can be used to probe a wide variety of different physical phenomena: interference effects, diffusional or hopping motions of atoms, rotational modes of molecules, acoustic modes and molecular vibrations, recoil in quantum fluids and magnetic quantum excitations [1].

In the causal interpretation of nonrelativistic quantum mechanics, a particle such as a neutron possesses a definite position and a momentum at all times. The possible trajectories are determined by the gradient of real phase function (or quantum potential) in the total wavefunction (pilot wave) [2]. We show a very simple model of a time-dependent collision of two neutrons, without spin or magnetic moment, neglecting the influence of gravitation and quark structure and with low momentum, displayed in a three-dimensional configuration space.

Two neutrons represented by two three-dimensional Gaussian wave profiles with different initial positions and momenta are used as projectiles. These interact in some regions, if the initial momenta are chosen appropriately [3]. In an elastic neutron scattering event, the momentum is transferred from one neutron to the another.

For a symmetric initial momentum distribution of the two waves (monochromatic beam), but with opposite signs in one direction, for example, in the direction, the model can be interpreted as a neutron interferometer (beam-splitter). After splitting by amplitude division (Mach–Zehnder type) via Bragg reflection, but with only one neutron present in the device at a time, the interference effect still appears. In this case, the neutron wave packet is split into two coherent waves (sub-beams) and the possible trajectories of one particle are affected by the wave that is not carrying the other particle (empty wave) [4].

x

In the graphics you see the wave density (if enabled), the initial momentum (large red arrows), the velocity vector field, the initial starting points of the eight trajectories (red points, shown as small red spheres), the actual position (colored points, shown as small spheres) and eight possible trajectories of the two neutrons.