Hydrogen and compounds containing hydrogen are among the most frequently studied objects in neutron scattering. It is therefore important that the n-p scattering process is understood in detail for a correct interpretation of experimental data. The very high value for the bound proton cross section (σ = 81.9 barns) is caused by a specific feature in the deuteron, a virtual 0+ state close to its binding level.
In this report the compound nucleus formation is studied on the atto-second time-scale by calculating the neutron-proton entanglement during the scattering process.
The excitation of the 0+ state causes a negative phase shift δs in the outgoing neutron wave function which is not taken into account in the standard description using the Fermi pseudo-potential. It increases linearly with the transferred momentum and it is shown here that it can have important consequences for interpretation of inelastic scattering already at the 1 eV level since it is associated with an energy shift DE ≈ ds × h/Dt.
The figure shows the variation of this transient energy transfer and the estimated probability for exciting the water 0.46 eV vibration at different neutron flight times within the n-p scattering length.It explains excitations below 16 Å-1 which are not predicted by standard theory, but can be observed in modern instruments with separate momentum and energy determination, such as the SEQUOIA at SNS. On a deeper level, it is of interest as an example of an energy transfer connected with the breaking of a quantum entanglement.
Figure 1. Variation of this transient energy transfer and the estimated probability for exciting the water 0.46 eV vibration at different neutron flight times within the n-p scattering length.
It is expected that the present theory will be able to explain further details in high precision experiments on hydrogen, like those carried out in SEQUOIA at SNS.
Full article can be found at Physica Scripta 95, 025003 (2 Jan. 2020)