We study the reconnection of vortices in a quantum fluid with a roton minimum, by numerically solving the Gross-Pitaevskii (GP) equations. A non-local interaction potential is introduced to mimic the experimental dispersion relation of superfluid $^4mathrm{He}$. We begin by choosing a functional shape of the interaction potential that allows to reproduce in an approximative way the so-called roton minimum observed in experiments, without leading to spurious local crystallization events. We then follow and track the phenomenon of reconnection starting from a set of two perpendicular vortices. A precise and quantitative study of various quantities characterizing the evolution of this phenomenon is proposed: this includes the evolution of statistics of several hydrodynamical quantities of interest, and the geometrical description of a observed helical wave packet that propagates along the vortex cores. Those geometrical properties are systematically compared to the predictions of the Local Induction Approximation (LIA), showing similarities and differences. The introduction of the roton minimum in the model does not change the macroscopic properties of the reconnection event but the microscopic structure of the vortices differs. Structures are generated at the roton scale and helical waves are evidenced along the vortices. However, contrary to what is expected in classical viscous or inviscid incompressible flows, the numerical simulations do not evidence the generation of structures at smaller or larger scales than the typical atomic size.
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