In the context of the PN model, the GSF surface reflects the inter-atomic interactions in the system and serves to model the details of the dislocation core on the atomic scale. Finally, the stress term of Eq. (4) accounts for the work done by any external stresses, where τ e and τ s denote the magnitude of the components of the stress tensor that couple to the edge and screw displacements, respectively [1]. The quantities that specify the model for dislocations in a particular material are the elastic parameters µ and ν , the GSF surface γ ( ⃗ δ ) associated with the glide plane of interest, and Δ x . Here, we employ the SWF model based on the parameter set of Ref.[17] to determine these quantities for solid hcp 4 He (space group 194). In order to determine its elastic properties, we employ a computational cell containing 720 particles at a density of 0.0294 Å − 3 , which corresponds to lattice parameters a =3.63668 Å and c=5.93866 Å, subject to standard pe- riodic boundary conditions. Sampling configurations according to the quantum-mechanical probability density of the SWF model using the Metropolis algorithm, we then compute expectation values of the stress tensor [19] associated with the six independent deformations of the periodic cell, imposing strain levels of 0.25%. Using the standard relationship between the stress and strain tensors [20], we extract the five independent elastic constants of the hcp structure. The results, which, to the best of our knowledge represent the first complete estimate of the elastic constants in hcp 4 He, are reported in Table I. The shear modulus µ = C 44 = 17 . $^{1}$±0 . 8 MPa, is in good agreement with the value of 14 MPa that follows from the ratio of the experimental shear stress and strain values reported in [21]. Poisson’s ratio, obtained from the results in Table I, is found to be ν = 0 . 151 . Both theoretical values are those corresponding to shear directions in the basal plane, in which hexagonal crystals are isotropic [22]. Since basal slip is known to be the dominant dislocation glide mechanism in hcp solid $^{4}$He [23] we focus on the properties of these particular dislocations and compute the GSF surface associated with the basal plane. For this purpose, we utilize the 720-atom cell and impose a series of 400 slip vectors ⃗ δ in the basal plane by adjusting the periodic boundary condition along the c -axis. The shadow degrees of freedom of the atoms immediately adjacent to the slip plane are allowed to vary only along the c -direction to maintain the relative displacement. Using the Metropolis algorithm we then sample configurations according to the SWF and compute the expectation value of the Hamiltonian as a function of ⃗ δ . Subtracting the expectation value at ⃗ δ = 0 and dividing by the area, we then obtain the GSF surface. 4