Charge Form Factor of the Alpha Particle

We calculate analytically the charge form factor $F_E\left(q^2\right)$ of the $\alpha$ particle (${\mathrm{He}}^4$) with a modified Irving wave function. The parameters of the wave function have been determined from a variational calculation of the binding energy of ${\mathrm{He}}^4$ using a central velocity-dependent potential. We find good agreement between our values of $F_E\left(q^2\right)$ and those obtained from electron-helium elastic-scattering experiments. Also, the agreement with calculations using hard-core potentials is satisfactory.