Longitudinal and transverse electron scattering form factors for the $2^{+}$ state at 1.37 MeV of the ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ nucleus were evaluated with rotational model wave functions. Four different approaches were used for the transverse E2 form factor: projected Hartree Fock, cranking model, rigid rotor, and irrotational flow. For the nuclear intrinsic wave function, the Nilsson model was assumed in all approaches yielding the calculation of the form factor in the plane-wave and distorted-wave Born approximations. The results are discussed and compared with a recent measurement performed for 180° electrons scattered from this state. The distorted-wave Born approximation calculation, taking into account first-order corrections due to 〈$J_{\perp }^2$${〉}^{\mathrm{-}1}$, shows that projected Hartree Fock and irrotational flow models give the best agreement with the available data and compete in quality with more complex calculations performed in the ‘‘shell model’’ approach.

• Received 5 December 1988

DOI:https://doi.org/10.1103/PhysRevC.39.1242