Inelastic electron scattering form factors for the excitation of the2+states in the1f72nuclei

Coulomb form factors for the $0_{\mathrm{gnd}}^{+}$→$2^{+}$ transitions in the even-even $1f_{\frac{7}{2}}$-shell nuclei are studied in terms of the shell model within the $f_{\frac{7}{2}}^n+f_{\frac{7}{2}}^{n-1\mathrm{}}{p}_{\frac{3}{2}}$ configurations and with the effective interactions. It is shown that the characteristics of the $C2$ form factors in the higher-momentum-transfer region, not explained by the simple $f_{\frac{7}{2}}^n$ model, can be interpreted by the mixing of the one-particle excitations into the $p_{\frac{3}{2}}$ orbit in the shell-model wave functions. $E2$ transition strengths and $Q$ moments are also discussed in connection with the $C2$ form factors.