Comparison of the electromagnetic responses of ${}^{12}\mathrm{C}$ obtained from the Green's function Monte Carlo and spectral function approaches

The electromagnetic responses of carbon obtained from the Green's function Monte Carlo and spectral function approaches using the same dynamical input are compared in the kinematical region corresponding to momentum transfer in the range 300–570 MeV. The results of our analysis, aimed at pinning down the limits of applicability of the approximations involved in the two schemes, indicate that the factorization ansatz underlying the spectral function formalism provides remarkably accurate results down to momentum transfer as low as 300 MeV. On the other hand, it appears that at 570 MeV relativistic corrections to the electromagnetic current not included in the Monte Carlo calculations may play a significant role in the transverse channel.

Figure 1

Electromagnetic response of carbon in the longitudinal channel at $\left|\mathbf{q}\right|=300$ MeV. The shaded area shows the results of the GFMC calculation, with the associated uncertainty arising from the inversion of the Euclidean response. All the remaining curves have been obtained within the SF approach, including the effects of Pauli blocking and FSI. The lines marked with dots and hollow squares correspond to nonrelativistic and fully relativistic calculation, respectively. Those marked with triangles and filled squares have been obtained by performing hybrid calculations: nonrelativistic current and relativistic phase space (triangles), or relativistic current and nonrelativistic phase space (filled squares).

Figure 2

Same as Fig. 1 for $\left|\mathbf{q}\right|=380$ MeV.

Figure 3

Same as Fig. 1 for $\left|\mathbf{q}\right|=570$ MeV.

Figure 4

Electromagnetic response of carbon in the transverse channel at $\left|\mathbf{q}\right|=300$ MeV. The shaded area shows the results of the GFMC calculation, with the associated uncertainty arising from the inversion of the Euclidean response. All the remaining curves have been obtained within the SF approach, including the effects of Pauli blocking and FSI. The lines marked with dots and hollow squares correspond to nonrelativistic and fully relativistic calculation, respectively, while the one marked with triangles has been obtained performing a hybrid calculation: relativistic current and nonrelativistic phase space.

Figure 5

Same as Fig. 4 for $\left|\mathbf{q}\right|=380$ MeV.

Figure 6

Same as Fig. 4 for $\left|\mathbf{q}\right|=570$ MeV.