Electromagnetic Response of ${}^{12}\mathrm{C}$: A First-Principles Calculation

The longitudinal and transverse electromagnetic response functions of ${}^{12}\mathrm{C}$ are computed in a “first-principles” Green’s function Monte Carlo calculation, based on realistic two- and three-nucleon interactions and associated one- and two-body currents. We find excellent agreement between theory and experiment and, in particular, no evidence for the quenching of the measured versus calculated longitudinal response. This is further corroborated by a reanalysis of the Coulomb sum rule, in which the contributions from the low-lying $J^{\pi }=2^{+}$, $0_2^{+}$ (Hoyle), and $4^{+}$ states in ${}^{12}\mathrm{C}$ are accounted for explicitly in evaluating the total inelastic strength.

Figure 1

Electromagnetic longitudinal response functions of ${}^{12}\mathrm{C}$ for $q$ in the range 300–570 MeV. Experimental data are from Refs. [9, 10]. See the text for further explanations.

Figure 2

Same as Fig. 1 but for the electromagnetic transverse response functions. Because pion production mechanisms are not included, the present theory underestimates the (transverse) strength in the $\mathrm{\Delta }$ peak region; see in particular the $q=570\mathrm{MeV}/c$ case.

Figure 3

Coulomb sum rule in ${}^{12}\mathrm{C}$: theory (black solid line labeled $1b+2b$) and analyses of experimental data (blue empty and full circles labeled EXP-TR and EXP) are from Ref. [5]; the (red square) data points, labeled EXP-TFF, include the contributions of the low-lying $J^{\pi }=2^{+}$, $0_2^{+}$ (Hoyle), and $4^{+}$ states,; see the text for explanations.