Charge Form Factor and Sum Rules of Electromagnetic Response Functions inC12

Abstract

An ab initio calculation of the 12 C elastic form factor, and sum rules of longitudinal and transverse response functions measured in inclusive (e, e ) scattering, is reported, based on realistic nuclear potentials and electromagnetic currents. The longitudinal elastic form factor and sum rule are found to be in satisfactory agreement with available experimental data. A direct comparison between theory and experiment is difficult for the transverse sum rule. However, it is shown that the calculated one has large contributions from two-body currents, indicating that these mechanisms lead to a significant enhancement of the quasi-elastic transverse response. This fact may have implications for the anomaly observed in recent neutrino quasi-elastic charge-changing scattering data off 12 C. The current picture of the nucleus as a system of protons and neutrons interacting among themselves via two-and three-body forces and with external electroweak probes via one-and two-body currents-a dynamical framework we will refer to below as the standard nuclear physics approach (SNPA)-has been shown to reproduce satisfactorily a variety of empirical properties of light nuclei with mass number A ≤ 12, including energy spectra [1][2][3][4][5][6][7], static properties [1,3,4,8,9] of low-lying states, such as charge radii, and magnetic and quadrupole moments, and longitudinal electron scattering [10,11]. However, it has yet to be established conclusively whether such a picture quantitatively and successfully accounts for the observed electroweak structure and response of these systems, at least those with A > 4, in a wide range of energy and momentum transfers. This issue has acquired new and pressing relevance in view of the anomaly seen in recent neutrino quasielastic charge-changing scattering data on 12 C [12], i.e., the excess, at relatively low energy, of measured cross section relative to theoretical calculations. Analyses based on these calculations have led to speculations that our present understanding of the nuclear response to chargechanging weak probes may be incomplete [13], and, in particular, that the momentum-transfer dependence of the axial form factor of the nucleon may be quite different from that obtained from analyses of pion electroproduction data [14] and measurements of neutrino and anti-neutrino reactions on protons and deuterons [15][16][17][18]. However, it should be emphasized that the calculations on which these analyses are based use rather crude models of nuclear structure-Fermi gas or local density approximations of the nuclear matter spectral function-as well as simplistic treatments of the reaction mechanism, and do not fit the picture outlined above. Conclusions based on them should therefore be viewed with caution.The present work provides the first step towards a comprehensive study, within the SNPA, of the quasi-elastic electroweak response functions of light nuclei. We report an exact quantum Monte Carlo (QMC) calculation of the elastic form factor and sum rules associated with the longitudi...

Chiral electroweak currents in nuclei

“…Later calculations of the charge form factors of 3 H, 3 He, and 4 He with realistic variational wave functions reaffirm the need for a substantial exchange charge effect for agreement with the empirical values [38]. This exchange current effect is most prominent in the lightest nuclei, and less so in the case of heavier nuclei as 16 O and 40 Ca, where the shell structure is most prominent [39,40]. The pion exchange effect nevertheless does improve slightly the agreement between the calculated and empirically extracted charge distributions throughout the periodic table [41].…”

Local chiral effective field theory interactions and quantum Monte Carlo applications

“…As a result, the method is very accurate but computationally very costly and allows one to access only nuclei with A 12 [20,21]. Larger particle numbers can be accessed with Auxiliary-Field Diffusion Monte Carlo (AFDMC), which in addition to the stochastic approach to the particle coordinates also stochastically evaluates the summations in spin-isospin space [22], however at the cost of using simpler variational wave functions than those used in nuclear GFMC.…”

From the lightest nuclei to the equation of state of asymmetric nuclear matter with realistic nuclear interactions

“…Recently, coupled cluster methods have been extended to study nuclear matter [19,20]. Quantum Monte Carlo methods, such as GFMC and AFDMC [21], have proved to be accurate for predicting properties of nuclei up to A=12 [22][23][24] and neutron matter [8,9]. Recently, new local versions of chiral forces have been fitted to scattering data, and can be included in GFMC and AFDMC.…”