Electromagnetic Response ofC12: A First-Principles Calculation

Abstract

The longitudinal and transverse electromagnetic response functions of 12 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 measured versus calculated longitudinal response. This is further corroborated by a re-analysis of the Coulomb sum rule, in which the contributions from the low-lying J π = 2 + , 0 + 2 (Hoyle), and 4 + states in 12 C are accounted for explicitly in evaluating the total inelastic strength.PACS numbers: 21.60. De, 25.30.Pt One of the challenges in quantum many-body physics is calculating the electroweak response of a nucleus by fully accounting for the dynamics of its constituent nucleons. In this paper we report the first such calculation for the electromagnetic response of the 12 C nucleus.The nucleons interact with each other via two-and three-body forces and with external electroweak fields via one-and two-body, and smaller many-body, currents. This dynamical picture of the nucleus in which the consequences of the nucleons' substructure on its structure and response are subsumed into effective many-body forces and currents is by now well established. When coupled to numerically exact methods, such as the Green's function Monte Carlo (GFMC) methods adopted in this work, it has led to a quantitative and successful "first-principles" understanding of many nuclear properties: the low-lying energy spectra of nuclei up to 12 C [1] (and references therein); their radii and magnetic moments [2,3]; their elastic and inelastic electromagnetic form factors [4,5]; electroweak transitions between their low-lying states (M 1 and E2 widths [2,3], and β-decay and electroncapture rates [6]); properties of their ground-state structure, such as the momentum distributions of nucleons and nucleon pairs [7]; insights into the role that the dominant features of the nuclear interaction-the short-range repulsion and long-range tensor nature-have in shaping their ground-state structure [8]; and more (for a recent review see [1]). One of the key features of this approach is the assumption that the couplings of the external fields to the nucleons are governed by those in free-space with modifications induced primarily by two-nucleon currents.Here we report calculations of the 12 C electromagnetic longitudinal and transverse response functions, denoted respectively as R L (q, ω) and R T (q, ω), where q and ω are the electron momentum and energy transfers. These response functions are obtained experimentally by Rosenbluth separation of inclusive (e, e ) scattering data [9,10]. The calculations are based on the AV18+IL7 combination of two and three-nucleon potentials [11,12] and accompanying set of two-body electromagnetic currents (for a review see [1] and references therein). GFMC methods are used to compute these responses as functions of imaginary time [13,14], and maximum-entrop...

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