Scattering Observables from One- and Two-Body Densities: Formalism and Application to $γ\,{}^3$He Scattering
Harald W. Griesshammer, Judith A. McGovern, Andreas Nogga, Daniel R. Phillips
备注：
44 pages LaTeX2e (pdflatex) including 4 figures as .pdf files using includegraphics. Improved proofs of symmetry relations and clarifications. Final version with minor changes and updates to reverences is text-identical with journal publication but more readable layout
We introduce the transition-density formalism, an efficient and general method for calculating the interaction of external probes with light nuclei. One- and two-body transition densities that encode the nuclear structure of the target are evaluated once and stored. They are then convoluted with an interaction kernel to produce amplitudes, and hence observables. By choosing different kernels, the same densities can be used for any reaction in which a probe interacts perturbatively with the target. The method therefore exploits the factorisation between nuclear structure and interaction kernel that occurs in such processes. We study in detail the convergence in the number of partial waves for matrix elements relevant in elastic Compton scattering on $^3$He. The results are fully consistent with our previous calculations in Chiral Effective Field Theory. But the new approach is markedly more computationally efficient, which facilitates the inclusion of more partial-wave channels in the calculation. We also discuss the usefulness of the transition-density method for other nuclei and reactions. Calculations of elastic Compton scattering on heavier targets like $^4$He are straightforward extensions of this study, since the same interaction kernels are used. And the generality of the formalism means that our $^3$He densities can be used to evaluate any $^3$He elastic-scattering observable with contributions from one- and two-body operators. They are available at https://datapub.fz-juelich.de/anogga.
The use of light front coordinates allows a fully relativistic description of a hadron's spatial densities to be obtained. These densities must be two-dimensional and transverse to a chosen spatial direction. We explore their relationship to the three-dimensional, non-relativistic densities, with a focus on densities associated with the energy momentum tensor. The two-dimensional non-relativistic densities can be obtained from the light front densities through a non-relativistic limit, and can subsequently be transformed into three-dimensional non-relativistic densities through an inverse Abel…
Deformation effects on reaction observables of beryllium nuclei from ab initio densities
School of Physics, Beihang University（北京航空航天大学物理学院）；Peng Huanwu Collaborative Center for Research and Education, International Institute for Interdisciplinary and Frontiers, Beihang University（北京航空航天大学交叉前沿国际研究院彭桓武研究中心）；Institute for Advanced Simulation (IAS-4), Forschungszentrum Jülich（于利希研究中心先进模拟研究所（IAS-4））
Densities associated with the energy-momentum tensor are calculated for spin-one targets. These calculations are done in a light front formalism, which accounts for relativistic effects due to boosts and allows for arbitrary spatial localization of the target. These densities include the distribution of momentum, angular momentum, and pressures over a two-dimensional plane transverse to the light front. Results are obtained for both longitudinally and transversely polarized targets, and the formalism is tailored to allow the possibility of massless targets. The momentum density and pressure di…
A microscopic study of proton elastic scattering from unstable nuclei at intermediate energies using a relativistic formalism is presented. We have employed both the original relativistic impulse approximation (IA1) and the generalised impulse approximation (IA2) formalisms to calculate the relativistic optical potentials, with target densities derived from relativistic mean field (RMF) theory using the NL3 and FSUGold parameter sets. Comparisons between the optical potentials computed using both IA1 and IA2 formalisms, and the different RMF Lagrangians are presented for both stable and unstab…
A Comment on General Formulae for Polarization Observables in Deuteron Electrodisintegration and Linear Relations
我们建立了Arenhövel，Leidemann，and Tomusiak在Few-Body Systems { \bf 15}，109（1993）中发表的用于处理氘核两体电蜕变中极化观测量的形式主义和本论文作者在Phys.~修订版~ C { \bf 40}，2479（1989）.我们对两组结果之间的重叠进行评论。
Multiple high precision $β$-decay measurements are being carried out these days on various nuclei, in search of beyond the Standard Model signatures. These measurements necessitate accurate standard model theoretical predictions to be compared with. Motivated by the experimental surge, we present a formalism for such a calculation of $β$-decay observables, with controlled accuracy, based on a perturbative analysis of the theoretical observables related to the phenomena, including high order nuclear recoil and shape corrections. The accuracy of the corrections is analyzed by identifying a hiera…
