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Register a new userExperimental study of isovector spin sum rules
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We present the Bjorken integral extracted from Jefferson Lab experiment EG1b for $0.05<Q^{2}<2.92$ GeV$^2$. The integral is fit to extract the twist-4 element $f_{2}^{p-n}$ which appears to be relatively large and negative. Systematic studies of this higher twist analysis establish its legitimacy at $Q^{2}$ around 1 GeV$^{2}$. We also performed an isospin decomposition of the generalized forward spin polarizability $gamma_{0}$. Although its isovector part provides a reliable test of the calculation techniques of Chiral Perturbation Theory, our data disagree with the calculations.
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We present a measurement of the spin-dependent cross sections for the vec{^3He}(vec{e},e)X} reaction in the quasielastic and resonance regions at four-momentum transfer 0.1 < Q^2< 0.9 GeV^2. The spin-structure functions have been extracted and used to evaluate the nuclear Burkhardt--Cottingham and extended GDH sum rules for the first time. Impulse approximation and exact three-body Faddeev calculations are also compared to the data in the quasielastic region.
The Gerasimov-Drell-Hearn sum rule and related dispersive integrals connect real and virtual Compton scattering to inclusive photo- and electroproduction. Being based on universal principles as causality, unitarity, and gauge invariance, these relations provide a unique testing ground to study the internal degrees of freedom that hold a system together. The present contribution reviews the spin-dependent sum rules and cross sections of the nucleon. At small momentum transfer, the data sample information on the long range phenomena (Goldstone bosons and collective resonances), whereas the primary degrees of freedom (quarks and gluons) become visible at large momentum transfer (short distance). The rich body of new data covers a wide range of phenomena from coherent to incoherent processes, and from the generalized spin polarizabilities on the low-energy side to higher twist effects in deep inelastic scattering.
Energies and spectroscopic factors of the first $7/2^-$, $3/2^-$, $1/2^-$ and $5/2^-$ states in the $^{35}$Si$_{21}$ nucleus were determined by means of the (d,p) transfer reaction in inverse kinematics at GANIL using the MUST2 and EXOGAM detectors. By comparing the spectroscopic information on the $^{35}$Si and $^{37}$S isotones, a reduction of the $p_{3/2} - p_{1/2}$ spin-orbit splitting by about 25% is proposed, while the $f_{7/2} -f_{5/2}$ spin-orbit splitting seems to remain constant. These features, derived after having unfolded nuclear correlations using shell model calculations, have been attributed to the properties of the 2-body spin-orbit interaction, the amplitude of which is derived for the first time in an atomic nucleus. The present results, remarkably well reproduced by using several realistic nucleon-nucleon forces, provide a unique touchstone for the modeling of the spin-orbit interaction in atomic nuclei.
Nucleon-transfer sum rules have been assessed via a consistent reanalysis of cross-section data from neutron-adding ($d$,$p$) and -removing ($d$,$t$) reactions on well-deformed isotopes of Gd, Dy, Er, Yb, and W, with $92leq Nleq108$, studied at the Niels Bohr Institute in the 1960s and 1970s. These are complemented by new measurements of cross sections using the ($d$,$p$), ($d$,$t$), and ($p$,$d$) reactions on a subset of these nuclei. The sum rules, defined in a Nilsson-model framework, are remarkably consistent. A single overall normalization is used in the analysis, which appears to be sensitive to assumptions about the reaction mechanism, and in the case of sums using the ($d$,$t$) reaction, differs from values determined from reactions on spherical systems.
The spin-structure functions $g_1$ and $g_2$, and the spin-dependent partial cross-section $sigma_mathrm{TT}$ have been extracted from the polarized cross-sections differences, $Delta sigma_{parallel}hspace{-0.06cm}left( u,Q^{2}right)$ and $Delta sigma_{perp}hspace{-0.06cm}left( u,Q^{2}right)$ measured for the $vec{^textrm{3}textrm{He}}(vec{textrm{e}},textrm{e})textrm{X}$ reaction, in the E97-110 experiment at Jefferson Lab. Polarized electrons with energies from 1.147 to 4.404 GeV were scattered at angles of 6$^{circ}$ and 9$^{circ}$ from a longitudinally or transversely polarized $^{3}$He target. The data cover the kinematic regions of the quasi-elastic, resonance production and beyond. From the extracted spin-structure functions, the first moments $overline{Gamma_1}hspace{-0.06cm}left(Q^{2}right)$, $Gamma_2hspace{-0.06cm}left(Q^{2}right)$ and $I_{mathrm{TT}}hspace{-0.06cm}left(Q^{2}right)$ are evaluated with high precision for the neutron in the $Q^2$ range from 0.035 to 0.24~GeV$^{2}$. The comparison of the data and the chiral effective field theory predictions reveals the importance of proper treatment of the $Delta$ degree of freedom for spin observables.
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