William & Mary ScholarWorks

Welcome! William & Mary ScholarWorks preserves and provides access to the research and creative output of William & Mary's faculty, staff, and students.

UPDATE 18th JUNE 2025: Our repository has migrated from Digital Commons to Open Repository DSpace as of this summer. Additional updates and improvements will continue through the Fall semester. Thank you for your patience during this transition.

Recent Submissions

Open Access
Covariant spectator theory of 𝑛𝑝 scattering: Phase shifts obtained from precision fits to data below 350 MeV
(2008) Gross, Franz; Stadler, Alfred; Data science
Using the covariant spectator theory (CST), we present two one-boson-exchange kernels that have been successfully adjusted to fit the 2007 world 𝑛𝑝 data (containing 3788 data) below 350 MeV. One model (which we designate WJC-1) has 27 parameters and fits with a 𝜒2/𝑁data=1.06. The other model (designated WJC-2) has only 15 parameters and fits with a 𝜒2/𝑁data=1.12. Both of these models also reproduce the experimental triton binding energy without introducing additional irreducible three-nucleon forces. One result of this work is a new phase-shift analysis, updated for all data until 2006, which is useful even if one does not work within the CST. In carrying out these fits we have reviewed the entire database, adding new data not previously used in other high precision fits and restoring some data omitted in previous fits. A full discussion and evaluation of the 2007 database is presented.
Open Access
Fixed-axis polarization states: covariance and comparisons
(2008) Gross, Franz; Ramalho, G.; Peña, M. T.; Data science
Addressing the recent criticisms of Kvinikhidze and Miller, we prove that the spectator wave functions and currents based on “fixed-axis” polarization states (previously introduced by us) are Lorentz covariant, and find an explicit connection between them and conventional direction-dependent polarization states. The discussion shows explicitly how it is possible to construct pure S-wave models of the nucleon.
Open Access
D-state effects in the electromagnetic 𝑁⁢𝛥 transition
(2008-12-17) Ramalho, G.; Peña, M. T.; Gross, Franz; Data science
We consider here a manifestly covariant quark model of the nucleon and the 𝛥, where one quark is off shell, and the other two quarks form an on-shell diquark pair. Using this model, we have shown previously that the nucleon form factors and the dominant form factor for the 𝛾⁢𝑁 →𝛥 transition (the magnetic dipole (M1) form factor) can be well described by nucleon and 𝛥 wave functions with S-state components only. In this paper, we show that nonvanishing results for the small electric (E2) and Coulomb (C2) quadrupole form factors can be obtained if D-state components are added to the 𝛥 valence quark wave function. We present a covariant definition of these components and compute their contributions to the form factors. We find that these components cannot, by themselves, describe the data. Explicit pion cloud contributions must also be added, and these contributions dominate both the E2 and the C2 form factors. By parametrizing the pion cloud contribution for the transition electric and Coulomb form factors in terms of the neutron electric form factor, we estimate that the contributions of the 𝛥 D-state coupled to quark core spin of 3/2 is of the order of 1%, and the contributions of the 𝛥 D-state coupled to quark core spin 1/2 is of the order of 4%.
Open Access
Covariant spectator theory for the electromagnetic three-nucleon form factors: Complete impulse approximation
(2009-05-20) Pinto, Sérgio Alexandre; Stadler, Alfred; Gross, Franz; Data science
We present the first calculations of the electromagnetic form factors of ³He and ³H within the framework of the Covariant Spectator Theory (CST). This first exploratory study concentrates on the sensitivity of the form factors to the strength of the scalar meson-nucleon off-shell coupling, known from previous studies to have a strong influence on the three-body binding energy. Results presented here were obtained using the complete impulse approximation (CIA), which includes contributions of relativistic origin that appear as two-body corrections in a nonrelativistic framework, such as “Z-graphs,” but omits other two and three-body currents. We compare our results to nonrelativistic calculations augmented by relativistic corrections of 𝒪⁢(𝑣/𝑐)⁢².
Open Access
Electric quadrupole and magnetic octupole moments of the Δ
(2009-07-27) Ramalho, G.; Peña, M. T.; Gross, Franz; Data science
Using a covariant spectator constituent quark model we predict an electric quadrupole moment QΔ⁺ = −0.043 e fm² and a magnetic octupole moment 𝒪Δ⁺ = −0.0035 e fm³ for the Δ⁺ excited state of the nucleon.