Spinon excitations in the XX chain: spectra, transition rates, observability

The exact one-to-one mapping between (spinless) Jordan-Wigner lattice fermions and (spin-1/2) spinons is established for all eigenstates of the one-dimensional s = 1=2 XX model on a lattice with an even or odd number N of lattice sites and periodic boundary conditions. Exact product formulas for the transition rates derived via Bethe ansatz are used to calculate asymptotic expressions of the 2-spinon and 4-spinon parts (for large even N) as well as of the 1-spinon and 3-spinon parts (for large odd N) of the dynamic spin structure factors. The observability of these spectral contributions is assessed for finite and infinite N.Comment: 19 pages, 10 figure

Interaction and thermodynamics of spinons in the XX chain

The mapping between the fermion and spinon compositions of eigenstates in the one-dimensional spin-1/2 XX model on a lattice with N sites is used to describe the spinon interaction from two different perspectives: (i) For finite N the energy of all eigenstates is expressed as a function of spinon momenta and spinon spins, which, in turn, are solutions of a set of Bethe ansatz equations. The latter are the basis of an exact thermodynamic analysis in the spinon representation of the XX model. (ii) For N -> infinity the energy per site of spinon configurations involving any number of spinon orbitals is expressed as a function of reduced variables representing momentum, filling, and magnetization of each orbital. The spins of spinons in a single orbital are found to be coupled in a manner well described by an Ising-like equivalent-neighbor interaction, switching from ferromagnetic to antiferromagnetic as the filling exceeds a critical level. Comparisons are made with results for the Haldane-Shastry model.Comment: 16 pages, 3 figure

Spectrum and transition rates of the XX chain analyzed via Bethe ansatz

As part of a study that investigates the dynamics of the s=1/2 XXZ model in the planar regime |Delta|<1, we discuss the singular nature of the Bethe ansatz equations for the case Delta=0 (XX model). We identify the general structure of the Bethe ansatz solutions for the entire XX spectrum, which include states with real and complex magnon momenta. We discuss the relation between the spinon or magnon quasiparticles (Bethe ansatz) and the lattice fermions (Jordan-Wigner representation). We present determinantal expressions for transition rates of spin fluctuation operators between Bethe wave functions and reduce them to product expressions. We apply the new formulas to two-spinon transition rates for chains with up to N=4096 sites.Comment: 11 pages, 4 figure

Optimised tracer-dependent dosage cards to obtain weight-independent effective doses

Purpose. The aim of this study was twofold: firstly, to determine whether the European Association of Nuclear Medicine (EANM) dosage card results in weight-independent effective doses or weight-independent count rates; secondly, to determine whether one dosage card is sufficient for 95 different radiopharmaceuticals, and, if not, how many cards we reasonably need to take into account inter-tracer variability. Methods. Normalisation factors for count rate and effective dose were calculated as a function of body weight, with 70 kg as standard. Calculations were performed, using whole-body absorption fractions and MIRDOSE 3 software, for seven anthropomorphic phantoms and ten radionuclides. An analytic function for both relations was proposed. Normalisation factors for effective dose for 95 radiopharmaceuticals were investigated using cluster analysis. Results. Normalisation factors for count rate and effective dose can be estimated accurately as a function of body weight W by (W/70) a holding only one parameter, called the a value. The a values for 95 radiopharmaceuticals were classified into three clusters (n A = 7, nB = 76, nC = 12). Cluster A contains tracers for renal studies. Cluster B contains all remaining tracers, except iodine-labelled tracers for thyroid studies and 89Sr for therapy, which belong to cluster C. Conclusion. Correction factors proposed by the EANM task group mainly correct for effective dose. They are very similar to the factors obtained for cluster A. Using the EANM factors for tracers belonging to clusters B and C results in significantly higher effective doses to children. We suggest using three tracer-dependent dosage cards for which the correction factors have been calculated to obtain weight-independent effective doses. © Springer-Verlag 2004.SCOPUS: ar.jinfo:eu-repo/semantics/publishe