Finite perturbation theory-density functional theory calculation of the spin-dipolar contribution to NMR spin-spin coupling constants

In this work an implementation of the FPT-DFT approach for calculating the spin-dipolar contribution to NMR spin-spin coupling constants is presented. This method was tested in a set of small molecules, giving results in excellent agreement when comparing them with values taken from the literature, which were obtained with state-of-the-art calculations. To obtain an insight into the relative importance of the spin-dipolar contribution in unsaturated compounds, calculations of J(F,C), J(F,F) and J(F,H) couplings in 1,2-, 1,3-, and 1,4-difluorobenzenes were performed. An important spin-dipolar contribution to ³ J(F, F) and ⁵ J(F,F) was found, suggesting that this term might be important in some cases. When performing DFT calculations the non-singlet instabilities usually found in unsaturated compounds are overcome.     

Many-body perturbation theory applied to dielectronic recombination resonances

A procedure to calculate dielectronic recombination cross-sections based on relativistic many-body perturbation in an all order formulation is presented. Complex rotation is employed in order to handle autoionizing states. The method is applied to recombination of lithium-like neon and lithium-like argon and the results are compared with experiments. This revised version was published online in July 2006 with corrections to the Cover Date.     

In-medium chiral perturbation theory

We report on how to tackle the problem of establishing a chiral effective field theory in nuclear matter with explicit pion fields and in the presence of external sources (Ann. Phys. 297, 27 (2002)). We have made use of the results of J.A. Oller (Phys. Rev. C 65, 025204 (2002)) where the generating functional for the in-medium chiral SU(2) x SU(2) Lagrangian has been derived. Within this approach we develop the so-called standard power counting rules for the calculation of in-medium pion properties if the residual nucleon energies are of the order of the pion mass. In addition, for the case of vanishing residual nucleon energies, a modified scheme (non-standard counting) is introduced. For both schemes the pertinent scales where the chiral expansions have to break down are established as well. We have performed a systematic analysis of n-point in-medium Green functions up to and including next-to-leading order when the standard rules apply. These include the in-medium contributions to quark condensates, pion propagators, pion masses and couplings of the axial-vector, vector and pseudoscalar currents to pions.Received: 30 September 2002, Published online: 22 October 2003PACS: 12.39.Fe Chiral Lagrangians - 11.30.Rd Chiral symmetries - 21.65. + f Nuclear matter     

In-medium chiral perturbation theory

This talk will report about a systematical implementation of a chiral effective field theory in nuclear matter with explicit pion fields and in the presence of external sources[1]. Within the generating functional approach of Ref.[2] the so-called standard power counting rules for the calculation of in-medium pion properties are developed that apply if the residual nucleon energies are of the order of the pion mass. In addition, for the case of vanishing residual nucleon energies, a modified scheme (non-standard counting) is introduced. For both schemes the pertinent scales where the chiral expansions have to break down are established as well. We report about a systematic analysis of n-point in-medium Green functions up to and including next-to-leading order when the standard rules apply. These include the in-medium contributions to quark condensates, pion propagators, pion masses and couplings of the axial-vector, vector and pseudoscalar currents to pions.     

A brief introduction to chiral perturbation theory

A brief introduction to the subject of chiral perturbation theory (Xpt) is presented, including a discussion of effective field theory and applications of Xpt in the arena of purely mesonic interactions as well as in the πN sector.     

Compilation of coupling constants and low-energy parameters

The electron capture decay ${}^{163}\text{Ho}\text{→}{}^{163}\text{Dy}{}^{\mathrm{<mtext>H</mtext>}}\text{+ν}{}_{\mathrm{<mtext>e</mtext>}}$ occurs with a record low energy release, Q ～ 2.6 keV. The daughter Dy^H atom has an electron hole, H, and predominantly decays by electron ejection Dy^H→Dy^H₁H₂+e^?. We investigate the neutrino mass sensitivity of the electron spectrum in the overall process Ho→Dy^H₁H₂+e^?+ν_e. In this spectrum, the fraction of events sensitive to a fixed non-zero neutrino mass in one to two orders of magnitude smaller than in the standard case of tritium β decay. But the electron energies in ¹⁶³Ho decay are considerably smaller than in ³H decay (Q ～ 18 keV). This suggests experiments whose energy resolution could be much better than that of the magnetic spectrometers conventionally used in the tritium case.     

Compilation of coupling constants and low-energy parameters

The double-pomeron coupling strength in the dual resonance model is found in both the inclusive and exclusive regions by comparison with experiments. Double-pomeron coupling occurs in inclusive experiments in the Mueller diagram for the central plateau region. Its strength can also be bounded from its non-observation in the two-particle to four-particle exclusive experiments. The dual resonance model is used to perform the analytic continuation of a six-point amplitude between these regions. The results show that the coupling strength for two forward pomerons in the exclusive region must be less than $\text{1}\text{300}$ of that in the inclusive region. This is experimental evidence for substantial forward double-pomeron decoupling in exclusive processes.     

Review of chiral perturbation theory

A review of chiral perturbation theory and recent developments on the comparison of its predictions with experiment is presented. Some interesting topics with scope for further elaboration are touched upon.     

Topics in chiral perturbation theory

I consider some selected topics in chiral perturbation theory (CHPT). For the meson sector, emphasis is put on processes involving pions in the isospin zero S-wave which require multi-loop calculations. The advantages and shortcomings of heavy baryon CHPT are discussed. Some recent results on the structure of the baryons are also presented.     

Topics in chiral perturbation theory

I consider some selected topics in chiral perturbation theory (CHPT). For the meson sector, emphasis is put on processes involving pions in the isospin zero S-wave which require multi-loop calculations. The advantages and shortcomings of heavy baryon CHPT are discussed. Some recent results on the structure of the baryons are also presented.     

The dominance of low-energy contributions to the Casimir energy in the chiral bag model

The smearing of the discrete mode sums leading to the Casimir energy and other vacuum quark contributions to baryon observables in the chiral bag model is shown to give smooth densities dominated by low-energy contributions. This observation provides support for methods previously adopted for the elimination of divergences in such calculations and leads to significant numerical improvements over standard mode sum techniques.     

Dispersion theory and the low-energy constants for neutral-pion photoproduction

The relativistic amplitudes of pion photoproduction are evaluated by dispersion relations at t = const. The imaginary parts of the amplitudes are taken from the MAID model covering the absorption spectrum up to center-of-mass energies W = 2.2GeV. For sub-threshold kinematics the amplitudes are expanded in powers of the two independent variables ν and t related to energy and momentum transfer. Subtracting the loop corrections from this power series allows one to determine the counter terms of covariant baryon chiral perturbation theory. The proposed continuation of the amplitudes into the unphysical region provides a unique framework to derive the low-energy constants to any given order as well as an estimate of the higher-order terms by global properties of the absorption spectrum.