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Register a new userDirect T-Matrix Approach to Determination of the Electric Polarizabilities of Quantum Bound Systems
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Added by
Vladislav Kharchenko
Publication date
2012
fields
Physics
and research's language is
English
Authors
V. F. Kharchenko
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A new general formalism for determining the electric multipole polarizabilities of quantum (atomic and nuclear) bound systems based on the use of the transition matrix in momentum space has been developed. As distinct from the conventional approach with the application of the spectral expansion of the total Greens function, our approach does not require preliminary determination of the entire unperturbated spectrum; instead, it makes possible to calculate the polarizability of a few-body bound complex directly based on solving integral equations for the wave function of the ground bound state and the transition matrix at negative energy, both of them being real functions of momenta. A formula for the multipole polarizabilities of a two-body bound complex formed by a central interaction potential has been derived and studied. To test, the developed $T$-matrix formalism has been applied to the calculation of the dipole, quadrupole and octupole polarizabilities of the hydrogen atom.
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We show that the Ocneanu algebra of quantum symmetries, for an ADE diagram (or for higher Coxeter-Dynkin systems, like the Di Francesco - Zuber system) is, in most cases, deduced from the structure of the modular T matrix in the A series. We recover in this way the (known) quantum symmetries of su(2) diagrams and illustrate our method by studying those associated with the three genuine exceptional diagrams of type su(3), namely E5, E9 and E21. This also provides the shortest way to the determination of twisted partition functions in boundary conformal field theory with defect lines.
A selfconsistent thermodynamic $T$-matrix approach is deployed to study the microscopic properties of the quark-gluon plasma (QGP), encompassing both light- and heavy-parton degrees of freedom in a unified framework. The starting point is a relativistic effective Hamiltonian with a universal color force. The input in-medium potential is quantitatively constrained by computing the heavy-quark (HQ) free energy from the static $T$-matrix and fitting it to pertinent lattice-QCD (lQCD) data. The corresponding $T$-matrix is then applied to compute the equation of state (EoS) of the QGP in a two-particle irreducible formalism including the full off-shell properties of the selfconsistent single-parton spectral functions and their two-body interaction. In particular, the skeleton diagram functional is fully resummed to account for emerging bound and scattering states as the critical temperature is approached from above. We find that the solution satisfying three sets of lQCD data (EoS, HQ free energy and quarkonium correlator ratios) is not unique. As limiting cases we discuss a weakly-coupled solution (WCS) which features color-potentials close to the free energy, relatively sharp quasiparticle spectral functions and weak hadronic resonances near $T_{rm c}$, and a strongly-coupled solution (SCS) with a strong color potential (much larger than the free energy) resulting in broad non-quasiparticle parton spectral functions and strong hadronic resonance states which dominate the EoS when approaching $T_{rm c}$.
The direct transition-matrix approach to determination of the electric polarizabilities of quantum bound systems developed in my recent work is applied to study the electric multipole polarizabilities of a two-particle bound complex with a central interaction between the particles. Expressions for the electric quadrupole and octupole polarizabilities of the deuteron are derived and their values in the case of the S-wave separable interaction potential are calculated.
We have applied relativistic coupled-cluster (RCC) theory to determine the isotope shift (IS) constants of the first eight low-lying states of the Li, Be$^+$ and Ar$^{15+}$ isoelectronic systems. Though the RCC theory with singles, doubles and triples approximation (RCCSDT method) is an exact method for these systems for a given set of basis functions, we notice large differences in the results from this method when various procedures in the RCC theory framework are adopted to estimate the IS constants. This has been demonstrated by presenting the IS constants of the aforementioned states from the finite-field, expectation value and analytical response (AR) approaches of the RCCSDT method. Contributions from valence triple excitations, Breit interaction and lower-order QED effects to the evaluation of these IS constants are also highlighted. Our results are compared with high-precision calculations reported using few-body methods wherever possible. We find that results from the AR procedure are more reliable than the other two approaches. This analysis is crucial for understanding the roles of electron correlation effects in the accurate determination of IS constants in the heavier atomic systems, where few-body methods cannot be applied.
The generalized Baldin sum rule at finite four-momentum transfer Q^2 is evaluated utilizing a structure function parameterization fit to recent experimental data. The most recent measurements on F_1 from Hall C at Jlab, as well as the F_2 structure function data from Hall B at Jlab and SLAC, were used in constructing our parameterization. We find that at Q^2 below 1 GeV^2 the dominant contribution to the electric and magnetic polarizabilities of the nucleon comes from the resonance region.
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