12 research outputs found
Quasilinearization Method and Summation of the WKB Series
Solutions obtained by the quasilinearization method (QLM) are compared with
the WKB solutions. Expansion of the -th QLM iterate in powers of
reproduces the structure of the WKB series generating an infinite number of the
WKB terms with the first terms reproduced exactly. The QLM quantization
condition leads to exact energies for the P\"{o}schl-Teller, Hulthen,
Hylleraas, Morse, Eckart potentials etc. For other, more complicated potentials
the first QLM iterate, given by the closed analytic expression, is extremely
accurate. The iterates converge very fast. The sixth iterate of the energy for
the anharmonic oscillator and for the two-body Coulomb Dirac equation has an
accuracy of 20 significant figures
Effects of Negative Energy Components in the Constituent Quark Model
Relativistic covariance requires that in the constituent quark model for
mesons the positive energy states as well as the negative energy states are
included. Using relativistic quasi-potential equations the contribution of the
negative energy states is studied for the light and charmonium mesons. It is
found that these states change the meson mass spectrum significantly but leave
its global structure untouched.Comment: 14 pages revtex 3.0, 4 figures uudecoded attached in postscript
format, THU-93/1
Relativistic effects and quasipotential equations
We compare the scattering amplitude resulting from the several quasipotential
equations for scalar particles. We consider the Blankenbecler-Sugar, Spectator,
Thompson, Erkelenz-Holinde and Equal-Time equations, which were solved
numerically without decomposition into partial waves. We analyze both
negative-energy state components of the propagators and retardation effects. We
found that the scattering solutions of the Spectator and the Equal-Time
equations are very close to the nonrelativistic solution even at high energies.
The overall relativistic effect increases with the energy. The width of the
band for the relative uncertainty in the real part of the scattering
matrix, due to different dynamical equations, is largest for
backward-scattering angles where it can be as large as 40%.Comment: Accepted for publication in Phys. Rev.
Unitarity and the Bethe-Salpeter Equation
We investigate the relation between different three-dimensional reductions of
the Bethe-Salpeter equation and the analytic structure of the resultant
amplitudes in the energy plane. This correlation is studied for both the
interaction Lagrangian and the system with -, -,
and -channel pole diagrams as driving terms. We observe that the equal-time
equation, which includes some of the three-body unitarity cuts, gives the best
agreement with the Bethe-Salpeter result. This is followed by other 3-D
approximations that have less of the analytic structure.Comment: 17 pages, 8 figures; RevTeX. Version accepted for publication in
Phys. Rev.
Energy and decay width of the pi-K atom
The energy and decay width of the pi-K atom are evaluated in the framework of
the quasipotential-constraint theory approach. The main electromagnetic and
isospin symmetry breaking corrections to the lowest-order formulas for the
energy shift from the Coulomb binding energy and for the decay width are
calculated. They are estimated to be of the order of a few per cent. We display
formulas to extract the strong interaction S-wave pi-K scattering lengths from
future experimental data concerning the pi-K atom.Comment: 37 pages, 5 figures, uses Axodra