Three-level Approximation Research Articles

Three-level approximation for interacting Boson transition-temperature calculation

The normal-superfluid phase-transition temperature of a dilute Bose system whose particles interact via a two-body potential composed of a hard core followed by a weak attractive tail is studied using the three-level approximation. It is found that, for such a system, the three-level approximation does give results, for the transition temperature, approximately equal to the lambda-transition temperature of liquid 4He. The condensed state is composed of ε 0 = 0, ε 1 = E 0/ N and ε 2, such that the states ε 0 and ε 1 lie below the cutoff momentum.

On the extrapolation of Galerkin methods for parabolic problems

The use of Richardson extrapolation in conjunction with several discrete-time Galerkin methods for the approximate solution of parabolic initialboundary value problems is investigated. It is shown that the extrapolation of certain two- and three-level Galerkin approximations which arep th order correct in time yields an improvement ofp orders of accuracy in time per extrapolation, wherep=1, 2. Both linear and quasilinear problems are considered.

Kinetic Cooling of a Gas by Absorption of CO2 Laser Radiation

The effect of kinetic cooling due to the absorption of 10.6-μ CO2 laser radiation in the atmosphere has recently been predicted. In this letter, experimental evidence for this effect is presented. Transient-density increases due to the kinetic cooling have been observed in CO2–N2 mixtures following the propagation of an ∼ 1-μsec 0.5-J CO2 laser pulse through the gas. The experiments were performed with varying concentrations of CO2 and the observed cooling and subsequent heating effects are explained using the usual three-level approximation for vibrational-energy transfer in CO2–N2, together with known relaxation rates.

Test of the Boundary-Condition Constraint Method for Nuclear Reactions

The boundary-condition constraint method (BCCM) is a generalization of $R$-matrix theory that permits the shell model to be used as a basis for nuclear-reaction calculations and which permits the correct farasymptotic behavior of the wave function to be imposed as a constraint on shell-model bound-state calculations. For practical application it is necessary to truncate sums over an infinite number of levels. The purpose of this paper is to investigate how effective the few-level approximation might be. The BCCM is used to calculate an $s$-wave bound state for a square well in the two- and three-level approximations. The BCCM results are found to compare favorably with the exact and shell-model results. The BCCM is used to calculate the $s$ and $p$-wave scattering from a square well in the two- and three-level approximations. The results are found to compare favorably with the exact and Wigner $R$-matrix-theory results. We note that within the $n$-level approximation there is some ambiguity in the form of the Green's function to be used with the BCCM.

GFactor in Metallic Zinc

A calculation of the $g$ factor for the small "needles" of the Fermi surface of Zn has been carried on in the three-level approximation. It is shown that for fields parallel to the hexagonal axis, $g$ is expected to be large with an upper bound of 133. This result rules out two of the three possibilities determined by Stark from experiment. It is found that three possible orderings of the levels can give the observed results, and the energy gaps are estimated in each case; the lattice potential and the spin-orbit splitting are of the same order of magnitude. The variation of the $g$ factor with angle is in agreement with experiment.