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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 127 records · Page 7
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DOE OSTI2025

Factorial growth in perturbation theory, power corrections: precise extraction of quark masses and $\alpha_\text{s}$

These proceedings summarize a newly found connection between the factorial growth of coefficients in perturbative QCD and power corrections to the perturbation series, discussed in refs. [1-4]. The improved convergence is shown for three quantities four which four terms in the series are available: the static energy, the quark pole mass, and the polarized Bjorken sum rule. Prospects for determinations of $\alpha_\text{s}$ with controlled truncation uncertainties are discussed, as was found earlier in quark-mass determinations [3,5].

Kronfeld, Andreas S. [Fermilab; TUM-IAS, Munich] (↗
NASA NTRS1980

Application of functional analysis to perturbation theory of differential equations

The deviation of the solution of the differential equation y' = f(t, y), y(O) = y sub O from the solution of the perturbed system z' = f(t, z) + g(t, z), z(O) = z sub O was investigated for the case where f and g are continuous functions on I x R sup n into R sup n, where I = (o, a) or I = (o, infinity). These functions are assumed to satisfy the Lipschitz condition in the variable z. The space Lip(I) of all such functions with suitable norms forms a Banach space. By introducing a suitable norm in the space of continuous functions C(I), introducing the problem can be reduced to an equivalent problem in terminology of operators in such spaces. A theorem on existence and uniqueness of the solution is presented by means of Banach space technique. Norm estimates on the rate of growth of such solutions are found. As a consequence, estimates of deviation of a solution due to perturbation are obtained. Continuity of the solution on the initial data and on the perturbation is established. A nonlinear perturbation of the harmonic oscillator is considered a perturbation of equations of the restricted three body problem linearized at libration point.

Bogdan, V. M.↗
NASA NTRS1980

Nonrelativistic hyperfine splitting in muonic helium by adiabatic perturbation theory

Huang and Hughes have discussed the hyperfine splitting delta mu of muonic helium using a variational approach. In this paper, the Born-Oppenheimer approximation is used to simplify the evaluation of delta mu in the nonrelativistic limit. The first-order perturbed wave function of the electron is obtained in closed form by modifying the method used by Dalgarno and Lynn. The result is close to those of Huang and Hughes which required a large Hylleraas expansion and considerable extrapolation.

Drachman, R. J.↗
NASA NTRS1996

The General Necessary Condition for the Validity of Dirac's Transition Perturbation Theory

For the first time, from the natural requirements for the successive approximation the general necessary condition of validity of the Dirac's method is explicitly established. It is proved that the conception of 'the transition probability per unit time' is not valid. The 'super-platinium rules' for calculating the transition probability are derived for the arbitrarily strong time-independent perturbation case.

Quang, Nguyen Vinh↗
NASA NTRS1979

The adiabatic semiclassical perturbation theory for vibrationally inelastic scattering. I - Collinear calculations. II - Three-dimensional treatment

A semiclassical approximation to treat vibrationally inelastic scattering is developed. The vibrational basis set used is adiabatic with respect to a reference potential which is chosen to be as close as possible to the true potential and also gives easily obtainable solutions to the vibrational wave equation. The radial wave functions are obtained using the WKB approximation, and the coupled Schroedinger equations are solved by a first-order perturbation method to yield a phase shift matrix which is exponentiated to give the full scattering matrix. Results were obtained for all the cases computed by Secrest and Johnson and by Clark and Dickinson, and the agreement is better than 10% for half of the cross-sections and rarely off by more than a factor of 2.

Cross, R. J., Jr.↗
NASA NTRS1965

Studies in Perturbation Theory. XI. Lower Bounds to Energy Eigenvalues, Ground State, and Excited States

The bracketing theorem in the partitioning technique for solving the Schrödinger equation may be used in principle to determine upper and lower bounds to energy eigenvalues. Practical lower bounds of any accuracy desired may be evaluated by utilizing the properties of ``inner projections'' on finite manifolds in the Hilbert space. The method is here applied to the ground state and excited states of a Hamiltonian H=H(sub 0)+V having a positive definite perturbation V. Even if inspiration is derived from the method of intermediate Hamiltonians, the final results are of bracketing type and independent of this approach. The method is numerically illustrated in some accompanying papers.

Loewdin, Per-Olov↗
NASA NTRS1973

Degenerate R-S perturbation theory

A concise, systematic procedure is given for determining the Rayleigh-Schrodinger energies and wave functions of degenerate states to arbitrarily high orders even when the degeneracies of the various states are resolved in arbitrary orders. The procedure is expressed in terms of an iterative cycle in which the energy through the (2n+1)st order is expressed in terms of the partially determined wave function through the n-th order. Both a direct and an operator derivation are given. The two approaches are equivalent and can be transcribed into each other. The direct approach deals with the wave functions (without the use of formal operators) and has the advantage that it resembles the usual treatment of nondegenerate perturbations and maintains close contact with the basic physics. In the operator approach, the wave functions are expressed in terms of infinite order operators which are determined by the successive resolution of the space of the zeroth order functions.

Hirschfelder, J. O.↗
NASA NTRS1974

Degenerate RS perturbation theory

A concise, systematic procedure is given for determining the Rayleigh-Schroedinger energies and wave functions of degenerate states to arbitrarily high orders even when the degeneracies of the various states are resolved in arbitrary orders. The procedure is expressed in terms of an iterative cycle in which the energy through the (2n + 1)-th order is expressed in terms of the partially determined wave function through the n-th order. Both a direct and an operator derivation are given. The two approaches are equivalent and can be transcribed into each other. The direct approach deals with the wave functions (without the use of formal operators) and has the advantage that it resembles the usual treatment of nondegenerate perturbations and maintains close contact with the basic physics. In the operator approach, the wave functions are expressed in terms of infinite-order operators which are determined by the successive resolution of the space of the zeroth-order functions.

Hirschfelder, J. O.↗