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At least 433 records · Page 24
All sourcesNASA NTRSDOE OSTI
NASA NTRS1971

Non-asymptotic effects in the approach to the far field sonic boom.

An extension is described for the Whitham theory (1952, 1954) which indicates small deviations from the ultimate N-wave for bodies with a continuous or discontinuous tangent. Some simple formulas are derived which yield a good reduction in the sonic boom intensity. The theory is elucidated by some numerical examples for a class of simple theoretically relevant shapes.

Henderson, L. F.↗
NASA NTRS1973

Asymptotic form for the cross section for the Coulomb interacting rearrangement collisions

It is shown that in a rearrangement collision leading to the formation of the highly excited hydrogenlike states the cross section in all orders of the Born approximation behaves as 1/n sq, with n the principal quantum number, thus invalidating the Brinkman-Kramers approximation for large n. Similarly, in high energy inelastic electron-hydrogenlike atom collisions the exchange cross section for sufficiently large n dominates the direct excitation cross section.

Omidvar, K.↗
NASA NTRS1972

Asymptotic solution to the problem of optimal low-thrust energy increase.

Consideration of the problem of optimal ascent from an initial circular planetary orbit to some specified final energy level by a spacecraft equipped with a low-thrust engine. Optimal is defined as minimum time. An accurate small parameter perturbation solution is presented, and the optimal trajectory is analyzed and compared with a tangential thrust trajectory.

Jacobson, R. A.↗
NASA NTRS1973

Asymptotic form for the cross section for the Coulomb interacting rearrangement collisions.

It is shown that in a rearrangement collision leading to the formation of highly excited hydrogenlike states the cross section at high energies behaves as 1/n-squared, with n the principal quantum number, thus invalidating the Brinkman-Kramers approximation for large n. Similarly, in high-energy inelastic electron-hydrogenlike-atom collisions the exchange cross section for sufficiently large n dominates the direct excitation cross section.

Omidvar, K.↗
NASA NTRS1975

Asymptotic form of the charge exchange cross section in the three body rearrangement collisions

A three body general rearrangement collision is considered where the initial and final bound states are described by the hydrogen-like wave functions. Mathematical models are developed to establish the relationships of quantum number, the reduced mass, and the nuclear charge of the final state. It is shown that for the low lying levels, the reciprocal of n cubed scaling law at all incident energies is only approximately satisfied. The case of the symmetric collisions is considered and it is shown that for high n and high incident energy, E, the cross section behaves as the reciprocal of E cubed. Zeros and minima in the differential cross sections in the limit of high n for protons on atomic hydrogen and positrons on atomic hydrogen are given.

Omidvar, K.↗
NASA NTRS1975

Asymptotic form of the charge-exchange cross section in three-body rearrangement collisions

A three-body general-type rearrangement collision is considered in which the initial and final bound states are described by hydrogen-like wave functions. It is shown that the charge-exchange amplitude in the first Born approximation can be expanded at all incident energies in terms of the inverse powers of the principal quantum number (n). By expanding the exchange amplitude in this way, it is demonstrated conclusively that the cross section for capture into the s, p, and d states as well as for the sum over all the angular-momentum states is proportional to 1/n-cubed plus terms proportional to higher inverse odd powers of n. It is found that the low-lying levels cannot be scaled to the 1/n-cubed law irrespective of the value of the incident energy except in the case of capture into the s states in accordance with the Oppenheimer-Brinkman-Kramers approximation. Zeros and minima in the differential cross sections are given in the limit of high principal quantum number for electron capture by protons from atomic hydrogen and for positronium formation by proton-atomic hydrogen collisions.

Omidvar, K.↗
NASA NTRS1974

Geodesic synchrotron radiation in the Kerr geometry by the method of asymptotically factorized Green's functions

The scalar, electromagnetic, and gravitational geodesic-synchrotron-radiation (GSR) spectra are determined for the case of a test particle moving on a highly relativistic circular orbit about a rotating (Kerr) black hole. It is found that the spectral shape depends only weakly on the value of the angular-momentum parameter (a/M) of the black hole, but the total radiated power drops unexpectedly for a value of at least 0.95 and vanishes as the value approaches unity. A spin-dependent factor (involving the inner product of the polarization of a radiated quantum with the source) is isolated to explain the dependence of the spectral shape on the spin of the radiated field. Although the scalar wave equation is solved by separation of variables, this procedure is avoided for the vector and tensor cases by postulating a sum-over-states expansion for the Green's function similar to that found to hold in the scalar case. The terms in this sum, significant for GSR, can then be evaluated in the geometric-optics approximation without requiring the use of vector or tensor spherical harmonics.

Chrzanowski, P. L.↗