Damping theory and its application to the interpretation of slow neutron scattering experiments
The damping theory, which includes the decay of quantum states, is developed in terms of the projection operators. The concept of probability that a transition from a given initial state will be towards a specified final state is introduced, and the probability is calculated by using the damping theory. When the decay of the final state is neglected, this probability reduces to the conditional probability, introduced by Heitler, that the system will be found in a specified final state after transition from the given initial state has definitely taken place, With this new probability concept, an approximate expression is obtained for the transition probability per unit time from the initial to the final state. This expression is the starting point of the present line shape theory, which is applicable to both neutron and photon spectra. In this work, only the scattering of slow neutrons by an anharmonic crystal is considered. However, the differential scattering cross section formula is obtained first for an arbitrary macroscopic medium, and then applied to a crystal. The cross section formula in the harmonic approximation follows from the present cross section formula when the width and shift of lines are neglected. The novel feature of this derivation is that it does not use Bloch's theorem. Explicit formulas for the width and the shift of the observed peaks in the energy spectrum of the elastically scattered slow neutrons by crystals are obtained, and compared in the case of a single-phonon event to those by Maradudin and Fein. It is found that the the shift formulas agree exactly at all temperatures, whereas the width formulas agree only in the zero temperature limit. The discrepancy in the width formulas at finite temperatures is discussed in terms of the concept of phonon lifetime. The application of the present line shape theory to the interpretation of the optical experiments is also discussed. (auth)
- Research Organization:
- Univ. of Michigan, Ann Arbor, MI (United States)
- Sponsoring Organization:
- National Science Foundation (NSF)
- DOE Contract Number:
- Grant No. G-20037
- NSA Number:
- NSA-18-028560
- OSTI ID:
- 4071924
- Report Number(s):
- CONF-481-58; AED-Conf-64-003-50
- Resource Relation:
- Conference: American Physical Society Annual Meeting, New York, NY (United States), 22-25 Jan 1964; Other Information: From American Physical Society Annual Meeting, New york, Jan. 1964. Orig. Receipt Date: 31-DEC-64; Related Information: Partial fulfillment of thesis
- Country of Publication:
- United States
- Language:
- English
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