The antimatter rocket described in Walter’s paper can achieve a specific impulse of about
0.58c (after correcting for a missed Lorentz factor). This is much higher than Walter’s figure of 0.21c, and it agrees with some calculations previously published by Vulpetti. Even better efficiency and even higher specific impulses could be achieved if a way to utilize gamma ray energy could be found. We point out that even if gamma ray reflectors are not feasible, gamma ray energy might still be utilized. For example, a gamma ray absorbing shield will radiate back into space the energy it absorbs. Moreover, the re-emitted radiation coming from the shield will be in the form of photons at near-optical frequencies. Thereby, the re-emmitted radiation can be collimated into an exhaust beam with relative ease. We calculated that if a pion drive were so equipped that it could effectively utilize half of the gamma ray energy for propulsion, then it could achieve a specific impulse of up to nearly 0.77c.
The first antimatter rocket design achieves its thrust by collimating (via electromagnetic fields) the charged pion products into an exhaust jet. The gamma rays simply escape into space as waste. A negligible amount of reaction products are absorbed by the spacecraft. This particular antimatter rocket design is often discussed elsewhere in the literature (see papers by Frisbee and references therein).
Using Gamma Rays [UPDATE: Westmoreland Proposed Gamma Ray Utilization Will Not Work]
The pion propulsion design can use at best 39.87% of the annihilation energy as exhaust energy. A large amount of energy is uselessly carried off into space by gamma rays.
Sanger famously proposed that one would need to create an extremely dense “pure electron gas” in order to reflect gamma rays efficiently. A parabolic reflector of this kind, with the annihilation point at its focus, would steer gamma rays into a well-collimated exhaust beam. However, the feasibility of this proposal is unclear.
Vulpetti has proposed a method of utilizing gamma ray energy by taking advantage of pair production phenomena. The gamma rays produced by proton-antiproton annihilations are of such a high energy that, by interacting with the electric field of a nucleus, they can be converted into real electron-positron pairs. Since they are charged particles, these electrons and positrons can be collimated by way of electromagnetic fields.
Another alternative is to use a gamma absorbing shield. The shield will reradiate, in all directions, the energy that it absorbs. The reradiated photons will tend to have optical or nearly optical wavelengths and so can be easily collimated. This was suggested to the author by Louis Crane. A similar concept has been discussed by Smith and by Sanger.
 U. Walter, (2006) “Relativistic rocket and space flight,” Acta Astronautica,
Vol. 59, pp. 453 – 461.
 G. Vulpetti, (1985) “Maximum terminal velocity of relativistic rocket,”
Acta Astronautica, Vol. 12, No. 2, pp. 81 – 90.
 G. P. Sutton, O. Biblarz, Rocket Propulsion Elements, 7th Edition, John
Wiley and Sons, New York, 2001.
 E. Sanger, (1953) “Zur Theorie der Photonraketen,” Ingenieur-Archiv,
Band 21, pp. 213 – 226 (in German).
 L. Crane and S. Westmoreland, (2009) “Are black hole starships possible?” arXiv:0908.1803 [gr-qc].
 R. H. Frisbee, (2003) “How to build an antimatter rocket for interstellar
missions,” 39th AIAA/ASME/SAE/ASEE Joint Propulsion Conference
and Exhibit, Huntsville, Alabama, July 20 – 23, 2003.
A 2003 paper by Robert Frisbee: How to Build an Antimatter Rocket for Interstellar Missions – – – – – Systems Level considerations in designing advanced propulsion Technology Vehicles.
 C. Amsler, et al., (2008) “Review of Particle Physics,” Physics Letters B,
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 D. L. Morgan, (1988) in Antiproton Science and Technology, ed. R. W.
Augenstein et al., pp. 530 – 565.
 E. Sanger, “Photon propulsion,” in Handbook of Astronautical Engineering,
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 G. Vulpetti, (1983) “A concept of low-thrust relativistic-jet-speed high efficiency matter-antimatter annihilation thruster,” International Astronautical
Federation 34th Congress, Budapest, October 1983.
 D. W. Smith, et al., (2005) “Thermal radiation studies for an electronpositron
annihilation propulsion system,” 41st AIAA/ASME/SAE/ASEE Joint Propulsion Conference, Tucson, Arizona, July 10 – 13, 2005.