Positronium: A Review of the Calculations

¡ Air Force Cambridge Research Laboratories, Air Force Systems Command, United States Air Force
āχāĻŦ⧁āĻ•
33
āĻĒ⧃āĻˇā§āĻ āĻž
āĻŽā§‚āĻ˛ā§āϝāĻžāĻ‚āĻ•āύ āφ⧰⧁ āĻĒā§°ā§āϝāĻžāϞ⧋āϚāύāĻž āϏāĻ¤ā§āϝāĻžāĻĒāύ āϕ⧰āĻž āĻšā§‹ā§ąāĻž āύāĻžāχ  āĻ…āϧāĻŋāĻ• āϜāĻžāύāĻ•

āĻāχ āχāĻŦ⧁āĻ•āĻ–āύ⧰ āĻŦāĻŋāĻˇā§Ÿā§‡

For typical magnetospheric densities, free positrons have a lifetime of between one million and one trillion seconds. A portion of the injected positrons undergo free annihilation and a portion form positronium. Results are given of the theoretical calculations of positronium properties without presenting the intermediate steps that depend on a knowledge of quantum electrodynamics. This paper is a review of the calculations of positronium state (1) decay rates, (2) energy levels, and (3) external field behavior. Theoretical results are compared with only the latest experimental results. The coverage is substantially complete from the pre-experimental years (1930 to 1950) to the present (1974). Emphasis is placed on stating final theoretical results and giving references to original work rather than giving a step-by-step account of the calculations. (Modified author abstract).

āĻāχ āχāĻŦ⧁āĻ•āĻ–āύāĻ• āĻŽā§‚āĻ˛ā§āϝāĻžāĻ‚āĻ•āύ āϕ⧰āĻ•

āφāĻŽāĻžāĻ• āφāĻĒā§‹āύāĻžā§° āĻŽāϤāĻžāĻŽāϤ āϜāύāĻžāĻ“āĻ•āĨ¤

āĻĒāĻĸāĻŧāĻžā§° āύāĻŋāĻ°ā§āĻĻ⧇āĻļāĻžā§ąāϞ⧀

āĻ¸ā§āĻŽāĻžā§°ā§āϟāĻĢ’āύ āφ⧰⧁ āĻŸā§‡āĻŦāϞ⧇āϟ
Android āφ⧰⧁ iPad/iPhoneā§° āĻŦāĻžāĻŦ⧇ Google Play Books āĻāĻĒāĻŸā§‹ āχāύāĻˇā§āϟāϞ āϕ⧰āĻ•āĨ¤ āχ āĻ¸ā§āĻŦāϝāĻŧāĻ‚āĻ•ā§āϰāĻŋāϝāĻŧāĻ­āĻžā§ąā§‡ āφāĻĒā§‹āύāĻžā§° āĻāĻ•āĻžāωāĻŖā§āϟ⧰ āϏ⧈āϤ⧇ āĻ›āĻŋāĻ‚āĻ• āĻšāϝāĻŧ āφ⧰⧁ āφāĻĒ⧁āύāĻŋ āϝ'āϤ⧇ āύāĻžāĻĨāĻžāĻ•āĻ• āϤ'āϤ⧇āχ āϕ⧋āύ⧋ āĻ…āĻĄāĻŋāĻ…'āĻŦ⧁āĻ• āĻ…āύāϞāĻžāχāύ āĻŦāĻž āĻ…āĻĢāϞāĻžāχāύāϤ āĻļ⧁āύāĻŋāĻŦāϞ⧈ āϏ⧁āĻŦāĻŋāϧāĻž āĻĻāĻŋāϝāĻŧ⧇āĨ¤
āϞ⧇āĻĒāϟāĻĒ āφ⧰⧁ āĻ•āĻŽā§āĻĒāĻŋāωāϟāĻžā§°
āφāĻĒ⧁āύāĻŋ āĻ•āĻŽā§āĻĒāĻŋāωāϟāĻžā§°ā§° ā§ąā§‡āĻŦ āĻŦā§āϰāĻžāωāϜāĻžā§° āĻŦā§āĻ¯ā§ąāĻšāĻžā§° āϕ⧰āĻŋ Google PlayāϤ āĻ•āĻŋāύāĻž āĻ…āĻĄāĻŋāĻ…'āĻŦ⧁āĻ•āϏāĻŽā§‚āĻš āĻļ⧁āύāĻŋāĻŦ āĻĒāĻžā§°ā§‡āĨ¤
āχ-ā§°ā§€āĻĄāĻžā§° āφ⧰⧁ āĻ…āĻ¨ā§āϝ āĻĄāĻŋāĻ­āĻžāχāϚ
Kobo eReadersā§° āĻĻ⧰⧇ āχ-āϚāĻŋ⧟āĻžāρāĻšā§€ā§° āĻĄāĻŋāĻ­āĻžāχāϚāϏāĻŽā§‚āĻšāϤ āĻĒā§āĻŋāĻŦāϞ⧈, āφāĻĒ⧁āύāĻŋ āĻāϟāĻž āĻĢāĻžāχāϞ āĻĄāĻžāωāύāĻ˛â€™āĻĄ āϕ⧰āĻŋ āϏ⧇āχāĻŸā§‹ āφāĻĒā§‹āύāĻžā§° āĻĄāĻŋāĻ­āĻžāχāϚāϞ⧈ āĻ¸ā§āĻĨāĻžāύāĻžāĻ¨ā§āϤ⧰āĻŖ āϕ⧰āĻŋāĻŦ āϞāĻžāĻ—āĻŋāĻŦāĨ¤ āϏāĻŽā§°ā§āĻĨāĻŋāϤ āχ-ā§°āĻŋāĻĄāĻžā§°āϞ⧈ āĻĢāĻžāχāϞāĻŸā§‹ āϕ⧇āύ⧇āĻ•ā§ˆ āĻ¸ā§āĻĨāĻžāύāĻžāĻ¨ā§āϤ⧰ āϕ⧰āĻŋāĻŦ āϜāĻžāύāĻŋāĻŦāϞ⧈ āϏāĻšāĻžāϝāĻŧ āϕ⧇āĻ¨ā§āĻĻā§ā§°āϤ āĻĨāĻ•āĻž āϏāĻŦāĻŋāĻļ⧇āώ āύāĻŋā§°ā§āĻĻ⧇āĻļāĻžā§ąāϞ⧀ āϚāĻžāĻ“āĻ•āĨ¤