Convergence of the Adiabatic Nuclear Potential. II

Journal Article · Sun Nov 15 00:00:00 UTC 1953 · Physical Review

DOI: https://doi.org/10.1103/physrev.92.1017 · OSTI ID:4426688

Klein, Abraham ^[1]

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1. Univ. of Rochester, NY (United States)

A conjecture made in a previous paper concerning the non-convergence of the series of adiabatic nuclear potentials for meson pair theory obtained by means of perturbation methods is shown to be incorrect. The correct series is derived and summed and is in agreement with a result given previously by Wentzel. The same methods suffice for the derivation and summation of two additional series of potentials of the pseudoscalar theory with pscudoscalar coupling. One of these has as its leading term the one-pair potential of fourth order, and the other begins with the leading term of sixth order. Each series has the same radius of convergence which is determined by the condition xe^x>2α, where x is the separation of the nucleons in units of the meson Compton wavelength and α = (g²/4π) (μ/2M). With (g²/4π) =15, perturbation theory converges for x>0.85; with (g²/4π) = 10, for x>0.57. The convergence for x≲1 is in any case very slow for these values of the coupling constant. Further, the possibility remains that for substantially smaller values of the coupling constant, as are suggested by the inclusion of radiative corrections, perturbation calculations of adiabatic potentials may yield a meaningful first approximation when used in conjunction with a suitable cut-off.

• Research Organization: Univ. of Rochester, NY (United States)
• Sponsoring Organization: US Atomic Energy Commission (AEC)
• NSA Number: NSA-07-006208
• OSTI ID: 4426688
• Report Number(s): NYO--3832
• Journal Information: Physical Review, Journal Name: Physical Review Journal Issue: 4 Vol. 92; ISSN 0031-899X
• Publisher: American Physical Society (APS)Copyright Statement
• Country of Publication: United States
• Language: English