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References
For references to earlier literature see the review articleThe scattering of nucleons by alpha-particles, byP. E. Hodgson:Adv. in Phys.,7, 1 (1958).
C. L. Chritchfield andD. C. Dodder:Phys. Rev.,76, 602 (1949).
J. D. Seagrave:Phys. Rev.,92, 1222 (1953).
E. Clementel andC. Villi:Nuovo Cimento,2, 1121 (1955).
As has been already emphasized in ref. (4), the normal and the inverted doublets correspond to the well known Fermi-Yang ambiguity in the elastic scattering of pions by protons. The preceding discussion can be readily extended to this case by regarding δ0 - α3, δ1/2 - α31, δ3/2 - α33 as theS andP wave phaseshifts for the isobaric spinT = 3/2. The behaviour ofk 3 cot α31 as a function ofk 2, calculated in terms of the Yang phaseshifts, deviates grossly from the linearity prescription of the effective range theory. This is an alternative argument for ruling out the Yang set without resorting to polarization measurements or even to comparison with spin-flip dispersion relations [W. C. Davidon andM. L. Goldberger:Phys. Rev.,104, 1119 (1956)]. The effective range theory has been first applied to the pion-proton scattering in theL = 1,J = 3/2;T = 3/2 state byK. A. Brueckner [Phys. Rev.,87, 1026 (1952)]. According to the preceding discussion, the scattering lengtha 3, determined byJ. Orear [Nuovo Cimento,4, 856 (1956)] from the low energy data of positive pions elastically scattered by protons, follows from the well known rigid sphere approximation (a 3 = − α3/k) and should be interpreted as the equivalent scattering length for the pure nuclear interaction. It would be interesting to examine the low energy data concerning the scattering of positive pions by protons, by taking into account the Coulomb effects in the effective range equations.
I. I. Levintov, A. V. Miller andV. N. Shamsev:Sov. Phys., Journ. Exp. Theor. Phys.,5, 258 (1957).
As far as the determination ofD waves is concerned, there is apparently some misunderstanding in the literature. So far,D waves have been extracted from the data bySeagrave (3) fork 0 = 0 and fork 0 ≠ 0 byD. C. Dodder andJ. L. Gammel [Phys. Rev.,88, 520 (1952)], byW. E. Kreger, W. Jentschke andP. C. Kruger [Phys. Rev.,93, 837 (1954)], byT. M. Putnam, J. E. Brolley andL. Rosen [Phys. Rev.,104, 1303 (1956)] and byK. W. Brockman [Phys. Rev.,102, 391 (1956)]. In this connection it has to be stressed that in a single channel reaction there exist four distinct sets of twoD phaseshifts (D 3/2,D 32), which are consistent with the data. This problem has been discussed byE. Clementel andC. Villi [Nuovo Cimento,5, 1343 (1957)] in the particular case of the scattering of positive pions by protons. The same situation occurs obviously for the nucleon-α scattering. TheD wave ambiguity is somewhat different from theP wave ambiguity, because two out of the four sets ofD phaseshifts are associated with the normalP doublet and the remaining two are associated with the inverted one. Thus, if one rules out the normalP doublet,there still remain two inverted P doublets each one associated with one set of D phaseshifts, which are equally good as far as the fit of the data is concerned. Which one of these two sets ofP andD waves represents a physical solution is at present unknown. A discrimination between them can be done by taking into account the constraints imposed by the effective range theory. According to this point of view, the energy dependence of theD 32 andD 32 phaseshifts, derived by previous analyses, does not appear to possess those features which should characterize a physical solution. This problem, however, deserves a further examination.
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This research has been sponsored by the Wright Air Development Center of the Air Research and Development Command, United Air Force, through its European Office, under Contract NO AF 61 (O52)-164.
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Pisent, G., Villi, C. Effective range theory in nucleon-alpha scattering. Nuovo Cim 11, 300–306 (1959). https://doi.org/10.1007/BF02859727
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DOI: https://doi.org/10.1007/BF02859727