Summary
Making an eikonal approximation in two relative momenta in a 3-body system, keeping trace of all recoil terms, and assuming that the ranges of forces responsible for πp and πn elastic scattering are small, we find the following form factor for the double-scattering term in πd → πd:
, whereϱ≡r[1+(Δμ/4kM)2]−1/2,B is the binding energy of the deuteron,μ, M are pion and nucleon masses, respectively,Δ is the momentum transfer in the πd → πd process. The above form factor should be compared with the ordinary one of Glauber
and with the form factor of Blankenbecler and Gunion, and Gottfried
, whereη≡Δ 2/8k.
Riassunto
Eseguendo un’approssimazione iconale in due impulsi relativi in un sistema di 3 corpi, prendendo la traccia di tutti i termini di rinculo e supponendo che i raggi d’azione delle forze responsabili dello scattering elastico πp e πn siano piccoli, si trova il seguente fattore di forma per il termine di scattering doppio nel processo πd → πd:
, doveϱ≡r[1+(Δμ/4kM)2]−1/2,B è l’energia di legame del deutone,μ, M sono rispettivamente le masse del pione e del nucleone,gD è l’impulso trasferito nel processo πd → πd. Il suddetto fattore di forma deve essere confrontato con quello ordinario di Glauber
, e con il fattore di forma di Blankenbecler e Gunion e di Gottfried
, doveη≡Δ 2/8k.
Реэуме
Исполяэуя зиконаляное приблизение по двум относителяным импулясам в трех-частичнои системе, сохраняя след всех членов отдали и предполагая, что области деиствия сил, ответственных эа πр и πп упругое рассеяние, являутся малыми по сравнениу с расстояниями мезду р и n в деитроне, мы получаем следуушии форм-фактор для члена двукратного рассеяния в πd→πd
, где В естя знергия свяэи деитрона, μ, М соответственно массы пиона и нуклона, а Л естя передаваемыи импуляс в процессе πd→πd. Полученныи выще форм-фактор долзен бытя сравнен с обычным форм-фактором Глаубера
, и с форм-фактором Бланкенбеклера и Гуниона и Готтфрида
, где η ≡ Δ2/8k.
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References
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In the application of the ordinary Glauber formula,i.e. that without recoil corrections, one usually takesk in the laboratory frame of reference, and, as shown byFranco andGlauber (10), the formula is the same as in the centre-of-mass system. However, for a discussion of recoil corrections a quantityΔ 2/8k is important, and in the c.m.s. it is much larger than in the laboratory system. For comparison, we put in Table 1 also the value ofΔ 2 whenk is the relative momentum in theπd c.m.s. In this last case our correction factor |F|2 can be 0.76 or even 0.15 in the double-scattering region or near by. Thus we can get a correction of about 0.50, or in other words about 2 depletion factors of the differential cross-section, which seems to be needed in the explanation of the experiment ofBradamante et al. (9). The importance of the πd c.m.s. and complications connected with it in considerations of the appropriate 2-body subsystems shall be given in our next report.
V. Franco andR. J. Glauber:Phys. Rev.,142, 1195 1966).
R. Blankenbecler andJ. F. Gunion:Phys. Rev. D,4, 718 (1971).
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Namysłowski, J.M. Recoil form factor for the deuteron. Nuov Cim A 12, 331–340 (1972). https://doi.org/10.1007/BF02729548
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DOI: https://doi.org/10.1007/BF02729548