Letters to the Editor Preg. Theor. Phys. Vol. 36 (1966), No. 6 1301 total cross section of -n:--p larger than -n:+-p. iii) The impact parameter approximation holds: On Pion-Nucleon Scattering at High Energies b~./zCZ+1)Ik i:.+'),kr~ab t-o Jo and where k is momentum in the center-of-mass system and t is square of four-momentum transfer. The spin flip amplitude is written in terms of the spin flip partial wave amplitude v(b) as Department of Physics Nagoya University, Nagoya *Department of Physics Kyusyu University, Fukuoka September 26, 1966 On the basis of an analysis of polarization (incident pion momentum Pz=1.7~25 GeVIc in laboratory system) it was reported in a previous noten that the imagi-_ nary part of spin flip partial.wave amplitude Im 11- (b) of -n:~ p elastic scattering is negative in the range ·of the impact parameter b = (1-2) X 10-13cm, independently of the incident energy.. We noted in I that this behaviour of Imv-(b) may be closely· connected with interactions responsible for construction of baryon resonances. In tl;le present note the analysis is extended to (1) the higher energy region Pz = 6~ 10 GeVIc where several new polarizaticm measurements 2l .have been made and to (2) the differential cross section for the charge, exchange process (-n:~p+°) in the energy region 3"""" 18 GeVIc. aJ Assumptions taken here are: i) The -n:--p elastic amplitude f-=-o-+ onh- is dominated by spin :qon-flip term uin the forward region. ii) The ratios a=Re.giimg and fl=Reh/ Im h are constant in ·the forward ·region for the .11:-- p elastic and charge exchange processes respectively. The spin non-flip amplitudes for the -n:-- p elastic and charge ~s 0- = exchange processes can be e~prsd k(a-+i) [(da-/dt)t=o expCr-t)l(1+anJ 1121 ..../7! and n•=k(ac---:i) [(da,.l dt)t=o exp(r.t)l 2 1'\ln (l+a~)1 respectively. Here r-and r. are parameters. The sign of Im Oc can be determined as negative because of the h(t) = (kl2) ~v(b)J1 (b.../ -t)bdb. iv) The following two types are assumed for v(b): (I) 11 (b) = Ab for OS:.bS:.R and 0 for R<b, (II) v(b) = Ab" exp( -b 2IR 2 ), (n=1, 3 or 5), where A is a complex and R is a real parameter.· The cross section and. the polarization of 11:-- p elastic process are written by ' and P-(t) =2..../-;;[(l+a-fl-)l..../1+an xim h-ICkvda~lt). The quantity [(1+a~fl-) oqtained from the experimenta] polarization in the forward direction (lti<0.8(GeV/c) 2 ) is ~hown in Fig. 1. In Fig. 2, ..../i+;B' Imv.(b) is snown which .is obtained from the ·spin flip part of · the charge exchange ·cross secti~n (da.ldt),, .. 'n;,=da.ldt-(da./dt)t=o e~p(r.t) The value of r. has to be taken larger than ~6 ( GeVI p) - 2 to satisfy the above equation. Hatched regions in Figs. 1 and 2 come mainly from uncertainties of the experimental data and of r. respectively. Though the sign respectively. ./1+a~]Imv-(b) Downloaded from https://academic.oup.com/ptp/article-abstract/36/6/1301/1821774 by guest on 11 June 2020 Katsuya HASEBE, Hiroyuki KANADA, Shoichiro 0TSUKI,* Shoji SAWADA and Masaru Y ASUNO 1302 0.05 Letters to the Editor [(l+a_4l// l+a!] Im u.. (b) Imv-(b) at a few GeV/c and decrease as energy increases. 0.15 0.05 0 -0.05 -0.10 0.15 -0.15 Fig. 3. Energy dependence of Im 1J1 (b) and ImtJa(b) at b=0.9xl0- 13 cm for case II with n=3. Fig. 1 and Fig. 2. Shown for tJ(b). for case II with n=3. Similar results are obtained for the other cases. of Im lie (b) cannot be determined by cross section only, we assume tentatively that it is positive as is expected from the reason mentioned in I. To obtain the amplitude of definite isospin state, i.e. Imv3(b)=Im{v-(b)+'\1"2vc(b)} and Imvl(b)=Im{v-(b)-vc(b)/'\1"2} -for I= 3/2 and I= 1/2 respectively, it is necessary to determine the values of «-, 8c and 8-- We take «-= -0.3 which is consistent with experiment. Though we have no knowledge of 8c and 8- at present, if we restrict them by 18c I ::::::;1 and 18-1 ::::::;1, we can obtain the values of lm /13 (b) and lm 111 (b) rather restrictively. In case II with n = 3 for 11 (b) the Im /13 (b) and lm 111 (b) have maximum and minimum values at b = 0.9 X 10-13 em respectively. These values, which are shown in Fig. 3, are relatively large compared with that of In the forward direction the experimental polarization seems to be nearly energy independent through the energy range 1.7 to 10 GeV /c. If this behaviour remains up to 20GeV/c, the value of Imv3(b) becomes approximately zero at about 20 GeV /c. From the above argument we expect that 1) the polarization of n+-.p elastic scattering in the forward direction is large positive at a few GeVIc and diminish as the energy increases and 2) the polarization of charge exchange process is negative. The polarization measurements which test the above results will play a significant role in understanding the interactive force between pion and nucleon which is responsible for the mass spectrum of nucleon isobars.n• 4 ) _More details of our results will be reported elsewhere. 1) 2) 3) K. Hasebe, S. Hayakawa, H. Kanada, S. Otsuki and M. Y asuno, Prog. Theor. ·Phys. 35 (1966), 755, referred to ·as I. In this note the same notation is as in I used. The suffices - and c indicate 11:--p elastic and charge exchange proces~, respectively. M. Borghini et al., Phys. Letters 21 (1966), 114. P. Sonderegger et al., Phys. Letters 20 (1966), 75. Downloaded from https://academic.oup.com/ptp/article-abstract/36/6/1301/1821774 by guest on 11 June 2020 0.10 Letters to the Editor 4) 1303 T. F. Kycia and K. F. Riley, Phys. Rev. LetterslO (1963), 266. S. Otsuki and S. Sawada, Prog. Theor. Phys. 36 (1966), 666. Downloaded from https://academic.oup.com/ptp/article-abstract/36/6/1301/1821774 by guest on 11 June 2020 Note added hi proof: After this note was completed, the authors had the opportunity to learn the prelimimtry results of the data on the polarization of w:•- p .and charge exchange processes reported in the ·High Energy Conference held at Berkeley (Aug. 1966). In both processes polarizations are positive in the forward direction. The former agrees well with ours and the latter suggests that the case IfJcl ?:;1 has to be treated.