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Comparison of the π+ and π− elastic scattering from 12C over the πN (3,3) resonance region
Volume 71B, number 2
PHYSICS LETTERS
21 November 1977
C O M P A R I S O N O F T H E 7r+ A N D re- E L A S T I C S C A T T E R I N G F R O M 12 C O V E R T H E lrN ( 3 , 3 ) R E S O N A N C E R E G I O N J. PIFFARETTI, R. CORFU, J.-P. EGGER, P. GRETILLAT, C. LUNKE, E. SCHWARZ lnstitut de Physique, Universitd de Neuchhtel 1, Rue A.-L. Breguet 1, CH-2000 Neuch~tel, Switzerland C. PERRIN Institut des Sciences Nucldaires, Universitd de Grenoble, B.P. 257, Centre de tri, F-38044 Grenoble-Cedex, France and B.M. PREEDOM Physics Department, University o f South Carolina 2, Columbia, SC 29208, USA Received 2 August 1977 Pion-carbon scattering was measured for both 7r÷ and lr- at 162 and 226 MeV. The significant differences observed between the 7r+ and ~r-elastic cross sections in the diffraction minima are shown to be of opposite sign below and above the 7rN (3,3) resonance. In addition, differences between the ~r+ and ~r- cross sections are also observed at 162 MeV at backward angles.
In a previous letter [1 ], we presented measurements of the Tr+ and 7r- cross sections from 12C at 148 MeV. This data did show significant differences between 7r+ and 7r- elastic cross sections in the diffraction minima. Germond and Wilkin recently explained this fact in terms of Coulomb distortion [2]. They compared their predictions with "on-line" results obtained later at SIN. We report here on the corresponding final results. The new measurements were undertaken at the Swiss Institute of Nuclear Research (SIN) with the same apparatus and method used earlier [1 ]. Angular distributions between 20 ° and 125 ° were obtained for both 7r+ and n - at 162 and 226 MeV. The analysis of the data was done as previously except for the following points. 1. Four angular bins of 2 ° width were accepted out of the full aperture of the spectrometer. This corresponds to 85% of the overall solid angle of 15.3 msr. 2. The calibration of the solid angles was obtained t Work supported in part by the Swiss National Science Foundation. 2 Supported in part by the National Science Foundation of USA. 324
by measuring the 7r+-p elastic scattering at 45 ° (polyethylene target) and using the accurate results of Bussey et al. [3]. The calibrations performed at the two energies are in complete agreement. 3. The cross sections were corrected for finite angular resolution by a method similar to the one used by Binon et al. on their 7 r - - 4 H e data [4]. In the diffraction minima the correction did not exceed 15%. The final results were checked to be "binning independent", the data gathered in bins of 2 °, 4 ° or 6 ° fullwidth giving, once corrected, compatible cross sections. As an additional check of the normalisation, the forward average nuclear cross section, 1
~(0) = ~ ( o _ ( o ) + o+(0)},
(1)
obtained from the independent fits of our rr+ and 7rdata were compared with the values predicted by the optical theorem o(0) = (kST/4~')2 (1 + p2),
(2)
where ¢7T the average total cross section and p the relative real part of the forward amplitude were taken from the work of Wilkin et al. [5]. This optical point prediction is 4% higher than our
Volume 71B, number 2
~10 ~
PHYSICS LETTERS
21 November 1977
.........
Pi minus
.......... Pi minus
• -
Pi plus
• -
Pi ptus
_=
o
~7 10' ~ - uJ --
I LL
10 o
10"
101
i
0
i
15
~
~
30
Fig. 1. C o m p a r i s o n
J
i
45
q
i
60
i
i
75
q
~
90
i
t
i
i
105 120 135 ANGLE (DEG.)
o f t h e 7T+ a n d 7r- e l a s t i c cross s e c t i o n s f r o m
12C at 162 MeV. The angles and cross sections are given in the lab system. The curves are independent fits of the form given by eq. (3). Note the peculiar cross-over of the two curves at 105 ° which does not appear either in the 148 MeV or in the 226 MeV data. extrapolation at 162 MeV and 10% larger at 226 MeV. As, on the other hand, our n - data at 226 MeV agrees perfectly with the one of Binon et al. [6], we attributed this discrepancy to systematic uncertainties o f the e x t r a p o l a t i o n and applied no c o r r e c t i o n to our cross sections. The n + and n - elastic cross sections o b t a i n e d at 162 and 226 MeV are shown in figs. 1 and 2. The 148 MeV data can be found in ref. [1 ]. The curves plotted are fits corresponding to scattering amplitudes of the form:
F(q) : F(q = 0). {]-2 ] (1 q2 \ qq21, I --~2 ) {1-q2~'e-1/2aq2, \ q21 (3)
0
15
30
45
60
75
90
105 120 135 ANGLE (DEG.)
Fig. 2. Comparison of the n + and ~r- elastic cross sections from 12C at 226 MeV. The angles and cross sections are given in the lab system. The curves are independent fits of the form given by eq. (3). No satisfactory fit was possible with two zeros only.
qi
where q is the m o m e n t u m transfer and are c o m p l e x zeros corresponding to the diffraction minima. The fits were p e r f o r m e d i n d e p e n d e n t l y for n + and n - without correcting for C o u l o m b distortion. It is to be n o t e d that no good fit was possible at the considered energies with two zeros only. The inversion o f the o - o+ difference in the first m i n i m u m is clear when comparing either the 148 or 162 MeV cross sections to the 226 MeV data. In fig. 2 o f ref. [2] the differences deduced from the fits are plotted as a f u n c t i o n o f the kinetic energy in comparison to the predictions o f G e r m o n d and Wilkin [2]. A qualitative agreement is reached. The behaviour of the cross section in the second m i n i m u m is a p p r o x i m a t e l y the same, the o - o+ difference changing also from positive at 148 MeV to negative at 226 MeV. 325
Volume 71 B, number 2
PHYSICS LETTERS
The preliminary analysis of the inelastic scattering data shows no significant difference b e t w e e n the 7r+ and 7r- cross sections at 226 MeV as was also the case at 148 MeV [1]. All these facts are in agreement with the C o u l o m b distortion picture [2] and one can conclude that with some more refinements in the calculation it should be possible to correct the pion-nucleus cross sections for C o u l o m b effects at least in the vicinity o f the first diffraction m i n i m u m . Therefore one m a y hope to use pion-nucleus scattering data to extract nuclear structure information. On the contrary, the cross-over o f the lr+ and n elastic cross sections appearing at 105 ° in the 162 MeV data (fig. 1) seems difficult to explain in the same model. More work, b o t h experimental and theoretical, will probably be necessary to understand completely the
326
21 November 1977
interplay of nuclear and C o u l o m b interactions at large angles. We wish to t h a n k Dr. J.-F. G e r m o n d for his help in the a d j u s t m e n t of his fitting code to our special needs.
References [1] [2] [3] [4]
J. Piffaretti et al., Phys. Lett. 67B (1977) 289. J.-F. Germond and C. Wilkin, Phys. Lett. 68B (1977) 229. P.J. Bussey et al., Nucl. Phys. B58 (1973) 363. F. Binon et al., Phys. Rev. Lett. 35 (1975) 145 and Nucl. Phys. B (to be published). [5] C. Wilkin et al., Nucl. Phys. B62 (1973) 61. [6] F. Binon et al., Nucl. Phys. B17 (1970) 168. [7] R.M. Edelstein et al., Phys. Rev. 122 (1961) 252; F.P.G. Valckx et al., Nuovo Cimento 23 (1962) 1005.
PHYSICS LETTERS
21 November 1977
C O M P A R I S O N O F T H E 7r+ A N D re- E L A S T I C S C A T T E R I N G F R O M 12 C O V E R T H E lrN ( 3 , 3 ) R E S O N A N C E R E G I O N J. PIFFARETTI, R. CORFU, J.-P. EGGER, P. GRETILLAT, C. LUNKE, E. SCHWARZ lnstitut de Physique, Universitd de Neuchhtel 1, Rue A.-L. Breguet 1, CH-2000 Neuch~tel, Switzerland C. PERRIN Institut des Sciences Nucldaires, Universitd de Grenoble, B.P. 257, Centre de tri, F-38044 Grenoble-Cedex, France and B.M. PREEDOM Physics Department, University o f South Carolina 2, Columbia, SC 29208, USA Received 2 August 1977 Pion-carbon scattering was measured for both 7r÷ and lr- at 162 and 226 MeV. The significant differences observed between the 7r+ and ~r-elastic cross sections in the diffraction minima are shown to be of opposite sign below and above the 7rN (3,3) resonance. In addition, differences between the ~r+ and ~r- cross sections are also observed at 162 MeV at backward angles.
In a previous letter [1 ], we presented measurements of the Tr+ and 7r- cross sections from 12C at 148 MeV. This data did show significant differences between 7r+ and 7r- elastic cross sections in the diffraction minima. Germond and Wilkin recently explained this fact in terms of Coulomb distortion [2]. They compared their predictions with "on-line" results obtained later at SIN. We report here on the corresponding final results. The new measurements were undertaken at the Swiss Institute of Nuclear Research (SIN) with the same apparatus and method used earlier [1 ]. Angular distributions between 20 ° and 125 ° were obtained for both 7r+ and n - at 162 and 226 MeV. The analysis of the data was done as previously except for the following points. 1. Four angular bins of 2 ° width were accepted out of the full aperture of the spectrometer. This corresponds to 85% of the overall solid angle of 15.3 msr. 2. The calibration of the solid angles was obtained t Work supported in part by the Swiss National Science Foundation. 2 Supported in part by the National Science Foundation of USA. 324
by measuring the 7r+-p elastic scattering at 45 ° (polyethylene target) and using the accurate results of Bussey et al. [3]. The calibrations performed at the two energies are in complete agreement. 3. The cross sections were corrected for finite angular resolution by a method similar to the one used by Binon et al. on their 7 r - - 4 H e data [4]. In the diffraction minima the correction did not exceed 15%. The final results were checked to be "binning independent", the data gathered in bins of 2 °, 4 ° or 6 ° fullwidth giving, once corrected, compatible cross sections. As an additional check of the normalisation, the forward average nuclear cross section, 1
~(0) = ~ ( o _ ( o ) + o+(0)},
(1)
obtained from the independent fits of our rr+ and 7rdata were compared with the values predicted by the optical theorem o(0) = (kST/4~')2 (1 + p2),
(2)
where ¢7T the average total cross section and p the relative real part of the forward amplitude were taken from the work of Wilkin et al. [5]. This optical point prediction is 4% higher than our
Volume 71B, number 2
~10 ~
PHYSICS LETTERS
21 November 1977
.........
Pi minus
.......... Pi minus
• -
Pi plus
• -
Pi ptus
_=
o
~7 10' ~ - uJ --
I LL
10 o
10"
101
i
0
i
15
~
~
30
Fig. 1. C o m p a r i s o n
J
i
45
q
i
60
i
i
75
q
~
90
i
t
i
i
105 120 135 ANGLE (DEG.)
o f t h e 7T+ a n d 7r- e l a s t i c cross s e c t i o n s f r o m
12C at 162 MeV. The angles and cross sections are given in the lab system. The curves are independent fits of the form given by eq. (3). Note the peculiar cross-over of the two curves at 105 ° which does not appear either in the 148 MeV or in the 226 MeV data. extrapolation at 162 MeV and 10% larger at 226 MeV. As, on the other hand, our n - data at 226 MeV agrees perfectly with the one of Binon et al. [6], we attributed this discrepancy to systematic uncertainties o f the e x t r a p o l a t i o n and applied no c o r r e c t i o n to our cross sections. The n + and n - elastic cross sections o b t a i n e d at 162 and 226 MeV are shown in figs. 1 and 2. The 148 MeV data can be found in ref. [1 ]. The curves plotted are fits corresponding to scattering amplitudes of the form:
F(q) : F(q = 0). {]-2 ] (1 q2 \ qq21, I --~2 ) {1-q2~'e-1/2aq2, \ q21 (3)
0
15
30
45
60
75
90
105 120 135 ANGLE (DEG.)
Fig. 2. Comparison of the n + and ~r- elastic cross sections from 12C at 226 MeV. The angles and cross sections are given in the lab system. The curves are independent fits of the form given by eq. (3). No satisfactory fit was possible with two zeros only.
qi
where q is the m o m e n t u m transfer and are c o m p l e x zeros corresponding to the diffraction minima. The fits were p e r f o r m e d i n d e p e n d e n t l y for n + and n - without correcting for C o u l o m b distortion. It is to be n o t e d that no good fit was possible at the considered energies with two zeros only. The inversion o f the o - o+ difference in the first m i n i m u m is clear when comparing either the 148 or 162 MeV cross sections to the 226 MeV data. In fig. 2 o f ref. [2] the differences deduced from the fits are plotted as a f u n c t i o n o f the kinetic energy in comparison to the predictions o f G e r m o n d and Wilkin [2]. A qualitative agreement is reached. The behaviour of the cross section in the second m i n i m u m is a p p r o x i m a t e l y the same, the o - o+ difference changing also from positive at 148 MeV to negative at 226 MeV. 325
Volume 71 B, number 2
PHYSICS LETTERS
The preliminary analysis of the inelastic scattering data shows no significant difference b e t w e e n the 7r+ and 7r- cross sections at 226 MeV as was also the case at 148 MeV [1]. All these facts are in agreement with the C o u l o m b distortion picture [2] and one can conclude that with some more refinements in the calculation it should be possible to correct the pion-nucleus cross sections for C o u l o m b effects at least in the vicinity o f the first diffraction m i n i m u m . Therefore one m a y hope to use pion-nucleus scattering data to extract nuclear structure information. On the contrary, the cross-over o f the lr+ and n elastic cross sections appearing at 105 ° in the 162 MeV data (fig. 1) seems difficult to explain in the same model. More work, b o t h experimental and theoretical, will probably be necessary to understand completely the
326
21 November 1977
interplay of nuclear and C o u l o m b interactions at large angles. We wish to t h a n k Dr. J.-F. G e r m o n d for his help in the a d j u s t m e n t of his fitting code to our special needs.
References [1] [2] [3] [4]
J. Piffaretti et al., Phys. Lett. 67B (1977) 289. J.-F. Germond and C. Wilkin, Phys. Lett. 68B (1977) 229. P.J. Bussey et al., Nucl. Phys. B58 (1973) 363. F. Binon et al., Phys. Rev. Lett. 35 (1975) 145 and Nucl. Phys. B (to be published). [5] C. Wilkin et al., Nucl. Phys. B62 (1973) 61. [6] F. Binon et al., Nucl. Phys. B17 (1970) 168. [7] R.M. Edelstein et al., Phys. Rev. 122 (1961) 252; F.P.G. Valckx et al., Nuovo Cimento 23 (1962) 1005.