- Email: [email protected]
c
Nuclear Physics B46 (1972) 630-636. North-Holland Publishing Company
7r- p FORWARD ELASTIC SCATTERING NEAR 1 GeV/c J.M. ABILLON, A. BORG , M. CROZON, Th. LERAY, J.P. MENDIBURU and J. TO CQ U EV I LLE Laboratoire de Physique A tomique et Moleculaire, Coll~ge de France, Paris 5
Received 19 May 1972
Abstract: We have measured the differential cross section of the reaction n - p ~ n - p in the range 0.92 < cos 0c.m. ~<0.99 at 15 momenta between 0.875 and 1.580 GeV/c. The results we report complete the available data; previous measurements of this reaction do not extend beyond cos 0c.m.=0.90. We compare our experimental results with dispersion relation predictions. A comparison of our results for B, the slope of the differential cross section, with earlier results shows many discrepancies.
1. INTRODUCTION The pion beam conditions are the same as in ref. [1 ]. The experimental array consisted mainly in 3 magnetostrictive spark chambers telescopes. One o f them determined the incident particle direction. After the scattering in a 40 cm long liquid hydrogen target, a second telescope measured the scattered n direction, and a third one its deflection through an analysing magnet. A suitable array of scintillators selected the events, rejecting most of the inelastic events. The collection of the data was done by an online computer, which monitored the performance of the equipment. The overall efficiency of the spark chambers was sufficiently good that more than 95% of the triggered events could be analysed, using the CERN MAGFIT 3 program procedure. To select the elastic events, two tests have been concurently used. (a) The vertex of the interaction had to be inside the target (fig. la). (b) The m o m e n t u m of the scattered n was selected in a -+ 3 standard deviations interval around its central value (fig. lb). Depending on the energy 40% to 70% of the analysed events satisfied these criteria and were considered to be elastic events. A Monte Carlo program was used to compute the solid angles and to estimate the errors on the solid angles. We have considered two kinds of errors: * Ce travail a b6n4fici~ de l'aide du Commissariat h l'Energie Atomique. ** D. Ph. P. E., C.E.N. Saclay.
J.M. A billon et aL, ¢r p f o r w a r d elastic scattering
6 31
N bet'of eveol5
60~
n
,J]
ra
5,~ E
4.O.$Geg//cl
,5 '~- cm CI
N be,- of eveni',.,s 206
"100
.4
.52
.64
.75
.88
Mo-,entu,-o
"~0
2'°'"2 "I.12
f24
(G~v/~)
b
Fig. 1. (a) z-coordinate (along the beam direction) of the vertex of the interaction for a sample of events at 1.03 GeV/c. The arrows indicate the locations of: the last scintillator of the beam telescope (sj), the entrance and outgoing windows of the target (Fe and Fs respectively). (b) Histogram of the momentum of the scattered pion for the same sample of events as in la). (a) The statistical errors include the errors due to the limited number of events and also the errors coming from the various uncertainties in the Monte Carlo computation and in the geometrical reconstruction. (b) The normalization errors affect as a whole the results at one energy and include errors on the measurement of the lepton contamination of the beam (measured with a gas (~erenkov counter) and possible systematic geometrical errors. They decrease when the energy increases. For each incident momentum, 2500 to 4000 "full target" events were collected, and 1000 to 2000 "empty target". The resulting differential cross sections are given in table 1 and plotted on fig. 2, together with those of refs. [2, 3]. In the table errors are separately mentioned, as quoted above. As far as a comparison is possible, our results are in good agreement with earlier experiments.
12.6
1 1 . 3 5 ± 1.6
1.580
± 1.65
± 1.6
1.505
1.180
11.2
± 1.0
9.8
1.120
1.440
± 0.85
12.2
1.085
8.95 ± 0.95
±0.95
12.6
1.055
1 0 . 6 5 ± 1.25
12.9
± 1.0
15.3
1.030
1.360
14.70±0.80
1 6 . 8 5 ± 1.0
1.000
1.280
15.0
1 9 . 0 5 +-0.95
0.975
±0.75
±0.80
± 0.80
±0.90
± 0.50
± 0.80
8.85 ± 0.75
9.1
12.45 ± 1.2
8.35 ±0.60
7.1
9.35 ± 0.65
7.95 ± 0.55
10.7
14.7
1 4 . 7 5 ± 1.0
0.950
+0.85
1 0 . 4 5 ± 0.81 15.0
± 1.0
1 4 . 7 5 ± 1.0
6.20 ± 0.60
7.15 ± 0 . 8 5
13.0
0.98 ~ 0.97
0.99 ~ 0.98
0.925
0.875
Momentum (GeV/c)
cos Oc.m. interval
±0.90
±0.70
'-+0780
±0.85
± 0.50
± 0.60
± 0.60
8.85 ± 0.60
8.5
9.45 ± 0.60
8.20± 0.60
7.8
7.8
9 . 0 5 +- 0 . 5 5
10.0
13.1
13.9
14.35 + 0.85
12.5
13.05±0.90
9.70 ± 0.70
6 . 6 5 -+ 0 . 5 5
0 . 9 7 --, 0 . 9 6
±0.95
±0.90
±0.90
± 0.60
± 0.50
7.5
8.4
8.7
± 0.55
± 0.60
± 0.55
7.75 ± 0 . 6 0
7.3
7.85 ± 0 . 6 0
9.6
9.55 + 0.75
14.8
14.5
14.55 ± 0.95
12.35± 0.95
12.5
8.95 ± 0.80
5.30 ± 0.60
0 . 9 6 --* 0 . 9 5
Table 1 D i f f e r e n t i a l cross s e c t i o n s ( m b / s r ) .
± 1.4
± 1.25
± 1.15
± 0.70
7.3
8.1
7.3
7.7
± 0.55
± 0.60
± 0.55
+- 0 . 6 0
6.55 ± 0.50
7.6
8.65 + 0.70
9.85-+ 0 . 9 0
11.95 + 1.05
13.2
13.7
1 2 . 8 5 ± 1.3
13.2
9 . 6 0 ± 1.20
6 . 1 5 ± 1.05
0 . 9 5 -+ 0 . 9 4
+ 1.35
± 0.75
6.4
6.5
6.6
± 0.55
± 0.60
± 0.60
7.15 ± 0 . 5 5
6.4
4 . 6 5 ± 0.85
7.75 ± 1.05
8.3
14.25 ± 2.05
0 . 9 4 -~ 0 . 9 3
3 3
7.4 ± 0 . 7 5
3
3
3
~.2
t.6
1
~.3
4.5
4.6
L8
5
5
5.2
Normal±sat±on error (%)
6.0 ± 0 . 8 0
0 . 9 3 -+ 0 . 9 2
bo
J.M. A billon et aL, n - p forward elastic scattering
633
10 °
sI
GeV/c
i
"--~e
o.v/~
]
10
10 5 1.36 GeV/c 10 1
"~4,4 OeV/c
OeV/c
10 5 20
"q
S
5~
I
.90
.80
.70
I
cos e
.90
80
.70
cos
Fig. 2. Differential cross section in mb/sr as function of cos 0c.m. at the different energies: this experiment. ~ Brody et ak ~, Duke et al. Solid lines axe best fits (see text). 2. C O U L O M B A N D N U C L E A R S C A T T E R I N G In the angular range here studied, the C o u l o m b effect is rather small but n o t negligible. In order to take account of it, we have used the theoretical formalism of West and Yennie [4] which includes b o t h real and imaginary radiative corrections.
J.M. Abillon et al., ~r- p forward elastic scattering
634
Table 2 do
Momentum
~-~ (0°c.m.)
B (GeV - 2
(GeV/c)
(mb/sr)
(log. slope at 0 ° )
0,875
6.70 _+ 1.00
7.20 -+ 1.40
0,925
11.30 -+ 1.10
10.80 ± 0.85
0.950
16.50 -+ 0.80
11.80 ± 0.60
0.975
17.10 ± 0.85
11.80 ± 0.80
1,000
18.50 ± 1.60
10.10 +- 0,45
1.030
18.50-+ 1.30
9.00 ± 0.65
1.055
17.30 ± 1.50
8.00 ± 0.80
1.085
12.50 ± 0.75
7.50-+ 0.50
1.120
12.00 +- 1.20
6.90 -+ 0.50
1.180
11.40 ± 1.15
7.80 ± 0.35
1.280
8.50 -+ 0.45
4.70 +- 0.70
1.360
10.50 ± 0.40
6.90 ± 0.40
1.440
11.50 ± 1.05
7.50 -+ 0.30
1.505
10.30 ± 0.50
6.90 ± 0.30
1.580
11.30 +- 0.55
7.10 -+ 0.35
It can be s h o w n t h a t , in t h e range o f s a n d t here c o n c e r n e d , t h e real radiative corr e c t i o n s are negligible. T h u s o n e c a n write the d i f f e r e n t i a l e x p e r i m e n t a l cross sections:
d o _ l f c l 2 + 2 f c I m f N [13 cos ~q5 -- sin ~ l dt
+ ( 1 + 182) Im f 2N
w h e r e f c is the C o u l o m b a m p l i t u d e ; f N is the n u c l e a r a m p l i t u d e , w i t h
Re & 18= i m f N
'
a4~ is an a n a l y t i c e x p r e s s i o n given in ref. [5] a n d r e p r e s e n t s t h e p h a s e b e t w e e n Coulomb and nuclear amplitudes. Having p a r a m e t r i z e d f N b y Im f N ( t ) = Im f N (0) exp ~ B t , we have f i t t e d the values o f dON/dt ( 0 °) a n d B o n the e x p e r i m e n t a l results (solid lines o n fig. 2). T a b l e 2 a n d fig. 3 give the results o f these fits.
J.M. A billon et al., 7r-p forward elastic scattering
635
20
a8
2o
,
I''t
40
! L
I
p,.~ [aov/c) b Fig. 3. (a) Differential cross section at 0 ° in mb/st extrapolated from data and given by dispersion relations predictions: ~i our results, o values given by Brody et al., - - predictions by Hohler and Straus, - - - prediction by Mendiburu. (b) Logarithmic slope of the differential cross sections at 0 ° (B) in GeV-2: ~i our results. $ a compilation by Lasinski et al. In fig. 3a the values of dON/d~2 (0 °) are plotted concurrently with 3 different predictions: (a) d o N / d ~ (0 °) o b t a i n e d by Brody et al. from their results. (b) Dispersion relations predictions by HOhler and Strauss [5]. In this computation, the dispersion integrals are written for the even and odd isospin c o m b i n a t i o n s o f the lrN amplitude. F u r t h e r m o r e , the odd c o m b i n a t i o n is decomposed into a low
636
J.M. A billon et aL, rt- p forward elastic scattering
energy term and a background term. The latter is fitted on experimental data for charge-exchange scattering. For the m o m e n t u m range 0,5 to 2.65 GeV/c, total cross sections by Carter et al. [6] are used. (c) Dispersion relations computed by one of us [7] who used a dispersion relation with three substractions for the 7r-N amplitudes. Here the results of Carter et al. [6] are left out because they seem to be shifted in energy [8]. Finally, the results for B (slope of the scattering amplitude) are plotted in fig. 3b, and compared with those given in a compilation by Lasinski et al. [9]. There are many discrepancies. They probably come from the fact that there were very few experimental points in the very forward region, and that made extrapolations hazardous.
REFERENCES [ 11 J.M. Abillon, A. Borg, M. Crozon, Th. Leray, J.P. Mendiburu and J. Tocqueville, Phys. Letters 32B (1970) 712. 121 P.J. Duke, D.P. Jones. M.A.R. Kemp, P.G. Murphy, J.D. Prentice and J.J. Thesher, Phys. Rev. 149 (1966) 1077. [31 A.D. Brody, R.J. Cashmore, A. Kernan, D.W.G.S. Leith, B.S. Levy, B.C. Shen, J.P. Berge, D.J. Herndon, R. Longacre, L.R. Price, A.H. Rosenfeld and P. S~ding, Phys. Rev. D3 (1971) 2619. [4] G.B. West and D.R. Yennie Phys. Rev. 172 (1968) 1413. [51 G. H6hler and R. Straus, Karlsruhe preprint, October 1970. 161 A.A, Caxter et aL, Phys. Rev. 144 (1966) 1101. [7] J.P. Mendiburu, thesis to be published. [8] Ayed and Bareyre, private communication. [9] T. Lasinski, R. Levi-Setti and E. Predazzi, Phys. Rev. 179 (1969) 1426; T. Lasisnski, R. Levi-Setti, B. Schwarzschild and P. Ukleja, Nucl. Phys. B37 (1972) 1.
7r- p FORWARD ELASTIC SCATTERING NEAR 1 GeV/c J.M. ABILLON, A. BORG , M. CROZON, Th. LERAY, J.P. MENDIBURU and J. TO CQ U EV I LLE Laboratoire de Physique A tomique et Moleculaire, Coll~ge de France, Paris 5
Received 19 May 1972
Abstract: We have measured the differential cross section of the reaction n - p ~ n - p in the range 0.92 < cos 0c.m. ~<0.99 at 15 momenta between 0.875 and 1.580 GeV/c. The results we report complete the available data; previous measurements of this reaction do not extend beyond cos 0c.m.=0.90. We compare our experimental results with dispersion relation predictions. A comparison of our results for B, the slope of the differential cross section, with earlier results shows many discrepancies.
1. INTRODUCTION The pion beam conditions are the same as in ref. [1 ]. The experimental array consisted mainly in 3 magnetostrictive spark chambers telescopes. One o f them determined the incident particle direction. After the scattering in a 40 cm long liquid hydrogen target, a second telescope measured the scattered n direction, and a third one its deflection through an analysing magnet. A suitable array of scintillators selected the events, rejecting most of the inelastic events. The collection of the data was done by an online computer, which monitored the performance of the equipment. The overall efficiency of the spark chambers was sufficiently good that more than 95% of the triggered events could be analysed, using the CERN MAGFIT 3 program procedure. To select the elastic events, two tests have been concurently used. (a) The vertex of the interaction had to be inside the target (fig. la). (b) The m o m e n t u m of the scattered n was selected in a -+ 3 standard deviations interval around its central value (fig. lb). Depending on the energy 40% to 70% of the analysed events satisfied these criteria and were considered to be elastic events. A Monte Carlo program was used to compute the solid angles and to estimate the errors on the solid angles. We have considered two kinds of errors: * Ce travail a b6n4fici~ de l'aide du Commissariat h l'Energie Atomique. ** D. Ph. P. E., C.E.N. Saclay.
J.M. A billon et aL, ¢r p f o r w a r d elastic scattering
6 31
N bet'of eveol5
60~
n
,J]
ra
5,~ E
4.O.$Geg//cl
,5 '~- cm CI
N be,- of eveni',.,s 206
"100
.4
.52
.64
.75
.88
Mo-,entu,-o
"~0
2'°'"2 "I.12
f24
(G~v/~)
b
Fig. 1. (a) z-coordinate (along the beam direction) of the vertex of the interaction for a sample of events at 1.03 GeV/c. The arrows indicate the locations of: the last scintillator of the beam telescope (sj), the entrance and outgoing windows of the target (Fe and Fs respectively). (b) Histogram of the momentum of the scattered pion for the same sample of events as in la). (a) The statistical errors include the errors due to the limited number of events and also the errors coming from the various uncertainties in the Monte Carlo computation and in the geometrical reconstruction. (b) The normalization errors affect as a whole the results at one energy and include errors on the measurement of the lepton contamination of the beam (measured with a gas (~erenkov counter) and possible systematic geometrical errors. They decrease when the energy increases. For each incident momentum, 2500 to 4000 "full target" events were collected, and 1000 to 2000 "empty target". The resulting differential cross sections are given in table 1 and plotted on fig. 2, together with those of refs. [2, 3]. In the table errors are separately mentioned, as quoted above. As far as a comparison is possible, our results are in good agreement with earlier experiments.
12.6
1 1 . 3 5 ± 1.6
1.580
± 1.65
± 1.6
1.505
1.180
11.2
± 1.0
9.8
1.120
1.440
± 0.85
12.2
1.085
8.95 ± 0.95
±0.95
12.6
1.055
1 0 . 6 5 ± 1.25
12.9
± 1.0
15.3
1.030
1.360
14.70±0.80
1 6 . 8 5 ± 1.0
1.000
1.280
15.0
1 9 . 0 5 +-0.95
0.975
±0.75
±0.80
± 0.80
±0.90
± 0.50
± 0.80
8.85 ± 0.75
9.1
12.45 ± 1.2
8.35 ±0.60
7.1
9.35 ± 0.65
7.95 ± 0.55
10.7
14.7
1 4 . 7 5 ± 1.0
0.950
+0.85
1 0 . 4 5 ± 0.81 15.0
± 1.0
1 4 . 7 5 ± 1.0
6.20 ± 0.60
7.15 ± 0 . 8 5
13.0
0.98 ~ 0.97
0.99 ~ 0.98
0.925
0.875
Momentum (GeV/c)
cos Oc.m. interval
±0.90
±0.70
'-+0780
±0.85
± 0.50
± 0.60
± 0.60
8.85 ± 0.60
8.5
9.45 ± 0.60
8.20± 0.60
7.8
7.8
9 . 0 5 +- 0 . 5 5
10.0
13.1
13.9
14.35 + 0.85
12.5
13.05±0.90
9.70 ± 0.70
6 . 6 5 -+ 0 . 5 5
0 . 9 7 --, 0 . 9 6
±0.95
±0.90
±0.90
± 0.60
± 0.50
7.5
8.4
8.7
± 0.55
± 0.60
± 0.55
7.75 ± 0 . 6 0
7.3
7.85 ± 0 . 6 0
9.6
9.55 + 0.75
14.8
14.5
14.55 ± 0.95
12.35± 0.95
12.5
8.95 ± 0.80
5.30 ± 0.60
0 . 9 6 --* 0 . 9 5
Table 1 D i f f e r e n t i a l cross s e c t i o n s ( m b / s r ) .
± 1.4
± 1.25
± 1.15
± 0.70
7.3
8.1
7.3
7.7
± 0.55
± 0.60
± 0.55
+- 0 . 6 0
6.55 ± 0.50
7.6
8.65 + 0.70
9.85-+ 0 . 9 0
11.95 + 1.05
13.2
13.7
1 2 . 8 5 ± 1.3
13.2
9 . 6 0 ± 1.20
6 . 1 5 ± 1.05
0 . 9 5 -+ 0 . 9 4
+ 1.35
± 0.75
6.4
6.5
6.6
± 0.55
± 0.60
± 0.60
7.15 ± 0 . 5 5
6.4
4 . 6 5 ± 0.85
7.75 ± 1.05
8.3
14.25 ± 2.05
0 . 9 4 -~ 0 . 9 3
3 3
7.4 ± 0 . 7 5
3
3
3
~.2
t.6
1
~.3
4.5
4.6
L8
5
5
5.2
Normal±sat±on error (%)
6.0 ± 0 . 8 0
0 . 9 3 -+ 0 . 9 2
bo
J.M. A billon et aL, n - p forward elastic scattering
633
10 °
sI
GeV/c
i
"--~e
o.v/~
]
10
10 5 1.36 GeV/c 10 1
"~4,4 OeV/c
OeV/c
10 5 20
"q
S
5~
I
.90
.80
.70
I
cos e
.90
80
.70
cos
Fig. 2. Differential cross section in mb/sr as function of cos 0c.m. at the different energies: this experiment. ~ Brody et ak ~, Duke et al. Solid lines axe best fits (see text). 2. C O U L O M B A N D N U C L E A R S C A T T E R I N G In the angular range here studied, the C o u l o m b effect is rather small but n o t negligible. In order to take account of it, we have used the theoretical formalism of West and Yennie [4] which includes b o t h real and imaginary radiative corrections.
J.M. Abillon et al., ~r- p forward elastic scattering
634
Table 2 do
Momentum
~-~ (0°c.m.)
B (GeV - 2
(GeV/c)
(mb/sr)
(log. slope at 0 ° )
0,875
6.70 _+ 1.00
7.20 -+ 1.40
0,925
11.30 -+ 1.10
10.80 ± 0.85
0.950
16.50 -+ 0.80
11.80 ± 0.60
0.975
17.10 ± 0.85
11.80 ± 0.80
1,000
18.50 ± 1.60
10.10 +- 0,45
1.030
18.50-+ 1.30
9.00 ± 0.65
1.055
17.30 ± 1.50
8.00 ± 0.80
1.085
12.50 ± 0.75
7.50-+ 0.50
1.120
12.00 +- 1.20
6.90 -+ 0.50
1.180
11.40 ± 1.15
7.80 ± 0.35
1.280
8.50 -+ 0.45
4.70 +- 0.70
1.360
10.50 ± 0.40
6.90 ± 0.40
1.440
11.50 ± 1.05
7.50 -+ 0.30
1.505
10.30 ± 0.50
6.90 ± 0.30
1.580
11.30 +- 0.55
7.10 -+ 0.35
It can be s h o w n t h a t , in t h e range o f s a n d t here c o n c e r n e d , t h e real radiative corr e c t i o n s are negligible. T h u s o n e c a n write the d i f f e r e n t i a l e x p e r i m e n t a l cross sections:
d o _ l f c l 2 + 2 f c I m f N [13 cos ~q5 -- sin ~ l dt
+ ( 1 + 182) Im f 2N
w h e r e f c is the C o u l o m b a m p l i t u d e ; f N is the n u c l e a r a m p l i t u d e , w i t h
Re & 18= i m f N
'
a4~ is an a n a l y t i c e x p r e s s i o n given in ref. [5] a n d r e p r e s e n t s t h e p h a s e b e t w e e n Coulomb and nuclear amplitudes. Having p a r a m e t r i z e d f N b y Im f N ( t ) = Im f N (0) exp ~ B t , we have f i t t e d the values o f dON/dt ( 0 °) a n d B o n the e x p e r i m e n t a l results (solid lines o n fig. 2). T a b l e 2 a n d fig. 3 give the results o f these fits.
J.M. A billon et al., 7r-p forward elastic scattering
635
20
a8
2o
,
I''t
40
! L
I
p,.~ [aov/c) b Fig. 3. (a) Differential cross section at 0 ° in mb/st extrapolated from data and given by dispersion relations predictions: ~i our results, o values given by Brody et al., - - predictions by Hohler and Straus, - - - prediction by Mendiburu. (b) Logarithmic slope of the differential cross sections at 0 ° (B) in GeV-2: ~i our results. $ a compilation by Lasinski et al. In fig. 3a the values of dON/d~2 (0 °) are plotted concurrently with 3 different predictions: (a) d o N / d ~ (0 °) o b t a i n e d by Brody et al. from their results. (b) Dispersion relations predictions by HOhler and Strauss [5]. In this computation, the dispersion integrals are written for the even and odd isospin c o m b i n a t i o n s o f the lrN amplitude. F u r t h e r m o r e , the odd c o m b i n a t i o n is decomposed into a low
636
J.M. A billon et aL, rt- p forward elastic scattering
energy term and a background term. The latter is fitted on experimental data for charge-exchange scattering. For the m o m e n t u m range 0,5 to 2.65 GeV/c, total cross sections by Carter et al. [6] are used. (c) Dispersion relations computed by one of us [7] who used a dispersion relation with three substractions for the 7r-N amplitudes. Here the results of Carter et al. [6] are left out because they seem to be shifted in energy [8]. Finally, the results for B (slope of the scattering amplitude) are plotted in fig. 3b, and compared with those given in a compilation by Lasinski et al. [9]. There are many discrepancies. They probably come from the fact that there were very few experimental points in the very forward region, and that made extrapolations hazardous.
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