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c
PHYSICS LETTERS
Volume SOB, number 3
lOJune
THE REAL PART OF THE FORWARD SCATTERING AMPLITUDE IN II*p ELASTIC SCATTERING BELOW 2 GeV/c P. BAILLON, C. BRICMAN' , Ph. EBERHARD’, M. FERRO-LUZZI, J.M. PERREAU, R.D. TRIPP’ and T. YPSILANTIS CERN, Geneva, Switzerland
Y. DECLAIS3 and J. SEGUINOT Universityof Caen4, France Received 1 April 1974 The differential cross section for rr*p elastic scattering below 2 GeV/c has been measured at small forward pion angles by an electronics experiment. The interference effects observed between the Coulomb and the nuclear interaction have been used to determine the magnitude and sign of the real parts of the n’p forward scattering amplitude. The latter are compared to the values predicted by the dispersion relations.
The differential cross sections of rr*p elastic scattering have been measured over the angular region between - 20 and - 200 mrad at several incident momenta below 2 GeV/c. The interference effects between Coulomb and nuclear scattering observed over the above angles have then been used to determine the real part of the n*p forward scattering amplitude. These results are the first direct measurements of the real part in np elastic scattering below 2 GeV/c. We compare them with the predictions from dispersion relations. The experiment was performed at the CERN proton-synchroton using the apparatus and procedure described in ref. [l] . Intensities of up to 2 X 105 pions per burst were used in data acquisition. The beam anticoincidence requirement (C4 of ref. [ 1 ] ) is much more useful in this case than in the K runs mainly because of the reduced decay rate. The increase in acquisition rate over that without the beam anticoincidence is of the order of 10 to 20. Another essential feature of the method is the 1-1detection system consisting of the iron bloc and C, counter [l] . In contrast with the Krc2 decay, the n-+p + v decay at our momenta exhibits a Jacobian peak just over the Coulomb-nuclar interference region. This, plus the fact that mul’ IISN. ’ LBL, University of California, Berkeley. 3 Now at CERN. 4 Work supported by IN2P3. * See next page.
tiple scattering spreads out the Jacobian peak for the full target runs, perturbs the full-empty subtraction to the point of simulating negative cross sections at the peak position. Therefore, the identification and rejection of the direct beam decays across the target is here an essential requirement. The reconstruction procedure is the same as in ref. [ 11. A summary of the data taken and accepted for each momentum and reaction is shown in table 1. The large reduction factor is essentially due to the small angle scatters retained by the C4 anticoincidence because of the beam spread. The corrections applied to the data in order to calculate the differential cross sections are similar to those introduced for the K data. The decay corrections are of course smaller; the backward-scattering contribution is important for n+p at 1 GeV/c (- 15 % between c = 0.002 and 0.02 GeV2) and negligible for rrp at 2 GeV/c. The corrected cross sections are plotted in fig. 1 as a function of the momentum transfer t. An example of the problems which may occur when the muon background is not removed can be noticed in the n+p data at 630 MeV/c. At such a low momentum the iron thickness needed for the absorption of the pions also stops most of the muons, thereby producing the spurious enhancement near t = 0.0018 GeV2. In this particular case we have been obliged to ignore the b-counter information and all data below t = 0.0023 GeV2 *. 387
PHYSICS LETTERS
Volume SOB, number 3
10June 1974
___-___... coulomb _---.-
nuclear - _._
interference
ti)
optical
point
”
0
0.5 Incident
1.5 1.0 lab. nwnentum
2.0 ( GeV/c )
2.5
Fig. 2. Predicted values of (Yfor n’p from dispersion relations (31 and measured values from this experiment. The shaded regions give an estimate of the error band of the dispersion relations calculation.
IO
IO’
IO2
IO 0
004
0.00
t
(GeV2)
’ Luckily the interference effects at this momentum are so spectacularly large that even the restricted t-range is sufficient to determine the real part of the forward scattering amplitude. Thus we have not gone through the alternative cumbersome procedure of folding in an artificial multiple scattering to the empty target events before the subtraction
Fig. 1. n+p and n-p differential cross sections as a function of the momentum transfer for the incident momenta given on the graphs. The full circles represent data for which the geometrical acceptance correction is either not needed or is smaller than _ 10%. The empty circles, not used in the fit, have been obtained with acceptance corrections larger than 1: 10%. The region of the interference is shown in detail by the insets. The points at t = 0 give the forward elastic cross section expected from the total cross section of ref. [3] vla the optical theorem for a zero real part. The curves in the insets show the contributions due to the Coulomb, nuclear and interference cross sections.
388
PHYSICS LETTERS
Volume 50B, number 3
Table 1 Total data taken (all categories) and number of events after reconstruction and cuts. F is for full- and E for empty-target data. A cut-off in momentum transfer q > 20 MeV/c is required on the accepted events. Momentum
Triggers (106)
(ceV/c)
F
E
Events accepted (103) F E
(a) r-p
1 .OlS 1.527 2.004
2.1 2.1 2.1
1.1 1.4 1.1
113.5 59.2 72.6
4.1 4.2 4.4
(b) n+p
0.619 1.009 1.521 1.999
1.8 2.1 2.5 2.8
1.1 1.1 1.1 1.1
92.4 85.1 204.8 140.4
45.4 11.2 11.0 11.0
As in ref. [ 11, we fit the data to the expression
do/dt =_4(flr)-2(1
+ r/O.71)-8 t Bof(l
-2Qot~(~cos6
+02)ebbt
+ Qsin6)(/3r)-’
(1 t r/O.71)-4 eebt12,
(1)
where (Yis the ratio of the real to the imaginary part of the forward scattering amplitude and b is the slope of the exponential representing the nuclear scattering. These are the two free parameters of the fit. The above three terms represent the Coulomb interaction, the nuclear interaction and the contribution due to the Coulomb-nuclear interference. The cross section units are mb, the momentum transfer r is in GeV2, the constants are A = 260.6 X 1OS6 and B = 0.05 11; Q is + 1 for rri: respectively. The Coulomb phase shift
10June1974
is 6 and has been given the form 6 = - [ln (9.5 r) + 0.577)/ 137 fl suggested by ref. [2]. For the total cross section ot we have used the values obtained in ref. [3] from a smooth interpolation of the available total cross section measurements. The results of the fit are given in table 2 and shown by the solid curve in fig. 1 (the data used in the fit are indicated by the full circles). The agreement between the fitted curves and the data is quite good and far from trivial if one recalls that the absolute normalisation of the Coulomb term in eq. (1) leaves little room for adjustment in the sensitive small-r region (shown in the insets of fig. 1). We have also systematically fitted the data using more flexible parametrizations such as: (i) assuming a linear t-dependence on either OLorb, (ii) leaving ot as a free parameter, (iii) introducing an overall free scale factor on the cross sections. The conclusion of this study is that fits with more than the two original parameters are not warranted by the data. In particular, the hypothesis of a constant (Yand b over the fitted range of r (see table 2) is consistent with our measurements. Fig. 2 shows our values of cwcompared to those calculated in ref. [3] by means of dispersion relations. The uncertainties associated to the latter calculation are not easy to assess. The shaded areas along the curves of fig. 2 represent an estimate of the typical error band which could be associated to the dispersion relations calculation [4]. We have also taken into account the observed variation between different tabulations available in the literature [3,5]. This, together with the additional source of uncertainty coming from the momentum scale (particularly important in the region of steeply rising (Y’S)allows us to conclude that
Table 2 Results of the fits. The number of degrees of freedom ND is indicated beside the x2. The limits of the fitted region are rmin and rmax. The real part of the forward scattering amplitude (D) is in the laboratory system and has been derived from cxand ot. Momentum (&V/c
OL
)
b
xzWD)
rmin lrnax (lo-2 GeV2)
D
(fm)
(a) n-p
1.015 1.527 2.004
-0.03 f 0.03 -0.15 f 0.03 -0.11 f 0.02
6.0 f 0.5 6.3 i -0.2 7.7 + 0.2
28.9(31) 57.8(52) 48.6(54)
0.09 0.12 0.14
3.8 9.0 9.7
-0.06 f 0.06 -0.32 f 0.05 -0.31 * 0.06
(b) rr+p
0.619 1.009 1.521 1.999
-1.98 -0.29 -0.22 -0.29
0.5 0.2 6.5 5.4
9.4(14) 28.3(30) 50.5(54) 52.3(53)
0.23 0.15 0.12 0.16
1.7 4.0 10.0 9.7
-0.97 -0.29 -0.55 -0.68
i f f f
0.05 0.02 0.02 0.02
* 3.3 f 0.7 + 0.1 f 0.2
* 0.02 f 0.02 + 0.04 f 0.05
389
Volume 50B, number 3
PHYSICS LETTERS
lOJune
the overall agreement between dispersion relations and measurements is quite good throughout the region examined.
[2] M.P. Lecher, Nucl. Pbys. B2 (1967) 525. [ 31 G. Hijhler and H.P. Jakob, Tables of pion-nucleon forward amplitudes, Karlsrube University (1972) unpublished. [4] E. Ferrari, University of Rome. Internal note 382 (1972)
References
unpublished. [5 ] G. H6hler and R. Strauss, Karlsruhe University report (1971) unpublished; A.A. Carter and J.R. Carter, Queen Mary College Report. (London 1973) unpublished.
[l] P. Baillon et al., whys. Lett. 50B (1974) 377.
390
Volume SOB, number 3
lOJune
THE REAL PART OF THE FORWARD SCATTERING AMPLITUDE IN II*p ELASTIC SCATTERING BELOW 2 GeV/c P. BAILLON, C. BRICMAN' , Ph. EBERHARD’, M. FERRO-LUZZI, J.M. PERREAU, R.D. TRIPP’ and T. YPSILANTIS CERN, Geneva, Switzerland
Y. DECLAIS3 and J. SEGUINOT Universityof Caen4, France Received 1 April 1974 The differential cross section for rr*p elastic scattering below 2 GeV/c has been measured at small forward pion angles by an electronics experiment. The interference effects observed between the Coulomb and the nuclear interaction have been used to determine the magnitude and sign of the real parts of the n’p forward scattering amplitude. The latter are compared to the values predicted by the dispersion relations.
The differential cross sections of rr*p elastic scattering have been measured over the angular region between - 20 and - 200 mrad at several incident momenta below 2 GeV/c. The interference effects between Coulomb and nuclear scattering observed over the above angles have then been used to determine the real part of the n*p forward scattering amplitude. These results are the first direct measurements of the real part in np elastic scattering below 2 GeV/c. We compare them with the predictions from dispersion relations. The experiment was performed at the CERN proton-synchroton using the apparatus and procedure described in ref. [l] . Intensities of up to 2 X 105 pions per burst were used in data acquisition. The beam anticoincidence requirement (C4 of ref. [ 1 ] ) is much more useful in this case than in the K runs mainly because of the reduced decay rate. The increase in acquisition rate over that without the beam anticoincidence is of the order of 10 to 20. Another essential feature of the method is the 1-1detection system consisting of the iron bloc and C, counter [l] . In contrast with the Krc2 decay, the n-+p + v decay at our momenta exhibits a Jacobian peak just over the Coulomb-nuclar interference region. This, plus the fact that mul’ IISN. ’ LBL, University of California, Berkeley. 3 Now at CERN. 4 Work supported by IN2P3. * See next page.
tiple scattering spreads out the Jacobian peak for the full target runs, perturbs the full-empty subtraction to the point of simulating negative cross sections at the peak position. Therefore, the identification and rejection of the direct beam decays across the target is here an essential requirement. The reconstruction procedure is the same as in ref. [ 11. A summary of the data taken and accepted for each momentum and reaction is shown in table 1. The large reduction factor is essentially due to the small angle scatters retained by the C4 anticoincidence because of the beam spread. The corrections applied to the data in order to calculate the differential cross sections are similar to those introduced for the K data. The decay corrections are of course smaller; the backward-scattering contribution is important for n+p at 1 GeV/c (- 15 % between c = 0.002 and 0.02 GeV2) and negligible for rrp at 2 GeV/c. The corrected cross sections are plotted in fig. 1 as a function of the momentum transfer t. An example of the problems which may occur when the muon background is not removed can be noticed in the n+p data at 630 MeV/c. At such a low momentum the iron thickness needed for the absorption of the pions also stops most of the muons, thereby producing the spurious enhancement near t = 0.0018 GeV2. In this particular case we have been obliged to ignore the b-counter information and all data below t = 0.0023 GeV2 *. 387
PHYSICS LETTERS
Volume SOB, number 3
10June 1974
___-___... coulomb _---.-
nuclear - _._
interference
ti)
optical
point
”
0
0.5 Incident
1.5 1.0 lab. nwnentum
2.0 ( GeV/c )
2.5
Fig. 2. Predicted values of (Yfor n’p from dispersion relations (31 and measured values from this experiment. The shaded regions give an estimate of the error band of the dispersion relations calculation.
IO
IO’
IO2
IO 0
004
0.00
t
(GeV2)
’ Luckily the interference effects at this momentum are so spectacularly large that even the restricted t-range is sufficient to determine the real part of the forward scattering amplitude. Thus we have not gone through the alternative cumbersome procedure of folding in an artificial multiple scattering to the empty target events before the subtraction
Fig. 1. n+p and n-p differential cross sections as a function of the momentum transfer for the incident momenta given on the graphs. The full circles represent data for which the geometrical acceptance correction is either not needed or is smaller than _ 10%. The empty circles, not used in the fit, have been obtained with acceptance corrections larger than 1: 10%. The region of the interference is shown in detail by the insets. The points at t = 0 give the forward elastic cross section expected from the total cross section of ref. [3] vla the optical theorem for a zero real part. The curves in the insets show the contributions due to the Coulomb, nuclear and interference cross sections.
388
PHYSICS LETTERS
Volume 50B, number 3
Table 1 Total data taken (all categories) and number of events after reconstruction and cuts. F is for full- and E for empty-target data. A cut-off in momentum transfer q > 20 MeV/c is required on the accepted events. Momentum
Triggers (106)
(ceV/c)
F
E
Events accepted (103) F E
(a) r-p
1 .OlS 1.527 2.004
2.1 2.1 2.1
1.1 1.4 1.1
113.5 59.2 72.6
4.1 4.2 4.4
(b) n+p
0.619 1.009 1.521 1.999
1.8 2.1 2.5 2.8
1.1 1.1 1.1 1.1
92.4 85.1 204.8 140.4
45.4 11.2 11.0 11.0
As in ref. [ 11, we fit the data to the expression
do/dt =_4(flr)-2(1
+ r/O.71)-8 t Bof(l
-2Qot~(~cos6
+02)ebbt
+ Qsin6)(/3r)-’
(1 t r/O.71)-4 eebt12,
(1)
where (Yis the ratio of the real to the imaginary part of the forward scattering amplitude and b is the slope of the exponential representing the nuclear scattering. These are the two free parameters of the fit. The above three terms represent the Coulomb interaction, the nuclear interaction and the contribution due to the Coulomb-nuclear interference. The cross section units are mb, the momentum transfer r is in GeV2, the constants are A = 260.6 X 1OS6 and B = 0.05 11; Q is + 1 for rri: respectively. The Coulomb phase shift
10June1974
is 6 and has been given the form 6 = - [ln (9.5 r) + 0.577)/ 137 fl suggested by ref. [2]. For the total cross section ot we have used the values obtained in ref. [3] from a smooth interpolation of the available total cross section measurements. The results of the fit are given in table 2 and shown by the solid curve in fig. 1 (the data used in the fit are indicated by the full circles). The agreement between the fitted curves and the data is quite good and far from trivial if one recalls that the absolute normalisation of the Coulomb term in eq. (1) leaves little room for adjustment in the sensitive small-r region (shown in the insets of fig. 1). We have also systematically fitted the data using more flexible parametrizations such as: (i) assuming a linear t-dependence on either OLorb, (ii) leaving ot as a free parameter, (iii) introducing an overall free scale factor on the cross sections. The conclusion of this study is that fits with more than the two original parameters are not warranted by the data. In particular, the hypothesis of a constant (Yand b over the fitted range of r (see table 2) is consistent with our measurements. Fig. 2 shows our values of cwcompared to those calculated in ref. [3] by means of dispersion relations. The uncertainties associated to the latter calculation are not easy to assess. The shaded areas along the curves of fig. 2 represent an estimate of the typical error band which could be associated to the dispersion relations calculation [4]. We have also taken into account the observed variation between different tabulations available in the literature [3,5]. This, together with the additional source of uncertainty coming from the momentum scale (particularly important in the region of steeply rising (Y’S)allows us to conclude that
Table 2 Results of the fits. The number of degrees of freedom ND is indicated beside the x2. The limits of the fitted region are rmin and rmax. The real part of the forward scattering amplitude (D) is in the laboratory system and has been derived from cxand ot. Momentum (&V/c
OL
)
b
xzWD)
rmin lrnax (lo-2 GeV2)
D
(fm)
(a) n-p
1.015 1.527 2.004
-0.03 f 0.03 -0.15 f 0.03 -0.11 f 0.02
6.0 f 0.5 6.3 i -0.2 7.7 + 0.2
28.9(31) 57.8(52) 48.6(54)
0.09 0.12 0.14
3.8 9.0 9.7
-0.06 f 0.06 -0.32 f 0.05 -0.31 * 0.06
(b) rr+p
0.619 1.009 1.521 1.999
-1.98 -0.29 -0.22 -0.29
0.5 0.2 6.5 5.4
9.4(14) 28.3(30) 50.5(54) 52.3(53)
0.23 0.15 0.12 0.16
1.7 4.0 10.0 9.7
-0.97 -0.29 -0.55 -0.68
i f f f
0.05 0.02 0.02 0.02
* 3.3 f 0.7 + 0.1 f 0.2
* 0.02 f 0.02 + 0.04 f 0.05
389
Volume 50B, number 3
PHYSICS LETTERS
lOJune
the overall agreement between dispersion relations and measurements is quite good throughout the region examined.
[2] M.P. Lecher, Nucl. Pbys. B2 (1967) 525. [ 31 G. Hijhler and H.P. Jakob, Tables of pion-nucleon forward amplitudes, Karlsrube University (1972) unpublished. [4] E. Ferrari, University of Rome. Internal note 382 (1972)
References
unpublished. [5 ] G. H6hler and R. Strauss, Karlsruhe University report (1971) unpublished; A.A. Carter and J.R. Carter, Queen Mary College Report. (London 1973) unpublished.
[l] P. Baillon et al., whys. Lett. 50B (1974) 377.
390