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c
Physics Letters B 305 (1993) 18-22 North-Holland
PHYSICS LETTERS B
Antiproton-4He interactions at 200 MeV/c PS 179 Collaboration F. Balestra a,b Yu.A. Batusov c, G. Bendiscioli d S. Bossolasco a,b M.P. Bussa a,b L. Busso a,b, S.A. Bunyatov c, K.M. Danielsen e, I.V. Falomkin c, L. Fava a,b, L, Ferrero a.b, V. Filippini d, C. Guaraldo f A. Haatuft g, A. Halsteinslid g, T. Jakobsen e, E. Lodi-Rizzini h.b, A. Maggiora a,b, K. Myklebost g, F. Nichitiu f'~, J.M. Olsen g, D. Panzieri a.b, G. Piragino a,b, G.B. Pontecorvo e, A. Rotondi d, A.M. Rozhdestvensky ¢, P. Salvini d, M.G. Sapozhnikov ~, F. Tosello a,b, V.I. Tretyak d,~ and A. Zenoni d b ¢ d e f s h
Istituto di Fisica Generale "A. Avogadro", University of Turin, 1-10125 Turin Italy 1NFN-Sezionedi Torino, 1-10125 Turin, Italy Joint Institute for Nuclear Research, 101 000 Dubna, Russian Federation Dipartimento di Fisica Nucleare e Teorica, University of Pavia, and INFN - Sezione di Pavia, 1-27100 Pavia, Italy Physics Department, University of Oslo, N-0316 Oslo, Norway Laboratori Nazionali di Frascati dell7NFN, 1-00044 Frascati, Italy Physics Department, University of Bergen, N-5007 Bergen, Norway Dipartimento di Automazione Industriale, University of Brescia, Brescia Italy
Received 3 November 1992; revised manuscript received 25 February 1993
The differential cross sections for antiproton elastic scattering on 4He at 192.8 MeV/c are measured. The annihilation cross section aa= (377.6_+8.0) mb, the elastic cross section ae~=(206.3-+6.6) mb and the total p 4He interaction cross section ato,= (583.9 + 10.4) mb are determined. The ratio of the real to imaginary part of the forward p 4He amplitude is found: p= 0.17+024--0.33 Partial wave analysis reveals that the S, P and D waves are essential in this energy region. •
The experimental data on a n t i p r o t o n interaction with light nuclei provide valuable information for an u n d e r s t a n d i n g of the a n t i p r o t o n - n u c l e u s dynamics, for example, for determining the parameters of the a n t i p r o t o n - n u c l e u s potential. Since a reliable description of the elastic scattering is a necessary condition for any adequate model ofpA-scattering, any new information on the differential elastic scattering cross sections serves as a test for the various models of/TA-interaction. Besides this, the data on elastic scattering on the lightest nuclei can be used for determ i n i n g the parameters of the elementary amplitude of the a n t i p r o t o n - n e u t r o n interaction which, owing to the absence of good antineutron beams, are not well known. At present data are available on the elastic scatterOn leave from JINR, Dubna, Russian Federation. 18
ing of antiprotons on deuterium [ 1,2], on 12C, 4°Ca and 2°Spb at 300 and 600 M e V / c [3,4], and on 160 and 180 at 600 M e V / c [5] and on 4He [6] as well. The last result was obtained by our group in the PSI 79 ( C E R N ) experiment. We have observed that at 600 M e V / c the p 4He elastic scattering exhibits a diffraction pattern typical of scattering on a strongly absorbing disk. The fuzzyblack-disk model [7] and Glauber model calculations [8] were found to provide a good agreement with the experimental data. Here we present the results of the PS-179 ( C E R N ) experiment on the investigation of the p 4He interaction at 192.8 M e V / c ( Tki, = 19.6 MeV). At this energy the 6 4He interaction includes only elastic scattering and annihilation, being below the threshold for charge-exchange (fl, a) and 4He break-up (p, f f ) reactions.
0370-2693/93/$ 06.00 © 1993 Elsevier Science Publishers B.V. All rights reserved.
Volume 305, number 1,2
PHYSICS LETTERS B
The measurements were performed in the LEAR antiproton beam at CERN using a streamer chamber filled with helium at atmospheric pressure placed in a magnetic field. A detailed description of the experimental apparatus can be found in ref. [ 9 ]. Approximately l05 pictures were processed. We scanned them twice. A zone 54 cm long at the center of the chamber was chosen for multiplicity and cross sections measurements. As a result we have found 2135 events which multiplicity other than 2, which are obviously annihilation events, and 1431 two-prong events, which may be either elastic scattering or annihilation events. The efficiency of scanning was equal to 99.9%. 1414 of the found two-prong events were measured. The geometrical reconstruction of the measured events was performed by means of a program written within the HYDRA system [ 10 ]. The input errors used for the HYDRA geometrical reconstruction program were the same as in our previous work [ 11 ]. 1237 of these events passed the geometrical reconstruction. So the measurement and reconstruction procedure efficiency was e= 86.4°/0. The final sample of events comprises 1053 events with the CM scattering angle 0> 12 °. For the identification of the elastic scattering events we compared the characteristics of the secondary particles (momentum, scattering angle, range, etc. ) for each event with the corresponding quantities calculated assuming elastic scattering kinematics. Criteria involving the following four quantities were used to select elastic scattering events: ( 1 ) recoil nucleus angle; (2) coplanarity; (3) recoil nucleus range (if it stopped) or its momentum (if it does not stop ); (4) scattered antiproton momentum. 977 events passed all four criteria. The remaining 76 events are annihilations. Considering the measurement and reconstruction efficiency, the total number of annihilation two-prong events is (76.1237/1053)/0.864= 103. So the total number of the observed annihilation events is 2238. The corresponding/~ 4He annihilation cross section was obtained equal to tra= 377.6_+ 8.0 rob.
(1)
A systematic error was estimated to be less than 2.5% due to uncertainties in the target transparency and in the beam counting. Our previous measurements [ 12,13 ] of aa and of the multiplicities involving a
6 May 1993
lower statistics (only 600 events were measured) agree within the statistical errors with the present results. The charged prong multiplicity distribution is compared with those for annihilation of stopped antiprotons and at 608 MeV/c in table 1. One can see that the energy dependence of the multiplicity distribution is rather weak. Of special interest (see for instance, for astrophysics, refs. [ 15,16 ] ) are the reactions with 3He formation in the final state. The signature of these reactions in p 4He annihilation is unambiguous: they are the only processes with even number of prongs in the final state. The branching ratios of the 3He production at different energies are also given in table 1. One can see that they are decreasing with energy owing to the increasing of the final state interactions which destroyed 3He nuclei. It must be stressed that a streamer chamber operating at normal pressure represents a very good instrument for studying charged-particle multiplicities. For instance, the tracks of a 250 keV a-particle or a 160 keV proton are 1 cm long in the chamber and are quite visible. The differential cross sections were calculated taking into account the efficiencies of scanning, measurement and of geometrical reconstruction of events (which varies from e = 0.73 at small scattering angles up to e= 0.93 at large scattering angles), and also the efficiency due to the downstream anticoincidence counter (which increases from 0.83 to 1.0 with the
Table 1 Charged prong multiplicity distributions (5%) in p 4He annihilation at different energies [ 13,14]. M
At rest
1 2 3 4 5 6 7 8 9
3.36 5.03 33.48 12.26 35.68 3.51 6.24 0.19 0.24
(M) 3He+X(%)
+0.35 _+0.42 +-0.92 +_0.63 _+0.93 +_0.36 _+0.47 _+0.08 _+0.10
4.097_+0.072 21.0
+_0.9
198 MeV/c
608 MeV/c
5.94 4.60 32.62 10.81 36.51 2.64 6.40 0.22 0.22
5.80 4.32 29.53 8.12 41.17 2.99 8.07 0.19 0.12
+_0.50 +0.44 +-0.99 +_0.66 +_1.01 +_0.34 _+0.52 +0.10 +-0.10
4.025+-0.078 18.3
+_0.5
+_0.43 +-0.38 +-0.85 +0.51 _+0.92 +_0.31 _+0.51 +-0.08 _+0.07
4.181+_0.074 15.6
+_0.7
19
Volume 305, n u m b e r 1,2
PHYSICS LETTERS B
scattering angle in the laboratory system changing from 10 ° to 18 ° ). The obtained da/d£2 values are given in table 2. The experimental differential elastic scattering cross sections were fitted by the following expression:
(2)
da/dg2= IFco,l(0) +Fnud(0) I2 ,
where the nuclear amplitude Fnud (0) was taken in the form Fnucl(0) =ato, k ( i + p ) exp( - ½Bt) ( 1 - t / t o ) / 4 n . (3) Here k is the CM momentum of p, B is the slope parameter, t = 2k 2( 1 - cos 0) is the squared momentum transfer, atot is the total/~ 4He scattering cross section, p = Re Fnu~l( 0 ) / I m F,u~l (0), to is a complex parameter, corresponding to the zero of the scattering amplitude. Re to is determined by the position of the minimum in da/dg2, while Im to is related to the value o f d a / d t 2 at the minimum. The Coulomb amplitude Fcoul(0) was evaluated taking into account the finite dimensions of the 4He nucleus and of the antiproton applying the method described in ref. [ 17 ]. Table 2
de/d~2 at 192.8 MeV/c. da/dl2
6 May 1993
To determine the parameters of the amplitude Fnud(0) such as atot, P and B one should take into account that they are strongly correlated. To reduce the correlations we fixed some of them from additional experimental information and proceeded by steps. First we fitted the differential cross section in the whole angular range of our measurements. Two solutions were obtained, which differ by the sign of Im to. Both solutions give very close values of the other parameters and the same Z 2 in the fitting procedure. The quantity of the fit is put in evidence in fig. 1; it turns out that x 2 / N D F = 1.5. The set of parameters with Im to> 0 was used to calculate the total cross section of the elastic scattering: ~e~= f [Fnud(0)12d~=206.3-+6.6 m b .
(4)
From this value and using aa from ( 1 ) we obtained the total p 4He interaction cross section: ~tot =aa + a ~ =583.9_+ 10.4 m b .
(5)
Then, for a better determination of thep and B parameters that depend on the Fnuc~behavior in the forward direction, we fixed in (3) the value of ato, from (5) and fitted da/dg2 only for a small scattering angle region (0< 50 ° ) without the factor ( 1 - t / t o ) in (3). The following results were obtained:
(mb/sr)
Statistical error (mb/sr)
0cut (deg)
Bin width (deg)
P = --0-17+0"24-0.33
124.94 92.49 74.69 74.89 65.25 51.80 51.23 35.86 34.25 16.63 13.30 9.28 4.14 2.01 1.17 0.52 0.36 1.19 1.58 0.87 1.10
15.15 10.21 8.20 7.27 6.22 5.23 4.95 3.98 3.74 2.54 2.22 1.82 1.19 0.58 0.44 0.30 0.25 0.49 0.60 0.50 0.63
14.2 19.5 24.5 29.3 34.5 39.5 44.6 49.4 54.6 59.3 64.2 68.7 74.7 82.3 94.1 105.6 111.5 122.8 132.3 144.8 153.0
5 5 5 5 5 5 5 5 5 5 5 5 5 10 l0 10 10 10 10 10 10
The analysis of our elastic scattering data at 600 MeV/c [6] yielded the value p = 0 . 2 2 + 0 . 5 5 and B = 58.7 _+ 1.4 ( G e V / c ) - 2 . At 200 MeV/c the errors on the parameter p are quite large because the da/dl2 was measured starting from 0> 12 ° where the sensitivity to the variation o f p is not too strong. Nevertheless it seems that p changes sign in this region. It may be a reflection of the behavior ofp in thepp elastic amplitude. It is known [ 18-20] that near the threshold the parameter p varies very rapidly with energy. Whereas from p-atomic data it follows that p is large and negative ( p = - 1.08_+ 0.09 [ 18 ] ), the data at 200 MeV/c [19,20] reveal that p is close to zero. Owing to the Fermi smearing of the nucleon bound in 4He one may also expect the p parameter in p 4He scattering tends to be negative. However, a detailed analysis taking into account the pn interaction is needed. The knowledge of the parameters of the amplitude
20
,
B=83.1 _+4.1 (GeV/c) -2
(6)
Volume 305, number 1,2
PHYSICSLETTERSB
6 May 1993
Fnud(O) allows to perform the partial wave projection and to determine the partial wave amplitudes TL:
TL=½k(2L+ 1 ) ~ F , ud(0) PL(cos 0)d(cos 0) ,
i\
100
(7) where PL(cos 0) are Legendre polynomials. The values of TL are given in table 3. From inspection of table 3 one may conclude that in order to reproduce da/dg2 at 200 MeV/c it is necessary to take into account only S, P and D partial waves. This differs from the situation at 600 MeV/c where the partial waves up to L=7 contribute to da/df2 [6]. In fig. 1 the comparison with the "fuzzy black disk" model, i.e. a black disk with a diffuse boundary [ 21 ], is performed. This model was proved to be rather successful in the phenomenological analysis of antiproton elastic scattering on different nuclei [ 7 ]. In this model the effect of the surface diffuseness is taken into account by the function
D(O) = e x p [ -A2k2sin2(½0) ] ,
(8)
and the scattering cross section is given by IT
l...,", 2
da/d~: (kR2)21~) D 2 ( 0 ) ,
Table 3 Partial wave amplitudes TLfrom eq. (7).
0 1 2 3
set II ( (Im to<0)
setl (lm to>0)
cn
10
.Q
E 1 b 0.1
I I iI I I
0,01
LI
o .......
's'o . . . . . . .
1'6b . . . . . . .
i~b .....
CMS angle (degrees) Fig. 1. Differential p 4He elastic cross section at 192.8 MeV/c. Solid curve: Glauber model calculation. Dashed lines: black disk fit (short dashes) and fit by formula (2) (long dashes).
(9)
where x = 2kR sin(½0). The dashed line in fig. 1 corresponds to a fuzzy black disk model fit with R = 3 . 0 4 + 0 . 0 3 fm and A= 1.17+0.07 fm. Performing this fit we have averaged the calculated cross sections over bins of the angular distribution. One can see that this model is good in the forward direction but can not reproduce da/dO around the minimum and at large angles. In fig. 1 also a comparison between the experimental data and the predictions of the Glauber model (solid line) is performed. The calculations have been
L
"2"
Re TL
Im Tz
Re TL
Im Tz
-0.325 -0.221 - 0.073 -0.016
0.465 0.395 0.145 0.032
-0.045 -0.233 - 0.099 -0.024
0.537 0.387 0.129 0.027
made as described in refs. [8,22]. One can see that the Glauber model prediction overestimates da/dl2 in the forward direction by a factor of 1.5-2. However, at such low energy the very applicability of the Glauber model is strongly questionable. In conclusion, the antiproton-4He interaction at 192.8 MeV/c is investigated. Charged prong multiplicities in p 4He annihilation and the differential elastic cross section are measured. The/~ 4He annihilation cross section is found to be aa=377.6 +8.0 mb. The elastic cross section ae1=206.3+6.6 mb and the total/~ 4He cross section atot= 583.9 + 10.4 mb are obtained. From the fit of the differential elastic cross section the ratio of the real to imaginary part of the forward antiproton-nucleus amplitude is found: p = 0 17 +0.24 -- " --0.33" The partial wave decomposition of the antiproton-nucleus amplitude reveals that S, P and D-~vaves are essential at this energy. The fuzzy-black-disk model and Glauber model calculations do not provide the same good descrip21
Volume 305, number 1,2
PHYSICS LETTERS B
tion of the p 4He elastic scattering at 200 MeV/c, the one obtained at 600 MeV/c.
as
References [ 1 ] R. Bizzarri et al., Nuovo Cimento A 22 (1974) 225. [2] G. Bruge et al., Phys. Rev. C 37 (1988) 1345. [ 3 ] D. Garreta et al., Phys. Lett. B 135 (1984) 266. [4] D. Garreta et al., Phys. Lett. B 149 (1984) 64. [5] G. Bruge et al., Phys. Lett. B 169 (1986) 14. [6] Yu. A. Batusov et al., Sov. J. Nucl. Phys. 52 (1990) 776. [ 7 ] J. Lichtenstadt et al., Phys. Rev. C 32 (1985) 1096. [ 8 ] F. Balestra et al., in: Proc. First biennial Conf. on Low energy antiproton physics (World Scientific, Singapore, 1991 ) p. 245. [9 ] F. Balestra et al., Nucl. Instrum. Methods 234 (1985 ) 30.
22
6 May 1993
[ 10] W.G. Moorhead, Report CERN 60-33 (3/62); R.K. B~Sckand J. Zoll, Report CERN/D.PH.2°/Progr. 744. [ 11 ] F. Balestra et al., Nucl. lnstrum. Methods A 257 (1987) 114. [12] F. Balestra et al., Phys. Lett. B 165 (1985) 265. [ 13 ] F. Balestra et al., Nuovo Cimento A 100 ( 1988 ) 323. [ 14] G. Bendiscioli, Report FNT/BE-91/34 (Pavia, 1991 ). [15] V.M. Chechetkin et al., Phys. Len. B 118 (1982) 329. [ 16] Yu. A. Batusov el al., JINR Rapid Comm. 6 (1985) 11; Lett. Nuovo Cimento 41 (1984) 223. [ 17] K.M. Das and B.B. Deo, Phys. Rev. C 26 (1982) 211. [ 18] C.J. Batty, Rep. Prog. Phys. 52 (1989) 1165. [ 19 ] W. Briickner et al., Phys. Lett. B 158 ( 1985 ) 180. [20] L. Linsen et al., Nucl. Phys. A469 (1987) 726. [21 ] E.V. Inopin and Yu. A. Berezhnoy, Nucl. Phys. 63 (1965) 689. [ 22 ] G. Bendiscioli et al., Report FNT/BE-91/03 (Pavia, 1991 ), Nuovo Cimento, in press.
PHYSICS LETTERS B
Antiproton-4He interactions at 200 MeV/c PS 179 Collaboration F. Balestra a,b Yu.A. Batusov c, G. Bendiscioli d S. Bossolasco a,b M.P. Bussa a,b L. Busso a,b, S.A. Bunyatov c, K.M. Danielsen e, I.V. Falomkin c, L. Fava a,b, L, Ferrero a.b, V. Filippini d, C. Guaraldo f A. Haatuft g, A. Halsteinslid g, T. Jakobsen e, E. Lodi-Rizzini h.b, A. Maggiora a,b, K. Myklebost g, F. Nichitiu f'~, J.M. Olsen g, D. Panzieri a.b, G. Piragino a,b, G.B. Pontecorvo e, A. Rotondi d, A.M. Rozhdestvensky ¢, P. Salvini d, M.G. Sapozhnikov ~, F. Tosello a,b, V.I. Tretyak d,~ and A. Zenoni d b ¢ d e f s h
Istituto di Fisica Generale "A. Avogadro", University of Turin, 1-10125 Turin Italy 1NFN-Sezionedi Torino, 1-10125 Turin, Italy Joint Institute for Nuclear Research, 101 000 Dubna, Russian Federation Dipartimento di Fisica Nucleare e Teorica, University of Pavia, and INFN - Sezione di Pavia, 1-27100 Pavia, Italy Physics Department, University of Oslo, N-0316 Oslo, Norway Laboratori Nazionali di Frascati dell7NFN, 1-00044 Frascati, Italy Physics Department, University of Bergen, N-5007 Bergen, Norway Dipartimento di Automazione Industriale, University of Brescia, Brescia Italy
Received 3 November 1992; revised manuscript received 25 February 1993
The differential cross sections for antiproton elastic scattering on 4He at 192.8 MeV/c are measured. The annihilation cross section aa= (377.6_+8.0) mb, the elastic cross section ae~=(206.3-+6.6) mb and the total p 4He interaction cross section ato,= (583.9 + 10.4) mb are determined. The ratio of the real to imaginary part of the forward p 4He amplitude is found: p= 0.17+024--0.33 Partial wave analysis reveals that the S, P and D waves are essential in this energy region. •
The experimental data on a n t i p r o t o n interaction with light nuclei provide valuable information for an u n d e r s t a n d i n g of the a n t i p r o t o n - n u c l e u s dynamics, for example, for determining the parameters of the a n t i p r o t o n - n u c l e u s potential. Since a reliable description of the elastic scattering is a necessary condition for any adequate model ofpA-scattering, any new information on the differential elastic scattering cross sections serves as a test for the various models of/TA-interaction. Besides this, the data on elastic scattering on the lightest nuclei can be used for determ i n i n g the parameters of the elementary amplitude of the a n t i p r o t o n - n e u t r o n interaction which, owing to the absence of good antineutron beams, are not well known. At present data are available on the elastic scatterOn leave from JINR, Dubna, Russian Federation. 18
ing of antiprotons on deuterium [ 1,2], on 12C, 4°Ca and 2°Spb at 300 and 600 M e V / c [3,4], and on 160 and 180 at 600 M e V / c [5] and on 4He [6] as well. The last result was obtained by our group in the PSI 79 ( C E R N ) experiment. We have observed that at 600 M e V / c the p 4He elastic scattering exhibits a diffraction pattern typical of scattering on a strongly absorbing disk. The fuzzyblack-disk model [7] and Glauber model calculations [8] were found to provide a good agreement with the experimental data. Here we present the results of the PS-179 ( C E R N ) experiment on the investigation of the p 4He interaction at 192.8 M e V / c ( Tki, = 19.6 MeV). At this energy the 6 4He interaction includes only elastic scattering and annihilation, being below the threshold for charge-exchange (fl, a) and 4He break-up (p, f f ) reactions.
0370-2693/93/$ 06.00 © 1993 Elsevier Science Publishers B.V. All rights reserved.
Volume 305, number 1,2
PHYSICS LETTERS B
The measurements were performed in the LEAR antiproton beam at CERN using a streamer chamber filled with helium at atmospheric pressure placed in a magnetic field. A detailed description of the experimental apparatus can be found in ref. [ 9 ]. Approximately l05 pictures were processed. We scanned them twice. A zone 54 cm long at the center of the chamber was chosen for multiplicity and cross sections measurements. As a result we have found 2135 events which multiplicity other than 2, which are obviously annihilation events, and 1431 two-prong events, which may be either elastic scattering or annihilation events. The efficiency of scanning was equal to 99.9%. 1414 of the found two-prong events were measured. The geometrical reconstruction of the measured events was performed by means of a program written within the HYDRA system [ 10 ]. The input errors used for the HYDRA geometrical reconstruction program were the same as in our previous work [ 11 ]. 1237 of these events passed the geometrical reconstruction. So the measurement and reconstruction procedure efficiency was e= 86.4°/0. The final sample of events comprises 1053 events with the CM scattering angle 0> 12 °. For the identification of the elastic scattering events we compared the characteristics of the secondary particles (momentum, scattering angle, range, etc. ) for each event with the corresponding quantities calculated assuming elastic scattering kinematics. Criteria involving the following four quantities were used to select elastic scattering events: ( 1 ) recoil nucleus angle; (2) coplanarity; (3) recoil nucleus range (if it stopped) or its momentum (if it does not stop ); (4) scattered antiproton momentum. 977 events passed all four criteria. The remaining 76 events are annihilations. Considering the measurement and reconstruction efficiency, the total number of annihilation two-prong events is (76.1237/1053)/0.864= 103. So the total number of the observed annihilation events is 2238. The corresponding/~ 4He annihilation cross section was obtained equal to tra= 377.6_+ 8.0 rob.
(1)
A systematic error was estimated to be less than 2.5% due to uncertainties in the target transparency and in the beam counting. Our previous measurements [ 12,13 ] of aa and of the multiplicities involving a
6 May 1993
lower statistics (only 600 events were measured) agree within the statistical errors with the present results. The charged prong multiplicity distribution is compared with those for annihilation of stopped antiprotons and at 608 MeV/c in table 1. One can see that the energy dependence of the multiplicity distribution is rather weak. Of special interest (see for instance, for astrophysics, refs. [ 15,16 ] ) are the reactions with 3He formation in the final state. The signature of these reactions in p 4He annihilation is unambiguous: they are the only processes with even number of prongs in the final state. The branching ratios of the 3He production at different energies are also given in table 1. One can see that they are decreasing with energy owing to the increasing of the final state interactions which destroyed 3He nuclei. It must be stressed that a streamer chamber operating at normal pressure represents a very good instrument for studying charged-particle multiplicities. For instance, the tracks of a 250 keV a-particle or a 160 keV proton are 1 cm long in the chamber and are quite visible. The differential cross sections were calculated taking into account the efficiencies of scanning, measurement and of geometrical reconstruction of events (which varies from e = 0.73 at small scattering angles up to e= 0.93 at large scattering angles), and also the efficiency due to the downstream anticoincidence counter (which increases from 0.83 to 1.0 with the
Table 1 Charged prong multiplicity distributions (5%) in p 4He annihilation at different energies [ 13,14]. M
At rest
1 2 3 4 5 6 7 8 9
3.36 5.03 33.48 12.26 35.68 3.51 6.24 0.19 0.24
(M) 3He+X(%)
+0.35 _+0.42 +-0.92 +_0.63 _+0.93 +_0.36 _+0.47 _+0.08 _+0.10
4.097_+0.072 21.0
+_0.9
198 MeV/c
608 MeV/c
5.94 4.60 32.62 10.81 36.51 2.64 6.40 0.22 0.22
5.80 4.32 29.53 8.12 41.17 2.99 8.07 0.19 0.12
+_0.50 +0.44 +-0.99 +_0.66 +_1.01 +_0.34 _+0.52 +0.10 +-0.10
4.025+-0.078 18.3
+_0.5
+_0.43 +-0.38 +-0.85 +0.51 _+0.92 +_0.31 _+0.51 +-0.08 _+0.07
4.181+_0.074 15.6
+_0.7
19
Volume 305, n u m b e r 1,2
PHYSICS LETTERS B
scattering angle in the laboratory system changing from 10 ° to 18 ° ). The obtained da/d£2 values are given in table 2. The experimental differential elastic scattering cross sections were fitted by the following expression:
(2)
da/dg2= IFco,l(0) +Fnud(0) I2 ,
where the nuclear amplitude Fnud (0) was taken in the form Fnucl(0) =ato, k ( i + p ) exp( - ½Bt) ( 1 - t / t o ) / 4 n . (3) Here k is the CM momentum of p, B is the slope parameter, t = 2k 2( 1 - cos 0) is the squared momentum transfer, atot is the total/~ 4He scattering cross section, p = Re Fnu~l( 0 ) / I m F,u~l (0), to is a complex parameter, corresponding to the zero of the scattering amplitude. Re to is determined by the position of the minimum in da/dg2, while Im to is related to the value o f d a / d t 2 at the minimum. The Coulomb amplitude Fcoul(0) was evaluated taking into account the finite dimensions of the 4He nucleus and of the antiproton applying the method described in ref. [ 17 ]. Table 2
de/d~2 at 192.8 MeV/c. da/dl2
6 May 1993
To determine the parameters of the amplitude Fnud(0) such as atot, P and B one should take into account that they are strongly correlated. To reduce the correlations we fixed some of them from additional experimental information and proceeded by steps. First we fitted the differential cross section in the whole angular range of our measurements. Two solutions were obtained, which differ by the sign of Im to. Both solutions give very close values of the other parameters and the same Z 2 in the fitting procedure. The quantity of the fit is put in evidence in fig. 1; it turns out that x 2 / N D F = 1.5. The set of parameters with Im to> 0 was used to calculate the total cross section of the elastic scattering: ~e~= f [Fnud(0)12d~=206.3-+6.6 m b .
(4)
From this value and using aa from ( 1 ) we obtained the total p 4He interaction cross section: ~tot =aa + a ~ =583.9_+ 10.4 m b .
(5)
Then, for a better determination of thep and B parameters that depend on the Fnuc~behavior in the forward direction, we fixed in (3) the value of ato, from (5) and fitted da/dg2 only for a small scattering angle region (0< 50 ° ) without the factor ( 1 - t / t o ) in (3). The following results were obtained:
(mb/sr)
Statistical error (mb/sr)
0cut (deg)
Bin width (deg)
P = --0-17+0"24-0.33
124.94 92.49 74.69 74.89 65.25 51.80 51.23 35.86 34.25 16.63 13.30 9.28 4.14 2.01 1.17 0.52 0.36 1.19 1.58 0.87 1.10
15.15 10.21 8.20 7.27 6.22 5.23 4.95 3.98 3.74 2.54 2.22 1.82 1.19 0.58 0.44 0.30 0.25 0.49 0.60 0.50 0.63
14.2 19.5 24.5 29.3 34.5 39.5 44.6 49.4 54.6 59.3 64.2 68.7 74.7 82.3 94.1 105.6 111.5 122.8 132.3 144.8 153.0
5 5 5 5 5 5 5 5 5 5 5 5 5 10 l0 10 10 10 10 10 10
The analysis of our elastic scattering data at 600 MeV/c [6] yielded the value p = 0 . 2 2 + 0 . 5 5 and B = 58.7 _+ 1.4 ( G e V / c ) - 2 . At 200 MeV/c the errors on the parameter p are quite large because the da/dl2 was measured starting from 0> 12 ° where the sensitivity to the variation o f p is not too strong. Nevertheless it seems that p changes sign in this region. It may be a reflection of the behavior ofp in thepp elastic amplitude. It is known [ 18-20] that near the threshold the parameter p varies very rapidly with energy. Whereas from p-atomic data it follows that p is large and negative ( p = - 1.08_+ 0.09 [ 18 ] ), the data at 200 MeV/c [19,20] reveal that p is close to zero. Owing to the Fermi smearing of the nucleon bound in 4He one may also expect the p parameter in p 4He scattering tends to be negative. However, a detailed analysis taking into account the pn interaction is needed. The knowledge of the parameters of the amplitude
20
,
B=83.1 _+4.1 (GeV/c) -2
(6)
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Fnud(O) allows to perform the partial wave projection and to determine the partial wave amplitudes TL:
TL=½k(2L+ 1 ) ~ F , ud(0) PL(cos 0)d(cos 0) ,
i\
100
(7) where PL(cos 0) are Legendre polynomials. The values of TL are given in table 3. From inspection of table 3 one may conclude that in order to reproduce da/dg2 at 200 MeV/c it is necessary to take into account only S, P and D partial waves. This differs from the situation at 600 MeV/c where the partial waves up to L=7 contribute to da/df2 [6]. In fig. 1 the comparison with the "fuzzy black disk" model, i.e. a black disk with a diffuse boundary [ 21 ], is performed. This model was proved to be rather successful in the phenomenological analysis of antiproton elastic scattering on different nuclei [ 7 ]. In this model the effect of the surface diffuseness is taken into account by the function
D(O) = e x p [ -A2k2sin2(½0) ] ,
(8)
and the scattering cross section is given by IT
l...,", 2
da/d~: (kR2)21~) D 2 ( 0 ) ,
Table 3 Partial wave amplitudes TLfrom eq. (7).
0 1 2 3
set II ( (Im to<0)
setl (lm to>0)
cn
10
.Q
E 1 b 0.1
I I iI I I
0,01
LI
o .......
's'o . . . . . . .
1'6b . . . . . . .
i~b .....
CMS angle (degrees) Fig. 1. Differential p 4He elastic cross section at 192.8 MeV/c. Solid curve: Glauber model calculation. Dashed lines: black disk fit (short dashes) and fit by formula (2) (long dashes).
(9)
where x = 2kR sin(½0). The dashed line in fig. 1 corresponds to a fuzzy black disk model fit with R = 3 . 0 4 + 0 . 0 3 fm and A= 1.17+0.07 fm. Performing this fit we have averaged the calculated cross sections over bins of the angular distribution. One can see that this model is good in the forward direction but can not reproduce da/dO around the minimum and at large angles. In fig. 1 also a comparison between the experimental data and the predictions of the Glauber model (solid line) is performed. The calculations have been
L
"2"
Re TL
Im Tz
Re TL
Im Tz
-0.325 -0.221 - 0.073 -0.016
0.465 0.395 0.145 0.032
-0.045 -0.233 - 0.099 -0.024
0.537 0.387 0.129 0.027
made as described in refs. [8,22]. One can see that the Glauber model prediction overestimates da/dl2 in the forward direction by a factor of 1.5-2. However, at such low energy the very applicability of the Glauber model is strongly questionable. In conclusion, the antiproton-4He interaction at 192.8 MeV/c is investigated. Charged prong multiplicities in p 4He annihilation and the differential elastic cross section are measured. The/~ 4He annihilation cross section is found to be aa=377.6 +8.0 mb. The elastic cross section ae1=206.3+6.6 mb and the total/~ 4He cross section atot= 583.9 + 10.4 mb are obtained. From the fit of the differential elastic cross section the ratio of the real to imaginary part of the forward antiproton-nucleus amplitude is found: p = 0 17 +0.24 -- " --0.33" The partial wave decomposition of the antiproton-nucleus amplitude reveals that S, P and D-~vaves are essential at this energy. The fuzzy-black-disk model and Glauber model calculations do not provide the same good descrip21
Volume 305, number 1,2
PHYSICS LETTERS B
tion of the p 4He elastic scattering at 200 MeV/c, the one obtained at 600 MeV/c.
as
References [ 1 ] R. Bizzarri et al., Nuovo Cimento A 22 (1974) 225. [2] G. Bruge et al., Phys. Rev. C 37 (1988) 1345. [ 3 ] D. Garreta et al., Phys. Lett. B 135 (1984) 266. [4] D. Garreta et al., Phys. Lett. B 149 (1984) 64. [5] G. Bruge et al., Phys. Lett. B 169 (1986) 14. [6] Yu. A. Batusov et al., Sov. J. Nucl. Phys. 52 (1990) 776. [ 7 ] J. Lichtenstadt et al., Phys. Rev. C 32 (1985) 1096. [ 8 ] F. Balestra et al., in: Proc. First biennial Conf. on Low energy antiproton physics (World Scientific, Singapore, 1991 ) p. 245. [9 ] F. Balestra et al., Nucl. Instrum. Methods 234 (1985 ) 30.
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[ 10] W.G. Moorhead, Report CERN 60-33 (3/62); R.K. B~Sckand J. Zoll, Report CERN/D.PH.2°/Progr. 744. [ 11 ] F. Balestra et al., Nucl. lnstrum. Methods A 257 (1987) 114. [12] F. Balestra et al., Phys. Lett. B 165 (1985) 265. [ 13 ] F. Balestra et al., Nuovo Cimento A 100 ( 1988 ) 323. [ 14] G. Bendiscioli, Report FNT/BE-91/34 (Pavia, 1991 ). [15] V.M. Chechetkin et al., Phys. Len. B 118 (1982) 329. [ 16] Yu. A. Batusov el al., JINR Rapid Comm. 6 (1985) 11; Lett. Nuovo Cimento 41 (1984) 223. [ 17] K.M. Das and B.B. Deo, Phys. Rev. C 26 (1982) 211. [ 18] C.J. Batty, Rep. Prog. Phys. 52 (1989) 1165. [ 19 ] W. Briickner et al., Phys. Lett. B 158 ( 1985 ) 180. [20] L. Linsen et al., Nucl. Phys. A469 (1987) 726. [21 ] E.V. Inopin and Yu. A. Berezhnoy, Nucl. Phys. 63 (1965) 689. [ 22 ] G. Bendiscioli et al., Report FNT/BE-91/03 (Pavia, 1991 ), Nuovo Cimento, in press.