p -4He break-up cross section at 180 MeV

Volume 194, number 3

PHYSICS LETTERS B

13 August 1987

~-4He BREAK-UP CROSS SECTION AT 180 MeV F. B A L E S T R A a, R. B A R B I E R I b, Yu.A. B A T U S O V c, G. B E N D I S C I O L I b, S. BOSSOLASCO a, M.P. B U S S A a, L. B U S S O a, I.V. F A L O M K I N c, L. F E R R E R O a, C. G U A R A L D O d, L.A. K O N D R A T Y U K e, E. L O D I R I Z Z I N I r, A. M A G G I O R A d, F. N I C H I T I U c, D. P A N Z I E R I a, G. P I R A G I N O a, G.B. P O N T E C O R V O c, A. R O T O N D I b, p. SALVINI b, M.G. S A P O Z H N I K O V c, F. T O S E L L O a and A. Z E N O N I b a lstituto di Fisica Generale dell'Universitiz di Torino, and INFNSezione di Torino, 1-10125 Turin, Italy b Dipartimento di Fisica Nucleare e Teorica dell'Universiti~ di Pavia, andlNFN Sezione di Pavia, 1-27100 Pavia, Italy c Joint Institute for Nuclear Research. Dubna, P.O. Box 79, I01000 Moscow, USSR Laboratori Nazionali di Frascati dell'INFN. 1-00044 Frascati, Italy Institute of Theoretical and Experimental Physics, 117259 Moscow, USSR r Dipartimento di Automazione lndustriale dell'Universitgl di Brescia, and INFN Sezione di Pavia, 1-10125 Pavia, Italy

Received 17 February 1987

We have measured a value of 15.5 _+2.9 mb for the 15-4He break-up cross section at 179.6 MeV. This low value is in agreement with the prediction of the Glauber model and is due to the large probability for the antiproton to annihilate into the nuclei, which makes only a surface layer of the nuclear volume effective for the break-up process.

1. M e a s u r e m e n t o f the break-up cross section. In previous papers we reported the reaction cross section o f the p - 4 H e interaction at 19.6, 48.7 and 179.6 MeV [1,2] a n d the charged prong multiplicity distribution at the same energies [1,2] a n d at rest [3] o b t a i n e d with a self-shunted streamer c h a m b e r in a magnetic field [4] at the L E A R facility o f CERN. In this p a p e r we report the first m e a s u r e m e n t o f the ~-4He break-up cross section at 179.6 MeV. The 13-4He interaction includes elastic scattering ( E L ) , a n n i h i l a t i o n ( A N N ) , charge exchange ( CEX ) and break-up ( B U ) reactions. The a n n i h i l a t i o n contributes to events with any charged prong multiplicity (from 1 to 9); CEX contributes to one-prong events: the elastic scattering and the BU reaction

13-4He~13n 3He

(1)

to the two-prong events and the BU reactions 13-4 He--.iSp 3He ~13 2p 2n --.13 2H 2H o13pn2H

(2)

to the three-prong events. C E X and BU reactions are f o r b i d d e n below about 25 MeV in the laboratory system (ref. [ 2 ] ) . We define the inelastic cross section O-IN, the reaction cross section aR, the scattering cross section (with a D in the final state) O-so a n d the total cross section O-v as follows: O'IN =O-BU -~ aCEX,

(3)

O-R = O-ANN + O-BU + ffCEX,

(4)

a s c = a , u +aEL,

(5)

aT =fiR +O-EL =O-SC +O'ANN + O'CEX.

(6)

In ref. [2] we e s t i m a t e d roughly that O-INis less than about 3% o f O-R, SO that annihilation is by far the d o m i n a n t m e c h a n i s m in the l~-4He interaction, a result in agreement with the m e a s u r e m e n t on the 13_12C interaction [ 5 ]. A subsequent simplified analysis o f the d a t a led to the following e s t i m a t i o n o f the break-up cross section at 48.7 and 179.6 MeV: 8 . 9 + 19.1 m b and 13.6+ 12.3 mb, respectively [6].

0370-2693/87/$ 03.50 © Elsevier Science Publishers B.V. ( N o r t h - H o l l a n d Physics Publishing D i v i s i o n )

343

Volume 194, number 3

PHYSICS LETTERSB

In this paper we give the values of the cross section of the reactions (1) and (2) at 179.6 MeV (600 MeV/¢) obtained directly by measuring a sample of p-4He events. We reconstructed the tracks by the CERN standard geometry programs and identified in some cases the mass of single prongs utilizing the track ionisation. This allows, for instance, to separate pions from heavy particles so helping in distinguishing annihilations (where pions are present) from the other events. Details of the resolution of our measurements are given in ref. [7]. Concerning the two-prong events, firstly we separated the elastic ones from the others. To do this, we compared the measured momenta and directions of each event with the corresponding quantities calculated for an elastic event with the same scattering angle of the negative prong and the nominal value for the beam momentum. The events were considered to be elastic when the measured quantities were equal to the calculated ones within 3 a. The mean coplanarity angle of these events was 8.8 X 10 3o with a mean error of 1.1 ° The BU events were separated from the annihilations by fitting the non-elastic events to reaction (1) and by help of the track ionisation mentioned above. The CERN standard kinematics programs were used. We found 87.7% of elastic events, 11.1% of non-elastic events and 1.2% of ambiguous events. The recognized BU events were 3.2%, the annihilations 7.1% and the undefined non-elastic events 0.8%. We analyzed with similar criteria the three-prong events, which consist only of BU and annihilation events, and found 75.9% of annihilation, 13.5% of BU events and 10.6% of undefined events. The ambiguity in the identification was due mainly to accidental facts such as an unfavorable stereoscopy and a bad quality of some pictures. As these facts affect statistically all types of events, these events were neglected in calculating the relative percentages of BU and annihilation events given below. As a test of the efficiency of our filter procedure, we analyzed a sample of events below the BU threshold and did not recognize any event as BU. In conclusion we have found that the two-prong non-elastic events are for (30.8-+9.0)% BU events (reaction (1)) and 69.2% annihilations; the three344

13 August 1987

prong events are for (15.1 _+3.4)% BU events (reactions (2)) and 84.9% annihilations. In the present analysis we have found for the twoprong, three-prong and total reaction cross sections the values 13.5_+1.1 mb, 75.2___2.6 mb and 239.2___5.0 mb, respectively. They are somewhat higher than those of ref. [ 2 ] but more reliable as we used a higher statistics and a more accurate procedure for separating the two-prong non-elastic events from the elastic ones. However, the differences are within the errors considering, besides the quoted statistical errors, also the systematic errors due to the target transparency (2.5%) and to the multiplicity identification (refs. [1,2]). Combining these values with the preceding percentages, we found for the two-prong, three-prong and total BU cross sections the values 4.2_+ 1.3 rob, 11.3 _+2.6 mb and 15.5 _+2.9 mb, respectively. The BU cross section is affected by a further systematic error due to the undetected inelastic D emitted into a small forward cone defined by a beam scintillation counter behind the streamer chamber [4]. The maximum undetected scattering angle varies from about 3 ° up to about 13 °, depending on the vertex position along the beam trajectory. The inefficiency can be revealed by analyzing the vertex distribution of the events along the beam path, which is expected to be uniform in the case of no lack of events. Within the limits of the statistics considered, we have not observed any loss of BU events. Then, to evaluate this effect, we have calculated the angular distribution predicted for the BU events by the Glauber model discussed in the next section. Through some formulae reported in ref. [8] we obtained at small angles a flat distribution depressed in the forward direction, which allowed, with a Monte Carlo method, to evaluate a BU cross section defect less than 1.5 mb. Hence, the systematic errors to be considered are about 3% on the total reaction cross section and 12% on the BU cross section. It is important to note that the 10-4He break-up channel appears to be depressed if compared with the same reactions induced at low energy by other hadrons such as nucleons [9] and pions [ 10,11 ]. For instance, the value of 15 mb is much smaller than the value of 107.7 _+4.4 mb found for the p-4He breakup at 53 MeV [9] and the branching ratio 0 " B y / 0 " R ~" 6% is much smaller than that for the/~-4He

Volume 194, number 3

PHYSICS LETTERS B

interaction, which is 70-80% even in the region of the A-resonance excitation [ 11 ].

2. Glauber theory analysis and discussion. Here we study the physical reasons of the abovementioned break-up suppression. The Glauber theory [ 8 ], which is in practice the eikonal approximation to the first order in the Watson multiple scattering expansion [ 12], is the most direct and simple way to perform this analysis. The reasons for the applicability of this method in low energy p-nucleus scattering are explained in some detail in refs. [ 3,13 ]; we recall only that, because o f the large annihilation probability, the elementary p-nucleon amplitude assumes a typical diffractive structure, so that the eikonal approximation is valid even at low m o m e n t a ( < 3 0 0 MeV/c). Under the assumption of the completeness of the nuclear wave functions we can write the break-up cross section, in the Glauber approximation, as follows [8,14]: O'BU

=(f ~u*({r,))F*(b, {s,))F(b, {s,})q/({ri})dZb × H i d 3 r , ) --aEL,

(7)

where ~ is the nuclear ground state wave function, b is the impact parameter, {r~} are the coordinates of the nucleons, {s,.} their transverse components and F(b, {s~}) is the nuclear profile function, which can be expressed in a standard form [8 ] in terms o f the 0-nucleon scattering amplitude:

f ( q) - ( k/4n)aj( i + pj)exp( - ½fl~q2).

(8)

Here aj is the total cross section o f the 0 - P and 0 - n interaction ( j = n , p, i.e., neutron or proton), fl~ the slope parameter, pj= R e ~ ( 0 ) / I m f j ( 0 ) , k the projectile wave number and q the transferred momentum. As in ref. [81, we calculate eq. (7) assuming ~({r,}) as a product wave function and using one particle densities deduced from the harmonic oscillator basis for the light nuclei (A < 16) and W o o d s - S a x o n densities for the heavier ones. For numerical details on these calculations see refs. [ 8,14,15 ].

13 August 1987

Table 1 Experimental and calculated total cross sections for the 15-4He interaction at 180 MeV. Only statistical errors are quoted; for the systematic ones, see text. The input parameters for the Glauber model are: ap=150 mb, an=135 mb, fl2=21 (GeV/c) 2, pp=pn=0.2 (see text). The calculations are performed for two different values of fl~, corresponding to the conditions an/ap=fi2,/fl~ (case a) and ft,'-=fl~ (case b). Here, f12 is in (GeV/c) 2 and the cross sections are in rob. The nuclear radius for 4He has been fixed at RN= 1.37 fm. case fl~ a b

a~

18.9 233.2 21.0 236.7

ainu

a~

a~,x. . . . aBu

16.2 14.7

131.0 239.2_+5.0 15.5_+2.9 130.8

The calculations require the determination of the six parameters an, p2n,fl~, ap,pp,fl 2 in eq. (8). The existing data on the proton parameters, deduced from P-P scattering experiments, are summarized by the empirical formulae of refs. [16,17], which at 600 MeV/c give ao= 150 rob, fl2=21 (GeV/c) 2 and pp= - 0 . 2 . We note that the values of ap are 5-10% higher than those recently measured at LEAR [ 18 ]. In the following we neglect this small discrepancy and refer to the detailed discussion o f ref. [3 ]. For the neutron parameters, we use the results of recent analyses of total 0-nucleus cross sections [ 3,17,19 ]. All these analyses give consistent values of a, and predict a ratio R = an/ap < 1 for 0.2 < p < 0.6 GeV/c, in agreement with the results given recently in refs. [18,20]. Here we use the results of ref. [3], which predict R = 0 . 9 at p = 0 . 6 GeV/c, that is an = 135 mb. For the other parameters, it results that Pn and pp affect negligibly the total cross section, so that usually one puts p, =Po, and that a change of 10% in the slope parameters leads to a 2% change in aR and eEL [14,17]. Hence, usually one puts [3,13,19,21] flz=fl2p o r R = anla o-fl.lflp. _ 2 2 We have found that, a , being fixed, the calculation of aBu by eq. (7) is insensitive to the values of Pn and pp, whereas it is determined mainly by the values of the slope parameters. Indeed, a 10% change in f12 leads to a 15% change in aBv. For this reason, we have fixed a , = 135 mb, p n = P p = 0 . 2 and have calculated O'BU according to the two generally accepted values for

~.

The results, reported in table 1, show that the model is in fair agreement with our data. In table 2 we report also the calculated values of the reaction 345

Volume 194, number 3

PHYSICS LETTERS B

Table 2 Theoretical reaction and break-up cross sections (this work) and experimental reaction cross sections (mb) on various nuclei at 600 MeV/c (C from refs. [5,22], Ne from ref. [ 19], AI and Cu from ref. [22] and Ca from ref. [5]). The parameters for the p-nucleon scattering amplitudes are those of case (b) of table 1. The radii RN and the diffusenesses a (expressed in fm) refer to the point-nucleon densities and are taken from ref. [ 17]. nucleus

RN

a

a~.~p

o'~

~2C -~°Ne 27A1 4°Ca Cu

1.62 2.74 2.84 3.51 4.20

0.500 0.526 0.520 0.527

4 9 2 _ + 2 0 476.4 619_+21 674.2 737 _+30 766.8 990+50 963.0 1213_+40 1235.3

-exp[-at

34.7 52.4 55.8 62.7 71.8

{exp[-oa T(b)] T(b)]},

(9)

w h e r e aa a n d a, are the a v e r a g e d 13-p a n d 13-n a n n i h i l a t i o n and total cross sections, respectively, a n d T ( b ) is the nuclear thickness f u n c t i o n [ 8 ]. In the case o f sharp nuclear surface, f r o m this e q u a t i o n we o b t a i n O'BU ~

!~(2~ --2t2)[ 1 + O ( J . t / R N ) ] , 4

(10)

w h e r e 2 = (n{y) - ~ with n = 0.17 f 3 is the m e a n free length c o r r e s p o n d i n g to a n n i h i l a t i o n or total p - n u c l e o n scattering. Since at 600 M e V / c oa = 90 m b a n d a . = 1 5 0 m b [ 2 3 ] , f r o m eq. (10) we o b t a i n amj -~ 2 mb, a v a l u e e v e n s m a l l e r t h a n t h o s e r e p o r t e d in tables 1 and 2. T h i s shows that, d u e to the large a n n i h i l a t i o n p r o b a b i l i t y , the b r e a k - u p cross section is a small q u a n t i t y d e t e r m i n e d m a i n l y by the 13 interaction on the surface layer o f the nucleus.

346

To test this surface d e p e n d e n c e , we h a v e calculated aR, aEe a n d eBu for 4°Ca, v a r y i n g the n u c l e a r r a d i u s a n d the diffuseness p a r a m e t e r in such a way to keep the R M S radius fixed at 3.43 fm. We h a v e f o u n d t h a t a 10% change in the diffuseness determ i n e s a 1% change in aR a n d aEL a n d a 10% change in Onu.

a~j

and break-up cross sections for o t h e r nuclei for which e x p e r i m e n t a l d a t a on the r e a c t i o n cross section exist. To u n d e r s t a n d m o r e clearly the possible r e a s o n s o f the low v a l u e o f the b r e a k - u p cross section o b s e r v e d e x p e r i m e n t a l l y , let us c o n s i d e r a 13 s c a t t e r i n g on a n u c l e u s w i t h sharp surface, i.e. w i t h a s q u a r e well d e n s i t y o f r a d i u s RN. In the optical l i m i t for the G l a u b e r a p p r o x i m a t i o n , w h e r e A >> 1 a n d f12 << R 2 a n d p = 0, one has

amj = t d2b

13 August 1987

References [ 1 ] F. Balestra et al., Phys. Lett. B 149 (1984) 69. [2] F. Balestra et al., Phys. Lett. B 165 (1985) 265. [3] F. Balestra et al., Report CERN-EP-/86-104 (1986); Nucl. Phys. A 465 (1987) 714. [4] F. Balestra et al., Nucl. Instrum. Methods A 234 ( 1985 ) 30. [5] D. Garreta et al., Phys. Lett. B 135 (1984) 266; D. Garreta, Proc. third LEAR Workshop on Physics with antiprotons at LEAR in the ACOL era, eds. U. Gastaldi, R. Klapisch, J.M. Richard and J. Tran Thanh Van (Editions Fronti~res, Gifsur Yvette, 1985) p. 599. [6] Yu.A. Batusov et al., JINR Rapid Commun.12 (1985) 6. [7] F. Balestra et al., Report CERN-EP/86-163 (1986); Nucl. Instrum. Methods, to be published. [8] R.J. Glauber and G. Matthiae, Nucl. Phys, B 212 (1970) 135. [9] D.J. Cairns et al., Nucl. Phys. 60 (1964) 369. [ 10 ] D. Ashery et al., Phys. Rev. C 23 (1981 ) 2173. [ 11 ] F. Balestra et al., Nucl. Phys. A 340 (1980) 372. [ 12] V.B. Mandelzweig and S.J. Wallace, Phys. Rev. C 25 (1982) 61; V.B. Belyaev and S.A. Rakityanskii, Sov. J. Nucl. Phys. 42 (1985) 867. [13] L.A. Kondratyuk, M.Zh. Shmatikov and R. Bizzarri, Sov. J. Nucl. Phys. 33 (1981) 413. [ 14] G.D. Alkhazov, S.L. Belostotsky and A.A. Vorobyov, Phys, Rep. 42 (1978) 89. [ 15] G.D. Alkhazov, Nucl. Phys. A 280 (1977) 330. [ 16 ] H. lwasaky et al., Nucl. Phys. A 433 (1985) 580. [ 17 ] LA. Kondratyuk and M.G. Sapozhnikov, Dubna preprint E4-86-487 (1986); Sov. J. Nucl. Phys., to be published. [18] W. Brfickner et al., Phys. Lett. B 158 (1985) 180; B 166 (1986) 113. [19] F. Balestra et al., Nucl. Phys. A452 (1986) 573. [ 20 ] T. Armstrong et al., Report PSU HEP/86-10 ( 1987). [21] O.D. Dalkarov and V.A. Karmanov, Nucl. Phys. A 445 (1985) 579. [22] K. Nakamura et al., Phys. Rev. Lett. 52 (1984) 731. [23] V. Flaminio et al., Report CERN-HERA 84-01 (1984).