nucleon

Volume 82B, number 1

PHYSICS LETTERS

12 March 1979

PRODUCTION OF PIONS IN HEAVY ION REACTIONS BELOW 500 MeV/NUCLEON B. JAKOBSSON 1

NORDITA, Blegdamsvej 1 7, DK-2100 Copenhagen (k, Denmark and J.P. BONDORF and G. FAI 2

The Niels Bohr Institute, University of Copenhagen, DK.21 O0 Copenhagen O, Denmark Received 7 June 1978 Revised manuscript received 21 December 1978

Pion production and subsequent absorption in heavy ion reactions at lab. energies 200-500 MeV/N has been calculated using an independent nucleon-nucleon scattering description based on Glauber multiple scattering formalism, and a two step isobar model for pion absorption. Calculated pion production cross sections are compared to results from recent emulsion and streamer chamber experiments.

Contradictory experimental results on pion production cross sections in heavy ion reactions in the hundreds of MeV/N region have recently been reported [ 1 - 4 ] . The first very large cross section (~3 b) for Ne + emulsion at 1 0 0 - 2 8 0 MeV/N is not supported by more recent results from emulsion and streamer chamber experiments [ 2 - 4 ] . The low production cross sections from the latter experiments are in qualitative agreement with the predictions made in an independent particle description [5]. In the present model we make use of an improved independent particle picture in which we put emphasis on the heavy ion scattering geometry and on the reabsorption of pions. For the heavy ion collision A + B we assume straight line trajectories and that at most one pion can be produced in the first scattering between a beam and a target nucleon. These assumptions limit our model to an energy interval 200 ~< E A/iV <~ 500 MeV. Throughout the calculations we use W o o d s - S a x o n density distributions with central density 0.17 fm - 3 , diffuseness 0.546 fm and a radius 1 On leave of absence from University of Lund, Lund, Sweden. 2 On leave of absence from the Roland E6tv6s University, Budapest, Hungary.

given by the normalisation to the nucleon number. The average probability that an incident beam nucleon scatters at least once, is calculated through the optical multiple scattering picture introduced b y Glauber [6]

P(b) = 1 - e x p ( - ~ ( T ( b ) ) ) ,

(1)

where

f f TA (s--)Ts(6 - ~-)d2s -

,

(2)

I: A or B .

(3)

f i t A (s~ d2s and TI(~) = . f

p l ( E , z ) dz,

is here the impact parameter, z the beam direction and ~- = (Sx, Sy) is the position vector in the plane through the plane through the center of the target, perpendicular to z. The effective n u c l e o n - n u c l e o n (biN) cross section ~ is taken to be the experimental one [7] reduced b y a blocking factor due to the Pauli principle. This factor is given by the ratio between the available phase space in the medium and the one of 35

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free NN scattering. The probability distribution P(Ni, b), that N i independent beam nucleons will scatter at least once is

P(Ni, b):(Ai)[P(b)lNi[1- P(b)l A-Ni .

(4)

In fig. 1 we show some examples of P(N i, b) distributions obtained in calculations for 20Ne induced reactions in a light (160), a medium (l°8Ag) and a heavy target nucleus (238U). It can be seen, that for small values of b, there is a large probability for a large N i and thus a large pion production. The probability for all 20 Ne nucleons to scatter on the ;target is negligible for surface nuclei like 160, but is of importance for the impact parameter integrated probability, P(Ni), when the target is a heavy nucleus. Using an isotropic Fermi distribution with PF = 260 MeV/c we calculate a distribution S(e) of the total energy e of the two nucleons in their c.m. system for each beam energy. The pion production cross sec-

12 March 1979

tion is assumed to be the same as for free N - N scattering. The ratio between the charged pion production cross section ~'chTrand the total N - N cross section as a function of e,

R(e)

= ~ch 7r(e)/rtot(e),

(5)

is obtained from experimental cross sections of pp scattering [7] and an assumption of isospin conservation to calculate the weights for nn and pn cross sections [8]. The total pion production cross section for a heavy ion reaction, weighted over all impact parameters is now given by A

7ch~r = 27r(R)Fbl ; b db(N~i=lP(Ni, b)Ni) ,

(6)

0 where emax

= [

deR(e) S(e) ,

(7)

0

Q8

'°.~.'0

~.__0.8

' ~

t°Ne+ '~g

and Fbl is the ratio between the inelastic and the tota] Pauli blocking factors. The detectable pion flux from a heavy ion reaction will be strongly reduced by reabsorption in the nuclei, since the mean free path for pion absorption in nuclear matter is comparable to or less than the dimensions of the nuclei. In [5] it is suggested that only 1/3 of the created pions survive from a 160 + 238U collision. In our model the reabsorption is determined in a Monte-Carlo calculation. The average depth of the primary 7r-meson production is calculated by

'

I

z o.~

~

,_2 8 ~ f . . / /

m

\

o

o.a

'*N,~U

I

'S 2

o:

2

L, b(fm) 6

8

I 10

Fig. 1. The calculated probability that N i beam nucleons will scatter at least once in 2 0 Ne+ 16 O, 20 Ne + 108 Ag and 20 Ne + 238U reactions as a function of b. The curves are labelled by N i and the arrows indicate the sum of the hard sphere radii of the colliding nuclei. 36

-boo

f Z($ X ,

z exp[--~'chTrZPB(b-- s-,z)] dz

Sy) - - +~~,

f

(8) exp[--~'chTrZPB(b- S-,Z)] dz

At each production point (Sx, Sy) there is a probability of pion production proportional to the product of TA(s-)and T B ( b - s-). We generate the pion momentum isotropically in the N-N center of velocity frame, taking into account the Fermi motion in A and B, using energy and momentum conservation. If b < IR A - RBI the pion is

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PHYSICS LETTERS

always supported to move in the larger nucleus otherwise in A or B according to the direction of the pion momentum. We assume that A and B are in their closest mutual position, frozen during the time which the pion spends in the system. For/:-~ ~ E~tit we describe the absorption by the isobar model [9]. The pion decays through the A33 resonance in two competing processes: 1r + N -+ A ,

A + N' ~ N" + N ' " ,

(%)

~r + N ~ 2 x ,

A-+Tr' + N' .

(9b)

The mean free path for (9b) is taken directly from [9], while the one for (9a) has been adjusted to experimental lr+ absorption data on 12C as suggested in [9]. For the delta decay process we have used both complete forward pion propagation and an isotropic decay but the differences in the final absorption probabilities are negligible as a result of the randomization of the direction of the initial pion momentum, For ETr < E~crit ~ 50 MeV the physical picture underlying the isobar model does not work. However, since absorption is strongly dominant for low energy p i o n - n u c l e u s reactions [101, we assume in our model a complete absorption o f pions with ETr < 50 MeV. The average absorption probability in 20Ne induced reactions at 250 MeV/N is shown in fig. 2a as a function of the impact parameter. The strong correlation between a small impact parameter and a strong absorption is noticeable. This connection is especially marked when the target is heavy. The statement that a very large pion production should be a signal for a small impact parameter in a heavy ion reaction [11 ] is therefore not always correct. In fig. 2b we exhibit the total number o f escaping charged pions in 250 MeV/N 20Ne induced heavy ion reactions. For a Ne + U reaction we notice that the largest charged 7rmultiplicities are to be expected when b is about 5 fm, while for the reaction between two light nuclei zero impact parameter is most favourable for pion production. Table 1 gives a summary of the results of our calculations for some 250 MeV/N collisions. The model gives a charged pion production cross section for 160 + Emulsion and 20Ne + emulsion collisions which is not in contradiction with experiments [2] and [3]. It should also be noted that the cross section before absorption for 160 and 238U corresponds to an aver-

12 March 1979

loc 8O

c .Q

~( ~q 2o o

I

I

Cn

._c D. 0

"5 .0 Z

Io

b(fm)

Fig. 2. (a) The calculated absorption probability for pions produced in 250 MeV/N 2°Ne + 160, l°8Ag and Z38U reactions as a function of impact parameter (b). (b) The number of escaping charged pions per event produced in 250 MeV]N ~°Ne induced reactions in 160, 1°SAg and 238U as a function of the impact parameter (b). age number of pions per collision, 0.12, slightly larger than the one (1/9) given in ref. [5]. In table 2 we compare 7r- multiplicities given by our model to streamer chamber data [4]. The error bars on the calculated results are due to the uncertainties in the experimental N - N and the heavy ion cross sections we use as input. The calculated multiplicities are within the limits of error in agreement with the Table 1 Calculated charged pion production cross sections before and after reabsorption in nuclei for heavy ion reactions at 250 MeV/N. Reaction

Primary Absorption rch~rafter Zch~r probability absorption (rob) (%) (rob)

2°Ne + 160 2°Ne + l°8Ag 2°Ne + 238U 160 + 238U

62 325 608 476

61 66 67 66

25 111 200 162

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Volume 82B, number 1

PHYSICS LETTERS

12 March 1979

Table 2 Experimental and theoretical multiplicities of pions in 12C, 2°Ne and 4°Ar induced reactions at 250 and 400 MeV/N. Experimental data are taken from refs. [2] and [4]. In the 12C and 4°Ar induced reactions only 7r- are registered while in the 2°Ne + emulsion (H, C, N, O, Ag, Br) case all charged pions are registered. Reaction

12C + LiH 12C + NaF 12C + BaI2 12C + Pb304 20 Ne+emulsion 4OAr+LiH 4°Ar+NaF 4°Ar+BaI2 40Ar+Pb3 O4

Energy (MeV/N)

400 400 400 400 250 400 400 400 400

Average multiplicity of pions Experiment

Theory

0.02 0.038 0.078 0.066 <0.13 0.043 0.034 0.107 0.099

0.021 0.040 0.062 0.062 0.030 0.030 0.075 0.161 0.124

experimental ones except for heavy projectile + heavy target reactions where we predict slightly larger multiplicities than the measured. We attribute the discrepancy to an u n d e r e s t i m a t i o n o f pion absorption in heavy nuclei by the isobar m o d e l . One thing which could alter the absorption probability is, that in the heavy p r o j e c t i l e - t a r g e t system, large volumes o f nuclear m a t t e r m a y be o f high density. The cross section for absorption in such regions is not k n o w n but could be m u c h higher than the absorption for normal density which was used in this paper. In conclusion we can state that the i n d e p e n d e n t particle m o d e l for p i o n p r o d u c t i o n including subsequent reabsorption b e l o w 500 M e V / N is in qualitative agreem e n t w i t h present experiments. The authors acknowledge fruitful discussions w i t h Drs. F. Myhrer and J. R a n d r u p . The kind hopsitality o f the Niels Bohr Institute and N O R D I T A is gratefully appreciated as well as the financial support o f the Danish Research Council and the C o m m e m o r a t i v e Association o f the Japan World Exposition.

38

Detected pions

-+ 0.01 ± 0.013 ~+0.014 +- 0.014 ± 0.022 ± 0.015 ± 0.019 ± 0.020

+- 0.004 -+ 0.008 ± 0.011 +- 0.012 -+ 0.006 -+ 0.006 ± 0.015 +- 0.031 -+0.024

~r7rn7rrr-+ 7r~r7r~r-

References [1] P.J. McNulty et al., Phys. Rev. Lett. 38 (1977) 1519. [2] P.J. Lindstrom et al., Phys. Rev. Lett. 40 (1978) 93. [3] R. Kullberg, A. Oskarsson and 1. Otterlund, Phys. Rev. Lett. 40 (1978) 289. [4] S.Y. Fung et al., Phys. Rev. Lett. 40 (1978) 292. [5] G.F. Bertsch, Phys. Rev. C15 (1977) 713. [6] R.J. Glauber, Lectures on theoretical physics, Vol. 1 (Interscience, New York, 1959). [7] E. Bracci et al., CERN/HERA Report 73-1 (1973); O. Benary, R. Price and G. Alexander, UCRL-Report 20000 NN (1970). [8] E. Fermi, Phys. Rev. 92 (1953) 452. [9] J.N. Ginocchio, Phys. Rev. C17 (1978) 195, and references therein. [10] K. Stricker, H. McManus and J.A. Carr, Cyclotron Labo. ratory Preprint, Michigan State University (1978). [11] R.K. Smith and M. Danos, in: Proc. of the Meeting on Gross Properties of Nuclei, Hirschegg, Austria, 1977.