Differential cross sections of the pp → ppπ0 reaction from 310 to 425 MeV

~ ~

~

ELSEVIER

Nuclear Physics A663&664 (2000) 452c-456c www.elsevier.nl/locate/npe

Differential cross sections of the pp

--t

PP7r° reaction from 310 to 425 MeV

J. Zlomanczuk", R. Bilger", W. Brodowski", H. Calen" H. Clement", J. Dyring",

C. Ekstrom", G. Faldta , K. Franssen", L. Gustafsson", S. Haggstrom", B. Hoistad", J. Johanson", A. Johansson", T. Johansson", K. Kiliand, S. Kullander", A. Kupsc", P. Marciniewski", B. Morosov", A. Mortsell", W. Oelert", R.J.M.Y. Huber", U. Schuberth", P. Sundberg", B. Shwartz", J. Stepaniak-, A. Sukhanov", A. Turowiecki'', G.J. Wagner", Z. Wilhelmi", C. Wilkin i , J. Zabierowski', A. Zernov " "Department of Radiation Sciences, Uppsala University, S-751 21 Uppsala, Sweden bphysikalisches Institut, Tubingen University, D-72076 Tubingen, Germany CThe Svedberg Laboratory, S-751 21 Uppsala, Sweden dIKP - Forschungszentrum Julich GmbH, D-52425 Julich, Germany e Joint

Institute for Nuclear Research Dubna, 101000 Moscow, Russia

fBudker Institute of Nuclear Physics, Novosibirsk 630 090, Russia gInstitute for Nuclear Studies, PL-00681 Warsaw, Poland hlnstitute of Experimental Physics, Warsaw University, PL-0061 Warsaw, Poland 'Physics and Astronomy Dept., University College London, London WC1E 6BT, U.K. -Institute for Nuclear Studies, PL-90137 L6dz, Poland Measurements of the differential cross sections of the PP --+ PP7r° reaction at 310, 320, 340,360,400 and 425 MeV have been carried out at the CELSIUS storage ring in Uppsala. An attempt has been made to describe the distributions obtained in terms of the five partial waves Ss, Ps, Pp, Sd and Ds. The relative contributions from the different states depend significantly upon the energy. For instance, that of the S s state drops from about 80% at 310 MeV to around 10% at 425 MeV.

1. INTRODUCTION

Measurements of the pp --+ PP7r° reaction near threshold [1] have triggered a lot of theoretical activity in recent years [2] but there are still some unanswered questions, such as the relative importance of heavy meson exchanges and off-shellpion rescattering. It has also been pointed out that partial waves higher than Ss (we are using here the standard notation, LI, with L representing the internal angular momentum of the pp pair and I 0375-9474/00/$ - see front matter © 2000 Elsevier Science B.Y. All rights reserved. PH S0375-9474(99)00629-6

J. Zlomanczuk et al. / Nuclear Physics A 663&664 (2000) 452c-456c

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being the 71" angular momentum in the overall centre-of-mass system) may be important for a consistent description of the N N ---+ N N7I" reactions [3,4] near threshold. Recently, in a polarized-beam polarized-target experiment carried out at IUCF [5], the admixtures of the Ps and Pp states were measured. The results obtained are in qualitative agreement with earlier TRlUMF data [6]. However, in the analyses of both experiments, only partial waves up to Pp were considered, whereas in a recent Uppsala experiment it was shown that, already at 310 MeV, the Sd state strongly influences pion angular distributions via its interference with the Ss state [7]. In this contribution we report on new measurements of the differential cross sections, da / dq, where q is the two-proton relative momentum, and do / d cos((),,), of the pp ---+ PP7l"° reaction at 310, 320, 340, 360,400 and 425 MeV carried out at the CELSIUS storage ring in Uppsala. An attempt has been made to describe the distributions obtained in terms of the five partial waves, Ss, Ps, Pp, Sd and Ds.

2. EXPERIMENT The experiment was carried out using the PROMICE-WASA experimental set-up at the CELSIUS storage ring of the The Svedberg Laboratory. The detector system is described elsewhere [8J and only the main components are mentioned here. In the experiment both protons were measured by the forward scintillator hodoscope and the tracker (FD), though some were lost through a small hole, subtending an angle of ±4.5°, which accommodated the beam pipe. This is the principal source of detection inefficiency for the two protons, giving a geometrical acceptance of about 70% at 310 MeV. At higher energies the maximum proton angle is greater than the largest angle measured in the FD (20°), and the acceptance is consequently reduced. The overall efficiencyis further diminished by "-'20%, mainly through the interaction of protons in the scintillator. Since, at all the energies considered here, protons from 71"0 production stop in the hodoscope, their energies and angles can be measured with accuracies of 4.5% and 0.5° (r.m.s.) respectively. The 71"0 is then reconstructed through the missing mass and no use is made in this analysis of the information collected in parallel on the photons arising from the 71"0 decay. Careful calibration of the FD elements leads to narrow, nearly background-free, missing mass peaks, with a FWHM ranging from 2.2 MeV/c z at 310 MeV to about 7 MeV/c z at 425 MeV.

3. ANALYSIS To evaluate the detector acceptance, we require a reasonable phenomenological description of the differential cross sections. In this work we have added two extra states, Sd and Ds, to the Ss, Ps and Pp states used by Handler [9]. The transitions which lead to the Sd and Ds states, 3 Pz ---+ lSod, 3 Fz ---+ lSod and 3 Pz ---+ 1 Dzs, 3 Fz ---+ 1 Dzs, may interfere with the 3 Po ---+ lS0S transition and thus influence the angular distributions. Making several simplifying assumptions on the energy and angular dependence, we arrive at the following expression for the terms contributing to the absolute square of the matrix element:

454c

J Zlomanczuk et a/.! Nuclear Physics A663&664 (2000) 452c-456c

Iss

ah} ,

Ips

[1 + ,81 (Ji~ - ~) ] , 2 ,0k q2[1 + ,1 (Ji~ - k) + ,2(Ji~ - ~)] 00h}k 4 [1+ 01 (Ji~ - k) + 02 (Jit - i)], Eohb [1 + El (Ji~ - k) + E2 (Ji~ - i)] ,80 q2

I Pp

I

ISd IDs

I

I SsSd

= (h}k 2 [JL%- ~l

ISsD.

=

nbebo [JL~ -

'

k] ·

Here the hS(q2) and h D(q2) functions describe the two-proton final state interaction in ISO and 1 D 2 states, respectively, JLk = cosek, N), = cos(ij, N) with N being the beam direction, and k is the pion momentum in the reaction centre-of-mass system. The parameters a, ,8, " 0, E, ( and 1] are considered to be constan t at a given beam energy and are found by fitting the experimental distributions. To account for the ISO proton-proton final state interaction, we have used the scat tering wave function calculated for the Paris potential [10] at a radius of 1 frn, while the h D(q2) have been calculated within the effectiverange approximation using the expansion parameters taken from the same paper. At the beam energy of 400 and 425 MeV, the assumption that the Ps and Pp partial amplit udes are proportional to qL x k l [9] may no longer hold. Therefore we have replaced the q2 factor in Ip s and fpp with combinations of P-state scattering wave functions calculated for the Paris potential [lOJ at the same radius as in the ISO case. Since two transitions may: contribute to the Ps state, ISO ---t 3 Pos and 1 D 2 ---t 3 P2s , for the Ips 3 3 we have used the ~ Po + P2 combination of the scattering functions. Similarly, for the I P p st ate we have taken th e sum: 3 Po + ~ 3 PI + 3 P2 • This change of the matrix element affects only slightly the description of the 310 data since all P scattering wave functions follow the q2 dependence up to nearly 100 MeV[c , but at higher energies the contribution from Ps and Pp states is reduced at high q.

Jiq

!

i

k

4. RESULTS AND DISCUSSION Our results shown in Figs 1-3 have been normalised using the pp elastic scattering data collected simultaneously with the 7fo data. The values of the pp elastic differential cross section have been obtained from the SAID program [11] . Distributions of the acceptanc ecorrected two-proton relativ e momentum obtained for th e pp -> pp7fo reaction at six beam energies are compared in Fig. 1 with th e results of the Monte-Carlo simulation . Th e acceptance-corrected c.m. pion angle distributions presented in Fig. 2 show a clear change from a negative slope at 310 MeV to a positive one at higher energies. In the region of small q, shown in Fig. 3, there is a strong influence of the Sd state. At low energies this is mostly due to interference with the Ss state (cos2 0" behaviour) but at higher energies I Sd is significant and a cos4 0" term shows up.

1. Zlomanczuk et al./Nuclear Physics A 663&664 (2000) 452c-456c

455c

~F6l: :~ ~"" -~......,===""-' 340 MeV

, - - -- - --

-----, 1000

o

800

50

100

0 50 100 150 , - - -- - - - -----,

4ClQM4IV

600 400 200 O loo":::c....;:.a:..=.::::.:;=~

50

100

150

200

0

50

100

150 200 250

50 100 150 200 250

q (MeV/c)

Fig. 1. Acceptance-corrected distributions in the proton-proton relative momentum q at six beam energies.

::EJ 800B 200

310 MeV

o

1500LJ

:

1:

320 MeV

o

~:EJ'" 1000

360 MeV

o

800~

o 02 0.4 0.6 0.8 1

8000

~

0

r====l1~

340 MeV

r=:==1

4OOO~1:~ o

0

o 02 0.4 0.6 0.8

1

0 02 0.4 0.6 0.8 1

cos~"

Fig. 2. Acceptance-corrected distributions in the cosine of the c.m.

'~D :a

200 150

100

'C'

.s OJ

~ "C

50

310MeV

0

100 50

~ 320 MeV

0

~E;] 2oo~ 100 360 MeV

~E;J 0

0 o 02 0.4 0.6 0.8 1

o 0.2 0.4 0.6 0.8

2

cos

1

7l'0

angle.

2OO~ ~8 150 100

50 0 400 300

200 100

+

340MeV

~

425 MeV

0 o 0.2 0.4 0.6 0.8

1

e"

Fig. 3. AB Fig. 2 for events with q < 53 MeV[c: The preliminary results on the total cross sections and relative contributions from different partial waves are summarized in the table below. The errors in the total cross section are believed to be less than 10%.

456c

T (MeV) 310 320 340 360 400 425

1. Zlomanczuk et al. / Nuclear Physics A663&664 (2000) 452c-456c

O"tot

(/1-6)

4.96 7.37 15.1 26.6 97.3 168.0

Ss 0.77 0.65 0.46 0.31 0.13 0.09

Ps 0.04 0.07 0.15 0.23 0.31 0.33

Pp 0.15 0.21 0.29 0.37 0.48 0.50

Sd 0.01 0.02 0.02 0.02 0.02 0.01

Ds 0.02 0.05 0.07 0.06 0.06 0.07

It should be stressed that the decomposition into partial waves presented here is based on the assumptions we have made about the matrix element and depends, for instance, on the choice of the two-proton final state interaction functions. On the other hand, the total cross section, da / dq and angular distributions depend only weakly on the details of the matrix element (through the acceptance). These may provide a valuable source of information to constrain theoretical models.

5.

ACKNO~EDGMENTS

We are very grateful to the TSL/ISV personnel for their continued help during the course of this work. Discussions with K. Tamura about the theoretical calculations of the N N -+ N N 7r reactions were much appreciated. Financial support for this experiment and its analysis was provided by the Swedish Natural Science Research Council, the Swedish Royal Academy of Science, the Swedish Institute, the Japanese Ministry of Education, Deutsche Forschung Gesellschaft (Mu 705/3 Graduiertenkolleg), the Polish Scientific Research Committee, the Russian Academy of Science, the German Bundesministerium fur Bildung und Forschung [06TU886 and DAADj, and the European Science Exchange Programme. One of us (JZ1) would like to express his gratitude for the hospitality and financial support he received during his stay at RCNP of Osaka University.

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