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arXiv:nucl-ex/0112012v3 14 Jan 2002

Analyzing power of the ? pp → ppπ0reaction at

beam energy of 390 MeV

Y.Maedaa,b,∗, M.Segawaa, H.P.Yoshidaa, M.Nomachic,

Y.Shimbarac, Y.Sugayac, K.Yasudad, K.Tamurae, T.Ishidaf,

T.Yagitaf, A.Kacharavab,g

aResearch Center for Nuclear Physics, Osaka University, Ibaraki,Osaka 567-0047,

Japan

bInstitut f¨ ur Kernphysik, Forschungszentrum J¨ ulich, 52425 J¨ ulich, Germany1

cDepartment of Physics, Osaka University, Toyonaka, Osaka 560-0043, Japan

dThe Wakasa Wan Energy Research Center, Fukui 914-0192, Japan

ePhysics Division, Fukui Medical University, Fukui 910-1193, Japan

fDepartment of Physics, Kyushu University, Fukuoka 812-8581, Japan

gLaboratory of Nuclear Problems, Joint Institute for Nuclear Research, Dubna,

141980, Russia

Abstract

The analyzing power of ? pp → ppπ0reaction has been measured at the beam energy

of 390 MeV. The missing mass technique of final protons has been applied to iden-

tify the π0production event. The dependences of the analyzing power on the pion

emission-angle and the relative momentum of the protons have been obtained. The

angular dependence could be decomposed by the Legendre polynomial and the rela-

tive contribution of the P21to P11function is less than 20%. The P-state amplitude

is found to be the dominant component of the π production near the threshold.

The momentum dependence of the analyzing power has been studied to obtain the

information about the pion production mechanism. It has been deduced that the

pion production due to the long range interaction plays an important role in the

momentum dependence of the P-state amplitude.

Key words: Meson production

PACS: 13.60.Le

∗Corresponding author. E-mail address: y.maeda@fz-juelich.de

1Present address.

Preprint submitted to Elsevier Science6 February 2008

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In the last few years, both experimental and theoretical investigations for

various NN → NNπ reactions have been performed. The total cross sec-

tion of the pp → ppπ0reaction has been measured at IUCF very precisely

near the threshold [1]. In theoretical calculations, it has been shown that the

large contribution of the s-wave pion-production amplitude is necessary to

reproduce the experimental data. The proposed short-range effect between

the nucleons gives an essential contribution into the s-wave amplitude where

the final protons couple to a S-state [2]. In order to understand the s-wave

pion-production mechanisms systematical studies based on the chiral effective

theory are also still progressing [3]. Recently the investigations of the polar-

ization observables have attracted interest from the viewpoint of the partial

waves amplitude (PWA) analysis . These studies are expected to make a break-

through in the elucidation of the origin of the large s-wave amplitude. The

analyzing power and spin correlation coefficients integrated over the pion an-

gle and energy have been obtained at four bombarding energies between 325

and 400 MeV [4]. These data are compared with the theoretical calculations

in [5] and [6]. Only these two currently existing models are able to predict

polarization observables. The calculations provide a good fit to the cross sec-

tion close to the threshold but underestimate the contribution of the s-wave

pion-production amplitude, where final protons are in a P-state, as deduced

from the measurement of polarization observables. Therefore the origin of the

s-wave pion-production amplitude is not clear for the P-state as well as for

the S-state.

In this article, we report the experimental results of the analyzing power (Ay)

as a function of the pion emission angle (θπ) in the center-of-mass system

(C.M.S.) in order to obtain information about the relative strength of the

s-wave pion production, where the final protons are in P-state and S-state.

Based on few partial wave amplitudes, the deduced angular dependence of

the Ay× spin-averaged cross section is expressed in terms of the associated

Legendre polynomials P11(cosθπ) and P21(cosθπ) which are symmetrical and

asymmetrical around θπ = 90◦, respectively. The strength of the P11 term

corresponds to the contribution of the pion s-wave amplitude from a P-state,

whereas that of the P21term is determined by the contribution from the S-

and higher state. The angular dependence is expected to be sensitive to the

relative strength between the S-state and P-state amplitudes and will give

useful information to make the origin of the s-wave amplitudes more clear.

The analyzing power is also shown as a function of the relative momentum of

final protons with the angular integration, which enable one to select the term

of the P11function and to observe the momentum dependence of the P-state

amplitude. The momentum dependence of the P-state amplitude is studied in

terms of the interaction range of the pion production mechanism.

Experiment has been carried out using the 390 MeV polarized proton beam

from Ring Cyclotron at Research Center for Nuclear Physics (RCNP), Osaka

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University, Japan. The schematic view of the experimental setup is shown

in Fig.1. The used liquid hydrogen target (L.H target) and cooling system

has been developed by Kyushu University group [7]. The target thickness

is 8.5 mm. The measurements with the gas hydrogen target have been also

performed to study the amount of background events coming from construc-

tion materials. The Faraday cup installed in the beam dump monitors the

beam intensity. The array of plastic scintillators is employed to detect the

outgoing particles and measure the kinematical variables: scattering angles

and energies of two protons, on the basis of coplanar geometries. The number

of measured variables is sufficient to determine the kinematics of three-body

final state. The energy of protons is measured by the plastic scintillator (E-

counter) which can stop protons up to the 250 MeV kinetic energy. The energy

resolution of the E-counter was better than 2% at 200 MeV (FWHM). The

plastic scintillator hodoscope (Hodoscope) mounted in front of the E-counter

is used to determine the direction of the outgoing particles. The angle cov-

ered by one hodoscope is ±17 mrad horizontally and ±30 mrad vertically.

Our detector can measure outgoing protons in the scattering angular range of

15◦−35◦, which corresponds to the relative momentum of final protons from

150 MeV/c to the maximal kinematically allowed momentum (≃ 220 MeV/c)

and covers the polar angle of the relative momentum from 40◦to 140◦. Antico-

incidence counter (Anticounter) identifies the background events coming from

the random coincidences of the pp elastic scattering. The beam polarization

has been monitored by detecting the pp elastic scattering event from the liq-

uid hydrogen target using the set of scintillator counters (Polarimeter) placed

at 60◦±1◦. The analyzing power at the angle of 60◦±1◦is found to be −0.36

from a database of SAID [8]. The beam polarization during the experiment

has been 65−75%.

The π0-production event is identified by the missing mass technique. The

background due to the random coincidence of the elastic scattering events

and inelastic scattering events from other construction materials has been

subtracted. After subtracting background, the events that do not deposit the

full energy on the E-counter still are left as a tail in the missing mass spectrum.

These events are caused by the elastic scattering and charge exchange nuclear

reaction in the scintillator (nonfull-peak event). The tail is involved into the

systematical error.

Figure 2 shows the angular dependence of Ay for three relative-momentum

regions. The errors in the figure are only systematical mainly coming from

the energy measurement of the E-counters and the estimation of the nonfull-

peak events. The statistical error is below 5%. In order to obtain the relative

strength of the coefficients of the Legendre polynomials P11and P21, the ex-

perimental data has been fitted by

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Ay= [a P11(cosθπ) + b P21(cosθπ)]/σ(θπ), (1)

where a and b are the strength parameters. The spin-averaged angular distri-

bution σ(θπ) is obtained independently by fitting the experimental data on

the spin-averaged angular distribution with the function of σ0(1 + ccos2θπ).

The σ0and c are free parameters, and the magnitude of the c is 0.5-0.6. In

Fig.2, dashed lines show the results of the fitting with Eq.(1). The main con-

tribution comes from the P11 term and the fraction of the P21 term to the

contribution of the P11is below 20%, which makes the angular dependence

of Ay slightly asymmetrical. IUCF data at close energies also show a large

P11 component [9]. In terms of few PWAs (Ss,Ps,Pp,Sd), the coefficient a

is determined by the Ps × Pp whereas the coefficient b is determined by the

Ss × Sd and |Pp|2amplitudes. Here, the capital and small letters show the

angular momentum state of final protons and pion, respectively. Therefore the

main contribution of the P11term indicates that the strength of P-state am-

plitude dominates over the S-state amplitude. On the other hand the model

calculations of RCNP group (Fig.2) show more asymmetrical behavior than

the experimental results and the model calculations overestimates the data.

That means the calculated strength of the P-state amplitude is much smaller

than the experimental one. More theoretical studies are needed for elucidating

the origin of this disagreement.

Figures 3 (a) and (b) show the relative momentum distribution (dN/dk) and

integrated analyzing power as a function of the relative momentum of final

protons (k), respectively. The value of Ayincreases with k. Since the term of

the P21function in Eq.(1) becomes zero after the integration over the pion

angle, the dependence of the Aycan be expressed by the P-state amplitudes

and dN/dk as

Ay= Ps × Pp ρ(k)/(dN/dk), (2)

where ρ(k) is a phase space factor. Thus one can find from Eq.(2) that the

momentum dependence of P-state amplitude can be obtained utilizing the

known dependence of dN/dk and ρ(k). From the theoretical point of view,

the PWA is calculated by

?drr2uk

between the pion-production operatorsˆΠ(r) and the radial wave function of

initial protons up

the momentum of initial protons and of a pion in C.M.S, respectively. lπ is

the angular momentum of a pion. For example, the analytic forms of the s-

wave pion-production amplitude where the final protons are in S-state are

presented in Ref.[10]. According to the argument of Ref.[9], the strong mo-

mentum dependence of the P-state amplitude comes from the dependence of

the radial wave function of final protons and a pion, and the pion-production

operator is commonly considered as momentum independent. In the overlap

integral the pion-production operator selects typical region of the radial wave

f(r)φq

lπ(r)ˆΠ(r)up

i(r), i.e. the overlap integral

i(r), final protons uk

f(r), and pion φq

lπ(r), where p and q is

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functions when integrated over the relative distance of protons. Accordingly,

the radial wave function of final state shows different momentum dependence

on that selected region. Therefore the wave function of final state with a fixed

distance of protons gives a general estimation about the typical interaction

region of the pion-production operator in a certain PWA. For this purpose,

the dependence of the P-state amplitude with a fixed distance (r) between

protons is estimated by Ps × Pp ∼ (j1(kr))2j1(1

the spherical Bessel functions with an orbital angular momentum (l), which

is used for the undistorted wave function of final protons and pion (distorted

wave function for P-state protons does not change the final result). Results are

shown in Fig.3 (b). The value of dN/dk is taken from the solid line of Fig.3 (a)

that gives the best fit to the data. The calculations performed at several dis-

tances (r=1,2,3,3.5 fm) show that the momentum dependence becomes close

to the experimental data as the distance increases. The r∼3 fm (dash-double-

dotted line) is more preferable. The long range part of the wave function gives

the proper dependence and it implies that the contribution of the long range

production mechanism is more preferable than the short range one r∼1 fm

(dotted line). One must keep in mind that the above discussions are based an

assumption that the momentum dependence of the pion-production operator

is quite small. Therefore, the long range mechanism might not be the only

way to explain the momentum dependence of experimental data. However

as suggested by Ref.[6], the discrepancy between the theoretical calculations

and experimental data on the analyzing power presented in this article (both

angular dependence and momentum dependence in Fig.3 (b)) indicates the

necessity of some long-range mechanisms for s-wave pion production in P-

state amplitude to improve the predicted Ay. Such a behavior corresponds

to the expectation since the probability of the P-state at short distance is

much smaller than the probability of S-state and therefore the short-range

mechanism does not support the P-state amplitude.

2qr)j0(1

2qr), where jl(x) is

In summary, we have measured the angular and momentum dependence of

the analyzing power for the ? pp → ppπ0reaction at the incident energy of 390

MeV . The angular dependence shows the dominated contribution of P11and

that the contribution of the s-wave pion production comes mainly from the

P-state of final protons at this energy. The long range part of the P-state

wave function gives a general explanation to the experimental momentum

behavior of analyzing power and it is deduced that the long range interaction

is important for the pion production from the P-state nucleons and further

study is needed to pin down the production mechanism with a long range

interaction.

The authors are grateful to the RCNP cyclotron staff for their support through-

out the presented experiments. We acknowledge K. Sagara for the liquid hy-

drogen target system. This experiment was performed under the programmed

No. E140 at RCNP.

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References

[1] H.O. Meyer et al., Phys. Rev. Lett. 65, (1990) 2846; Nucl. Phys. A539, (1992)

633.

[2] T.-S.H. Lee, D.O. Riska, Phys. Rev. Lett. 70, (1993) 2237.

[3] C. Hanhart, G. A. Miller, F. Myhrer, T. Sato, U. van Kolck, Phys. Rev. C63,

(2001) 044002 and references therein.

[4] H.O. Meyer et al., Phys. Rev. Lett. 81, (1998) 3096; Phys. Rev. Lett. 83, (1999)

5439.

[5] C. Hanhart, J. Haidenbauer, O. Krehl and J. Speth Phys. Lett. B444, (1998)

25-31; Phys. Rev. C61, (2000) 064008.

[6] K. Tamura, Y. Maeda, N. Matsuoka, Nucl. Phys. A663-664, (2000) 457c-460c

; Nucl. Phys. A684, (2001) 392c-396c.

[7] K. Sagara et al., in RCNP Annual Report 1995, p.158.

[8] R.A. Arndt, I.I. Strakovsky and R.L. Workman, Phys. Rev. C50, (1994) 2731.

[9] H.O. Meyer et al., Phys. Rev. C63, (2001) 064002.

[10] C.J. Horowitz, H.O. Meyer, D.K. Griegel, Phys. Rev. C49, (1994) 1337.

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Fig. 1. Experimental setup. The shadow region shows liquid hydrogen target.

Fig. 2. The angular dependence of the analyzing power of the ? pp → ppπ0

reaction for three regions of relative momentum of final protons at the beam

energy of 390 MeV. The momenta range is shown at the top of figures. The

horizontal axis shows the emitted angle of a pion in C.M.S. Solid lines show

the result of RCNP model and shaded area indicates uncertainties for the

calculation [6]. Dashed lines show the fitted result of the Legendre polynomial,

see Eq.(1).

Fig. 3. (a) Relative momentum distribution of final protons. The vertical axis

shows the normalized yields in arbitrary unit. The solid line is the fitted result.

(b) Relative momentum dependence of the analyzing power. The solid line

shows the model calculations (same one of Fig.2). The dotted, dash-dotted,

dashed-double-dotted and dashed lines show the results with Bessel function

at distances r=1, 2, 3 and 3.5 fm, respectively.

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L.H target

50cm

Anticounter

E-counter

Beam

Hodoscope

Polarimeter

Fig.1

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-0.4

-0.3

-0.2

-0.1

0

Ay

160-180 MeV/c 180-200 MeV/c200-220 MeV/c

0

?(deg)

180

0

?(deg)

180

0

?(deg)

180

-0.4

-0.3

-0.2

-0.1

0

-0.4

-0.3

-0.2

-0.1

0

Fig.2

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-0.3

-0.2

-0.1

0

160 180

k (MeV/c)

(b)

200220

Integrated Ay

0

20

40

60

k (MeV/c)

(a)

160180200220

(arbitrary unit)

dN/dk

Fig.3

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