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Analyzing power of the reaction pp→ppπ0 at a beam energy of 390 MeV
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Nuclear Physics A721 (2003) 6290632~ www.elsevier.com/locate/npe
Analyzing power of the reaction pfp-+ppn’ at a beam energy of 390 MeV Y. Maedaa*, M. Segawab, H.P. Yoshidab, M. Nomachic, Y. Shimbarac, Y. Sugayac , K. Yasuda*, K. Tammae, T. Ishida’, T. Yagita’, A. Kacharavas aInstitut fiir Kernphysik, Forschungszentrum Jiilich, 52425 Jiilich, Germany bResearch Center for Nuclear Physics, Osaka University, Ibaraki, Osaka 567-0047, Japan CDepartment of Physics, Osaka University, Toyonaka, Osaka 560-0043, Japan *The 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 sPhysics Institute II, University Erlangen-Niirnberg,
91058 Erlangen, Germany
The analyzing power of the reaction jip+ppn’ has been measured at a beam energy of 390 MeV. The dependences of the analyzing power on the pion emission-angle and the relative momentum of two outgoing protons have been obtained. The angular dependence could be decomposed by Legendre polynomial and the relative contribution of the P21 to the PII function is less than 4%. The momentum dependence of the analyzing power has been studied to obtain information about the pion-production mechanism. It has been deduced that pion production due to the long-range interaction plays an important role in the momentum dependence of the P-state amplitude. 1. Introduction Over the last decade the total cross section of the pp+ppn’ reaction has been measured very precisely near the pion-production threshold at IUCF [l] and TSL [2]. In theoretical calculations [3] it has been shown that a large contribution of the s-wave pion-production amplitude is necessary to reproduce the experimental data. A proposed short-range interaction between the nucleons gives an essential contribution into the s-wave amplitude where the final protons couple to an S-state. In order to understand the s-wave pionproduction mechanisms, systematical studies based on the chiral effective theory are still in progress [4]. Recently, differential cross sections and the polarization observabies of no production have been measured at TSL [5] and IUCF [S] at several bombarding energies up to 425 MeV. Especially for the case of analyzing power A, and the spin correlation coefficient (1 - Ax - A,,)/4 existing models [7,8] predict a 3-10 times smaller value than the experimental data even though the calculations provide a good fit to the total cross *e-mail:y.maedaOfz-juelich.de 0375-9474/03/$ - see front matter 0 2003 Published by Elsevier Science B.V doi:lO.l016/S0375-9474(03)01139-4
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Z Maeda et al. /Nuclear Physics A721 (2003) 629~632~
section close to the threshold [8]. The experimental data show that there is a large contribution from the Ps amplitude, where the pion is emitted in an s-wave relative to the protons of P-state, and some essential pion-production mechanisms are still missing in the models. In this article, we report the experimental results of the analyzing power (A,) as functions of the pion emission angle (0,) in the center-of-mass system and the relative momentum (p) of the final protons. The deduced angular dependence of A, x the spin-averaged cross section is expressed in terms of the associated Legendre polynomials Pri (cos 0,) and Pzr(cos0,) which are symmetrical and asymmetrical around 8, = 90”, respectively. The strength of the Prr term corresponds to the contribution of the pion s-wave amplitude from a P-state, whereas that of the Pzl term is determined by the contribution from the S- and higher states. The angular dependence is expected to be sensitive to the relative strength between the S-state and P-state amplitudes. The momentum dependence of A, integrated over the angular range enables to select the part of the function Prr and to determine the momentum dependence of the P-state amplitude. The interaction range of the pion-production mechanism on P-state amplitude is studied together with the TSL and IUCF data. 2. Experiment
Experiment has been carried out using the 390 MeV polarized proton beam from the Ring Cyclotron at the Research Center for Nuclear Physics (RCNP), Osaka University, Japan. The used liquid hydrogen target (L.H.) and cooling system have been developed by a group from Kyushu University. The container windows of the target were made of 12.5pm thick aramid foil. The contribution of the target foil has been measured by an “empty target” run with a hydrogen gas. An array of plastic scintillators is employed to detect the outgoing particles and measures the kinematical MEAN 135.0 (Me”) variables: scattering angles (@I, 0,) and kinetic energies XccQ mvtm 1.4(ueV) i n of two protons (Ti, Tz), on the basis of coplanar geometries ((pr=O, (pz=180”). The number of measured variables is sufficient to determine the three-body finalstate kinematics. The kinetic energy of the protons can be reconstructed from the amplitude signal of the E counter for stopped particles. The plastic scintillator hodoscope mounted in front of the E-counter is used to determine the direction of the outgoing particles. The angle covered by one hodoscope element is 4~17 mrad 1. missing-mass horizontally and f30 mrad vertically. Our detector sys- FIGURE tem covers the scattering angular range from 15” to 35” spectrum of the pp+ppX’. in the laboratory system. The beam polarization has been monitored by detecting pp elastic scattering events using a set of scintillator counters placed at 60”fl”. The analyzing power at this angle of -0.36 has been taken from the SAID. The beam polarization varied between 65-75%. no-production events have been identified by the missing mass technique. Figure 1 shows
Y: Maeda et al. /Nuclear Physics A721 (2003) 629c-632c
631~
the spin-averaged missing mass spectrum. A clear peak located around the no mass is seen in case of the L.H. target (Solid). The background from random coincidences of elastically scattered events (Dashed) and inelastic scattering events (Dotted) from the target foils, which was measured during the “empty run”, are also shown. 3. Result and Discussion Figure 2 shows the angular depen160-l 80 MeV/c 180-200 MeVlc 200-220 MeV/c dence of A, for three relative momentum regions. The error is the systematic, one which mainly comes from the uncertainty of the energy measurement. The solid lines show the result of fits with Legendre polynomial functions. The main contribution comes from the Prr term and the contribu- FIGURE 2. Angular dependence of the analyaing power for three regions of relative motion of the Psi term is below 4%, which mentum of the final protons. means the Ps amplitude gives the dominate contribution compared of the S-state amplitude. In addition, the value of A, increases towards higher momenta, Figure 3 shows the integrated analyzing power as function of the relative momentum (p) normalized to the maximum momentum (p,,& The data show that the value of A, increases with p. The dependence of A, can be expressed by the P-state amplitudes as
where p(p) is a phase space factor and dN/dp is a spin 0.7 o,a, 0.9 1 averaged cross section. Thus one can find from Eq.(l) P’m that the momentum dependence of the P-state ampli- PWSTRE 3. Relative momentude can be obtained utilizing the known dependence of turn dependenceof the analyzing dN/dp and p(p). power. Prom the theoretical point of view, the partial-wave amplitude (PWA) is calculated by .f dtpa~Pf(r)~~~(r)n(~)~i(r), ie. the overlap integral between the pion-prodmtiop opera tom I?(p) and the radial wave function of the initial protons Us, final protons VT(V), and pion &(r), where 1, is the pioa angular momentum. The strong momentum dependence of the amplitude comes from the dependence of the radial wave function of final protans and a pion. &me the shape of the radial wave fun&ion strongly depends on the atlgular momentum state, the pion-pro&&ion operator fptbrs out the typical region of the radial wave functions depending on the angular momentum state when integrated over the relative distawa. Accmdingly, the radial wave function of the 4nal state shows different momentum dependence on that selected region. Therefore, the radial wave function of the Anal state with a fixed distance instead of the integration provides a general estimation about the typical interaction region of the pion-production operator in a certain PWA.
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I: Maeda et al. /Nuclear Physics A721 (2003) 629c-632~
For this purpose the partial wave analysis has been carried out by usI ing available data which are da/dp c from TSL [5] at 400 MeV and RCNP z,, (present work) at 390 MeV, and Ax 2 and A,, from IUCF [6] at 400 MeV. These experimental data are given by the incoherent sum of three amplitudes FIGURE 4. The momentum dependence of (Ss,Ps,Pp). In the calculation, the spin-averagedcross section, Ax and A,,. momentum dependence of each PWA is given by ~~((T)(P~,(T)with a fixed nucleon distance (r). The nucleon wave function was taken from Paris potential and spherical Bessel functions were used for the pion. The typical interaction region of each Ps and Pp amplitude was evaluated to fit these data. In Figure 4, the solid lines show the best fit. The nucleon distance for the Ss amplitude is fixed and varies from 0.5 to 2.0 fm (Hatched area). The evaluated nucleon distances are typically 2.5 fm for Ps and 1.5 fm for Pp. Subsequently, the momentum dependence of A, is calculated by using Eq.(l) with the evaluated nucleon distances (Solid line in Fig.3). Our data show stronger momentum dependence than the solid line. In order to reproduce the momentum dependence of A,, nucleon distance above 2.5 fm is also necessary in the Pp amplitude, which is shown by the dotted line in Fig.3. According to the semi-phenomenological partial wave analysis, the data indicate that the long-range interaction of the pion-production operator, which has a magnitude around 2.5 fm, would give an important contribution to the Ps amplitude. In summary, we have measured the angular and momentum dependences of the analyzing power for the reaction p’p+ppxO at an incident energy of 390 MeV. The angular dependence shows the dominant contribution of PII and that the main contribution to s-wave pion-production comes from the P-state of the 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 the analyzing power and it is deduced that the long-range interaction is important for the pion-production from the P-state nucleons. Further theoretical studies are needed to pin down the production mechanism with a long-range interaction. REFERENCES 1. 2. 3. 4. 5.
H.O. Meyer et al., Nucl. Phys. A539, (1992) 633. A. Bondar et al., Phys. Lett. B356, (1995) 8. T.-S.H. Lee, D.O. Riska, Phys. Rev. Lett. 70, (1993) 2237. C. Hanhart, U. van Kolck, G.A. Miller, Phys. Rev. Lett 85, (2000) 2905. J. Zlomanczuk et al., Nucl. Phys. A693, (2001) 633. 6. H.O. Meyer et al., Phys. Rev. C63, (2001) 064002. 7. C. Hanhart, J. Haidenbauer, 0. Krehl, J. Speth, Phys. Lett. B444, (1998) 25. 8. K. Tamura, Y. Maeda, N. Matsuoka, Nucl. Phys. A684, (2001) 392c.
Nuclear Physics A721 (2003) 6290632~ www.elsevier.com/locate/npe
Analyzing power of the reaction pfp-+ppn’ at a beam energy of 390 MeV Y. Maedaa*, M. Segawab, H.P. Yoshidab, M. Nomachic, Y. Shimbarac, Y. Sugayac , K. Yasuda*, K. Tammae, T. Ishida’, T. Yagita’, A. Kacharavas aInstitut fiir Kernphysik, Forschungszentrum Jiilich, 52425 Jiilich, Germany bResearch Center for Nuclear Physics, Osaka University, Ibaraki, Osaka 567-0047, Japan CDepartment of Physics, Osaka University, Toyonaka, Osaka 560-0043, Japan *The 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 sPhysics Institute II, University Erlangen-Niirnberg,
91058 Erlangen, Germany
The analyzing power of the reaction jip+ppn’ has been measured at a beam energy of 390 MeV. The dependences of the analyzing power on the pion emission-angle and the relative momentum of two outgoing protons have been obtained. The angular dependence could be decomposed by Legendre polynomial and the relative contribution of the P21 to the PII function is less than 4%. The momentum dependence of the analyzing power has been studied to obtain information about the pion-production mechanism. It has been deduced that pion production due to the long-range interaction plays an important role in the momentum dependence of the P-state amplitude. 1. Introduction Over the last decade the total cross section of the pp+ppn’ reaction has been measured very precisely near the pion-production threshold at IUCF [l] and TSL [2]. In theoretical calculations [3] it has been shown that a large contribution of the s-wave pion-production amplitude is necessary to reproduce the experimental data. A proposed short-range interaction between the nucleons gives an essential contribution into the s-wave amplitude where the final protons couple to an S-state. In order to understand the s-wave pionproduction mechanisms, systematical studies based on the chiral effective theory are still in progress [4]. Recently, differential cross sections and the polarization observabies of no production have been measured at TSL [5] and IUCF [S] at several bombarding energies up to 425 MeV. Especially for the case of analyzing power A, and the spin correlation coefficient (1 - Ax - A,,)/4 existing models [7,8] predict a 3-10 times smaller value than the experimental data even though the calculations provide a good fit to the total cross *e-mail:y.maedaOfz-juelich.de 0375-9474/03/$ - see front matter 0 2003 Published by Elsevier Science B.V doi:lO.l016/S0375-9474(03)01139-4
630~
Z Maeda et al. /Nuclear Physics A721 (2003) 629~632~
section close to the threshold [8]. The experimental data show that there is a large contribution from the Ps amplitude, where the pion is emitted in an s-wave relative to the protons of P-state, and some essential pion-production mechanisms are still missing in the models. In this article, we report the experimental results of the analyzing power (A,) as functions of the pion emission angle (0,) in the center-of-mass system and the relative momentum (p) of the final protons. The deduced angular dependence of A, x the spin-averaged cross section is expressed in terms of the associated Legendre polynomials Pri (cos 0,) and Pzr(cos0,) which are symmetrical and asymmetrical around 8, = 90”, respectively. The strength of the Prr term corresponds to the contribution of the pion s-wave amplitude from a P-state, whereas that of the Pzl term is determined by the contribution from the S- and higher states. The angular dependence is expected to be sensitive to the relative strength between the S-state and P-state amplitudes. The momentum dependence of A, integrated over the angular range enables to select the part of the function Prr and to determine the momentum dependence of the P-state amplitude. The interaction range of the pion-production mechanism on P-state amplitude is studied together with the TSL and IUCF data. 2. Experiment
Experiment has been carried out using the 390 MeV polarized proton beam from the Ring Cyclotron at the Research Center for Nuclear Physics (RCNP), Osaka University, Japan. The used liquid hydrogen target (L.H.) and cooling system have been developed by a group from Kyushu University. The container windows of the target were made of 12.5pm thick aramid foil. The contribution of the target foil has been measured by an “empty target” run with a hydrogen gas. An array of plastic scintillators is employed to detect the outgoing particles and measures the kinematical MEAN 135.0 (Me”) variables: scattering angles (@I, 0,) and kinetic energies XccQ mvtm 1.4(ueV) i n of two protons (Ti, Tz), on the basis of coplanar geometries ((pr=O, (pz=180”). The number of measured variables is sufficient to determine the three-body finalstate kinematics. The kinetic energy of the protons can be reconstructed from the amplitude signal of the E counter for stopped particles. The plastic scintillator hodoscope mounted in front of the E-counter is used to determine the direction of the outgoing particles. The angle covered by one hodoscope element is 4~17 mrad 1. missing-mass horizontally and f30 mrad vertically. Our detector sys- FIGURE tem covers the scattering angular range from 15” to 35” spectrum of the pp+ppX’. in the laboratory system. The beam polarization has been monitored by detecting pp elastic scattering events using a set of scintillator counters placed at 60”fl”. The analyzing power at this angle of -0.36 has been taken from the SAID. The beam polarization varied between 65-75%. no-production events have been identified by the missing mass technique. Figure 1 shows
Y: Maeda et al. /Nuclear Physics A721 (2003) 629c-632c
631~
the spin-averaged missing mass spectrum. A clear peak located around the no mass is seen in case of the L.H. target (Solid). The background from random coincidences of elastically scattered events (Dashed) and inelastic scattering events (Dotted) from the target foils, which was measured during the “empty run”, are also shown. 3. Result and Discussion Figure 2 shows the angular depen160-l 80 MeV/c 180-200 MeVlc 200-220 MeV/c dence of A, for three relative momentum regions. The error is the systematic, one which mainly comes from the uncertainty of the energy measurement. The solid lines show the result of fits with Legendre polynomial functions. The main contribution comes from the Prr term and the contribu- FIGURE 2. Angular dependence of the analyaing power for three regions of relative motion of the Psi term is below 4%, which mentum of the final protons. means the Ps amplitude gives the dominate contribution compared of the S-state amplitude. In addition, the value of A, increases towards higher momenta, Figure 3 shows the integrated analyzing power as function of the relative momentum (p) normalized to the maximum momentum (p,,& The data show that the value of A, increases with p. The dependence of A, can be expressed by the P-state amplitudes as
where p(p) is a phase space factor and dN/dp is a spin 0.7 o,a, 0.9 1 averaged cross section. Thus one can find from Eq.(l) P’m that the momentum dependence of the P-state ampli- PWSTRE 3. Relative momentude can be obtained utilizing the known dependence of turn dependenceof the analyzing dN/dp and p(p). power. Prom the theoretical point of view, the partial-wave amplitude (PWA) is calculated by .f dtpa~Pf(r)~~~(r)n(~)~i(r), ie. the overlap integral between the pion-prodmtiop opera tom I?(p) and the radial wave function of the initial protons Us, final protons VT(V), and pion &(r), where 1, is the pioa angular momentum. The strong momentum dependence of the amplitude comes from the dependence of the radial wave function of final protans and a pion. &me the shape of the radial wave fun&ion strongly depends on the atlgular momentum state, the pion-pro&&ion operator fptbrs out the typical region of the radial wave functions depending on the angular momentum state when integrated over the relative distawa. Accmdingly, the radial wave function of the 4nal state shows different momentum dependence on that selected region. Therefore, the radial wave function of the Anal state with a fixed distance instead of the integration provides a general estimation about the typical interaction region of the pion-production operator in a certain PWA.
632~
I: Maeda et al. /Nuclear Physics A721 (2003) 629c-632~
For this purpose the partial wave analysis has been carried out by usI ing available data which are da/dp c from TSL [5] at 400 MeV and RCNP z,, (present work) at 390 MeV, and Ax 2 and A,, from IUCF [6] at 400 MeV. These experimental data are given by the incoherent sum of three amplitudes FIGURE 4. The momentum dependence of (Ss,Ps,Pp). In the calculation, the spin-averagedcross section, Ax and A,,. momentum dependence of each PWA is given by ~~((T)(P~,(T)with a fixed nucleon distance (r). The nucleon wave function was taken from Paris potential and spherical Bessel functions were used for the pion. The typical interaction region of each Ps and Pp amplitude was evaluated to fit these data. In Figure 4, the solid lines show the best fit. The nucleon distance for the Ss amplitude is fixed and varies from 0.5 to 2.0 fm (Hatched area). The evaluated nucleon distances are typically 2.5 fm for Ps and 1.5 fm for Pp. Subsequently, the momentum dependence of A, is calculated by using Eq.(l) with the evaluated nucleon distances (Solid line in Fig.3). Our data show stronger momentum dependence than the solid line. In order to reproduce the momentum dependence of A,, nucleon distance above 2.5 fm is also necessary in the Pp amplitude, which is shown by the dotted line in Fig.3. According to the semi-phenomenological partial wave analysis, the data indicate that the long-range interaction of the pion-production operator, which has a magnitude around 2.5 fm, would give an important contribution to the Ps amplitude. In summary, we have measured the angular and momentum dependences of the analyzing power for the reaction p’p+ppxO at an incident energy of 390 MeV. The angular dependence shows the dominant contribution of PII and that the main contribution to s-wave pion-production comes from the P-state of the 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 the analyzing power and it is deduced that the long-range interaction is important for the pion-production from the P-state nucleons. Further theoretical studies are needed to pin down the production mechanism with a long-range interaction. REFERENCES 1. 2. 3. 4. 5.
H.O. Meyer et al., Nucl. Phys. A539, (1992) 633. A. Bondar et al., Phys. Lett. B356, (1995) 8. T.-S.H. Lee, D.O. Riska, Phys. Rev. Lett. 70, (1993) 2237. C. Hanhart, U. van Kolck, G.A. Miller, Phys. Rev. Lett 85, (2000) 2905. J. Zlomanczuk et al., Nucl. Phys. A693, (2001) 633. 6. H.O. Meyer et al., Phys. Rev. C63, (2001) 064002. 7. C. Hanhart, J. Haidenbauer, 0. Krehl, J. Speth, Phys. Lett. B444, (1998) 25. 8. K. Tamura, Y. Maeda, N. Matsuoka, Nucl. Phys. A684, (2001) 392c.