- Email: [email protected]
Study of spin parts of three nucleon forces via d→p breakup reactions at intermediate energies
Nuclear Physics A 790 (2007) 450c–453c
breakup reactions at Study of spin parts of three nucleon forces via dp intermediate energies K. Sekiguchi, a H. Sakai,a b N. Sakamoto,a H. Kuboki,b M. Sasano,b Y. Takahashi,b K. Yako,b T. Kawabata, c Y. Maeda,c S. Sakaguchi,c Y. Sasamoto,c K. Suda,c T. Uesaka,c H. Okamura,d K. Itoh, e and T. Wakasa, f a
RIKEN, the Institute of Physical and Chemical Research, Saitama 351-0198, Japan.
b c
Center for Nuclear Study, University of Tokyo, 113-0033, Japan.
d e f
Department of Physics, University of Tokyo, 113-0033, Japan.
Research Center for Nuclear Physics, Osaka University, Osaka 567-0047, Japan.
Department of Physics, Saitama University, Saitama 338-8570, Japan.
Department of Physics, Kyushu University, 812-8581, Japan.
Measurements of deuteron–proton breakup reactions at 135 MeV/A have been made at RIKEN Accelerator Research Facility, focusing on the specific coplanar configurations. The obtained results are compared with the Faddeev calculations based on the modern nucleon–nucleon forces together with the Tucson-Melbourne99, and UrbanaIX three nucleon forces. 1. INTRODUCTION Recently the study of three-nucleon force properties has been extensively performed for proton–deuteron (pd) elastic scattering at intermediate energies (E/A ∼ 100 MeV) by comparing the precisely measured data and rigorous numerical Faddeev calculations based on the modern nucleon–nucleon (NN) potentials, e.g. CDBonn [1], AV18 [2], Nijimegen I and II [3] (see Ref. [4]). Cross section data for elastic pd scattering have shown large disagreement between data and the theoretical predictions with the modern NN forces, especially in the angular range where the cross sections take minimum. Combination of the NN forces and 2π–exchange type 3NFs removes this discrepancy and leads to a good description of the measured cross sections. However spin observables are not always explained by addition of the 3NFs. Elastic pd scattering shows the ability of 3NF study at the intermediate energies. In complete breakup (d+p → p+p+n) experiments, the situation would be more interesting since they cover different kinematic conditions. Also the total cross sections of the breakup reactions have been predicted to be larger than the elastic ones as the incident nucleon energy increases (e.g. σbreakup ∼ 2.5σela. at 135 MeV/A) [5], and then the larger 3NF effects could be seen in the breakup reactions than the elastic scattering at these energies. 0375-9474/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysa.2007.03.174
451c
K. Sekiguchi et al. / Nuclear Physics A 790 (2007) 450c–453c
Therefore we have extended the measurement to dp breakup reactions to access further 3NF effects. The measurement we have made are focused on the polarization transfer y coefficients Kyy and all deuteron analyzing powers (Ady , Ayy , Axx , Axz ) for the specific pp)n reaction at 135 MeV/A at the angles of the emerging coplanar configurations of 1 H(d, ◦ ◦ two protons (θ1 = 27 –33 , θ2 = 31◦ , φ1 −φ2 = 180◦ ). Note, the configurations include the p2 n final state interactions . For these configurations large 3NF effects are theoretically predicated [6]. 2. EXPERIMENT The experiment was performed at the RIKEN Accelerator Research Facility using the the vector and tensor polarized deuteron beams at 270 MeV (135 MeV/A) [7]. A liquid hydrogen with the thickness of 71 mg/cm2 was used as a hydrogen target. The two emerging protons (p1 , p2 ) were detected in coincidence to determine the dp breakup events. The p1 was momentum analyzed by the magnetic spectrograph SMART [8] and its polarizations were measured with the focal plane polarimeter EPOL [9]. The p2 was detected by the E–dE counters consisting of NaI(Tl) and plastic scintillators installed in a scattering chamber. The schematic view of the experimental setup is shown in Fig. 1. The kinetic energies were covered from 160 MeV–180 MeV for the p1 and 30 MeV–80 MeV for the p2 , respectively.
Magnetic Spectrograph SMART
}
EPOL
SMART
d
Liq.H2 target
p1
θ1 θ2
n
EPOL Analyzer Target (Carbon)
beam
p2
NaI(Tl)-Plastic (Scattering Chamber)
Figure 1. Schematic view of the experimental setup for the dp breakup measurement.
452c
K. Sekiguchi et al. / Nuclear Physics A 790 (2007) 450c–453c
Figure 2. Parts of the measured data of analyzing powers (Ady , Axx ) and deuteron to y for d–p breakup reaction at 135 MeV/A. proton polarization transfer coefficient Kyy 3. DISCUSSION In Fig. 2 parts of the experimental results are shown with open circles along with the kinematical curves of the emerging two protons (S-curve). The errors are statistical ones only. The statistical errors are smaller than 0.02 for all deuteron analyzing powers y . The data were obtained with the and 0.03 for the polarization transfer coefficient Kyy S–curve energy bin of 10 MeV. The dark (light) shaded bands in the figure are the Faddeev calculations with (w/o) Tucson-Melbourne99 (TM99) 3NF [10] based on the modern NN potentials, namely CDBonn, AV18, Nijimegen I and II. The dashed lines are the calculations with including Urbana IX 3NF [11] based on AV18 potential. All predictions shown here are also integrated with the S-curve energy bin of 10 MeV for the direct comparison between the data and the calculations. Based on the comparison between the data and the predictions based on the NN forces y only, clear discrepancies exist for Axx and Kyy . The agreements are improved by adding
K. Sekiguchi et al. / Nuclear Physics A 790 (2007) 450c–453c
453c
the 3NFs, especially the Urbana IX 3NF. However for the vector analyzing power Ady the agreement is deteriorated by taking into account the 3NFs. The data are well reproduced by the predictions with the NN forces only. The results of the comparison for the coplanar configurations of the breakup reaction show that additional components other than 2π-exchange 3NFs are needed and also show that the measured spin observables are useful to clarify the spin dependence of 3NFs. It would be interesting to see how well the theoretical approaches, e.g. addition of 3NFs other than 2π exchange types, relativistic treatment [12], and the potentials based on chiral effective field theory [13] describe these obtained data. 4. SUMMARY We have extended the measurement from elastic dp scattering to dp breakup reactions in order to study the 3NF properties. The measured data are all deuteron analyzing y powers (Ady , Axx , Ayy , Axz ) and deuteron to proton polarization transfer coefficient Kyy for the coplanar configurations at the incident deuteron energy of 270 MeV (135 MeV/A). The data are compared with the Faddeev calculations with and without the TucsonMelbourne99 3NF or the UrbanaIX 3NF. Not all spin observables are reproduced by the present 3NFs, indicating that components other than 2π–exchange 3NFs are required to describe the data. ACKNOWLEDGEMENT We would like to thank H. Witala, W. Gl¨ockle, H. Kamada, J. Golak and A. Nogga for their strong theoretical support. We would also like to thank A. Deltuva, P. U. Sauer and A. C. Fonseca for their useful comments on theory. We would like to express the appreciation for the continuous help of the staff of RIKEN Accelerator Research Facility. REFERENCES 1. 2. 3. 4.
5. 6. 7. 8. 9. 10. 11. 12. 13.
R. Machleidt, Phys. Rev. C 63 (2001) 024001. R. B. Wiringa et al., Phys. Rev. C 51 (1995) 38. V. G. J. Stoks, et al., Phys. Rev. C 49 (1994) 2950. For example, K. Sekiguchi et al., Phys. Rev. C 65 (2002) 034003; K. Hatanaka et al., ibid 66 (2002) 044002; K. Ermisch et al., ibid 68 (2003) 051001; R. V. Cadman et al., Phys. Rev. Lett. 86 (2001) 967. ˙ lnierczuk et al., Phys. Rev. C 66 (2002) 024003. J. Kuro´s-Zo H. Witala, private communications. H. Okamura et al., AIP Conf. Proc. 293 (1994) 84; H. Okamura et al., ibid. 343 (1995) 123. T. Ichihara et al., Nucl. Phys. A 569 (1994) 287c. T. Saito, Ph.D. thesis, University of Tokyo. S. A. Coon, and M. T. Pe˜ na, Phys. Rev. C 48 (1993) 2559. B. S. Pudliner et al., Phys. Rev. C 56 (1997) 1720. H. Witala et al., Phys. Lett. B 634 (2006) 374. E. Epelbaum Prog. Part. Nucl. Phys. 57 (2006) 654.
breakup reactions at Study of spin parts of three nucleon forces via dp intermediate energies K. Sekiguchi, a H. Sakai,a b N. Sakamoto,a H. Kuboki,b M. Sasano,b Y. Takahashi,b K. Yako,b T. Kawabata, c Y. Maeda,c S. Sakaguchi,c Y. Sasamoto,c K. Suda,c T. Uesaka,c H. Okamura,d K. Itoh, e and T. Wakasa, f a
RIKEN, the Institute of Physical and Chemical Research, Saitama 351-0198, Japan.
b c
Center for Nuclear Study, University of Tokyo, 113-0033, Japan.
d e f
Department of Physics, University of Tokyo, 113-0033, Japan.
Research Center for Nuclear Physics, Osaka University, Osaka 567-0047, Japan.
Department of Physics, Saitama University, Saitama 338-8570, Japan.
Department of Physics, Kyushu University, 812-8581, Japan.
Measurements of deuteron–proton breakup reactions at 135 MeV/A have been made at RIKEN Accelerator Research Facility, focusing on the specific coplanar configurations. The obtained results are compared with the Faddeev calculations based on the modern nucleon–nucleon forces together with the Tucson-Melbourne99, and UrbanaIX three nucleon forces. 1. INTRODUCTION Recently the study of three-nucleon force properties has been extensively performed for proton–deuteron (pd) elastic scattering at intermediate energies (E/A ∼ 100 MeV) by comparing the precisely measured data and rigorous numerical Faddeev calculations based on the modern nucleon–nucleon (NN) potentials, e.g. CDBonn [1], AV18 [2], Nijimegen I and II [3] (see Ref. [4]). Cross section data for elastic pd scattering have shown large disagreement between data and the theoretical predictions with the modern NN forces, especially in the angular range where the cross sections take minimum. Combination of the NN forces and 2π–exchange type 3NFs removes this discrepancy and leads to a good description of the measured cross sections. However spin observables are not always explained by addition of the 3NFs. Elastic pd scattering shows the ability of 3NF study at the intermediate energies. In complete breakup (d+p → p+p+n) experiments, the situation would be more interesting since they cover different kinematic conditions. Also the total cross sections of the breakup reactions have been predicted to be larger than the elastic ones as the incident nucleon energy increases (e.g. σbreakup ∼ 2.5σela. at 135 MeV/A) [5], and then the larger 3NF effects could be seen in the breakup reactions than the elastic scattering at these energies. 0375-9474/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysa.2007.03.174
451c
K. Sekiguchi et al. / Nuclear Physics A 790 (2007) 450c–453c
Therefore we have extended the measurement to dp breakup reactions to access further 3NF effects. The measurement we have made are focused on the polarization transfer y coefficients Kyy and all deuteron analyzing powers (Ady , Ayy , Axx , Axz ) for the specific pp)n reaction at 135 MeV/A at the angles of the emerging coplanar configurations of 1 H(d, ◦ ◦ two protons (θ1 = 27 –33 , θ2 = 31◦ , φ1 −φ2 = 180◦ ). Note, the configurations include the p2 n final state interactions . For these configurations large 3NF effects are theoretically predicated [6]. 2. EXPERIMENT The experiment was performed at the RIKEN Accelerator Research Facility using the the vector and tensor polarized deuteron beams at 270 MeV (135 MeV/A) [7]. A liquid hydrogen with the thickness of 71 mg/cm2 was used as a hydrogen target. The two emerging protons (p1 , p2 ) were detected in coincidence to determine the dp breakup events. The p1 was momentum analyzed by the magnetic spectrograph SMART [8] and its polarizations were measured with the focal plane polarimeter EPOL [9]. The p2 was detected by the E–dE counters consisting of NaI(Tl) and plastic scintillators installed in a scattering chamber. The schematic view of the experimental setup is shown in Fig. 1. The kinetic energies were covered from 160 MeV–180 MeV for the p1 and 30 MeV–80 MeV for the p2 , respectively.
Magnetic Spectrograph SMART
}
EPOL
SMART
d
Liq.H2 target
p1
θ1 θ2
n
EPOL Analyzer Target (Carbon)
beam
p2
NaI(Tl)-Plastic (Scattering Chamber)
Figure 1. Schematic view of the experimental setup for the dp breakup measurement.
452c
K. Sekiguchi et al. / Nuclear Physics A 790 (2007) 450c–453c
Figure 2. Parts of the measured data of analyzing powers (Ady , Axx ) and deuteron to y for d–p breakup reaction at 135 MeV/A. proton polarization transfer coefficient Kyy 3. DISCUSSION In Fig. 2 parts of the experimental results are shown with open circles along with the kinematical curves of the emerging two protons (S-curve). The errors are statistical ones only. The statistical errors are smaller than 0.02 for all deuteron analyzing powers y . The data were obtained with the and 0.03 for the polarization transfer coefficient Kyy S–curve energy bin of 10 MeV. The dark (light) shaded bands in the figure are the Faddeev calculations with (w/o) Tucson-Melbourne99 (TM99) 3NF [10] based on the modern NN potentials, namely CDBonn, AV18, Nijimegen I and II. The dashed lines are the calculations with including Urbana IX 3NF [11] based on AV18 potential. All predictions shown here are also integrated with the S-curve energy bin of 10 MeV for the direct comparison between the data and the calculations. Based on the comparison between the data and the predictions based on the NN forces y only, clear discrepancies exist for Axx and Kyy . The agreements are improved by adding
K. Sekiguchi et al. / Nuclear Physics A 790 (2007) 450c–453c
453c
the 3NFs, especially the Urbana IX 3NF. However for the vector analyzing power Ady the agreement is deteriorated by taking into account the 3NFs. The data are well reproduced by the predictions with the NN forces only. The results of the comparison for the coplanar configurations of the breakup reaction show that additional components other than 2π-exchange 3NFs are needed and also show that the measured spin observables are useful to clarify the spin dependence of 3NFs. It would be interesting to see how well the theoretical approaches, e.g. addition of 3NFs other than 2π exchange types, relativistic treatment [12], and the potentials based on chiral effective field theory [13] describe these obtained data. 4. SUMMARY We have extended the measurement from elastic dp scattering to dp breakup reactions in order to study the 3NF properties. The measured data are all deuteron analyzing y powers (Ady , Axx , Ayy , Axz ) and deuteron to proton polarization transfer coefficient Kyy for the coplanar configurations at the incident deuteron energy of 270 MeV (135 MeV/A). The data are compared with the Faddeev calculations with and without the TucsonMelbourne99 3NF or the UrbanaIX 3NF. Not all spin observables are reproduced by the present 3NFs, indicating that components other than 2π–exchange 3NFs are required to describe the data. ACKNOWLEDGEMENT We would like to thank H. Witala, W. Gl¨ockle, H. Kamada, J. Golak and A. Nogga for their strong theoretical support. We would also like to thank A. Deltuva, P. U. Sauer and A. C. Fonseca for their useful comments on theory. We would like to express the appreciation for the continuous help of the staff of RIKEN Accelerator Research Facility. REFERENCES 1. 2. 3. 4.
5. 6. 7. 8. 9. 10. 11. 12. 13.
R. Machleidt, Phys. Rev. C 63 (2001) 024001. R. B. Wiringa et al., Phys. Rev. C 51 (1995) 38. V. G. J. Stoks, et al., Phys. Rev. C 49 (1994) 2950. For example, K. Sekiguchi et al., Phys. Rev. C 65 (2002) 034003; K. Hatanaka et al., ibid 66 (2002) 044002; K. Ermisch et al., ibid 68 (2003) 051001; R. V. Cadman et al., Phys. Rev. Lett. 86 (2001) 967. ˙ lnierczuk et al., Phys. Rev. C 66 (2002) 024003. J. Kuro´s-Zo H. Witala, private communications. H. Okamura et al., AIP Conf. Proc. 293 (1994) 84; H. Okamura et al., ibid. 343 (1995) 123. T. Ichihara et al., Nucl. Phys. A 569 (1994) 287c. T. Saito, Ph.D. thesis, University of Tokyo. S. A. Coon, and M. T. Pe˜ na, Phys. Rev. C 48 (1993) 2559. B. S. Pudliner et al., Phys. Rev. C 56 (1997) 1720. H. Witala et al., Phys. Lett. B 634 (2006) 374. E. Epelbaum Prog. Part. Nucl. Phys. 57 (2006) 654.