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Production of projectile-like fragments at intermediate energies
Nuclear Physics A 701 (2002) 150c–155c www.elsevier.com/locate/npe
Production of projectile-like fragments at intermediate energies S. Momota a,∗ , M. Notani a , S. Ito a , A. Ozawa a , T. Suzuki a,1 , I. Tanihata a , N. Aoi a , H. Sakurai a , T. Teranishi a , Y. Watanabe a , A. Yoshida a , A. Inabe a , T. Kubo a , H. Okuno a , N. Fukuda b , H. Iwasaki b , K. Yoneda b , H. Ogawa c , A. Kitagawa d , M. Kanazawa d , M. Torikoshi d , M. Suda d , A. Ono e a The Institute of Physical and Chemical Research (RIKEN), Hirosawa 2-1, Wako, Saitama 351-0198, Japan b Department of Physics, University of Tokyo, Tokyo 113-0033, Japan c Department of Applied Physics, Tokyo Institute of Technology, Tokyo 152-8551, Japan d National Institute of Radiological Sciences (NIRS), Chiba 263-8555, Japan e Department of Physics, Tohoku University, Miyagi 980-8578, Japan
Abstract The momentum distributions of projectile-like fragments produced in the 40 Ar + 9 Be reaction at E/A = 90 MeV and the 16 O + 12 C reaction at E/A = 290 MeV were observed. A correlation between the width of the transverse momentum distribution and the velocity was found at E/A = 90 MeV. Coulomb final-state interaction and AMD calculation cannot explain this correlation. A good agreement between EPAX2 and the production cross sections derived from observed momentum distribution of the fragments was found. 2002 Elsevier Science B.V. All rights reserved. Keywords: Nuclear reaction; Fragmentation reactions; Momentum distribution; Production cross section
1. Introduction A momentum distribution of projectile-like fragments (PLFs) provides information on the nuclear structure and the mechanism of a nuclear reaction through which fragments are * Corresponding author. Present address: Kochi University of Technology, Tosayamada, Kochi 782-8502, Japan. E-mail address: [email protected] (S. Momota). 1 Present address: Department of Physics, Niigata University, Niigata 950-2181, Japan.
0375-9474/02/$ – see front matter 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 5 - 9 4 7 4 ( 0 1 ) 0 1 5 6 4 - 0
S. Momota et al. / Nuclear Physics A 701 (2002) 150c–155c
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produced. The distribution is also very important in designing experiments with radioactive nuclear beams. At relativistic energies of E/A > 1 GeV, direct processes such as the projectile fragmentation process are dominant. The momentum distribution of PLFs can be understood by a simple model based on Fermi momentum of removed nucleons inside the projectile nucleus introduced by Goldhaber [1]. The production cross sections of PLFs can be predicted by an empirical parametrization, such as EPAX [2]. At an intermediate energy E/A ∼ 100 MeV, both the direct and multistep processes are included in the nuclear reaction. In this article, we concentrate on the transverse momentum (PT ) distribution and the production cross sections (σ (prod.)) of PLFs.
2. Apparatus and method An 40 Ar beam at E/A = 90 MeV accelerated by RIKEN Ring Cyclotron impinged on a 0.5-mm-thick 9 Be target to produce PLFs. The produced PLFs were separated and identified by an isotope separator, RIPS. The beam current was monitored by two sets of monitor counters consisting of three plastic scintillators. The momentum acceptance of RIPS was P /P = ±0.5% and the angular acceptance was ±12.5 mrad in θx and θy . The angle of incidence of the 40 Ar beam was deflected by the RIPS swinger magnet located at the upstream side of the 9 Be target. The scattering angle of fragments was defined by the 4D slit, which was located just after the 9 Be target. The PT distribution was observed at Bρ = 3.71 Tm. To derive the production cross section of fragments, the magnetic rigidity of RIPS was varied stepwise over the range Bρ = 2.52–4.14 Tm. An 16 O beam at E/A = 290 MeV accelerated by HIMAC at NIRS impinged on a 1.0-mm-thick 12 C target to produce PLFs. The beam current was monitored by a secondary electron monitor at the 12 C target. The momentum acceptance of an isotope separator was P /P = ±2.5% and the angular acceptance was ±13.0 mrad in θx and θy . The magnetic rigidity of the separator was varied stepwise over the range Bρ = 2.36–7.06 Tm. Particle identification was performed by simultaneous measurements of the time of flight (TOF) and the energy loss in silicon detectors (E) event by event at RIKEN and NIRS. The typical value for errors of the production rate derived from the experimental results was about 10%. The main part of this error came from the ambiguity of the beam-current monitor.
3. Results and discussion The PT distributions of PLFs measured at RIKEN are shown in Fig. 1. As shown in the figure, the observed distributions, except for a few isotopes, could be fitted by Gaussian and their standard deviations (σT ’s) were derived. The σT ’s derived from the observed PT distributions are shown in Fig. 2 as a function of the mass of PLF with that derived from a model calculation. The observed σT are larger than the calculated σT in which the contribution of Fermi momentum of removal
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S. Momota et al. / Nuclear Physics A 701 (2002) 150c–155c
Fig. 1. Observed PT distribution of N isotopes measured at PL = 7782 MeV/c.
Fig. 2. Observed σT as a function of mass of PLFs. The dotted line shows the calculated σT ’s in which the contributions of σ (Fermi) and σ (def.) are included. The solid line and the dashed line show the calculated σT ’s in which the contribution of Coulomb final-state interaction is included in addition to the above calculations.
nucleons, σ (Fermi) [1] and the deflection of projectile in the field of the target, σ (def.) [3] are included. Values of σ0 = 90 MeV/c and σD = 195 MeV/c were used to calculate σ (Fermi) and σ (def.), respectively. Coulomb final-state interaction introduced in Ref. [4] fails to explain this systematic enhancement as shown in Fig. 2. In Fig. 3(a), the observed σT ’s are shown as a function of the velocity of PLFs. The velocity of the 40 Ar beam corresponds to PL /A = 413 MeV/c. The correlation between
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Fig. 3. (a) Observed σT as a function of velocity. (b) Observed σT as a function of velocity. The arrows and the dotted lines shows the velocity of primary beam, 40 Ar.
σT and PL /A, which is independent on any isotope, was found. By subtracting the contributions of σ (Fermi) and of σ (def.), (σT )2 = σT2 − σ (Fermi)2 + σ (def.)2 , (1) this correlation can be extracted more clearly (Fig. 3(b)). The agreement between the observed σT ’s and the calculated σT ’s at higher momentum implies that the fragments with
Fig. 4. σT ’s and σT ’s for O isotopes calculated by AMD. The solid line indicates to observed σT ’s.
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Fig. 5. σ (prod.) of PLFs measured at (a) RIKEN and (b) NIRS with EPAX2 predictions.
higher momentum are produced through a direct process. The enhancement of the σT ’s at lower momentum implies the contamination of other reaction mechanisms. To understand this correlation, the reaction 40 Ar + 9 Be at E/A = 90 MeV was simulated by antisymmetrized molecular dynamics (AMD), which is a microscopic calculation. The PT distribution derived from this simulation is Gaussian and the σT ’s were determined by fitting. The typical results derived from AMD calculation are shown in Fig. 4. The AMD calculation failed to reproduce the correlation between σT and PL /A. By integrating the observed production rates over PL and PT , σ (prod.) was derived. The σ (prod.)’s of PLFs measured at RIKEN and at NIRS are shown along with EPAX2 predictions in Fig. 5. The good agreement between EPAX2 and the observed results is easily seen. σ (prod.) was measured at MSU [5] under almost the same condition as in the RIKEN experiment. A rather good agreement has been found for nuclei near to the stable line and differences were found for neutron rich nuclei.
4. Conclusion The momentum distribution of PLFs at intermediate energies were measured at E/A = 90 and 290 MeV. The obvious systematics between σT and PL /A is derived from the PT distribution observed at an energy of E/A = 90 MeV. Coulomb final-state interaction and AMD calculation fail to explain the systematics. To understand this correlation, further experimental and theoretical studies are required.
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σ (prod.)’s are derived from the observed PT and PL distributions. The good agreement between the observed σ (prod.)’s and EPAX2 predictions supports the validity of EPAX2 at intermediate energies. The present results also give important information for applications. σT and σ (prod.) of PLFs given in this study will help us design experiments in which a radioactive beam can be utilized.
Acknowledgements The staff and crew of the RIKEN Ring Cyclotron and of HIMAC of NIRS are appreciated for their hospitality and cooperation. Part of this work was supported by RIKEN Special Researchers’ Basic Science Program.
References [1] A.S. Goldhaber, Phys. Lett. 53B (1974) 306. [2] Sümmerer, B. Blank, Phys. Rev. C 61 (2000) 034607. [3] K. Van Bibber, D.L. Hendrie, D.K. Scott, H.H. Weiman, L.S. Schröder, J.V. Geage, S.A. Cessin, R. Treuhaft, Y.J. Grossiord, J.O. Rasmussen, C.Y. Wong, Phys. Rev. Lett. 43 (1979) 840. [4] C.-Y. Wong, K. Van Bibber, Phys. Rev. C 25 (1982) 2990. [5] M. Fauerbach, D.J. Morrissey, W. Benenson, B.A. Brown, M. Hellström, J.H. Kelley, R.A. Kryger, R. Pfaff, C.F. Powell, B.M. Sherrill, Phys. Rev. C 53 (1996) 647.
Production of projectile-like fragments at intermediate energies S. Momota a,∗ , M. Notani a , S. Ito a , A. Ozawa a , T. Suzuki a,1 , I. Tanihata a , N. Aoi a , H. Sakurai a , T. Teranishi a , Y. Watanabe a , A. Yoshida a , A. Inabe a , T. Kubo a , H. Okuno a , N. Fukuda b , H. Iwasaki b , K. Yoneda b , H. Ogawa c , A. Kitagawa d , M. Kanazawa d , M. Torikoshi d , M. Suda d , A. Ono e a The Institute of Physical and Chemical Research (RIKEN), Hirosawa 2-1, Wako, Saitama 351-0198, Japan b Department of Physics, University of Tokyo, Tokyo 113-0033, Japan c Department of Applied Physics, Tokyo Institute of Technology, Tokyo 152-8551, Japan d National Institute of Radiological Sciences (NIRS), Chiba 263-8555, Japan e Department of Physics, Tohoku University, Miyagi 980-8578, Japan
Abstract The momentum distributions of projectile-like fragments produced in the 40 Ar + 9 Be reaction at E/A = 90 MeV and the 16 O + 12 C reaction at E/A = 290 MeV were observed. A correlation between the width of the transverse momentum distribution and the velocity was found at E/A = 90 MeV. Coulomb final-state interaction and AMD calculation cannot explain this correlation. A good agreement between EPAX2 and the production cross sections derived from observed momentum distribution of the fragments was found. 2002 Elsevier Science B.V. All rights reserved. Keywords: Nuclear reaction; Fragmentation reactions; Momentum distribution; Production cross section
1. Introduction A momentum distribution of projectile-like fragments (PLFs) provides information on the nuclear structure and the mechanism of a nuclear reaction through which fragments are * Corresponding author. Present address: Kochi University of Technology, Tosayamada, Kochi 782-8502, Japan. E-mail address: [email protected] (S. Momota). 1 Present address: Department of Physics, Niigata University, Niigata 950-2181, Japan.
0375-9474/02/$ – see front matter 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 5 - 9 4 7 4 ( 0 1 ) 0 1 5 6 4 - 0
S. Momota et al. / Nuclear Physics A 701 (2002) 150c–155c
151c
produced. The distribution is also very important in designing experiments with radioactive nuclear beams. At relativistic energies of E/A > 1 GeV, direct processes such as the projectile fragmentation process are dominant. The momentum distribution of PLFs can be understood by a simple model based on Fermi momentum of removed nucleons inside the projectile nucleus introduced by Goldhaber [1]. The production cross sections of PLFs can be predicted by an empirical parametrization, such as EPAX [2]. At an intermediate energy E/A ∼ 100 MeV, both the direct and multistep processes are included in the nuclear reaction. In this article, we concentrate on the transverse momentum (PT ) distribution and the production cross sections (σ (prod.)) of PLFs.
2. Apparatus and method An 40 Ar beam at E/A = 90 MeV accelerated by RIKEN Ring Cyclotron impinged on a 0.5-mm-thick 9 Be target to produce PLFs. The produced PLFs were separated and identified by an isotope separator, RIPS. The beam current was monitored by two sets of monitor counters consisting of three plastic scintillators. The momentum acceptance of RIPS was P /P = ±0.5% and the angular acceptance was ±12.5 mrad in θx and θy . The angle of incidence of the 40 Ar beam was deflected by the RIPS swinger magnet located at the upstream side of the 9 Be target. The scattering angle of fragments was defined by the 4D slit, which was located just after the 9 Be target. The PT distribution was observed at Bρ = 3.71 Tm. To derive the production cross section of fragments, the magnetic rigidity of RIPS was varied stepwise over the range Bρ = 2.52–4.14 Tm. An 16 O beam at E/A = 290 MeV accelerated by HIMAC at NIRS impinged on a 1.0-mm-thick 12 C target to produce PLFs. The beam current was monitored by a secondary electron monitor at the 12 C target. The momentum acceptance of an isotope separator was P /P = ±2.5% and the angular acceptance was ±13.0 mrad in θx and θy . The magnetic rigidity of the separator was varied stepwise over the range Bρ = 2.36–7.06 Tm. Particle identification was performed by simultaneous measurements of the time of flight (TOF) and the energy loss in silicon detectors (E) event by event at RIKEN and NIRS. The typical value for errors of the production rate derived from the experimental results was about 10%. The main part of this error came from the ambiguity of the beam-current monitor.
3. Results and discussion The PT distributions of PLFs measured at RIKEN are shown in Fig. 1. As shown in the figure, the observed distributions, except for a few isotopes, could be fitted by Gaussian and their standard deviations (σT ’s) were derived. The σT ’s derived from the observed PT distributions are shown in Fig. 2 as a function of the mass of PLF with that derived from a model calculation. The observed σT are larger than the calculated σT in which the contribution of Fermi momentum of removal
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S. Momota et al. / Nuclear Physics A 701 (2002) 150c–155c
Fig. 1. Observed PT distribution of N isotopes measured at PL = 7782 MeV/c.
Fig. 2. Observed σT as a function of mass of PLFs. The dotted line shows the calculated σT ’s in which the contributions of σ (Fermi) and σ (def.) are included. The solid line and the dashed line show the calculated σT ’s in which the contribution of Coulomb final-state interaction is included in addition to the above calculations.
nucleons, σ (Fermi) [1] and the deflection of projectile in the field of the target, σ (def.) [3] are included. Values of σ0 = 90 MeV/c and σD = 195 MeV/c were used to calculate σ (Fermi) and σ (def.), respectively. Coulomb final-state interaction introduced in Ref. [4] fails to explain this systematic enhancement as shown in Fig. 2. In Fig. 3(a), the observed σT ’s are shown as a function of the velocity of PLFs. The velocity of the 40 Ar beam corresponds to PL /A = 413 MeV/c. The correlation between
S. Momota et al. / Nuclear Physics A 701 (2002) 150c–155c
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Fig. 3. (a) Observed σT as a function of velocity. (b) Observed σT as a function of velocity. The arrows and the dotted lines shows the velocity of primary beam, 40 Ar.
σT and PL /A, which is independent on any isotope, was found. By subtracting the contributions of σ (Fermi) and of σ (def.), (σT )2 = σT2 − σ (Fermi)2 + σ (def.)2 , (1) this correlation can be extracted more clearly (Fig. 3(b)). The agreement between the observed σT ’s and the calculated σT ’s at higher momentum implies that the fragments with
Fig. 4. σT ’s and σT ’s for O isotopes calculated by AMD. The solid line indicates to observed σT ’s.
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Fig. 5. σ (prod.) of PLFs measured at (a) RIKEN and (b) NIRS with EPAX2 predictions.
higher momentum are produced through a direct process. The enhancement of the σT ’s at lower momentum implies the contamination of other reaction mechanisms. To understand this correlation, the reaction 40 Ar + 9 Be at E/A = 90 MeV was simulated by antisymmetrized molecular dynamics (AMD), which is a microscopic calculation. The PT distribution derived from this simulation is Gaussian and the σT ’s were determined by fitting. The typical results derived from AMD calculation are shown in Fig. 4. The AMD calculation failed to reproduce the correlation between σT and PL /A. By integrating the observed production rates over PL and PT , σ (prod.) was derived. The σ (prod.)’s of PLFs measured at RIKEN and at NIRS are shown along with EPAX2 predictions in Fig. 5. The good agreement between EPAX2 and the observed results is easily seen. σ (prod.) was measured at MSU [5] under almost the same condition as in the RIKEN experiment. A rather good agreement has been found for nuclei near to the stable line and differences were found for neutron rich nuclei.
4. Conclusion The momentum distribution of PLFs at intermediate energies were measured at E/A = 90 and 290 MeV. The obvious systematics between σT and PL /A is derived from the PT distribution observed at an energy of E/A = 90 MeV. Coulomb final-state interaction and AMD calculation fail to explain the systematics. To understand this correlation, further experimental and theoretical studies are required.
S. Momota et al. / Nuclear Physics A 701 (2002) 150c–155c
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σ (prod.)’s are derived from the observed PT and PL distributions. The good agreement between the observed σ (prod.)’s and EPAX2 predictions supports the validity of EPAX2 at intermediate energies. The present results also give important information for applications. σT and σ (prod.) of PLFs given in this study will help us design experiments in which a radioactive beam can be utilized.
Acknowledgements The staff and crew of the RIKEN Ring Cyclotron and of HIMAC of NIRS are appreciated for their hospitality and cooperation. Part of this work was supported by RIKEN Special Researchers’ Basic Science Program.
References [1] A.S. Goldhaber, Phys. Lett. 53B (1974) 306. [2] Sümmerer, B. Blank, Phys. Rev. C 61 (2000) 034607. [3] K. Van Bibber, D.L. Hendrie, D.K. Scott, H.H. Weiman, L.S. Schröder, J.V. Geage, S.A. Cessin, R. Treuhaft, Y.J. Grossiord, J.O. Rasmussen, C.Y. Wong, Phys. Rev. Lett. 43 (1979) 840. [4] C.-Y. Wong, K. Van Bibber, Phys. Rev. C 25 (1982) 2990. [5] M. Fauerbach, D.J. Morrissey, W. Benenson, B.A. Brown, M. Hellström, J.H. Kelley, R.A. Kryger, R. Pfaff, C.F. Powell, B.M. Sherrill, Phys. Rev. C 53 (1996) 647.