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1. Pairing Forces Govern Population of Doubly Magic Ca54 from Direct Reactions

Author

J. M. Gheller, S. Y. Park, K. Yoneda, Masaki Sasano, P. A. Söderström, D. Sohler, D. Körper, H. Simon, A. Gillibert, K. Miki, Satoshi Takeuchi, Yasuhiro Togano, M. MacCormick, R.-B. Gerst, Duo Yan, Tomohiro Uesaka, Fabia Schindler, V. Wagner, B. D. Linh, M. Holl, A. Corsi, N. Paul, Igor Gašparić, H. N. Liu, P. Koseoglou, E. Sahin, Yosuke Kondo, T. Lokotko, T. Isobe, Victor Vaquero, M. L. Cortés, V. Werner, Takashi Nakamura, W. Rodriguez, Zaihong Yang, A. Delbart, S. Franchoo, F. Château, V. Lapoux, P. Doornenbal, K. I. Hahn, L. Stuhl, I. Murray, C. Caesar, Kazuyuki Ogata, C. Lehr, T. Kobayashi, X. X. Xu, C. Hilaire, Si-Ge Chen, Yutaka Utsuno, V. Panin, A. Giganon, Jenny Lee, N. L. Achouri, L. X. Chung, Y. L. Sun, K. Moschner, Yuya Kubota, D. M. Rossi, H. Baba, F. Flavigny, Masahiro Yasuda, L. Zanetti, Kathrin Wimmer, Dong-Wook Kim, O. Aktas, F. Browne, S. Wang, A. Obertelli, J. Kahlbow, Hiroyoshi Sakurai, T. Motobayashi, Julien Gibelin, K. Boretzky, D. Calvet, David Steppenbeck, H. Törnqvist, Thomas Aumann, Nobuyuki Chiga, T. Koiwai, Kazuki Yoshida, Hideaki Otsu, Hirofumi Yamada, and J. Tscheuschner

Subjects
Physics, education.field_of_study, Proton, 010308 nuclear & particles physics, Nuclear Theory, Population, Nuclear shell model, General Physics and Astronomy, 01 natural sciences, 7. Clean energy, Pairing, Excited state, 0103 physical sciences, Neutron, Atomic physics, Nuclear Experiment, 010306 general physics, Nucleon, Ground state, education
Abstract

Direct proton-knockout reactions of ^{55}Sc at ∼220 MeV/nucleon were studied at the RIKEN Radioactive Isotope Beam Factory. Populated states of ^{54}Ca were investigated through γ-ray and invariant-mass spectroscopy. Level energies were calculated from the nuclear shell model employing a phenomenological internucleon interaction. Theoretical cross sections to states were calculated from distorted-wave impulse approximation estimates multiplied by the shell model spectroscopic factors, which describe the wave function overlap of the ^{55}Sc ground state with states in ^{54}Ca. Despite the calculations showing a significant amplitude of excited neutron configurations in the ground-state of ^{55}Sc, valence proton removals populated predominantly the ground state of ^{54}Ca. This counterintuitive result is attributed to pairing effects leading to a dominance of the ground-state spectroscopic factor. Owing to the ubiquity of the pairing interaction, this argument should be generally applicable to direct knockout reactions from odd-even to even-even nuclei.

Published
2021
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2. Experimental Study of $^{4}n$ by Directly Detecting the Decay Neutrons

Author

Atsumi Saito, Yohei Shimizu, H. Törnqvist, B. Monteagudo, T. Isobe, M. Caamaño, H. Scheit, S. Kiyotake, J. Tscheuschner, M. L. Cortés, F. M. Marqués, N. Fukuda, N. A. Orr, J. M. Gheller, A. Gillibert, A. Matta, K. Yoneda, L. Stuhl, Z. Elekes, I. Kuti, V. Wagner, M. Miwa, Z. Halász, A. Obertelli, S. Kim, A. Revel, L. Zanetti, N. L. Achouri, S. Takeuchi, F. Dufter, C. A. Douma, S. Masuoka, Stefanos Paschalis, R. Gernhäuser, S. Chen, Nobuyuki Chiga, S. Storck, T. Shimada, M.N. Harakeh, P. Koseoglou, T. Harada, B. Yang, M. Matsumoto, H. Takeda, D. S. Ahn, Yuya Kubota, H. Yamada, Yasuhiro Togano, A. Hirayama, Y. Yasuda, T. Fujino, D. M. Rossi, Nasser Kalantar-Nayestanaki, J. Tanaka, M. Böhmer, N. Inabe, Didier Beaumel, S. Park, Thomas Aumann, H. Baba, Tomohiro Uesaka, F. Schindler, J. Feng, Zaihong Yang, I. Murray, Julien Gibelin, K. Boretzky, S. W. Huang, B. Fernández-Domínguez, S. Reichert, Takashi Nakamura, Yu-xin Liu, K. Wimmer, Yukie Maeda, L. Yang, H. Sato, E. Tronchin, P. Doornenbal, Dmytro Symochko, D. Cortina, J. Kahlbow, S. Shimoura, H. Suzuki, Hideaki Otsu, M. Potlog, P. J. Li, J. Mayer, H. Miki, Masaki Sasano, Toshio Kobayashi, Z. Ge, D. Kim, Juzo Zenihiro, T. Tomai, I. Stefan, M. Parlog, H. Simon, V. Panin, Igor Gašparić, C. Lehr, Yosuke Kondo, C. Lenain, U. Forsberg, Laboratoire de physique corpusculaire de Caen (LPCC), Université de Caen Normandie (UNICAEN), Normandie Université (NU)-Normandie Université (NU)-École Nationale Supérieure d'Ingénieurs de Caen (ENSICAEN), Normandie Université (NU)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS), Institut de Physique Nucléaire d'Orsay (IPNO), Université Paris-Sud - Paris 11 (UP11)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS), Institut de Recherches sur les lois Fondamentales de l'Univers (IRFU), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay, Grand Accélérateur National d'Ions Lourds (GANIL), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS), Normandie Université (NU)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3), Centre National de la Recherche Scientifique (CNRS)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Université Paris-Sud - Paris 11 (UP11), Centre National de la Recherche Scientifique (CNRS)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3), Research unit Nuclear & Hadron Physics, and Nuclear Energy

Subjects
Nuclear structure and force, tetraneutron, direct reactions, radioactive beams, Physics, Nuclear physics, 010308 nuclear & particles physics, 0103 physical sciences, Tetraneutron, Neutron, [PHYS.NEXP]Physics [physics]/Nuclear Experiment [nucl-ex], 010306 general physics, 01 natural sciences, Atomic and Molecular Physics, and Optics, 3. Good health
Abstract

The tetraneutron has attracted the attention of nuclear physicists during the past decades, but there is still no unambiguous confirmation of its existence or non-existence. A new experiment based on $$^{8}$$ He(p, 2p) $$^{7}$$ H{t+ $$^{4}n$$ } reaction, with direct detection of the four neutrons, has been carried out at RIBF, which can hopefully help to draw a definite conclusion on the tetraneutron system.

Published
2021
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3. Unperturbed inverse kinematics nucleon knockout measurements with a carbon beam

Author

S. Morozov, T. Atovullaev, O. Gavrischuk, I. Rufanov, D. M. Rossi, I. Slepnev, V. Tcholakov, V. Zhezher, Yu. Potrebenikov, E.P. Segarra, A. Timoshenko, A. Taranenko, A. Corsi, A. Shutov, D. Blaschke, A. Terletsky, G. Musulmanbekov, A. Kuznetsov, A. Vishnevsky, Herbert A. Simon, V. Vasendina, E. Piasetzky, V. Lenivenko, R. Kattabekov, D. Sakulin, A. Dmitriev, S. Lobastov, P. Dulov, Yu. Ivanova, O. Warmusz, N. Topilin, V. Rogov, M. Duer, P. Senger, V. Spaskov, D. Suvarieva, A. Morozov, Alexander Schmidt, N. Lashmanov, Kh. U. Abraamyan, I. Slepov, K. Gertsenberger, N. Zamiatin, D. Baranov, M. Strikhanov, V. Yurevich, K. Boretzky, V. Babkin, V. Samsonov, G. Agakishiev, N. Karpushkin, D. Bogoslovsky, V. Kekelidze, D. Peresunko, Y.-G. Ma, I. Filippov, A. Ciszewski, A. Ivashkin, D. Egorov, B. Topko, A. Zinchenko, M. Patsyuk, V. Shumikhin, V. Plotnikov, O. Petukhov, S. Bazylev, V. Shutov, Carlos A. Bertulani, M. Buryakov, A. Fediunin, V. Tikhomirov, E. Litvinenko, A. Makankin, I. Korover, D. Blau, S. Khabarov, Yu. Kiryushin, S. Piyadin, A. Stavinskiy, V. Kolesnikov, D. Finogeev, A. Kovalenko, M. Golubeva, M. Kapishin, A. Chebotov, D. Nikitin, A. Dryablov, J. Tanaka, Oleg B. Tarasov, Igor Gašparić, S. Kakurin, Or Hen, J. Kahlbow, F. Guber, Yu. Kopylov, O. Teryaev, V. Wagner, I. Selyuzhenkov, A. Malakhov, O. Streltsova, A. Kolozhvari, V. Burtsev, P. Alekseev, M. Rumyantsev, H. Törnqvist, E. Zherebtsova, S. Sedykh, P. Rukoyatkin, I. Gabdrakhmanov, A. Bolozdynya, A. Kugler, M. Shitenkov, N. Barbashina, N. Zhigareva, A. Izvestnyy, Yu. Kovalev, S. Kuklin, K. Roslon, N. Tarasov, O. Rogachevsky, A. Galavanov, S. Merts, Thomas Aumann, B. Dabrowska, V. Palchik, L. Kovachev, E. Atkin, R. Nagdasev, A. Maksymchyuk, V. Golovatyuk, N. Sukhov, J. Chen, G. Laskaris, E. Zubarev, V. Slepnev, T. Aushev, A. Sorin, B. Löher, S. Sergeev, V. Panin, V. Karjavin, A. Sheremeteva, E. Kulish, V. Sosnovtsev, G. Pokatashkin, G. Johansson, S. Buzin, K. Filippov, E. Streletskaya, M. Peryt, I. Mardor, Yu.P. Petukhov, V. Tarasov, H. Scheit, M. Zuev, P. Batyuk, V. Balandin, A. Shchipunov, I. Yaron, E. Ladygin, Song Zhang, D. Dabrowski, R. Cruz-Torres, A. Beck, T. Starecki, N. Voytishin, I. Tyapkin, A. Kisiel, and S. Afanasiev

Subjects
Physics, Hydrogen, Isotope, Scattering, Nuclear Theory, General Physics and Astronomy, chemistry.chemical_element, nuclear structure, experiments with inverse kinematics, quasi-free scattering, short-range correlations, 01 natural sciences, 010305 fluids & plasmas, Ion, Nuclear physics, chemistry, 0103 physical sciences, Particle, Facility for Antiproton and Ion Research, 010306 general physics, Nucleon, Wave function, Nuclear Experiment
Abstract

Particle knockout scattering experiments1,2 are fundamental for mapping the structure of atomic nuclei2–6, but their interpretation is often complicated by initial- and final-state interactions of the incoming and scattered particles1,2,7–9. Such interactions lead to reduction in the scattered particle flux and distort their kinematics. Here we overcome this limitation by measuring the quasi-free scattering of 48 GeV c–1 12C ions from hydrogen. The distribution of single protons is studied by detecting two protons at large angles in coincidence with an intact 11B nucleus. The 11B detection suppresses the otherwise large distortions of reconstructed single-proton distributions induced by initial- and final-state interactions. By further detecting residual 10B and 10Be nuclei, we also identified short-range correlated nucleon–nucleon pairs9–13 and provide direct experimental evidence for separation of the pair wavefunction from that of the residual many-body nuclear system9,14. All measured reactions are well described by theoretical calculations that include no distortions from the initial- and final-state interactions. Our results showcase the ability to study the short-distance structure of short-lived radioactive nuclei at the forthcoming Facility for Antiproton and Ion Research (FAIR)15 and Facility for Rare Isotope Beams (FRIB)16 facilities, which is relevant for understanding the structure and properties of nuclei far from stability and the formation of visible matter in the Universe. Initial- and final-state interactions distort the kinematics in particle knockout scattering experiments, complicating their interpretation. These effects are suppressed by detecting 11B nuclei in quasi-free scattering of 12C ions from hydrogen.

Published
2021

4. Extending the Southern Shore of the Island of Inversion to F28

Author

J. Mayer, Noritsugu Nakatsuka, Michael Thoennessen, A. Gillibert, Ákos Horváth, Q. Deshayes, Yosuke Kondo, J. Tscheuschner, Nasser Kalantar-Nayestanaki, J. M. Gheller, István Kuti, M. Shikata, Thomas Aumann, C. Caesar, J. Tsubota, A. Revel, N. L. Achouri, W. He, Z. Elekes, Calem Hoffman, Shoichiro Kawase, Heiko Scheit, J. Kahlbow, Masahiro Yasuda, H. Simon, H. Sato, K. Yoneda, A. Horvat, K. Nakano, Igor Gašparić, T. Ozaki, H. Chae, J. A. Tostevin, L. Stuhl, K. Miki, F. de Oliveira Santos, H. L. Crawford, D. Calvet, Stefanos Paschalis, S. Masuoka, T. Isobe, A. Obertelli, Tomoki Saito, Momoko Tanaka, N. A. Orr, Shoko Koyama, Nobuyuki Chiga, L. Atar, Y. Satou, P. Fallon, Atsumi Saito, Zsolt Dombrádi, H. Törnqvist, Jongwon Hwang, A. Corsi, Julien Gibelin, K. Boretzky, A. Delbart, D. M. Rossi, H. Baba, Masaki Sasano, D. Sohler, V. Lapoux, M. A. Najafi, S. K. Kim, A. Hirayama, H. Al Falou, K. Kisamori, T. Tomai, V. Panin, P. Schrock, Takashi Nakamura, Yasuhiro Togano, M.N. Harakeh, M. Holl, Zaihong Yang, F. Nowacki, T. Kobayashi, Cenxi Yuan, D. Körper, Tomohiro Uesaka, Thomas Nilsson, C. A. Douma, Simon Lindberg, Hideaki Otsu, O. Sorlin, T. Murakami, Yohei Shimizu, Fabia Schindler, Franck Delaunay, F. M. Marqués, and Satoshi Takeuchi

Subjects
Physics, Proton, Island of inversion, General Physics and Astronomy, 01 natural sciences, Spectral line, Momentum, 0103 physical sciences, Neutron, Atomic physics, 010306 general physics, Nucleon, Spectroscopy, Ground state
Abstract

Detailed spectroscopy of the neutron-unbound nucleus 28 F has been performed for the first time following proton/neutron removal from 29 Ne / 29 F beams at energies around 230 MeV / nucleon . The invariant-mass spectra were reconstructed for both the 27 F ( * ) + n and 26 F ( * ) + 2 n coincidences and revealed a series of well-defined resonances. A near-threshold state was observed in both reactions and is identified as the 28 F ground state, with S n ( 28 F ) = − 199 ( 6 ) keV , while analysis of the 2 n decay channel allowed a considerably improved S n ( 27 F ) = 1620 ( 60 ) keV to be deduced. Comparison with shell-model predictions and eikonal-model reaction calculations have allowed spin-parity assignments to be proposed for some of the lower-lying levels of 28 F . Importantly, in the case of the ground state, the reconstructed 27 F + n momentum distribution following neutron removal from 29 F indicates that it arises mainly from the 1 p 3 / 2 neutron intruder configuration. This demonstrates that the island of inversion around N = 20 includes 28 F , and most probably 29 F , and suggests that 28 O is not doubly magic.

Published
2020
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5. Lifetime measurement of the $^{26}0 g.s.$ at SAMURAI

Author

Hiroyuki Takeda, Takashi Nakamura, Hideaki Otsu, Olivier Sorlin, Masaki Sasano, Zaihong Yang, I. Murray, D. M. Rossi, Yuya Kubota, A. Hirayama, Thomas Aumann, Makoto Yasuda, K. I. Hahn, L. Atar, H. Baba, Sonja Storck, S. Choi, Z. Halász, Yohei Shimizu, C. Caesar, L. Stuhl, H. Scheit, C. Lehr, Nobuyuki Chiga, Yasuhiro Togano, Thomas Nilsson, Hans Törnqvist, Z. Elekes, D. Körper, M. Matsumoto, M. L. Cortés, Naohito Inabe, Yosuke Kondo, T. Murakami, D. S. Ahn, K. Yoneda, Marina Petri, Atsumi Saito, T. Tomai, Tomohiro Uesaka, M. Parlog, Simon Lindberg, V. Panin, M. Marques, D. Cortina-Gil, T. Isobe, H. Chae, S. K. Kim, István Kuti, Jongwon Hwang, Herbert A. Simon, P. Schrock, Naoki Fukuda, T. Kobayashi, J. Kahlbow, H. Suzuki, D. Sohler, H. Yamada, I. Syndikus, K. Boretzky, Q. Deshayes, P. Doornenbal, I. Gaparic, Stefanos Paschalis, Laboratoire de physique corpusculaire de Caen (LPCC), Université de Caen Normandie (UNICAEN), Normandie Université (NU)-Normandie Université (NU)-École Nationale Supérieure d'Ingénieurs de Caen (ENSICAEN), Normandie Université (NU)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS), Grand Accélérateur National d'Ions Lourds (GANIL), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS), SAMURAI20, Normandie Université (NU)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3), and Centre National de la Recherche Scientifique (CNRS)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)

Subjects
Physics, Superconductivity, History, Radionuclide, Spectrum analyzer, [PHYS.NEXP]Physics [physics]/Nuclear Experiment [nucl-ex], 01 natural sciences, 010305 fluids & plasmas, Computer Science Applications, Education, Nuclear physics, Stack (abstract data type), 0103 physical sciences, Physics::Accelerator Physics, ddc:530, Neutron, Radio isotopes, 010306 general physics, Ground state, Nuclear Experiment, Beam (structure)
Abstract

27th International Nuclear Physics Conference, INPC2019, Glasgow, United Kingdom, 29 Jul 2019 - 2 Aug 2019; Journal of physics / Conference series 1643(1), 012106 (2020). doi:10.1088/1742-6596/1643/1/012106, Published by IOP Publ., Bristol

Published
2020
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6. Experimental study of 4 n with 8He(p,2p) reaction

Author

M. Böhmer, Masaki Sasano, S. Reichert, Naohito Inabe, S. Chen, T. Shimada, M. Matsumoto, Susumu Shimoura, I. Stefan, J. Kahlbow, N. Kalantar-Nayestanaki, T. Harada, D. Symochko, István Kuti, S. W. Huang, D. Cortina, Tomohiro Uesaka, Z. Ge, N. L. Achouri, Yosuke Kondo, Hiroyuki Takeda, K. Yoneda, B. Fernández-Domínguez, U. Forsberg, Z. Elekes, Roman Gernhäuser, Y. Yasuda, H. Suzuki, Yohei Shimizu, D. Beaumel, D. Kim, C. A. Douma, Yukie Maeda, A. Hirayama, J. M. Gheller, Heiko Scheit, F. Dufter, T. Elidiano, Yasuhiro Togano, M. L. Cortés, M. Potlog, Nobuyuki Chiga, P. J. Li, Juzo Zenihiro, B. Yang, T. Isobe, M. Caamaño, Thomas Aumann, H. T. Törnqvsit, A. Gillibert, D. S. Ahn, F. Schindler, M.N. Harakeh, J. Feng, J. Tscheuschner, S. Kim, Atsumi Saito, L. Zanetti, P. Koseoglou, V. Wagner, M. Parlog, B. M. Godoy, N. Orr, Takashi Nakamura, Yu-xin Liu, J. Mayer, A. Obertelli, Yuya Kubota, Hideaki Otsu, S. Storck, S. Masuoka, K. Boretzky, Kathrin Wimmer, H. Miki, T. Tomai, F. M. Marqués, V. Panin, P. Doornenbal, Stefanos Paschalis, L. Yang, Satoshi Takeuchi, M. A. Knösel, Igor Gašparić, T. Kobayashi, C. Lehr, H. Yang, C. Lenain, M. Miwa, Z. Halász, A. Revel, H. Sato, T. Fujino, D. M. Rossi, H. Baba, S. Park, I. Murray, L. Stuhl, H. Yamada, J. Gibelin, J. Tanaka, Naoki Fukuda, RIKEN Nishina Center for Accelerator-Based Science, German Research Foundation, Federal Ministry of Education and Research (Germany), Laboratoire de physique corpusculaire de Caen (LPCC), Université de Caen Normandie (UNICAEN), Normandie Université (NU)-Normandie Université (NU)-École Nationale Supérieure d'Ingénieurs de Caen (ENSICAEN), Normandie Université (NU)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS), Institut de Physique Nucléaire d'Orsay (IPNO), Université Paris-Sud - Paris 11 (UP11)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS), Institut de Recherches sur les lois Fondamentales de l'Univers (IRFU), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay, Grand Accélérateur National d'Ions Lourds (GANIL), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS), Normandie Université (NU)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3), Centre National de la Recherche Scientifique (CNRS)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Université Paris-Sud - Paris 11 (UP11), and Centre National de la Recherche Scientifique (CNRS)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)

Subjects
Physics, Paper, History, 010308 nuclear & particles physics, tetraneutron, nuclear force, proton knock-out, radioactive beams, [PHYS.NEXP]Physics [physics]/Nuclear Experiment [nucl-ex], 01 natural sciences, Computer Science Applications, Education, ddc, Nuclear physics, 0103 physical sciences, Tetraneutron, Neutron, ddc:530, 010306 general physics
Abstract

7 pags., 3 figs. -- 27th International Nuclear Physics Conference (INPC2019), The tetraneutron has attracted the attention of nuclear physicists during the past decades, but there is still no unambiguous confirmation of its existence or nonexistence. A new experiment based on 8 He(p,2p)7H{t+4n} reaction, with direct detection of the four neutrons, has been carried out at RIBF, which can hopefully help to draw a definite conclusion on the tetraneutron system., We acknowledge the support of the RIBF accelerator staff and the BigRIPS team for providing the high-quality beam. Z. H. Yang acknowledges the financial support from the Foreign Postdoctoral Researcher program of RIKEN. T. Aumann acknowledges the support by DFG via SFB 1245. P. Koseoglou acknowledges the support from BMBF (NUSTAR.DA grant No.05P 15RDFN1).

Published
2020
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7. Quasifree Neutron Knockout from Ca54 Corroborates Arising N=34 Neutron Magic Number

Author

V. Wagner, V. Somà, F. Flavigny, K. Moschner, S. Y. Park, V. Panin, Kathrin Wimmer, M. MacCormick, S. Takeuchi, M. L. Cortés, S. Franchoo, Hideaki Otsu, D. Calvet, D. M. Rossi, Toshio Kobayashi, K. Yoneda, Tomohiro Uesaka, Masaki Sasano, T. Lokotko, P. Koseoglou, Dóra Sohler, H. Baba, N. Paul, P. A. Söderström, David Steppenbeck, Nobuyuki Chiga, E. Sahin, Petr Navrátil, Thomas Aumann, Takashi Nakamura, F. Browne, S. J. Chen, Donghang Yan, V. Werner, T. Isobe, R.-B. Gerst, P. Doornenbal, T. Koiwai, F. Château, A. Corsi, A. Gillibert, Takaharu Otsuka, Hiroyoshi Sakurai, A. Delbart, F. Raimondi, H. Yamada, Shuopei Wang, Y. L. Sun, Victor Vaquero, T. Motobayashi, L. X. Chung, H. Törnqvist, J. M. Gheller, Yasuhiro Togano, W. Rodriguez, Y. Chazono, A. Giganon, Carlo Barbieri, Kazuyuki Ogata, C. Lehr, Masahiro Yasuda, C. Hilaire, N. L. Achouri, Yosuke Kondo, Julien Gibelin, X. X. Xu, B. D. Linh, J. Kahlbow, Igor Gašparić, H. N. Liu, A. Obertelli, L. Zanetti, Yutaka Utsuno, Jenny Lee, Yuya Kubota, V. Lapoux, K. Yoshida, Dong-Wook Kim, O. Aktas, Zaihong Yang, I. Murray, K. I. Hahn, and L. Stuhl

Subjects
Physics, Hydrogen, Nuclear Theory, General Physics and Astronomy, chemistry.chemical_element, Impulse (physics), 01 natural sciences, Vertex (geometry), Isotopes of calcium, Transverse plane, chemistry, Excited state, 0103 physical sciences, Neutron, Atomic physics, Nuclear Experiment, 010306 general physics, Excitation
Abstract

Exclusive cross sections and momentum distributions have been measured for quasifree one-neutron knockout reactions from a ^{54}Ca beam striking on a liquid hydrogen target at ∼200 MeV/u. A significantly larger cross section to the p_{3/2} state compared to the f_{5/2} state observed in the excitation of ^{53}Ca provides direct evidence for the nature of the N=34 shell closure. This finding corroborates the arising of a new shell closure in neutron-rich calcium isotopes. The distorted-wave impulse approximation reaction formalism with shell model calculations using the effective GXPF1Bs interaction and ab initio calculations concur our experimental findings. Obtained transverse and parallel momentum distributions demonstrate the sensitivity of quasifree one-neutron knockout in inverse kinematics on a thick liquid hydrogen target with the reaction vertex reconstructed to final state spin-parity assignments.

Published
2019
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8. Study of multi-neutron systems with SAMURAI spectrometer

Author

K. Yoneda, Z. Elekes, Masaki Sasano, Heiko Scheit, Atsumi Saito, N. Inabe, I. Stefan, J. Tscheuschner, Mohsen Harakeh, Julien Gibelin, M. A. Knösel, K. Boretzky, Z. Ge, Takashi Nakamura, D. Kim, H. Sato, J. Kahlbow, Igor Gašparić, Y. Yasuda, Susumu Shimoura, T. Isobe, Juzo Zenihiro, M. Caamaño, Yosuke Kondo, S. Masuoka, H. Suzuki, A. Hirayama, S. W. Huang, C. A. Douma, B. M. Godoy, Z. Halász, H. Yamada, C. Lehr, M. Böhmer, Nobuyuki Chiga, A. Revel, N. L. Achouri, P. Koseoglou, Kathrin Wimmer, V. Wagner, N. A. Orr, M. Potlog, M. Miwa, B. Yang, A. Obertelli, T. Harada, H. T. Törnqvsit, S. Reichert, H. Miki, D. S. Ahn, T. Tomai, István Kuti, J. Mayer, J. Tanaka, S. Park, Yasuhiro Togano, M. Parlog, Naoki Fukuda, Yu-xin Liu, S. Chen, V. Panin, L. Zanetti, F. Schindler, S. Storck, T. Shimada, Tomohiro Uesaka, J. Feng, M. Matsumoto, Zaihong Yang, U. Forsberg, Roman Gernhäuser, I. Murray, F. Dufter, D. Symochko, L. Stuhl, J. M. Gheller, Hideaki Otsu, D. Beaumel, T. Kobayashi, H. Takeda, A. Gillibert, D. Cortina, P. Doornenbal, L. Yang, Nasser Kalantar-Nayestanaki, Satoshi Takeuchi, Thomas Aumann, Stefanos Paschalis, T. Fujino, D. M. Rossi, H. Baba, Yohei Shimizu, M. L. Cortés, F. M. Marqués, B. Fernández-Domínguez, Yuya Kubota, Yukie Maeda, S. K. Kim, P. J. Li, Laboratoire de physique corpusculaire de Caen (LPCC), Université de Caen Normandie (UNICAEN), Normandie Université (NU)-Normandie Université (NU)-École Nationale Supérieure d'Ingénieurs de Caen (ENSICAEN), Normandie Université (NU)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS), Institut de Physique Nucléaire d'Orsay (IPNO), Université Paris-Sud - Paris 11 (UP11)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS), Institut de Recherches sur les lois Fondamentales de l'Univers (IRFU), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay, Grand Accélérateur National d'Ions Lourds (GANIL), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS), Normandie Université (NU)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3), Centre National de la Recherche Scientifique (CNRS)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Université Paris-Sud - Paris 11 (UP11), and Centre National de la Recherche Scientifique (CNRS)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)

Subjects
Physics, Firm conclusion, Spectrometer, FOS: Physical sciences, [PHYS.NEXP]Physics [physics]/Nuclear Experiment [nucl-ex], 01 natural sciences, 010305 fluids & plasmas, Nuclear physics, 0103 physical sciences, Tetraneutron, Neutron, Nuclear Experiment (nucl-ex), 010306 general physics, Nuclear Experiment
Abstract

The tetraneutron has been drawing the attention of the nuclear physics community for decades, but a firm conclusion on its existence and properties is still far from being reached despite many experimental and theoretical efforts. New measurements have recently been performed at RIBF with the SAMURAI spectrometer by applying complementary reaction probes, which will help to pin down the properties of this four-neutron system., Comment: 5 pages, 2 figures, conference proceedings of XXII International Conference on Few-Body Problems in Physics (FB22), Caen, France, July 2018

Published
2018
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9. Strong neutron pairing in core+4n nuclei

Author

S. Beceiro-Novo, R. Thies, Jorge Machado, Andreas Martin Heinz, Tanja Heftrich, L. M. Fraile, A. Estrade, Marina Petri, T. Le Bleis, D. Cortina-Gil, L. Atar, T. Kröll, A. Knyazev, M. A. Najafi, G. L. Wilson, D. Rossi, Kai Zuber, A. Movsesyan, Z. Elekes, Simon Lindberg, I. Syndikus, P. Díaz Fernández, K. Göbel, Catherine Rigollet, Ángel Perea, R. Crespo, F. Farinon, J. Kahlbow, V. Volkov, M. Caamaño, W. N. Catford, A. Ignatov, S. Pietri, Carlos A. Bertulani, V. Panin, C. Langer, A. Kelic-Heil, O. Sorlin, Stefanos Paschalis, J. M. Boillos, Enrique Casarejos, J. Hagdahl, Iris Dillmann, M Vandebrouck, O. Ershova, K. Boretzky, A. Henriques, Roy Crawford Lemmon, J. S. Winfield, J. Benlliure, M. Labiche, Vladimir Avdeichikov, Enrique Nácher, H. Weick, Thomas Nilsson, F. Wamers, Rituparna Kanungo, M. Holl, C. Caesar, P. Velho, Håkan T Johansson, G. Ribeiro, Pavel Golubev, F. M. Marqués, M. Heine, Andreas Zilges, Hans Geissel, J. Enders, D. Galaviz, Daniel Bemmerer, Deniz Savran, Marielle Chartier, María José García Borge, Haik Simon, M. Freer, J. Taylor, Nasser Kalantar-Nayestanaki, Olof Tengblad, C. Wheldon, C. Nociforo, A. Revel, H. Alvarez-Pol, Joakim Cederkäll, Thomas Aumann, Rene Reifarth, L. Chulkov, J. Marganiec, Mikhail V. Zhukov, D. Yakorev, Björn Jonson, M. Röder, Philip Woods, R. Plag, U. Datta Pramanik, Andreas Wagner, R. Gernhäuser, E. Cravo, Y. Togano, H. Scheit, N. Kurz, M. Heil, Grand Accélérateur National d'Ions Lourds ( GANIL ), Commissariat à l'énergie atomique et aux énergies alternatives ( CEA ) -Institut National de Physique Nucléaire et de Physique des Particules du CNRS ( IN2P3 ) -Centre National de la Recherche Scientifique ( CNRS ), Laboratoire de physique corpusculaire de Caen ( LPCC ), Université de Caen Normandie ( UNICAEN ), Normandie Université ( NU ) -Normandie Université ( NU ) -Ecole Nationale Supérieure d'Ingénieurs de Caen ( ENSICAEN ), Normandie Université ( NU ) -Institut National de Physique Nucléaire et de Physique des Particules du CNRS ( IN2P3 ) -Centre National de la Recherche Scientifique ( CNRS ), Institut de Recherches sur les lois Fondamentales de l'Univers ( IRFU ), Commissariat à l'énergie atomique et aux énergies alternatives ( CEA ) -Université Paris-Saclay, Institut Pluridisciplinaire Hubert Curien ( IPHC ), Centre National de la Recherche Scientifique ( CNRS ) -Université de Strasbourg ( UNISTRA ), R3B, Technische Universität Darmstadt, Federal Ministry of Education and Research (Germany), National Science Foundation (US), Department of Energy (US), Grand Accélérateur National d'Ions Lourds (GANIL), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de physique corpusculaire de Caen (LPCC), Université de Caen Normandie (UNICAEN), Normandie Université (NU)-Normandie Université (NU)-École Nationale Supérieure d'Ingénieurs de Caen (ENSICAEN), Normandie Université (NU)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS), Institut de Recherches sur les lois Fondamentales de l'Univers (IRFU), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay, Institut Pluridisciplinaire Hubert Curien (IPHC), Université de Strasbourg (UNISTRA)-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3), Normandie Université (NU)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3), Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Université de Strasbourg (UNISTRA)-Centre National de la Recherche Scientifique (CNRS), Université de Strasbourg (UNISTRA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS), and Université de Strasbourg (UNISTRA)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Physics, Valence (chemistry), 010308 nuclear & particles physics, Astrophysics::High Energy Astrophysical Phenomena, Nuclear Theory, Aucun, General Physics and Astronomy, FOS: Physical sciences, [PHYS.NEXP]Physics [physics]/Nuclear Experiment [nucl-ex], 01 natural sciences, 7. Clean energy, Molecular physics, Pairing, 0103 physical sciences, Neutron, Física nuclear, Nuclear Experiment (nucl-ex), [ PHYS.NEXP ] Physics [physics]/Nuclear Experiment [nucl-ex], 010306 general physics, Nucleon, Nuclear Experiment, R3B radioactive beams nuclear structure neutron-rich Coulomb dissociation
Abstract

6 pags., 4 figs., The emission of neutron pairs from the neutron-rich N = 12 isotones C-18 and O-20 has been studied by high-energy nucleon knockout from N-19 and O-21 secondary beams, populating unbound states of the two isotones up to 15 MeV above their two-neutron emission thresholds. The analysis of triple fragment-n-n correlations shows that the decay N-19(-1p)18C*-> C-16 + n + n is clearly dominated by direct pair emission. The two- neutron correlation strength, the largest ever observed, suggests the predominance of a C-14 core surrounded by four valence neutrons arranged in strongly correlated pairs. On the other hand, a significant competition of a sequential branch is found in the decay O-21(-1n)O-20*-> O-18 + n + n, attributed to its formation through the knockout of a deeply bound neutron that breaks the O-16 core and reduces the number of pairs., This work was supported by the German Federal Ministry for Education and Research (BMBF Project No. 05P15RDFN1), and through the GSI-TU Darmstadt cooperation agreement. C. A. Bertulani acknowledges support by U.S. Department of Energy Grant No. DE-FG02-08ER41533 and U.S. National Science Foundation Grant No. 1415656.

Published
2018
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10. Quasifree ( p , 2p ) Reactions on Oxygen Isotopes: Observation of Isospin Independence of the Reduced Single-Particle Strength

Author

Rene Reifarth, J. Kahlbow, E. Y. Nikolskii, R. Thies, Jorge Machado, M. Heine, A. Estrade, Marina Petri, G. Ribeiro, J. Taylor, Daniel Bemmerer, M. A. Najafi, Haik Simon, M. Freer, Olof Tengblad, Enrique Casarejos, H. Alvarez-Pol, Kai Zuber, F. Farinon, C. Nociforo, D. Rossi, Nasser Kalantar-Nayestanaki, C. Wheldon, Thomas Aumann, K. Boretzky, L. Chulkov, Andreas Martin Heinz, C. Caesar, Vladimir Avdeichikov, Tanja Heftrich, J. M. Boillos, J. Hagdahl, V. Panin, D. Galaviz Redondo, Ángel Perea, T. Kröll, Joakim Cederkäll, A. Ignatov, Carlos A. Bertulani, N. Kurz, A. Hufnagel, M. Labiche, S. Pietri, V. Volkov, P. Díaz Fernández, Mikhail V. Zhukov, G. L. Wilson, Simon Lindberg, Carlo Barbieri, I. Syndikus, J. Benlliure, F. Wamers, M. Heil, Marine Vandebrouck, Catherine Rigollet, M. Caamaño, Enrique Nácher, H. Weick, S. Beceiro-Novo, C. Langer, O. Ershova, A. Kelic-Heil, P. Velho, A. Henriques, J. S. Winfield, Thomas Nilsson, A. Knyazev, E. Cravo, Håkan T Johansson, R. Crespo, María José García Borge, Pavel Golubev, O. Sorlin, H. Scheit, Marielle Chartier, M. Holl, Deniz Savran, I. Dillmann, Stefanos Paschalis, D. Yakorev, Y. Togano, J. Marganiec-Gałązka, T. Le Bleis, D. Cortina-Gil, Rituparna Kanungo, Hans Geissel, L. Atar, A. Movsesyan, L. M. Fraile, Björn Jonson, Philip Woods, Andreas Wagner, R. Gernhäuser, Andreas Zilges, J. Enders, R. Lemmon, M. Röder, Z. Elekes, K. Göbel, R. Plag, and W. N. Catford

Subjects
Physics, Range (particle radiation), 010308 nuclear & particles physics, Eikonal equation, media_common.quotation_subject, Nuclear Theory, Ab initio, General Physics and Astronomy, chemistry.chemical_element, 7. Clean energy, 01 natural sciences, Asymmetry, Oxygen, Isotopes of oxygen, Nuclear physics, chemistry, Isospin, 0103 physical sciences, Particle, Nuclear Experiment, 010306 general physics, media_common
Abstract

Quasifree one-proton knockout reactions have been employed in inverse kinematics for a systematic study of the structure of stable and exotic oxygen isotopes at the R3B/LAND setup with incident beam energies in the range of 300-450 MeV/u. The oxygen isotopic chain offers a large variation of separation energies that allows for a quantitative understanding of single-particle strength with changing isospin asymmetry. Quasifree knockout reactions provide a complementary approach to intermediate-energy one-nucleon removal reactions. Inclusive cross sections for quasifree knockout reactions of the type OA(p,2p)NA-1 have been determined and compared to calculations based on the eikonal reaction theory. The reduction factors for the single-particle strength with respect to the independent-particle model were obtained and compared to state-of-the-art ab initio predictions. The results do not show any significant dependence on proton-neutron asymmetry.

Published
2018
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11. Effective proton-neutron interaction near the drip line from unbound states in F25,26

Author

R. Crespo, Hans Geissel, Ralf Plag, J. Benlliure, Jason D. Holt, H. Hergert, Marine Vandebrouck, Christoph Langer, J. M. Boillos, Z. Elekes, J. Hagdahl, T. Kröll, J. Taylor, J. S. Winfield, A. Kelic-Heil, C. Caesar, Björn Jonson, Rene Reifarth, Roman Gernhäuser, A. Ignatov, D. M. Rossi, D. Galaviz, Joachim Enders, L. Chulkov, Deniz Savran, Ángel Perea, A. Lepailleur, F. Farinon, M. Heine, M. A. Najafi, Mikhail V. Zhukov, Nasser Kalantar-Nayestanaki, Andreas Wagner, T. Le Bleis, J. Kahlbow, Daniel Bemmerer, R. Kanungo, P. Velho, E. Y. Nikolskii, O. Sorlin, C. Wheldon, Thomas Aumann, M. Caamaño, D. Cortina-Gil, Stefanos Paschalis, Andreas Martin Heinz, L. Atar, Iris Dillmann, C. Nociforo, A. Henriques, R. Thies, Jorge Machado, O. Ershova, V. Panin, Marina Petri, Joakim Cederkäll, M. Holl, E. Cravo, Thomas Nilsson, A. Estrade, V. Volkov, W. N. Catford, Olof Tengblad, Vladimir Avdeichikov, Martin Freer, Marielle Chartier, F. Wamers, Simon Lindberg, M. J. G. Borge, Kai Zuber, Kathrin Göbel, Enrique Nácher, M. Röder, U. Datta Pramanik, Catherine Rigollet, H. Alvarez-Pol, Julien Gibelin, K. Boretzky, Yasuhiro Togano, M. Heil, I. Syndikus, L. M. Fraile, P. Díaz Fernández, A. Knyazev, S. R. Stroberg, S. Beceiro-Novo, Achim Schwenk, Tanja Heftrich, A. Movsesyan, D. Yakorev, A. Hufnagel, J. Marganiec, Helmut Weick, Håkan T Johansson, H. Scheit, Pavel Golubev, F. M. Marqués, Andreas Zilges, M. Labiche, G. L. Wilson, F. de Oliveira Santos, Carlos A. Bertulani, G. Ribeiro, P. J. Woods, S. Pietri, Enrique Casarejos, N. Kurz, Scott Bogner, Herbert A. Simon, and Roy Crawford Lemmon

Subjects
Physics, 010308 nuclear & particles physics, Binding energy, Ab initio, Resonance, 7. Clean energy, 01 natural sciences, Atomic mass, 0103 physical sciences, Bound state, Nuclear force, Neutron, Atomic physics, Nuclear Experiment, 010306 general physics, Multiplet
Abstract

Background: Odd-odd nuclei, around doubly closed shells, have been extensively used to study proton-neutron interactions. However, the evolution of these interactions as a function of the binding energy, ultimately when nuclei become unbound, is poorly known. The F-26 nucleus, composed of a deeply bound pi 0d(5/2) proton and an unbound v0d(3/2) neutron on top of an O-24 core, is particularly adapted for this purpose. The coupling of this proton and neutron results in a J(pi) = 1(1)(+) - 4(1)(+) multiplet, whose energies must be determined to study the influence of the proximity of the continuum on the corresponding proton-neutron interaction. The J(pi) = 1(1)(+), 2(1)(+), 4(1)(+) bound states have been determined, and only a clear identification of the J(pi) = 3(1)(+) is missing. Purpose: We wish to complete the study of the J(pi) = 1(1)(+) - 4(1)(+) multiplet in F-26, by studying the energy and width of the J(pi) = 3(1)(+) unbound state. The method was first validated by the study of unbound states in F-25, for which resonances were already observed in a previous experiment. Method: Radioactive beams of Ne-26 and Ne-27, produced at about 440AMeV by the fragment separator at the GSI facility were used to populate unbound states in F-25 and F-26 via one-proton knockout reactions on a CH2 target, located at the object focal point of the (RB)-B-3/LAND setup. The detection of emitted. rays and neutrons, added to the reconstruction of the momentum vector of the A - 1 nuclei, allowed the determination of the energy of three unbound states in F-25 and two in F-26. Results: Based on its width and decay properties, the first unbound state in F-25, at the relative energy of 49(9) keV, is proposed to be a J(pi) = 1/ 2(-) arising from a p1/2 proton- hole state. In F-26, the first resonance at 323(33) keV is proposed to be the J(pi) = 3(1)(+) member of the J(pi) = 1(1)(+) - 4(1)(+) multiplet. Energies of observed states in F-25,F-26 have been compared to calculations using the independent-particle shell model, a phenomenological shell model, and the ab initio valence-space in-medium similarity renormalization group method. Conclusions: The deduced effective proton- neutron interaction is weakened by about 30-40% in comparison to the models, pointing to the need for implementing the role of the continuum in theoretical descriptions or to a wrong determination of the atomic mass of F-26.

Published
2017
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12. Neutron radioactivity—Lifetime measurements of neutron-unbound states

Author

V. Panin, Heiko Scheit, C. Caesar, J. Kahlbow, Thomas Aumann, Stefanos Paschalis, and Herbert A. Simon

Subjects
Physics, Nuclear and High Energy Physics, 010308 nuclear & particles physics, Neutron emission, Neutron stimulated emission computed tomography, Nuclear Theory, 01 natural sciences, Neutron temperature, Neutron spectroscopy, Nuclear physics, medicine.anatomical_structure, 0103 physical sciences, Neutron cross section, medicine, Neutron, Atomic physics, 010306 general physics, s-process, Nuclear Experiment, Instrumentation, Nucleus
Abstract

A new technique to measure the lifetime τ of a neutron-radioactive nucleus that decays in-flight via neutron emission is presented and demonstrated utilizing MonteCarlo simulations. The method is based on the production of the neutron-unbound nucleus in a target, which at the same time slows down the produced nucleus and the residual nucleus after (multi-) neutron emission. The spectrum of the velocity difference of neutron(s) and the residual nucleus has a characteristic shape, that allows to extract the lifetime. If the decay happens outside the target there will be a peak in the spectrum, while events where the decay is in the target show a broad flat distribution due to the continuous slowing down of the residual nucleus. The method itself and the analysis procedure are discussed in detail for the specific candidate 26 O. A stack of targets with decreasing target thicknesses can expand the measurable lifetime range and improve the sensitivity by increasing the ratio between decays outside and inside the target. The simulations indicate a lower limit of measurable lifetime τ ∼ 0 . 2 ps for the given conditions.

Published
2017

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