Cross sections of knock out reactions from neutron rich gallium isotopes and their vicinity

Tiểu ban B: Vật lý hạt nhân, Số liệu hạt nhân, Phân tích hạt nhân Máy gia tốc Section B: Nuclear physics, Nuclear data, Nuclear analysis and Accelerator TIẾT DIỆN CỦA CÁC PHẢN ỨNG TÁCH NUCLEON CỦA ĐỒNG VỊ GALLIUM GIÀU NEUTRON VÀ CÁC ĐỒNG VỊ LÂN CẬN CROSS SECTIONS OF KNOCK-OUT REACTIONS FROM NEUTRON-RICH GALLIUM ISOTOPES AND THEIR VICINITY NGUYEN HONG HA (2) (3), LOUIS OLIVIER (1), SERGE FRANCHOO (1) IJCLab, CNRS-IN2P3, Paris–Saclay University Institute of Physics, Vietnam Academy of Science and Technology M1 General Physics, Paris–Saclay University E-mail: (1) franchoo@ijclab.in2p3.fr (2) (3) ha.nguyen@u-psud.fr Tóm tắt: Nghiên cứu trình bày kết thực nghiệm xác định tiết diện phản ứng tách nucleon từ đồng vị giàu neutron Đồng Gallium Thí nghiệm thực RIKEN Radioactive Isotope Beam Factory, chùm hạt sơ cấp 238U lượng cao gia tốc tạo phản ứng bia 9Be, tạo hỗn hợp hạt nhân lạ nằm xa vùng bền, sau hạt nhân đóng vai trò hạt nhân tới dẫn tới bia phản ứng chứa khí hydro nhiệt độ thấp để tạo phản ứng cần quan tâm Một số kết thu cho thấy phù hợp với nghiên cứu trước Paul cộng [1] phụ thuộc tiết diện phản ứng tách proton vào lượng tách neutron proton Khơng có hiệu ứng chẵn-lẻ proton mối quan hệ tiết diện tách neutron lượng tách neutron Tuy nhiên, tương quan ghép cặp neutron ảnh hưởng tới chế/hành vi phản ứng tách neutron Chúng nhận thấy tiết diện tách đơn neutron đạt giá trị cao hạt nhân tới có số neutron magic N=50, điều hứa hẹn phát số tính chất thú vị hạt nhân Từ khóa: Đồng vị Gallium, hạt nhân magic, hạt nhân lạ, hạt nhân giàu neutron, BigRIPS, ZeroDegree, MINOS Abstract: This work presents measurements of cross sections of nucleon-removal reactions from neutron-rich copper to gallium isotopes These experiments were carried out at the RIKEN Radioactive Isotope Beam Factory, where an incident beam of 238U at high energy collided with a 9Be target to create a cocktail of exotic nuclei, which then was sent to a cryogenic hydrogen target for the experiment Some of the results show good agreement with the previous study by Paul et al [1] regarding the dependence of the proton knock-out cross section on the neutron or proton separation energy No evenodd proton effect appears in the relationship between the neutron-removal cross sections and the nucleon separation energy Neutron-pairing correlations, however, affect the behavior of neutron knock-out reactions We find that the single-neutron knock-out cross section reaches the highest value for projectiles with the magic neutron number N = 50, revealing the underlying full shell structure Keywords: gallium isotopes, cross sections, magic nuclei, exotic nuclei, neutron-rich nuclei, pairing correlations, BigRIPS, ZeroDegree, MINOS INTRODUCTION Nuclear shell structure and magic numbers are important guides for understanding the overall properties of atomic nuclei, the widespread development of state-of-the-art experimental methods giving many new opportunities for studies of exotic nuclei The nucleon knock-out reactions are an ideal method to investigate the shell evolution in rich-neutron nuclei The latest study by Paul et al [1] showed a good agreement between measured (𝑝; 2𝑝) and (𝑝; 𝑝𝑛) cross section with intranuclear cascade (INCL) predictions, but the cross sections on 82.-.85Ga and their vicinity in different channels still need to be surveyed This research proposes an experimental study via nucleon knock-out reactions from neutron-rich gallium isotopes and their vicinity to explore the reaction mechanism and the influence of the even-odd effect to the dependence of nucleon separation energy and the inclusive cross section These experiments were carried out at the RIKEN Radioactive Isotope Beam Factory (RIBF) where exotic radioactive beams at high intensity have now become available This study is organized as follows Section describes the RIKEN Radioactive Isotope Beam Factory (RIBF) and the experimental set-up, which combines a heavy-ion accelerator, BigRIPS spectrometer, MINOS liquid-hydrogen target, DALI2 detector system, and ZeroDegree spectrometer This section also describes the TOF-Bρ-∆E identification method of the projectile and the reaction products Section gives the calculation of the transmission efficiency, our results on the inclusive cross section, and the dependence on the neutron separation energy (𝑆𝑛 ) and proton separation energy (𝑆𝑝 ) Finally, Section gives the discussion of the results and proposes further studies based on this work 165 Tuyển tập báo cáo Hội nghị Khoa học Cơng nghệ hạt nhân tồn quốc lần thứ 14 Proceedings of Vietnam conference on nuclear science and technology VINANST-14 EXPERIMENT Two experiments were conducted at the Radioactive Isotope Beam Factory (RIBF), operated by RIKEN, Japan The RIBF scheme shown in Figure combines five main components: the heavy-ion accelerator, BigRIPS, MINOS, DALI2, ZeroDegree 2.1 Heavy-ion accelerator The RIBF accelerator generates a high-energy 238U primary beam of 345 MeV/nucleon with intensity of 12 pnA (7.5×1010 particles/second) This beam collides on a 3-mm-thick 9Be target for in-flight fission and produces a cocktail of radioactive nuclei These isotopes are then sent to the entrance of the BigRIPS spectrometer [2][1] Figure 1: Schematic view of the RIBF experimental system [2] 2.2 BigRIPS spectrometer The function of BigRIPS is to discriminate the isotopes in the bunch of radioactive products in the reaction of 238U with 9Be The method used for isotope identification is 𝑇𝑂𝐹 − 𝐵𝜌 − ∆𝐸, which is based on the magnetic rigidity of the charged particle moving in a magnetic field 𝐵 and the energy lost ∆𝐸 by passing through an aluminum degrader The energy loss ∆E is measured with a tilted electrode gas ionization chamber [2] After this identification process, the isotopes are determined by their mass-to-charge ratio A/Q and their atomic number Z This is applied to the secondary beam that is sent to the MINOS target for inducing secondary reactions The particle identification of the secundary beam is shown in Figure [a] [b] Figure 2: (a) Seastar 2014 experiment (b) Seastar 2015 experiment Isotope identification in BigRIPS in terms of atomic number Z and mass-to-charge ratio A/Q of fission fragments produced in the 238U + 9Be reaction 166 Tiểu ban B: Vật lý hạt nhân, Số liệu hạt nhân, Phân tích hạt nhân Máy gia tốc Section B: Nuclear physics, Nuclear data, Nuclear analysis and Accelerator 2.3 MINOS target The secondary beams were delivered to MINOS (MagIc Numbers Off Stability), a system consisting of a liquid-hydrogen target for making nucleon knock-out reactions from exotic nuclei, coupled with a time-projection chamber (TPC) for reconstruction of the reaction vertex [2] The target cell is filled with cryogenic hydrogen at 20K and placed inside a polyethylene terephthalate cylindre In the first experiment – Seastar 2014, the density of the liquid hydrogen target was 70.97±7 kg/m3 and the length 𝐿𝑡𝑎𝑟𝑔𝑒𝑡 = 102±1 mm, corresponding to a density of (4.32±0.04) × 10 23 atoms/cm2 [2] In the second experiment – Seastar 2015, the density of the target was 73.22±8 kg/m 3, and the length 𝐿𝑡𝑎𝑟𝑔𝑒𝑡 = 99±1 mm, which is equivalent to a density of (4.33±0.04)×1023 atoms/cm2 [2] The TPC surrounding the target was used to track protons from (𝑝, 2𝑝) and (𝑝, 𝑝𝑛) knock-out reactions in order to reconstruct the vertex of the reactions of interest The tracking of the beam is done by PPAC detectors [2][3] 2.4 ZeroDegree spectrometer After reacting in the MINOS target, the daughter nuclei leaving the target are sent to the ZeroDegree spectrometer for identification The ZeroDegree uses the same particle identification principle as BigRIPS, that is the 𝑇𝑂𝐹 − 𝐵𝜌 − ∆𝐸 method The TOF was taken by plastic scintillators, the energy loss ΔE was measured by an ionization chamber, the information on the trajectory of the ions was determined by parallel plate avalanche counters (PPACs) MATERIAL AND METHOD The inclusive cross section σinc is the probability of reaction between two particles and defined as: 𝑍𝐷 𝐵𝑅 (1) 𝑁𝑑𝑎𝑢𝑔ℎ𝑡𝑒𝑟 = 𝜎𝑖𝑛𝑐 𝜀 𝑛𝑡 𝑁𝑚𝑜𝑡ℎ𝑒𝑟 where: 𝑛𝑡 is the number of the hydrogen atoms in the MINOS target as mentioned in Section 2.3 It 𝑍𝐷 𝐵𝑅 ⁄𝑁𝑚𝑜𝑡ℎ𝑒𝑟 is necessary to determine the total transmission efficiency 𝜀 = 𝑁𝑚𝑜𝑡ℎ𝑒𝑟 of the reaction channels of interest And 𝐵𝑅 𝑁𝑚𝑜𝑡ℎ𝑒𝑟 : number of mother isotopes in BigRIPS 𝑍𝐷 𝑁𝑚𝑜𝑡ℎ𝑒𝑟 : number of mother isotopes in ZeroDegree 𝑍𝐷 𝑁𝑑𝑎𝑢𝑔ℎ𝑡𝑒𝑟 : number of daughter isotopes in ZeroDegree 3.1 Transmission efficiency of BigRIPS When performing experiments with the MINOS liquid-hydrogen target, two components affect the efficiency of the detection system The first is the configuration of the beam line itself, including detectors and the deadtime of the measurement system, wihch we represent as εline The second effect is the scattering of the beam on the MINOS target and the stopping process in the magnetic dipoles for isotopes which have high momentum spread, represented by εloss The product of these two efficiencies is the transmission efficiency of the beamline This transmission efficiency can be determined from the flat part of the horizontally transversal particle distributions in the PPAC detectors in BigRIPS, conditioned on the incoming and the outgoing beam Figure shows the x-axis distribution of an interested isotope in BigRIPS and in ZeroDegree and the ratio between both distributions The transmission efficiency is calculated as: 𝑍𝐷 (2) 𝑁𝑚𝑜𝑡ℎ𝑒𝑟 𝜀 = 𝜀𝑙𝑖𝑛𝑒 𝜀𝑙𝑜𝑠𝑠 = 𝐵𝑅 𝑁𝑚𝑜𝑡ℎ𝑒𝑟 167 Tuyển tập báo cáo Hội nghị Khoa học Cơng nghệ hạt nhân tồn quốc lần thứ 14 Proceedings of Vietnam conference on nuclear science and technology VINANST-14 Figure 3: The figure on the left-hand side shows the horizontal distribution of the isotope of interest in BigRIPS in blue and the distribution in ZeroDegree in red The figure on the right-hand side shows the ratio between the two distributions, the red fitting line representing the value of the transmission efficiency 3.2 Reaction efficiency The ratio between the distributions corresponding to the daughter nuclei in ZeroDegree and the mother nuclei in BigRIPS is shown in Figure This ratio can be used to calculate the inclusive cross section of each reaction Figure 4: The figure on the left-hand side presents the horizontal distributions for 85Ge in BigRIPS (blue) and transmitted to ZeroDegree (red) The figure on the right-hand side shows the ratio between the two distributions, the red fitting line representing the value of the reaction efficiency RESULTS AND DISCUSSIONS 4.1 Inclusive cross sections The transmission efficiency was calculated in section 3.1 and the ratio between daughter nuclei and mother nuclei for each reaction channel in section 3.2 The inclusive cross section of each reaction channel is calculated by e.q (1) The result is given in table Figure shows the dependence of the cross section on the proton and neutron number of the projectile The cross section for single-neutron knock-out reactions is much higher than for knock-out of one proton, since the isotopes are all neutron-rich nuclei with 𝑁 > 𝑍 For (𝑝, 2𝑝) reactions (figure 5a), this work gives new cross sections which obey good systematic behavior with respect to Paul et al [1], while they have generally smaller errors and no sensitivity to the shell closure at Z = 28 The results for the (𝑝, 𝑝𝑛) reaction cross sections are shown in figure 5b, new cross sections were found at N = 50 and N = 52 to 54 The cross sections reach the highest value at the magic number N = 50 An odd-even effect appears with an odd-N projectile (N=53) having higher cross section than even-N projectiles (N=52 and N=54) Figure 5b also shows that increasing neutron numbers in each orbital offer an increase in neutron removal probabilities as the orbital is filling up, this confirms the theoretical calculation based on the eikonal model by Aumann et al [12] 168 Tiểu ban B: Vật lý hạt nhân, Số liệu hạt nhân, Phân tích hạt nhân Máy gia tốc Section B: Nuclear physics, Nuclear data, Nuclear analysis and Accelerator [b] [a] Figure 5: The inclusive reaction cross section of (𝑝, 2𝑝) and (𝑝, 𝑝𝑛) reactions measured in this work and from Paul et al [1] [a]: The (𝑝, 2𝑝) cross sections as a function of proton number of projectiles [b]: The (𝑝, 𝑝𝑛) cross section as a function of neutron number of projectiles Table 1: Inclusive cross section of reaction channels of interest: Reaction 86 Ge(p; 2p)85Ga 85 Ge(p; 2p)84Ga 84 Ge(p; 2p)83Ga 85 Ga(p; pn)84Ga 84 Ga(p; pn)83Ga 81 Ga(p; 2p)80Zn 81 Ga(p; 2p1n)79Zn 81 Ga(p; 2p2n)78Zn 81 Ga(p; 3p)79Cu 80 Zn(p; pn)79Zn Cross section (mb) 6.29±1.16 4.71±0.87 7.34±1.79 40.20±9.32 42.90±8.66 5.02±0.08 10.70±0.13 16.90±0.23 7.0×10−2±4.3×10−3 70.75±0.99 Reaction 80 Zn(p; p2n)78Zn 80 Zn(p; 2p)79Cu 80 Zn(p; 2p1n)78Cu 80 Zn(p; 2p2n)77Cu 79 Zn(p; pn)78Zn 79 Zn(p; 2p)78Cu 79 Zn(p; 2p1n)77Cu 79 Cu(p; pn)78Cu 79 Cu(p; p2n)77Cu 78 Cu(p; pn)77Cu Cross section (mb) 50.40±0.84 7.33±0.14 9.71±0.16 17.20±0.31 69.20±1.01 6.57±0.13 11.65±0.21 73.20±4.56 23.13±3.69 62.13±2.65 4.2 Odd-Even Splitting effect The odd-even splitting (OES) relates to the pairing coupling in nuclei To quantify the OES of proton knock-out cross sections (𝑂𝐸𝑆𝑝2𝑝 ) we define as follows [1]: 𝑂𝐸𝑆𝑝2𝑝 = [(−1)𝑍 (𝜎𝑒𝑣𝑒𝑛 (𝑆𝑛 ) − 𝑓𝑖𝑡𝑜𝑑𝑑 (𝑆𝑛 ))] (3) or vice versa for odd projectiles, where σ is the measured cross section 𝑓𝑖𝑡𝑜𝑑𝑑 is the value of the linear fitting function constructed from the cross sections of odd-Z projectiles and Sn is the neutron separation energy The OES of neutron knock-out reactions is quantified as [1]: 𝑂𝐸𝑆𝑝𝑝𝑛 = [(−1)𝑁 (𝜎𝑁 − 𝜎𝑁+1 )] (4) The nucleon separation energy is the minimum energy needed to remove a nucleon (proton or neutron) from a nucleus [11] The proton knock-out cross sections display two prominent properties as can be seen in figure The first feature is the weak 𝑆𝑛 and 𝑆𝑝 dependence with a naturally decreasing cross section towards neutronrich nuclei The second feature is an odd-even effect in which even-Z or even-N projectiles have a higher cross section than the odd-Z or odd-N projectiles at the same 𝑆𝑛 or 𝑆𝑝 value of the daughter nucleus This agrees with the study of Paul et al [1] This phenomenon can be explained by the pairing correlation, where odd-Z daughter nuclei have a higher number of final states available 169 Tuyển tập báo cáo Hội nghị Khoa học Công nghệ hạt nhân toàn quốc lần thứ 14 Proceedings of Vietnam conference on nuclear science and technology VINANST-14 [a] [b] Figure 6: Inclusive reaction cross section of (𝑝, 𝑝𝑛) and (𝑝, 2𝑝) reactions as a function of nucleon separation energy Data is taken from Paul et al [1] In figure 7, the linear fitting curves for the proton removal cross section as a function of −𝑆𝑛 in the daughter nucleus are plotted separately for even and odd Z projectiles The constructed 𝑓𝑖𝑡𝑜𝑑𝑑 function is then used to quantify the 𝑂𝐸𝑆𝑝2𝑝 This linear decreasing trend of the cross section and the OES conforms with the published data [1] Figure shows a systematically increasing trend in the 𝑂𝐸𝑆𝑝𝑝𝑛 as a function of the mass number of the projectile As discussed in section 4.1, a clear dependence of the neutron removal cross section on the filling of the neutron shell is observed Figure 7: (Above): Inclusive (𝑝, 2𝑝) cross sections measured in this work and from the study of Paul et al [1] The fitting function for odd-Z projectiles (black line) is 𝑓𝑖𝑡𝑜𝑑𝑑 (𝑆𝑛) = (−5.71 × 𝑆𝑛 + 1.68) × 10−4 The fitting function for even-Z projectiles (red line) is 𝑓𝑖𝑡𝑒𝑣𝑒𝑛 (𝑆𝑛 ) = (−9.24 × 𝑆𝑛 + 1.71) × 10−4 (Below): OES of proton knock-out reactions as a function of −𝑆𝑛 value 170 Tiểu ban B: Vật lý hạt nhân, Số liệu hạt nhân, Phân tích hạt nhân Máy gia tốc Section B: Nuclear physics, Nuclear data, Nuclear analysis and Accelerator Figure 8: (Above): Inclusive (𝑝, 𝑝𝑛) cross sections measured in this work and from the study of Paul et al [1] (Below): OES of neutron knock-out reactions as a function of atomic number The (𝑝, 𝑝𝑛) cross sections as a function of 𝑆𝑛 and 𝑆𝑝 for even and odd N and Z in the projectile are given in figure There is no sensitivity of the odd-even splitting effect here, which agrees with the conclusion of Paul et al [1] [a] [b] Figure 9: Single-neutron removal cross sections as a function of 𝑆𝑝 or 𝑆𝑛 CONCLUSION In summary, this research presents the measurement of 21 new cross sections of neutron-rich copper to gallium nuclei, providing important insights into the nuclear structure towards the nuclear drip line The dependence of the cross section on the nucleon number and nucleon separation energy has been considered A well pronounced shell structure effect appears for single-neutron knock-out reactions There is no such behavior for proton knock-out reactions, since likely for neutron-rich nuclei the protons lay deep inside and therefore require higher energy to be knocked out, equalizing the cross sections The contribution of this study confirms the theoretical calculation based on the eikonal model by Aumann et al [12] The odd-even splitting in neutron and proton removal reaction (𝑶𝑬𝑺𝒑𝟐𝒑 and 𝑶𝑬𝑺𝒑𝒑𝒏 ) has been compare with the study of Paul et al [1] and should enhance our understanding of the strength distribution 171 ... projectile The cross section for single -neutron knock- out reactions is much higher than for knock- out of one proton, since the isotopes are all neutron- rich nuclei with