The NSCL is funded in part by the National Science Foundation and Michigan State University. 55 Co S800 PID - 56 Ni(d, 3 He) 55 Co Target (p / d) 56 Ni Beam Φ To S800 Spectrograph 55 Ni / 55 Co (measure P,E,Φ) MCP's θ d / 3 He HiRA Results Experimental Setup Inverse kinematics at 37MeV/A, 80MeV/A R. Shane 1*, T. K. Ghosh 2, A. Sanetullaev 1 and M. B. Tsang 1 For the HiRA Collaboration 1 National Superconducting Cyclotron Laboratory, Michigan State Univ., East Lansing, MI 48824, USA 2 Variable Energy Cyclotron Centre, 1/AF, Bidhannagar, Kolkata , India * The global OM potentials obtained from systematic analysis of (p,d) and (d,p) transfer reactions at low-energy do not seem to work at higher energy. Work on extraction of the neutron and proton SF from the higher-energy data, as well as a consistent framework for comparison to the low-energy results, is in progress. HiRA + High Resolution Array (HiRA) 56 Ni: An alluring nucleus 56 Ni is outside the valley of stability and is doubly magic according to the Independent Particle Model (IPM) In the shell model, the magic number 28 is the first shell that requires the introduction of a strong spin-orbit interaction 56 Fe is the most abundant heavy element in the universe, yet 56 Ni is the first doubly-magic nucleus that is not stable 56 Ni is a “waiting point” nucleus in the astrophysical rapid proton (rp) capture process Understanding the shell structure of this doubly-magic, N=Z=28 nickel nucleus is therefore of considerable interest for both nuclear structure and astrophysics Study nucleon transfer reactions in inverse kinematics: 56 Ni(p,d) 55 Ni 56 Ni(p,d) 55 Ni at 37 MeV/A and 80 MeV/A to extract the neutron spectroscopic factor of 56 Ni and also its energy dependence 56 Ni(d, 3 He) 55 Co 56 Ni(d, 3 He) 55 Co at 80 MeV/A to extract the proton spectroscopic factor of 56 Ni These two reactions allow us to compare the neutron and proton SF in the f 7/2 shell Extracted spectroscopic factors are important benchmarks in evaluating different pf-shell model interactions that may be used to predict the structure of 78 Ni, a major waiting point in the path of the r-process. Goal of experimental study Ground-state neutron SF of Ni isotopes Measurement of the SF is essential in calibrating the theoretical shell model of the nucleus. Two possible shell structures of 56 Ni: Inert core of 56 Ni with 28 protons and 28 neutrons inside Inert core of 40 Ca with 8 protons and 8 neutrons outside IPM S800 Spectrograph Spectroscopic Factors from Transfer Reactions with Radioactive Beams 1.5mm Si 65μm Si CsI(Tl) HiRA PID - 56 Ni(d, 3 He) 55 Co 3 He Summary Implications: 56 Ni is not a good core Accurate description of Ni isotopes requires full model space with 40 Ca core. GXPF1A describes the data better than K3B interactions Reaction Model: (d  /d  ) RM calculated from 3-body model with global optical potentials and standard geometry of n-wave functions. The probe: Spectroscopic Factor N=2 N=8 N=20 N=28 Single-nucleon transfer reactions are a powerful tool to study single particle states. Spectroscopic Factor (SF) quantifies the nature and occupancy of the single particle orbits in a nucleus. SF provides information on nuclear structure and is a key input for astrophysics calculations. Lab Angle [degrees] Differential Cross section [arb. units] (d, MeV/A Shape of calculation section depends on potentials. Best match to data is for CH89 (p), Perey-Perey (d), and Bechetti-Greenlees ( 3 He). Deuteron Potentials: pp = Perey-Perey ADNTD 17 (1976) 3 He Potentials: gdp = GDP08 PRC 79 (2009) and ch=Chapel Hill 89 bg = Bechetti-Greenlees ADNTD 17 (1976) 80.7 MeV/A Differential Cross section [arb. units] Deuteron Potentials: pp = Perey-Perey ADNTD 17 (1976) js = Johnson-Soper PRC 1 (1970) 976 Proton Potential: ch = Chapel Hill 89 Phys. Rep. 201 (1991) 57 Lab Angle [degrees] 37 MeV/A SF is extracted by matching the magnitude of the calculated cross section to the data The value SF exp = 7 was determined for the f 7/2 neutron from data at 37 MeV/A js = Johnson-Soper PRC 1 (1970) 976 *Note: there seems to be a shift in angle between the data and calculations which is not yet understood