Nuclear Astrophysics and Exotics Artemis Spyrou Michigan State University Artemis Spyrou, Belfast 2017, 1 Overview Lecture 1: Intro to Nuclear Astrophysics - reactions Lecture 2: How to measure cross sections + activity Lecture 3: Nuclear structure for astrophysics Lecture 4: Exotic phenomena close to the drip lines Artemis Spyrou, Belfast 2017, 2 Abundances From M. Wiescher, JINA web Artemis Spyrou, Belfast 2017, 3 Nucleosynthesis paths Z 56Fe Stellar burning pp chain N Artemis Spyrou, Belfast 2017, 4 Paths beyond Iron Artemis Spyrou, Belfast 2017, 5 Nuclear Astrophysics Connections Numerical approximaons Astrophysical Nuclear Input condions Stellar modeling • Solar system abundances • Stellar observaons – Abundances Compare to • Meteori:c samples Observaons • Light output / Energy produc:on • Time scales Artemis Spyrou, Belfast 2017, 6 Nuclear input: What do we need? o Basic nuclear properties • Mass • Binding energy • Half life • Level structure • Angular • Nuclear radius/shape Momentum Artemis Spyrou, Belfast 2017, 7 Nuclear Input νp-process • Close to proton drip line • Masses, T1/2 mostly known • Most important (p,n) reactions rp-process r-process • Close to proton drip line 56Fe • Masses, T1/2 mostly known • Far from stability • Proton capture reactions • Most properties not known • Masses • T1/2 • Pn Burning • Neutron captures p-process • Nuclear reactions • Resonance properties • Close to stability i-process • Masses, T1/2 known s-process • Between s and r • γ-induced reaction rates • Along stability • Mass, T1/2 known • Most properties known • Missing neutron captures • Missing neutron captures Artemis Spyrou, Belfast 2017, 8 Nuclear Reactions in Stars Main focus on capture reactions Artemis Spyrou, Belfast 2017, 9 Y X υ r = NX NYυσ(υ) ∞ r N N f(υ)σ(υ)υdυ f (υ) = X Y ∫ 0 r: reaction rate Nx, Ny: number of particles υ:velocity r ∞ σ(υ): reaction cross section at υ συ = = f(υ)σ (υ)υdυ N N ∫ f(υ): velocity distribution X Y 0 <συ>: reaction rate per particle pair Rolfs and Rodney, “Cauldrons in the cosmos” Artemis Spyrou, Belfast 2017, 10 Maxwell – Boltzmann distribution 2 ⎛ mυ ⎞ 0.5 3/ 2 ⎜ ⎟ ⎜ − ⎟ 2 ⎛ m ⎞ ⎝ 2kT ⎠ f(υ) = 4πυ ⎜ ⎟ e 0.4 (E) 2πkT φ ⎝ ⎠ 0.3 0.2 Distribution Distribution 0.1 3/ 2 ⎛ E ⎞ ⎜ − ⎟ 2 ⎛ 1 ⎞ 1/ 2 kT φ(E) = ⎜ ⎟ E e⎝ ⎠ 0.0 π ⎝ kT ⎠ 0kT 2kT 4kT 6kT 8kT 10kT 12kT 14kT Energy E 1/2 ! E $ ! 8 $ 1 ∞ #− & (E)Ee" kT %dE συ = # & 3/2 ∫ σ "πµ % (kT) 0 Rolfs and Rodney, “Cauldrons in the cosmos” Artemis Spyrou, Belfast 2017, 11 Tunnel Effect – S-factor 2 Coulomb barrier ψ (Rn ) P = 2 ψ (Rc ) projecle Tunneling probability -> R n Rc Distance r increasing with energy Poten:al V(r) Nuclear radius Artemis Spyrou, Belfast 2017, 12 Cross section has two components: 1. Interaction between particles (pure nuclear) 2. The Coulomb force Astrophysical S-factor 1 (−2πη) σ (E) = e S(E) Contains all the pure nuclear E properties Z Z e2 η: Sommerfeld parameter η = 1 2 !υ Rolfs and Rodney, “Cauldrons in the cosmos” Artemis Spyrou, Belfast 2017, 12 Astrophysical region S-factor σ(Ε) Coulomb Barrier Log Scale Cross Section Extrapolation The dangers of extrapolation S(E) factor Linear Scale Energy E Artemis Spyrou, Belfast 2017, 13 Gamow Window Maxwell – Boltzmann distribu:on Tunneling probability ⎛ E ⎞ # & ∝ exp⎜− ⎟ EC ⎝ kT ⎠ ∝ exp%− ( $ E ' Gamow peak ΔE0 Relative probability E0 Energy Artemis Spyrou, Belfast 2017, 14 Gamow Window • Charged particles Burning: T= 0.01 – 0.1 GK o (p,γ): Ep= 0.02 – 0.2MeV Standard approximation o (α,γ): Eα= 0.05 -0.5 MeV p process: T= 1.8 – 3.3 GK 2 2 2 1/3 E0 = 0.12204(Z1 Z2 µT9 ) o (p,γ): Ep= 1 – 5 MeV [in MeV] o (α,γ): Eα= 4 -12 MeV E 0.237(Z 2Z 2 T 5 )1/6 Δ 0 = 1 2 µ 9 rp process: T= 1.1 – 1.3 GK o (p,γ): E = 0.8 – 2 MeV ΔE p Window: E + 0 νp process: T= 1.5 – 3.0 GK 0 2 o (p,γ): Ep= 1 – 4 MeV • Neutrons No Coulomb barrier, angular momentum 1 s process: T~ 0.3GK Eeff = 0.172T9 (ℓ + ) 2 o (n,γ): En= 25 - 75 keV [in MeV] i process: T= 0.1-0.3GK 1 o (n,γ): Ep= 10 – 75 MeV ΔEeff = 0.194T9 ℓ + 2 r process: T= 0.1 – 2.0 GK ΔEeff Window: E + o (n,γ): Ep= 10 – 500 keV eff 2 Rauscher, PRC 81 (2010) 045807 Kadonis.org : Gamow Calculator Artemis Spyrou, Belfast 2017, 15 Nuclear input: What do we need? o Nuclear reactions/Astrophysical reaction rates * a A B B Radiative capture reactions Incoming channel + → → +γ Resonant Statistical Direct A A A Q Q Q B B B Artemis Spyrou, Belfast 2017, 16 o Example: 24Mg(p,γ)25Al Marialuisa Aliotta, University of Edinburgh 11th Euro Summer School on Exotic Beams Artemis Spyrou, Belfast 2017, 17 Nuclear input: What do we need? o Nuclear reactions/Astrophysical reaction rates a + A → B* → B +γ Prompt Outgoing channel or other particle channels (Competing channels) n γ B-1n Delayed A Q β B n Τ1/2 γ C-1n C Artemis Spyrou, Belfast 2017, 18 Experiment Accelerator Facilities Artemis Spyrou, Belfast 2017, 19 Facilities Stable beam facilities (Intro Physics) • Van de Graaff (single-ended or tandem) • Cyclotrons • LINACS Artemis Spyrou, Belfast 2017, 20 Basic Components Analyzing magnet Accelerator Ion sources Beam Lines 5MV tandem accelerator @ Institute of Nuclear Physics, “Demokritos”, Athens, Greece Artemis Spyrou, Belfast 2017, 21 Radioactive Beams • Fragmenta0on: NSCL/FRIB, GSI/FAIR, RIKEN, … Target Fast RIB Stable beam Fragmentaon Separaon • Isotope Separaon On-Line (ISOL): TRIUMF, SPIRAL, ISOLDE, … Target Extrac:on Stable beam RIB Separaon Reacceleraon • Fission source: CARIBU/ANL Fission source Separaon Acceleraon RIB Extrac:on • Low energy reac0ons: ANL, FSU, Texas A&M, Notre Dame, … Target Low energy RIB Stable beam Reac:on Separaon? Artemis Spyrou, Belfast 2017, 22 NSCL@MSU • Naonal Superconduc0ng Cyclotron Laboratory “Stopped beam area” Gas Stopper ReAccelerator Facility K500 Cyclotron S800 Spectrograph A1900 Fragment Separator K1200 Cyclotron Artemis Spyrou, Belfast 2017, 23 Coupled Cyclotron Facility Example: 86Kr → 78Ni K500 ion sources coupling 86Kr14+, line 12 MeV/u K1200 A1900 focal plane Δp/p = 5% producon transmission stripping 86Kr34+, target foil of 65% of the 140 MeV/u produced 78Ni wedge fragment yield aer target fragment yield aer wedge fragment yield at focal plane Artemis Spyrou, Belfast 2017, 24 Neutron Facilities Time-of-Flight: e.g. nTOF@CERN, LANSCE@ Los Alamos, IRMM@Geel, Belgium, etc • High energy protons on heavy target, broad energy distribu:on, pulsed beam. Reac0on-based, quasi-monoenergec: Any low energy facility 2 2 3 • Reac:ons: H( H,n) He – Q= 3.3 MeV - En= 2.5 MeV 3 2 4 H( H,n) He – Q= 17.6 MeV - En = 14.1 MeV 7 7 Li(p,n) Be – Q= - 1.64 MeV – En=? – How can you get 25 keV? … Artemis Spyrou, Belfast 2017, 25 In the Laboratory Number of reactions • Yield of reaction: Y = Number of beam particles Yield of reaction N • Cross section: σ = = R Number of target particles Nb ⋅ NT To measure a cross section you need three things: 1. Number of target particles (NT) !!! 2. Number of beam particles (Nb) !!! 3. Number of reactions (NR) !!! Artemis Spyrou, Belfast 2017, 26 Number of target particles 1 • Rutherford backscattering 92 ΔΕ0 Mo target 0 Mo Ed = 1.35 MeV ΔΕ - experiment 0 0 Ε Ε Beam simulation ο 170 Ε1 Ε1-ΔΕ Al backing 1 Si detector # events ΔΕ # events 1 Energy (keV) Ε -ΔΕ Ε Ε 1 1 1 o Simulation with SIMNRA o Known detector geometry N : Avogadro number N Aξ A o Known cross section NT = A: Atomic mass A ξ: target thickness in g/cm2 o Free parameter: target thickness/composition Artemis Spyrou, Belfast 2017, 27 Tools 1 Si surface barrier detector – Semi-conductor hp://nsspi.tamu.edu/nssep/courses/basic-radiaon-detec:on/ semiconductor-detectors/introduc:on/introduc:on Artemis Spyrou, Belfast 2017, 28 Number of target particles 1 • X-ray Fluorescence (XRF) M L K M L K X-ray detector # events Energy (keV) Artemis Spyrou, Belfast 2017, 29 Tools 1 SiLi detector – Semi-conductor X-ray tube • Cooling • Addition of Li helps remove impurities hmp://nau.edu/cefns/labs/electron-microprobe/glg-510-class-notes/ detec:on-of-signals/ hmp://www.schoolphysics.co.uk/age16-19/Medical%20physics/text/ X_rays/index.html Artemis Spyrou, Belfast 2017, 30 Number of target particles 1 • Particle energy loss ΔΕ0 0 ΔΕ - 0 0 Ε α α Ε source source Si detector Si detector # events Ε Ε0-ΔΕ0 Ε0 o Many other techniques like resonance measurement, use of spectrometer or recoil separator, use a reaction, etc o If radioactive sample: activity from decay Artemis Spyrou, Belfast 2017, 31 In the Laboratory Number of reactions • Yield of reaction: Y = Number of beam particles Yield of reaction N • Cross section: σ = = R Number of target particles Nb ⋅ NT To measure a cross section you need three things: 1. Number of target particles (NT) !!! 2. Number of beam particles (Nb) !!! 3. Number of reactions (NR) !!! Artemis Spyrou, Belfast 2017, 32 Number of beam particles 2 • High beam intensities: measure deposited charge Collimator 1 Collimator 2 Target beam detector A Ammeter/ Current integrator e.g. 1H+ beam: each beam particle deposits 1.6 x 10-19 Cb (e- charge) 84Kr27+ beam: each beam particle deposits 27 x 1.6 x 10-19 Cb Artemis Spyrou, Belfast 2017, 33 Number of beam particles 2 • High beam intensities: measure deposited charge Collimator 1 Collimator 2 - Target e e- beam detector - - e - e e- e A Ammeter/ Current integrator Artemis Spyrou, Belfast 2017, 34 Number of beam particles 2 • High beam intensities: measure deposited charge Collimator 1 Collimator 2 - Target e- - e e- beam e detector - - e- e- e - e e- e- e e- A Ammeter/ Current integrator +- Beam: positive charge +1e + +-+- Measurement 1: +1e +- Measurement 2: +2e = false +- +- +- How do we fix it? Artemis Spyrou, Belfast 2017, 35 Number of beam particles 2 • Low beam intensities: measure each particle in detector 1.