Πυρηνοσύνθεση Βαρέων Στοιχείων και Πυρηνικές Αντιδράσεις Nuclear Reactions in Heavy-Element Nucleosynthesis Παρασκευή ηµητρίου ΙΠΦ, ΕΚΕΦΕ «ηµόκριτος»
Outline διαδικασίες πυρηνοσύνθεσης Βαρέων στοιχείων (>Fe) στοιχεία πυρηνικών αντιδράσεων των διαδικασιών πυρηνοσύνθεσης s-, r-, p-process παραδείγµατα στην p και r process συµπεράσµατα
nucleosynthesis of elements up to Fe
+e-captures, neutrino-interactions s process: slow neutron captures β - (n,γ) τ 10-10 4 yr, T (0.1-0.4)10 9 K, n>10 5 cm -3 p process: photodisintegrations+inverse (p,γ) (α,γ) (γ,n) (n,γ) (γ,α) (γ,p) T 2 10 9 K, n>10 8 cm -3 β + r process: rapid neutron captures β - (γ,n) (n,γ) + fission, + β-delayed fission heavy-element nucleosynthesis: > Fe τ 10-1 s, T (1.8-3.3)10 9 K, n>10 20 cm -3
role of fission end of r process re-cycling
nuclear reaction network reaction: i + j k + l elemental abundances abundance of element i: N i number of particles i per cm 3 N i ( Z A i ) + N j ( Z A j ) N k ( Z A k ) + N l ( Z A l ) rate equation: rate of change of abundance N i dn (α,n) i (α,γ) = N jn i συ + N k N συ N (t) dt (p,n) ij (p,γ) l + kl iλβi (α,p) jkl (γ,n) (n,γ) reaction rate per (p,α) particle pair: (γ,p) (n,p) συ (n,α) ϕ 2 number of reactions/nucleus X/unit time = ( υ) υσ ( υ) d υ σ(cm ) = 2 number of incident particles/cm /unit time υ : relative velocity σ(υ) :cross section for reaction ϕ( υ) : velocity distribution
stellar reaction rates velocity distribution in thermodynamic equilibrium: Maxwellian συ = µ 4π 2πkT 3/2 0 υ 3 σ(υ)exp 2 µυ dυ 2kT stellar temperature charged-particle reactions: Coulomb barrier 2 2πZ e Penetration exp 1Z 2 hυ Maxwellian distr. Gamov peak Gamow window Coulomb penetration relevant energy range hot astrophysical plasma: excited target nucleus i µ + j k + l relative population of levels µ : Maxwellian distribution συ * = 8 πµ 1/2 partition function : 1 3/2 (kt) G(T) G(T) = 0 µ µ µ (2J i + 1) µ E + ε σ (E)Eexp 0 (2J i + 1) kt µ µ 2J + 1 ε i exp i 0 2J i + 1 kt µ i reaction cross section nuclear level scheme de
nuclear reaction cross sections in stellar and/or explosive environments: T ~ 10 8 10 9 K E ~0.1-5 MeV (p,γ) (γ,n) (γ,α) (γ,p) (α,γ) (n,γ) channel a projectile Target A E r compound nucleus B In resonant state channel b Resonant reactions γ σ(e) Γ a,b (E E Γ :decay widths Γ = Γ a + Γ b +... E = E + Q r R Breit-Wigner: Γ a 2 R ) b + ( Γ/2) a,b 2 σ(e) E R width Γ E Non-resonant reactions σ(e) Compound nucleus (Hauser-Feshbach): compound nucleus B In continuum phase space projectile Final nucleus C γ σ ( E) T ( J b π J ) = π ν T (2J + 1) T ν b ( J Direct reactions: π a ) + ( J T π tot ) T ( J ( J b π ε, J, π ) π T ( ε, J b ) π ) ρ( ε, J, π ) dεdjdπ E σ γ B H γ A + x 2 Target A Final compound nucleus B H γ : electromagnetic operator
fission E inc Sn T n E,j,π Tγ T f Z,N+1 Compound nucleus T A T B spontaneous B A B B λ P σ sf X nf P A P B = Penetrabil T n T T k f k ity throug h barrier ; T f = P P A A + P B P B X deformation β decay + β-delayed emission n(p) p(n)+e - ( + )+ν(ν) 0 Z,N Z+1,N-2 Sn -Q T n E,j,π Tγ β - Z+1,N-1 T A T B T f B A B B λ β = 0 Q β S β (E)dE 1 2 2 Sβ (E) = G M (E) (Q E) 3 Ω Ω f Ω β 2π Ω Ω : Fermi,GT, First Forbidden transitions λ λ bdn bdf = = 0 Q 0 β Q β T n T n T n + T γ T f + T γ + T f + T f S β S β (E)dE (E)dE
nuclear data input Q values, S n nuclear masses ground-state properties: charge radii, deformations, shell effects nuclear level schemes : energy, spins, lifetimes of levels hot nucleus properties: nuclear level densities (NLD) particle transmission coefficients T optical potential (OP) γ-ray strength functions: giant dipole resonances fission barriers and level densities β-decay strength functions
p process s process r process
abundances of elements nuclear reaction rates reaction network: 20000 reactions and 2000 nuclei astrophysics models stellar sites neutron densities temperatures Exp. data nuclear models reproduce existing data with good accuracy-test theories global models: large-scale calculations microscopic models: extrapolations to experimentally unknown
nuclear models phenomenological (macroscopic-microscopic) models: Finite Range Droplet Model (FRDM), Fermi Gas Model (FG) etc shell, pairing etc corrections: empirical formulas advantage: simplicity, easy to compute disadvantage: free parameters adjusted on available data microscopic Effective NN interaction: Skyrme, Gogny many-body techniques: Hartree-Fock, Hartree-Fock-BCS, Hartree-Fock-Bogoliubov advantage: shell, pairing, deform. consistently disadvantage: computing power 1. Existing data in known mass regions masses (2135 Z 8): FRDM 1995 (rms=676 kev) ++ HF-BCS 2001 (rms=738 kev) ++ HFB 2002 (rms=660 kev) ++ NLDs (278): Back-Shifted FG 1997 (rms=1.94) ++ HF-BCS 2001 (rms=2.14) ++ 2. Extrapolations to unknown mass regions -- +-
Comparison of masses: M=M HFB -M FRDM
Comparison of state densities ω(u): r=10 [log ( ωhfbcs/ ωbsfg)]
Comparison of radiative capture rates r = συ συ max min (n,γ) ++ (p,γ) +- (α,γ) -- α OP!!!
α-nucleus optical potentials 144 Sm(α,γ) 148 Gd Data by A. Spyrou et al, INP, NCSR Demokritos OP I,II,III : Demetriou, Grama, Goriely NPA 707 142 (2002) OP III
p-process nucleosynthesis possible sites: O-Ne rich layers of massive stars (M>10M ) in pre- and SN phase (Type II) C-rich zones of Chandrasekhar-mass white dwarfs (Type Ia SN) exploding sub-chandrasekhar mass white dwarfs Example: impact of nuclear uncertainties on overproduction factor <F> of p nuclei in site: SN type II for M=25 M
Woosley and Howard, Ap. J. Suppl. 36, 285 (1978), Overproduction factors: σ σ AV mass fraction of produced p nucleus σ = solar mass fraction of the p nucleus σav = 1 35 i σi p-nuclei abundances: still a problem!!! S. Goriely, M. Arnould, I. Borzov, and M. Rayet : A&A 375, 35 (2001) no neutrino interactions
possible sites to date: core-collapse supernova (IIa,Ib) r-process nucleosynthesis 1. prompt explosion of massive stars 8-10M (Wheeler etal. 1998, Sumiyoshi etal. 2001) r-process in innermost layers (n n >10 20 cm -3, T >10 9 K) problems: triggering explosion 2. delayed explosion of very massive star 20M (Woosley&Hoffman 1992, Takahashi etal. 1994, Wanajo etal. 2001, Terasawa etal. 2002)) r-process in neutrino-driven winds from nascent neutron star problems: SN IIa cannot give necessary conditions (entropy) extremely massive neutron stars required (2M ) mergers of neutron stars (Schramm 1982; Meyer 1989; Ruffert & Janka 1998, Argast etal. 2003) extremely neutron-rich nuclear matter r-process during decompression phase (T 10 9 K) problems: low coalescence times too late injection of r-process matter in ISM [r/fe] disagree with observations EOS exotic nuclear physics
Decompression of initially cold neutron star matter - Neutron star mergers or neutron star-black hole mergers: M ejec = 10-3 -10-2 M o or 5 10-5 - 2 10-4 M o 10-2 (corotating) - 10-4 (counter-rotating) M o Galactic NSM rate: f NSM = 10-6 - 3 10-4 yr -1 Coalescence timescales: 100-1000 Myr (total amount of r-process matter in the Galaxy estimated to 10 4 M o ) - Possible site for the r-process nucleosynthesis - Ejection of n-rich material from the neutron star inner crust - No consistent r-process calculations - Lattimer et al (1977), Meyer (1989): decompression of cold matter - Freiburghaus et al. (1999): parametrized-y e and heated matter - Chemical evolution of the Galaxy not in favour R-process matter mixed with ISM leads to [r/fe] too high to be compatible with observation of [r/fe] in ultra-metal-poor stars!?!?!
The r-process of nucleosynthesis Expansion of neutron-rich matter Initial distribution of nuclei with Z 40-70 at the n-drip line Free neutrons: N n 10 34 cm -3 Temperature evolution followed by an adequate EOS (ρ < 10 11 g/cm 3 T < 10 9 K) Nuclear reaction network including (n,γ),(γ,n),β,βdn,βdf,nif,sf Many uncertainties: initial conditions (in part., Z-dist. at the n-drip line) EOS and temperature evolution during the r-process Role of neutrinos (heat, accelerate, change the composition?) neutron-capture rates at the n-drip line β -decay rates and energy generation due to β -decays fission rates and energy generation due to fission distribution of fission fragments
r-abundance distribution in the ejecta After t=0.91 s Relative Abundances 10-1 10-2 10-3 10-4 N n =10 22 cm -3 T 9 =0.05 Solar System t=0.91s 10-5 50 100 150 200 250 A
r-abundance distribution in the ejecta After t=3.23 s Relative Abundances 10-1 10-2 10-3 10-4 N n =10 20 cm -3 T 9 =0.05 Solar System t=3.23s 10-5 50 100 150 200 250 A
One sensitivity calculation Relative Abundances 10-1 10-2 10-3 10-4 Solar System log ft=-2.8; HFB-02 log ft=-5.5; HFB-08 10-5 50 100 150 200 250 A
Συµπεράσµατα Οι θερµοπυρηνικές αντιδράσεις αποτελούν το κύριο καύσιµο υλικό των άστρων και η κύρια αιτία αστρικής εξέλιξης και πυρηνοσύνθεσης η περιγραφή των πυρηνικών αντιδράσεων µε σηµασία στην πυρηνοσύνθεση Βαρέων στοιχείων αποτελεί έργο σύνθετο και απαιτεί γνώσεις πολλών πυρηνικών ιδιοτήτων (πυρηνικής δοµής, ιδιότητες βασικής στάθµης και διεγερµένων καταστάσεων) οι αβεβαιότητες στην περιγραφή των πυρηνικών αντιδράσεων έχουν επιπτώσεις και στον υπολογισµό των τελικών περιεκτικοτήτων των στοιχείων για την βελτίωση των πυρηνικών δεδοµένων απαιτούνται συγχρόνως παιρετέρω µετρήσεις ενεργών διατοµών σε ενέργειες σχετικές και ανάπτυξη γενικευµένων µικροσκοπικών µοντέλων για πιο ακριβείς υπολογισµούς πέρα από τις αβεβαιότητες της πυρηνικής φυσικής, σηµαντικές αβεβαιότητες παραµένουν και στο αστροφυσικό µέρος, ιδιαίτερα όσον αφορά το αστρικό περιβάλλον όπου λαµβάνει χώρα η διαδικασία πυρηνοσύνθεσης (p-, r-process)