(EXPERIMENTAL) NUCLEAR ASTROPHYSICS. study energy generation processes in stars study nucleosynthesis of the elements
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2 (EXPERIMENTAL) NUCLEAR ASTROPHYSICS Ø Ø study energy generation processes in stars study nucleosynthesis of the elements What is the origin of the elements? How do stars/galaxies form and evolve? What powers the stars? How old is the universe? NUCLEAR PHYSICS KEY for understanding MACRO-COSMOS intimately related to MICRO-COSMOS
3 ... Everything starts from the B 2 FH review paper of 1957, the basis of the modern nuclear astrophysics this work has been considered as the greatest gift of astrophysics to modern civilization The elements composing everything from planets to life were forged inside earlier generations of stars! Nuclear reactions responsible for both ENERGY PRODUCTION and CREATION OF ELEMENTS
4 nucleosynthesis processes 1. H burning à conversion of H to He 2. He burning à conversion of He to C, O 3. C, O and Ne burning à production of A: 16 to Si burning à production of A: 28 to s-, r- and p-processes à production of A>60 6. Li,Be, and B from cosmic rays
5 nuclear reac)on rates Nuclear reactions in stars: a) produce energy b) synthesise elements stars = cooking pots of the Universe for reaction: 1+2 à 3+4 Total reaction rate: R 12 = (1+δ 12 ) -1 N 1 N 2 <σv> 12 reactions cm -3 s -1 N i = number density σv = σ (v)φ(v)vdv Energy production rate: ε 12 = R 12 Q 12 reaction Q-value: Q=[(m 1 +m 2 )-(m 3 +m 4 )]c 2 Mean lifetime of nucleus 1 against destruction by nucleus 2 τ 2 (1) = 1 N 2 < σv > energy production as star evolves <σv> = KEY quantity change in abundance of nuclei X to be determined from experiments and/or theoretical considerations
6 stellar reaction rate σv = σ (v)φ(v)vdv a) velocity distribution need: a) velocity distribution φ(v) b) cross section σ(v) interacting nuclei in plasma are in thermal equilibrium at temperature T also assume non-degenerate and non-relativistic plasma Maxwell-Boltzmann velocity distribution µ φ(v) = 4π 2πkT with p 3/ 2 T v 2 2 µ v exp 2kT mpmt µ = reduced mass m + m arbitrary units max at E=kT v = relative velocity 0.0 kt ~ 8.6 x 10-8 T[K] kev energy [kev] example: Sun T ~ 15x10 6 K kt ~ 1 kev
7 reaction cross sections b) cross section no nuclear theory available to determine reaction cross section a priori cross section depends sensitively on: Ø the properties of the nuclei involved Ø the reaction mechanism and can vary by orders of magnitude, depending on the interaction examples: Reaction Force σ (barn) E proj (MeV) 15 N(p,α) 12 C strong He(α,γ) 7 Be electromagnetic p(p,e + ν)d weak barn = cm 2 = 100 fm 2 in practice, need experiments AND theory to determine stellar reaction rates
8 reaction mechanisms: I. direct (non-resonant) reactions II. resonant reactions
9 reaction mechanisms I. direct (non-resonant) process one-step process direct transition into a bound state example: radiative capture A(x,γ)B E cm γ Q A+x B σ γ B H A + x γ 2 H γ = electromagnetic operator describing the transition Ø reaction cross section proportional to single matrix element Ø can occur at all projectile energies Ø smooth energy dependence of cross section other direct processes: stripping, pickup, charge exchange, Coulomb excitation
10 reaction mechanisms II. resonant process two-step process example: resonant radiative capture A(x,γ)B 1. Compound nucleus formation (in an unbound state) 2. Compound nucleus decay (to lower excited states) S x A+x Q E cm E r γ Γ B σ γ f r 2 E H E E H A + γ r B x 2 B compound decay probability Γ γ compound formation probability Γ x Ø reaction cross section proportional to two matrix elements Ø only occurs at energies E cm ~ E r - Q Ø strong energy dependence of cross section N. B. energy in entrance channel (Q+E cm ) has to match excitation energy E r of resonant state, however all excited states have a width there is always some cross section through tails
11 reaction mechanisms example: resonant reaction A(x,α)B 1. Compound nucleus formation (in an unbound state) 2. Compound nucleus decay (by particle emission) S x A+x E cm Γ C C α B B+α S α σ γ r 2 B + α H E E H A + α r x x 2 compound decay probability Γ α compound formation probability Γ x N. B. energy in entrance channel (S x +E cm ) has to match excitation energy E r of resonant state, however all excited states have a width there is always some cross section through tails
12 reactions with charged particles
13 Nuclear reactions between charged particles charged particles Coulomb barrier energy available: from thermal motion V Coulomb potential during static burning: kt << E coul E coul ~ Z 1 Z 2 (MeV) E kin ~ kt (kev) T ~ 15x10 6 K (e.g. our Sun) kt ~ 1 kev nuclear well r 0 r reactions occur through TUNNEL EFFECT tunneling probability P exp(-2πη) relative probability Maxwell-Boltzmann distribution exp(-e/kt) Gamow peak ΔE 0 tunneling through Coulomb barrier exp(- ) E G / E Gamow peak: energy of astrophysical interest where measurements should be carried out kt << E 0 << E coul barn < σ < 10-9 barn kt E 0 energy major experimental challenges
14 Gamow peak: most effective energy region for thermonuclear reactions E 0 ± ΔE 0 /2 energy window of astrophysical interest E 0 = f(z 1, Z 2, T) varies depending on reaction and/or temperature Examples: T ~ 15x10 6 K (T 6 = 15) reaction Coulomb barrier (MeV) E 0 (kev) area under Gamow peak ~ <σv> p + p x10-6 α + 12 C x O + 16 O x STRONG sensitivity to Coulomb barrier separate stages: H-burning He-burning C/O-burning
15 measure σ(e) over as wide a range as possible, then extrapolate down to E 0! CROSS SECTION σ (E) = 1 exp(-2πη) S(E) E S-FACTOR S(E) = Eσ (E) exp(2πη) σ(e) LOG SCALE resonance non-resonant S(E) LINEAR SCALE extrapola)on direct measurement low-energy tail of broad resonance direct measurements sub-threshold resonance non resonant process E 0 extrapolation needed! E coul Coulomb barrier -E r 0 E r interac)on energy E DANGER OF EXTRAPOLATION!
16 Gamow peak for 12 C(α,γ) 16 O at T = 0.2GK cross section and astrophysical S-factor for non-resonant reaction Iliadis, Nuclear Physics of Stars, 2007 Iliadis, Nuclear Physics of Stars, 2007
17 reaction rate for resonant processes Reaction rate for resonant reactions σv = σ(v) φ(v)vdv = σ(e)exp( E/ kt)ede here Breit-Wigner cross section 2J + 1 Γ σ ( E) = π! 2 1 Γ 2 ( 2J 1 + 1) ( 2J T + 1) E E R ( ) 2 + ( Γ/2) 2 integrate over appropriate energy region E ~ kt for neutron induced reactions E ~ Gamow window for charged particle reactions if compound nucleus has an excited state (or its wing) in this energy range RESONANT contribution to reaction rate (if allowed by selection rules) typically: Ø resonant contribution dominates reaction rate Ø reaction rate critically depends on resonant state properties
18 summary stellar reaction rates include contributions from Ø direct transitions to the various bound states Ø all narrow resonances in the relevant energy window Ø broad resonances (tails) e.g. from higher lying resonances Ø broad subthreshold resonances with their higher energy tail Ø any interference term total rate σv = σv DCi + σv Ri i i + σv tails + σv int Rolfs & Rodney, 1988 Iliadis, 2007
19 Experimental approach Quiescent burning modes Explosive burning modes Ø stable nuclei Ø timescales ~ 10 9 y Ø E 0 ~ few kev Features Ø unstable nuclei Ø timescales ~ s Ø E 0 ~ MeV Ø barn < σ < 10-9 barn Ø extrapolations Ø background Problems Ø unknown nuclear properties Ø low beam intensities Ø beam-induced background Ø long measurements Ø pure targets Ø high beam currents Ø underground laboratories Requirements Ø radioactive ion beams Ø large area detectors Ø high detection efficiency
20 à we need to improve the signal-to-noise ratio
21 Laboratory for Underground Nuclear Astrophysics 1400 m-rock thickness above the Laboratory represents a natural shield for cosmic ray flux à reduction by one million times; 400 kv Accelerator : E beam kev I max 500 µa protons Energy spread 70 ev I max 250 µa alphas Long term stability 5eV/h
22 LUNA= Laboratory for Underground Nuclear Astrophysics LUNA Phase I: 50 kv accelerator ( ) investigate reactions in solar pp chain R. Bonetti et al.: Phys. Rev. Lett. 82 (1999) He( 3 He,2p) 4 He C. Casella et al.: Nucl. Phys. A706 (2002) d(p,γ) 3 lowest energy: σ ~ 20 fb à 1 lowest energy: σ ~ 9 pb à 50 counts/day only two reactions studied directly at Gamow peak
23 the underground solution Main Sources of Background: Ø natural radioac)vity (mainly from U and Th chains and from Rn) Ø cosmic rays (muons, 1,3 H, 7 Be, 14 C, ) Ø neutrons from (α,n) reac)ons and fission counts /h/kev typical γ-ray spectrum at surface lab Gran Sasso Boulby surface E-3 ambient neutron induced cosmic rays E γ [kev] ideal location: underground + low concentration of U and Th
24 but further problem at astrophysical energies à à à à S(E) enhancement experimentally found due to the Electron Screening Electron Screening S(E) s = S(E) b exp(πηu e /E) 3 He + 2 H à p + 4 He
25 Electron Screening In astrophysical plasma: - the screening, due to free electrons in plasma, can be different à we need S(E) b to evaluate reaction rates A theoretical approach to extract the electron screening potential U e in the laboratory is needed Experimental studies of reactions involving light nuclides have shown that the observed exponential enhancement of the cross section at low energies were in all cases significantly larger (about a factor of 2) than it could be accounted for from available atomic-physics model, i.e. the adiabatic limit (U e ) ad Although we try to improve experimental techniques to measure at very low energy à à S b (E)-factor extracted from extrapolation of higher energy data
26 - to measure cross sections at never reached energies (no Coulomb suppression), where the signal is below current detection sensitivity - to get independent information on U e - to overcome difficulties in producing the beam or the target (Radioactive ions, neutrons..) - NOTE: Measurements require careful validation. Data analysis needs nuclear reaction models v Coulomb dissociation to determine the absolute S(E) factor of a radiative capture reaction A+x à B+γ studying the reversing photodisintegration process B+γ A+x v Asymptotic Normalization Coefficients (ANC) to determine the S(0) factor of the radiative capture reaction, A+x à B+γ studying a peripheral transfer reaction into a bound state of the B nucleus v Trojan Horse Method (THM) to determine the S(E) factor of a charged particle reaction A+xàc+C selecting the Quasi Free contribution of an appropriate A+a(x+s)à c +C+s reaction
27 Basic principle: astrophysically relevant two-body σ from quasi- free contribution of an appropriate three-body reaction a: x s clusters A + a c + C + s à à à A + x c + C a Direct break-up S ü only x - A interaction E A > E Coul ü s = spectator (p s ~0) NO Coulomb suppression NO electron screening A x 2-body reaction C c E q.f. = E ax = m x /(m x + m A )E A B x-s ± intercluster motion plays a key role in compensating for the beam energy E q.f. 0!!!
28 Typical experimental setup for THM measurements Coincidence detection of any two of the three particles in the exit channel
29 Li burning 6 Li + d α + α via 6 Li+ 6 Li α+α+α S 0 = 16.9 MeV b 6 Li+d α + α U e (ad) U e (THM) 6 Li+d U e (Dir) 6 Li+d 186 ev 340 ± 50 ev 330 ± 120 ev 7 Li+p α+α via 7 Li+d α+α +n S 0 = 55 ± 3 kev b U e (ad) U e (THM) 7 Li+p U e (Dir) 7 Li+p 186 ev 330 ± 40 ev 300 ± 160 ev 7 Li+p α + α 6 Li+p à α + 3 He via 6 Li+d à α + 3 He+n S o = 3± 0.9 MeV b 6 Li+p α + 3 He U (ad) e U (THM) 6 e Li+p U (Dir) 6 e Li+p 186 ev 435 ± 40 ev 440 ± 80 ev C. Spitaleri et al., PRC60 (1999) C. Spitaleri et al., PRC63 (2001) A. Tumino et al., PRC67 (2003)
30 LUNA Reactions measured so far at or near Gamow region: 3 He( 3 He,2p) 4 He 1 H(p,γ) 3 He 14,15 N(p,γ) 15 O 3 He( 4 He,γ) 7 Be 25 Mg(p,γ) 26 Al 2 H( 4 He,γ) 6 Li 17 O(p,g) 18 F 17 O(p,α) 14 N Many critical reactions for astrophysics BEYOND current capabilities Some of the poorly known nuclear reactions with stable and photon beams Heavy ion reactions: 12 C+ 12 C, 16 O+ 16 O, 12 C+ 16 O Neutron sources: 13 C(a,n) 16 O, 22 Ne(a,n) 25 Mg, 17 O(a,n) 20 Ne Capture reactions: 3 He(a,γ) 7 Be, 12 C(a,γ) 16 O & 2π ) Most of these reactions are resonant: σv 12 = ( + ' µ 12 kt * 3 / 2 2 & ( ωγ) R exp E ) R ( + ' kt * NOTE exponential dependence on energy means: Ø small uncertainties in E R (even a few kev) imply large uncertainties in reaction rate
31 Other examples abundances of Ne, Na, Mg, Al, in AGB stars and nova ejecta affected by many (p,γ) and (p,a) reactions shaded areas indicate order of magnitude(s) uncertainties Iliadis et al. ApJ S134 (2001) 151; S142 (2002) 105; Izzard et al A&A (2007)
32 17 O(p,γ) 18 F 17 O(p,α) 14 N Both reac)ons involved in the explosive hydrogen burning in the novae and in the nucleosynthesis path of 18 F, of special interest in novae observa)ons in the γ-ray wavelengths à LUNA experiment In explosive condi)ons, the reac)on rate is dominated by contribu)ons from narrow resonances at E c.m. =65 and 183keV à THM experiment Experimental details: Direct experiment: LUNA underground 400 kv accelerator, E c.m. = kev, 200µA p-beam on solid Ta 2 O 5 targets. Deep underground environment of LNGS + 4pi 10cm thick lead shielding leads to a reduc)on of the background events by a factor of 2500 with respect to surface measurements. Prompt γ-rays detected by HPGe detectors + target ac)va)on technique. Since 18 F β + decays to the ground state of 18 O, it is possible to determine its ac)vity through the detec)on of the 511-keV γ ray from the positron annihila)on. Targets used solely for the ac)va)on measurements were irradiated for several hours in order to saturate the 18 F ac)vity, using the same experimental setup of the prompt γ-ray measurements. A. Di Leva et al. Phys. Rev. C (2014) THM experiment: 41 MeV 17 O beam on a CD 2 target, 150 µg/cm 2 thick. Detec)on setup consis)ng of telescopes made up of ioniza)on chambers/si detectors as ΔE and silicon PSD as E-detectors. M.L. Sergi et al. PRC (R) (2010) M.L. Sergi et al PRC (2015)
33 17 O(p,γ) 18 F 17 O(p,α) 14 N S(E) (kev b) LUNA activation LUNA primary Newton et al. Hager et al. Kontos et al. fit global fit LUNA only fit E c.m. (MeV) (ωγ) 183keV =1.67±0.12 µev (ωγ) 65keV = Reaction rate about 20% smaller than the most recent value reported in literature The abundance of key isotopes such as 18 F, 18 O, 19 F, 15 N evaluated through nova models calculations, are now obtained with a precision of 10%
34 importance: evolution of massive stars astrophysical energy: 1 3 MeV minimum measured E: 2.1 MeV (by γ-ray +part. spectroscopy) 12 C+ 12 C à α + 20 Ne 12 C+ 12 C à p + 23 Na extrapolations differ by 3 orders of magnitude complicated by the presence of resonant structures even in the low-energy part of the excitation function [MeV b] S * tot Spillane et al. Aguilera et al. Becker et al. High and Cujec Patterson et al E cm [MeV] Jiang et al. Gasques et al. Caughlan and Fowler PA KNS b 10-7 b large uncertainties in astrophysical models of stellar evolution and nucleosynthesis
35 12 C( 12 C,α) 20 Ne and 12 C( 12 C,p) 23 Na reactions via the Trojan Horse Method applied to the 12 C( 14 N,α 20 Ne) 2 H and 12 C( 14 N,p 23 Na) 2 H three-body processes 2 H from the 14 N as spectator s Observation of 12 C cluster transfer in the 12 C( 14 N,d) 24 Mg * reaction (R.H. Zurmȗhle et al. PRC 49(1994) 5) QUASI-FREE MECHANISM ü only 12 C - 12 C interaction ü d = spectator E 14N =30 MeV> E Coul 14 N NO Coulomb suppression NO electron screening 12 C Direct breakup 12 C 24 Mg* d a,p 20 Ne, 23 Na E QF = E 14N m m C N m 12 m C 12 + C m 12 C MeV C. Spitaleri et al., Phys. Rev. C 63, (2001) R. Tribble et al. Rep. Prog. Phys (2014)
36 12 C( 12 C,α) 20 Ne and 12 C( 12 C,p) 23 Na reactions via the Trojan Horse Method applied to the 12 C( 14 N,α 20 Ne) 2 H and 12 C( 14 N,p 23 Na) 2 H three-body processes 2 H from the 14 N as spectator s Observation of 12 C cluster transfer in the 12 C( 14 N,d) 24 Mg * reaction (R.H. Zurmȗhle et al. PRC 49(1994) 5) E 14N =30 MeV> E Coul p p Na * +d Na+d α Ne * +d α Ne+d
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