Nuclear Astrophysics: A Few Basic Concepts and Some Outstanding Problems Barry Davids, TRIUMF Exotic Beams Summer School 2012 Aims of Nuclear Astrophysics

How, when, and where were the chemical elements produced? What role do nuclei play in the liberation of energy in stars and stellar explosions? How are nuclear properties related to astronomical observables such as solar neutrino flux, γ rays emitted by astrophysical sources, light emitted by novae and x-ray bursts, et cetera? Nuclear Astrophysics

Nuclear reactions power the stars and synthesize the chemical elements We observe the elemental abundances through starlight and isotopic abundances in meteorites, and deduce the physical conditions required to produce them (Burbidge, Burbidge, Fowler and Hoyle, Reviews of Modern Physics 29, 547, 1957) Task of nuclear astrophysics is to understand abundances and energy release quantitatively Solar System Abundances Primordial Nucleosynthesis

The Astrophysical Journal,744:158(18pp),2012January10 Coc et al.

2 2 ΩBh =WMAP ΩBh =WMAP

2 3 4 3 4 10 10 10 10 10 -14 -14 Lightest nuclei 10 10 1 1 -1 p -1 12 10 4 10 C 13 n He -15 C -15 produced during 10 10 -3 -3 14 10 2 10 N H -16 -16 Mass fraction period of nuclear Mass fraction -5 -5 10 10 10 3 10 13 3H He N -17 15 -17 -7 -7 10 O 10 reactions in hot, dense, 10 10 16O -9 -9 -18 -18 10 10 10 10 expanding universe 7Li 7 -11 Be -11 -19 15 -19 10 10 10 N 10 2 3 6 14 -13 Li -13 C Accounts for H, He, 10 10 -20 -20 10 10 11 10 -15 C -15 C 18 4 7 10 11 10 O B -21 -21 He, and Li 10 10 17 -17 9 -17 10 Be 10 O -22 -22 10 10 10 -19 B -19 10 10 Figure from Coc et al., 8 Li -23 16 14 -23 10 N O 10 -21 8 -21 12 10 B 10 N Astrophysical Journal 9 Li -24 -24 -23 13 10 -23 10 10 10 B Be 10 744, 158 (2012) 12B -25 -25 -25 -25 10 10 10 10 2 3 4 3 4 10 10 10 10 10 Time (s) Time (s) Figure 12. Standard big bang nucleosynthesis production of H, He, Li, Be, and Figure 13. Standard big bang nucleosynthesis production of C, N, and O isotopes B isotopes as a function of time, for the baryon density taken from WMAP7. as a function of time. (Note the different time and abundance ranges compared (A color version of this figure is available in the online journal.) to Figure 12.) (A color version of this figure is available in the online journal.) 3.2. Improvement of Some Critical Reaction Rates

In this section, the above-mentioned critical reactions are Equations (11) and (14) of Angulo et al. (1999), where the low- analyzed and their rates re-evaluated on the basis of suited est four resonances in the 7Li(d,n)2α reaction center-of-mass reaction models. In addition, realistic uncertainties affecting system are considered, the corresponding resonant parameters these rates are estimated in order to provide realistic predictions being taken from RIPL-3 (Capote et al. 2009). For the direct part, for the BBN. Since each reaction represents a specific case the contribution is obtained by a numerical integration with a dominated by a specific reaction mechanism, they are analyzed constant S-factor of 150 MeV b is considered for the upper and evaluated separately below, see Figures 16, 17, 18,and19. limit (Hofstee et al. 2001)andof5.4MeVb for the lower limit

7 9 9 (Sabourov et al. 2006). The recommended rate is obtained by 3.2.1. Li(d,γ ) Be Affecting Be the geometrical means of the lower and upper limits of the total The total reaction rate consists of two contributions, namely rate. The final rate with the estimated uncertainties are shown aresonanceandadirectpart.Thedirectcontributionisobtained and compared with the TALYS and Boyd et al. (1993)ratesin by a numerical integration from the experimentally known Figure 18. S-factor (Schmid et al. 1993). The corresponding upper and lower limits are estimated by multiplying the S-factor by a 3.2.3. 7Li(t,n)9Be Affecting CNO and 9Be factor of 10 and 0.1, respectively. The resonance contribution is To estimate the 7Li(t,n)9Brate,experimentaldatafrom estimated on the basis of Equations (11) and (14) in the NACRE Brune et al. (1991)aswellastheoreticalcalculationsfrom evaluation (Angulo et al. 1999)wheretheresonanceparameters Yamamoto et al. (1993)areconsidered. and their uncertainties for the compound system 9Be are taken More precisely, the lower limit of the total reaction rate is from the RIPL-3 database (Capote et al. 2009). The final rate obtained from the theoretical analysis of Yamamoto et al. (1993) with the estimated uncertainties are shown and compared with based on the experimental determination of the 7Li(t,n )9B TALYS predictions in Figure 16. 0 cross section (where n0 denotes transitions to the ground 9 3.2.2. 7Li(d,n)2 4He Affecting CNO state of Be only) by Brune et al. (1991). The upper limit is assumed to be a factor of 25 larger than the lower limit. 7 9 Both the resonant and direct mechanisms contribute to This factor corresponds to the ratio between the Li(t, ntot) B 7 9 the total reaction rate. The resonance part is calculated by (which includes all neutron final states) and Li(t, n0) Bcross

9 Stars

Stars are hot balls of gas powered by internal nuclear energy sources The pressure at the centre must support the weight of the overlying layers: gravity tends to collapse a star under its own weight; as it shrinks, the pressure, temperature, and density all increase until the pressure balances gravity, and the star assumes a stable configuration For gas spheres at least 0.085 the mass of the Sun, the central temperature becomes hot enough to initiate thermonuclear fusion reactions Nuclear reactions in the hot, dense core are the power source of the Sun and all other stars The Sun

Solar centre is about 150 times the density of water (~8 times the density of uranium) Central pressure is > 200 billion atm Central temperature is 16 MK Adelberger et al.: Solar fusion cross .... II. The pp chain ... 201

and CNO bicycle are shown in Fig. 2. The SSM requires input rates for each of the contributing reactions, which are customarily provided as S factors, defined below. Typically cross sections are measured at somewhat higher energies, where rates are larger, then extrapolated to the solar energies of interest. Corrections also must be made for the differences in the screening environments of terrestrial targets and the solar plasma. The model is constrained to produce today’s solar  radius, mass, and luminosity. The primordial Sun’s metal abundances are generally determined from a combination of photospheric and meteoritic abundan- ces, while the initial 4He=H ratio is adjusted to repro- duce, after 4.6 Gyr of evolution, the modern Sun’s luminosity. The SSM predicts that as the Sun evolves, the core He abundance increases, the opacity and core temperature FIG. 1. The stellar energy production as a function of temperature rise, and the luminosity increases (by a total of 44% over for the pp chain and CN cycle, showing the dominance of the 4.6 Gyr). The details of this evolution depend on a variety of former at solar temperatures. Solar metallicity has been assumed. model input parameters and their uncertainties: the photon The dot denotes conditions in the solar core: The Sun is powered luminosity L , the mean radiative opacity, the solar age, the dominantly by the pp chain. diffusion coefficients describing the gravitational settling of He and metals, the abundances of the key metals, and the as a function of temperature, density, and composition rates of the nuclear reactions. allows one to implement this condition in the SSM. If the various nuclear rates are precisely known, the com- Energy is transported by radiation and convection. petition between burning paths can be used as a sensitive  The solar envelope, about 2.6% of the Sun by mass, is diagnostic of the central temperature of the Sun. Neutrinos convective. Radiative transport dominates in the inte- probe this competition, as the relative rates of the ppI, ppII, rior, r & 0:72R , and thus in the core region where and ppIII cycles comprising the pp chain can be determined thermonuclear reactions take place. The opacity is sen- from the fluxes of the pp=pep, 7Be, and 8B neutrinos. This sitive to composition. is one of the reasons that laboratory astrophysics efforts to The Sun generates energy through hydrogen burning, provide precise nuclear cross section data have been so  Eq. (2). Figure 1 shows the competition between the pp closely connected with solar neutrino detection. pp Chainschain and CNO cycles as a function of temperature: Helioseismology provides a second way to probe the solar The relatively cool temperatures of the solar core favor interior, and thus the physics of the radiative zone that the the pp chain, which in the SSM produces 99% of the SSM was designed to describe. The sound speed profile c r Sun’s energy. The reactions contributing to the pp chain has been determined rather precisely over the outer 90%ð ofÞ Nuclear reaction rates determine energy release, neutrino production, and nucleosynthesis in Sun and other stars Adelberger et al., Reviews of Modern

FIG. 2 (color online). The left frame shows the three principal cycles comprising the pp chain (ppI, ppII, and ppIII), with branching Physics 83, 195 3 4 percentages indicated, each of which is ‘‘tagged’’ by a distinctive neutrino. Also shown is the minor branch He p He eþ e, 7 3 þ ! þ þ which burns only 10À of He, but produces the most energetic neutrinos. The right frame shows the CNO bicycle. The CN cycle, marked I, (2011) produces about 1% of solar energy and significant fluxes of solar neutrinos.

Rev. Mod. Phys., Vol. 83, No. 1, January–March 2011 Adelberger et al.: Solar fusion cross .... II. The pp chain ... 201

and CNO bicycle are shown in Fig. 2. The SSM requires input rates for each of the contributing reactions, which are customarily provided as S factors, defined below. Typically cross sections are measured at somewhat higher energies, where rates are larger, then extrapolated to the solar energies of interest. Corrections also must be made for the differences in the screening environments of terrestrial targets and the solar plasma. The model is constrained to produce today’s solar  radius, mass, and luminosity. The primordial Sun’s metal abundances are generally determined from a combination of photospheric and meteoritic abundan- ces, while the initial 4He=H ratio is adjusted to repro- duce, after 4.6 Gyr of evolution, the modern Sun’s luminosity. The SSM predicts that as the Sun evolves, the core He abundance increases, the opacity and core temperature FIG. 1. The stellar energy production as a function of temperature rise, and the luminosity increases (by a total of 44% over for the pp chain and CN cycle, showing the dominance of the 4.6 Gyr). The details of this evolution depend on a variety of former at solar temperatures. Solar metallicity has been assumed. model input parameters and their uncertainties: the photon The dot denotes conditions in the solar core: The Sun is powered luminosity L , the mean radiative opacity, the solar age, the dominantly by the pp chain. diffusion coefficients describing the gravitational settling of He and metals, the abundances of the key metals, and the as a function of temperature, density, and composition rates of the nuclear reactions. allows one to implement this condition in the SSM. If the various nuclear rates are precisely known, the com- Energy is transported by radiation and convection. petition between burning paths can be used as a sensitive  The solar envelope, about 2.6% of the Sun by mass, is diagnostic of the central temperature of the Sun. Neutrinos convective. Radiative transport dominates in the inte- probe this competition, as the relative rates of the ppI, ppII, rior, r & 0:72R , and thus in the core region where and ppIII cycles comprising the pp chain can be determined thermonuclear reactions take place. The opacity is sen- from the fluxes of the pp=pep, 7Be, and 8B neutrinos. This sitive to composition. is one of the reasons that laboratory astrophysics efforts to The Sun generates energy through hydrogen burning, provide precise nuclear cross section data have been so  Eq. (2). Figure 1 shows the competition between the pp closely connected with solar neutrino detection. chain and CNO cycles as a function of temperature: Helioseismology provides a second way to probe the solar The relatively cool temperatures of the solar core favor interior, and thus the physics of the radiative zone that the the pp chain, which in the SSM produces 99% of the SSM was designed to describe. The sound speed profile c r Sun’s energy. The reactions contributing to the pp chain has been determined rather precisely over the outer 90%ð ofÞ CNO Cycles

FIG. 2 (color online). The left frame shows the three principal cycles comprising the pp chain (ppI, ppII, and ppIII), with branching 3 4 percentages indicated, each of which is ‘‘tagged’’ by a distinctive neutrino. Also shown is the minor branch He p He eþ e, 7 3 þ ! þ þ which burns only 10À of He, but produces the most energetic neutrinos. The right frame shows the CNO bicycle. The CN cycle, marked I, produces about 1% of solar energy and significant fluxes of solar neutrinos.

Rev. Mod. Phys., Vol. 83, No. 1, January–March 2011 HaxtonFig03.pdf 4/15/09 4:25:05 PM

HaxtonFig03.pdf 4/15/09 4:25:05 PM

7

HaxtonFig03.pdf 4/15/09 4:25:05 PM HaxtonFig03.pdfHaxtonFig03.pdf 4/15/09 4/15/09 4:25:05 4:25:05 PM PM HaxtonFig03.pdfHaxtonFig03.pdf 4/15/09 4/15/09 4:25:05 4:25:05 PM PM TABLE I The Solar Fusion II recommended values for S(0), its derivatives, and related quantities, andPM for4:25:05 the resulting4/15/09 PM HaxtonFig03.pdf 4:25:05 4/15/09 HaxtonFig03.pdf uncertainties on S(E) in the region of the solar Gamow peak, defined for a temperature of 1.55 107K characteristic of the Sun’s center. Also see Sec. VIII for recommended values of CNO electron capture rates, Sec. XI.B⇥ for other CNO S-factors, and Sec. X for the 8B neutrino spectral shape. Quoted uncertainties are 1⇤.

Reaction Section S(0) S⇥(0) S⇥⇥(0) Gamow peak (keV-b) (b) (b/keV) uncertainty (%) + 22 24 p(p,e ⇥e)d III (4.01 0.03) 10 (4.49 0.05) 10 0.7 3 ±+0.17 ⇥ 4 ±+0.18 ⇥ 6 +3.9 9 ± d(p,) He IV (2.14 0.16) 10 (5.56 0.20) 10 (9.3 3.4) 10 7.1 3 3 4 ⇥ 3 ⇥ ⇥ 3 ± He( He,2p) He V (5.33 0.10) 10 ? 3.43 0.94 ? (3.71 2.30) 10 ?? 3 4 7 ± ⇥ ± 4 a ± ⇥ 6 b He( He,) Be VI 0.56 0.03 ( 3.6 0.2) 10 (0.151 0.008) 10 5.1 3 + 4 ± 20 ± ⇥ ± ⇥ ± He(p,e ⇥e) He VII (8.6 2.6) 10 30 7 7 ± ⇥ ± Be(e, ⇥e) Li VIII See Eq. (37) 2.0 ± c p(pe,⇥e)d VIII See Eq. (43) 1.0 7 8 2 d 5 7 ± Be(p,) B IX (2.08 0.16) 10 ( 3.1 0.3) 10 (2.3 0.8) 10 7.5 14 15 ± ⇥ ± ⇥ 3 a ± ⇥ 5 b ± N(p,) O XI.A 1.66 0.12 ( 3.3 0.24) 10 (4.4 0.32) 10 7.2 ± ± ⇥ ± ⇥ ± a p + p ! 2H + e+ + ν p + e– + p ! 2H + ν S (0)/S(0) taken from theory; error is that due to S(0). See text. e 2 + e – 2 ⇥ p + p ! H + e + νe p + e + p ! H + νe Thermonuclearb Power Sources S⇥⇥(0)/S(0) taken from theory; error is that due to S(0). See text. c 99.76 % 0.24 % estimated error in the ratio of the pep and pp rates: see Eq. (43) 99.76 % 0.24 % derror dominated by theory 2H + p ! 3He + γ 2H + p ! 3He + γ

2 + – 2 p + p ! H + e + νe 83.20 % p + e + p ! H + νe 1 2 + 83.20 % – 2 1 !* p + pp ! +2 p2H + 2eH+ – + eν+ + ν p + p !p + 2 Hp 2 +p! e+ + He p++ – ++ ν– epe –! +2 pν2H + 2 νH + ν p + e–p + + p e!+ 2 p2 H !+ ν H + ν e ν + H !! p + e + e p e e ν + H e ν ! + p + e ee + + H p e! ! p + ep e e ν + e + H ! p e + p e 3 3 4 3 4 7 99.76 % He + He ! He + 2p 0.243He % + 3He ! He4He + + 2pHe ! Be + γ 3He + 4He ! 7Be + γ ( => 9?90@ 99.76% 99.76 % 0.24 % 99.76 %99.76% 0.24 % 0.24% 0.24% 99.76 % 0.24 % % 0.24 99.76 % 2 3 H + p ! He + γ 99.88 % 99.88 % 0.12 % 0.12 % & 2H + 2pHγ ! ++ p3He He !3 +3! He γp ++ γH 2 2H + p2 !H +γ 3 Hep+ ! +He 3 3γHe! p + + γ H 2

7 – 7 7 8 . 7 – 7 7 8 83.20 % Be16.70 + e ! % Li + νe Be Be+ e + ! p !Li +B ν +e γ Be + p ! B + γ $ 83.20% 83.20 % 16.70 % 83.20 %83.20% 16.70 % 1 % 16.7083.20 % 1 !"#$%% 16.70&'83.20 % 51067 3He + 3He ! 4He + 2p 3He + 4He ! 7Be + γ 3 3 3 7 3 4 4 4 3 3 33 7 334 3 44 44 4 43 7 3 7 3 3 8 34 84 4 7 3 + 7 3 8 8 + ,343 " Heγ ++ He HeBe + !He! He !He + + He 2pHe + 2p He + γ HeHe + +!Be He HeHe2p ! + ! +He He He2ppHe He ++ ! ! +He He He 2p Be He ! + Be γHe + γ He +2p B pHe + He! ! +He !Be* HeHe ! Be + ! e He + γ++ Be ν e+He γ B ! Be* + e + νe !* 88/9:6;< 99.88 % !* 0.12 % 012 * % 0.12 99.88% 99.88 %0.12 % % 99.88 99.88 99.88% % 0.12 % 0.12%99.88 % 0.12 %0.12 % pp(I ppII =>pp 9?90@I ppppIIIII ppIII 7 – 7 7 8 8 7 Be + e7 !8 – Li + νe7 7 Be + p !7 B– + γ 7 γ + B p + Be ν + 7 γ Li + B 7 –&e p + 7–+ Be Be 7 ν 7+ Li 7 7 e 8+ – Be 87 7 8 ! e Be + Be! e ! !+ e Li ! + νLi + νe e 7 Be +BeBe– p! !++ 7ep B !! + γBLi + + γ ν 7 Be +8 p ! B + γ /" . e Be + e ! Li + νe e Be + p ! B + γ $ 51067

7 ,343 " 4 8 8 +

Li + p ! !* 2 He B ! Be* + e + ν /$ + 8 8 4 + 7 8 7 8 4 4 8 8 e7 + e ν + e + Be* ! B e ν He 7+ 2 e ! + p + Be* Li 4! B 8 88/9:6; !'A of the!#= former at solar temperatures.!$> !'A D ,8C . D

D D !# !% !' ,8C . > EA EE B that the SSM was designed to capture. The sound speed ,8C . D ,8C . profile c(r) has been determined to high accuracy over the !# !% !' !" ,8C . !% ,8C . !& outer> 90% of theE Sun and, asA previously EE discussed, isB now = > A in conflict with the SSM, when recent abundance deter- minations from 3D photosphericD absorption line analyses FIG. 2 The upper frame shows the three principal cycles com- are used.,8C . ,8C . prising the pp chain (ppI, ppII, and ppIII), with branching percentages indicated, each of which is “tagged” by a dis- ,8C . ,8C . tinctive neutrino. Also shown is the minor branch 3He+p !" !% !& 4 + 7 3 = > A He+e +⇥e, which burns only 10 of He, but pro- A. Rates and S-factors ⌅ ⇤ duces the most energetic neutrinos. The lower frame shows Sunday, February 28, 2010 the CNO bi-cycle. The CN cycle, marked I, produces about The SSM requires a quantitative description of relevant 1% of solar energy and significant fluxes of solar neutrinos. nuclear reactions. Both careful laboratory measurements constraining rates at near-solar energies and a supporting theory of sub-barrier fusion reactions are needed. Solar Neutrino Fluxes Adelberger et al.: Solar fusion cross .... II. The pp chain ... 219

4.5 1012

1011 pp

4 1010

9 10 13 N 3.5 108

7

) (%) 10 e 15

(E O 3 6 13 10

Capt N

) g 8 Neutrino Flux 5 17 π B / 10 F

α 15 17 ( 2.5 4 O + F 10

3 pep 10 7 7 hep 2 Be Be 102

101 1.5 0.1 0.3 1 3 10 0 2 4 6 8 10 Neutrino Energy (MeV)

Ee (MeV) FIG. 7 (color online). Solar neutrino fluxes based on the ‘‘OP’’ FIG. 6 (color online). Calculated radiative corrections for p calculations of Bahcall et al. (2005), with the addition of the new 7 7 þ 2 1 p eÀ d e (dashed line) and Be eÀ Li e (dotted line features from CNO reactions. Line fluxes are in cmÀ sÀ and þ ! þ þ !Stonehill,þ Formaggio, and2 Robertson,1 1 PRC 69, 015801 (2004) line). The solid line is for p eÀ n e. From Kurylov et al., spectral fluxes are in cmÀ sÀ MeVÀ . From Stonehill et al., 2004. 2003. þ ! þ

Because Eq. (40) corresponds to a ratio of stellar and theory uncertainty in Eq. (46). However, scrutiny of the terrestrial electron-capture rates, the radiative corrections presently unknown hadronic and nuclear effects in should almost exactly cancel: Although the initial atomic g E ;Q would be worthwhile. As one of the possible state in the solar plasma differs somewhat from that in a Captð e Þ strategies for more tightly constraining the neutrino mixing terrestrial experiment, the short-range effects that dominate angle  is a measurement of the pep flux, one would like to the radiative corrections should be similar for the two cases. 12 reduce theory uncertainties as much as possible. (Indeed, this is the reason the pp and 7Be electron corrections The electron-capture decay branches for the CNO isotopes shown in Fig. 6 are nearly identical.) However, the same 13N, 15O, and 17F were first estimated by Bahcall (1990). In argument cannot be made for the ratio of pep electron his calculation, only capture from the continuum was con- capture to pp decay, as the electron kinematics for these sidered. More recently, Stonehill et al. (2004) reevaluated processes differ. With corrections, Eq. (41) becomes these line spectra by including capture from bound states. Between 66% and 82% of the electron density at the nucleus Crad pep is from bound states. Nevertheless, the electron-capture com- R pep h ð Þi 1:102 1 0:01 10 4 = ð Þ¼ Crad pp ð Æ Þ À ð eÞ ponent is more than 3 orders of magnitude smaller than the h ð Þi 1=2 þ component for these CNO isotopes, and it has no effect on TÀ 1 0:02 T 16 R pp ; (45)  6 ½ þ ð 6 À ފ ð Þ energy production. However, the capture lines are in a region of the neutrino spectrum otherwise unoccupied except for 8B where the radiative corrections have been averaged over neutrinos, and they have an intensity that is comparable to the reaction kinematics. Kurylov et al. (2003) found a 1.62% 8B neutrino intensity per MeV (Fig. 7), which may provide a radiative correction for the -decay rate, Crad pp 1:016 spectroscopically cleaner approach to measuring the CNO (see discussion in Sec. III), while Crad peph ð 1:Þ042i . Thus fluxes than the continuum neutrinos do. Crad pep = Crad pp 1:026, soh thatð ourÞi final result be- The recommended values for the ratio of line neutrino flux hcomesð Þi h ð Þi  to total neutrino flux are listed in Table VI. The ratio depends weakly on temperature and density, and thus on radius in the Sun. The values given are for the SSM R pep 1:130 1 0:01 10 4 = ð Þ¼ ð Æ Þ À ð eÞ and do not depend significantly on the details of the model. 1=2 The branching ratio for 7Be decay to the first excited state in TÀ 1 0:02 T6 16 R pp : (46)  6 ½ þ ð À ފ ð Þ the laboratory is a weighted average of the results from Balamuth et al. (1983), Davids et al. (1983), Donoghue While certain improvements could be envisioned in the et al. (1983), Mathews et al. (1983), Norman et al. (1983a, calculation of Kurylov et al. (2003)—for example, in the 1983b), and an average of earlier results, 10:37% 0:12% matching onto nuclear degrees of freedom at some character- [see (Balamuth et al. (1983)]. The adoptedÆ average, istic scale GeV—rather large changes would be needed to 10:45% 0:09% decay to the first excited state, is corrected impact the overall rate at the relevant 1% level. For this by a factorÆ of 1.003 for the average electron energy in the reason, and because we have no obvious basis for estimating solar plasma, 1.2 keV (Bahcall, 1994), to yield a recom- the theory uncertainty, we have not included an additional mended branching ratio of 10:49% 0:09%. Æ

Rev. Mod. Phys., Vol. 83, No. 1, January–March 2011 Solar Neutrino Flux Measurements

3He(α,γ)7Be and 7Be(p,γ)8B cross sections needed for predictions of solar neutrino fluxes 8B solar ν flux now measured to ± 4.0% by SNO, 7Be flux measured to ± 4.8% by Borexino

S34(0) is the astrophysical S factor for the 3He + α → 7Be + γ reaction at zero energy; most probable energy for reaction is 23 keV; S17(0) is the comparable quantity for the 7Be(p,γ)8B reaction

8 0.81 B flux ∝ S34(0) , S17(0)

7 0.86 Be flux ∝ S34(0) Reaction Rates

• r = np nt s v f v v ‚v = np nt < sv >, (1) 0 1 1 t t = , and analogously t p = . p ‡ H L H L t (2) np < sv > nt < sv >

1 n 1 H L= . H L (3) t t i=1 ti t

3 E ‚ 8 - • - = H L k T 2 E s E „ k T ‚E. (4) p m 0

H L ‡ H L Nonresonant Reaction Rates

2 2 2 p Zp Zt e 2 p Zp Zt e S E - s E = „ — v , or S E = E s E „ — v . (1) E

2 H L p Zp Zt e 2 m EG H L S E - HSLE - H L (2) s E = „ — E = „ E , where E E

pZ Z e2 2 H L p t 2 H L 2 EG = 2m = 2 mc p Zp Zt a (3) H L —

E EG 3 - + 8 - •I Mk T E < sv >= k T 2 S E „ ‚E. (4) p m 0

E EG H L 3 ‡ H L - + 8 - • k T E < sv >= k T 2 S E0 „ ‚E. (5) p m 0

2 H L H L d E EG ‡ kT EG 3 + = 0, or E0 = . (6) dE k T E 2 E=E0 Solar Interior

Solar plasma is to good approximation an Relative Probability MaxwellBoltzmann 0.5

⇥ ideal gas 0.4

0.3 Described by 0.2 Maxwell- 0.1 Energy keV 5 10 15 20

Boltzmann ⇥ distribution of thermal energies Coulomb Penetrability

For non-resonant s-wave capture below the Coulomb barrier, charged Relative Probability Gamow Factor particle induced reaction 0.007 0.006 ⇥ probability governed by 0.005 0.004 -2πη the Gamow factor e , 0.003 0.002 where η=2πZpZt/(hv) 0.001 Energy keV 5 10 15 20

Coulomb barrier for p+p ⇥ reaction is hundreds of keV Gamow Peak

Resulting asymmetric distribution known as the Gamow peak, centred about the most effective Relative Probability energy for thermonuclear 1.4· 10-6 reactions 1.2· 10-6 1· 10-6

Is only 6 keV for pp 8· 10-7 reaction and 20 keV for 6· 10-7 7Be(p,γ)8B reaction 4· 10-7 210· -7

Energy keV Implies important role for 5 10 15 20 theory in extrapolation ⇥ from energies accessible in laboratory Reactions1969ApJS...18..247W at Astrophysical Energies Coulomb repulsion strongly inhibits charged particle- induced reactions Neutron-induced reactions are hindered only by the centrifugal barrier Resonances

— G = , (1) t 1 G P E = , (2) 2 2 2 p E - Ei + G 2 sresonance µ Gp G - Gp P Er , and its magnitude is therefore H L H L p H êGLp G - Gp (3) sresonance = 2 l + 1 . 2 2 2 I k M EH -LEr + G 2

2 J + 1 p I GMp Ge p Gp Ge sp,e = H L ∫ w . 2 2 2 2 2 2 (4) 2 Jp + 1 2 Jt + 1H k EL - EH r ê +L G 2 k E - Er + G 2 H L I M H L H L H ê L H L H ê L Narrow Resonance Radiative Capture Reaction Rates

3 E 8 - • - rpt = np nt < sv >= np nt k T 2 E s E „ k T ‚E. (1) p m 0

E H L H L 8 Er - r • p ‡ Gp Er Gg rpt = np nt „ k T w ‚E 3 2 2 2 p m 0 k E - Er + G 2 k T 2 H L E ‡ 8 Er - r p H • L H1 ê L = np nt H L„ k T w Gp Gg ‚E 3 2 2 2 p m k 0 E - Er + G 2 k T 2

Er E ‡Arctan E 8 Er - r p H G 2 L H ê L 8 Er - r p p 2 (2) = np nt H L „ k T w Gp Gg > np nt „ k T w Gp Gg p m 3 k2 G 2 p m 3 k2 G 2 2 2 k T ê k T J N ê 2 3 8 E Er p — p 2 p Gp Gg Er r - ê 2 2 - ê = np nt H L „ k T w Gp Gg = np nt — w H L „ k T p m 3 2 m E G m k T G k T 2

3 2 p Er 2 2 - ∫ np nt — wg „ k T , m k TH L Direct and Indirect Measurements of Resonant Rates Direct measurement not generally feasible at all energies Must identify and measure energies of resonances with favourable spin and parity When resonances are narrow and don’t interfere, decay properties can be measured to deduce strength Major Stellar Fusion Processes Threshold Fuel Major Products Temperature (K)

Hydrogen Helium, Nitrogen 4 Million

Helium Carbon, Oxygen 100 Million

Oxygen, Neon, Carbon 600 Million Sodium, Magnesium Magnesium, Sulfur, Oxygen 1 Billion Phosphorous, Silicon

Silicon Cobalt, Iron, Nickel 3 Billion Heavy Element Abundances

~1/2 of chemical elements w/ A > 70 produced in the rapid neutron capture (r) process: neutron captures on rapid timescale (~1 s) in a hot (1 billion K), dense environment ( >1020 neutrons cm-3) The other half are produced in the slow neutron capture process The r Process Site?

Core-collapse supernovae favoured astrophysical site; explosion liberates synthesized elements, distributes throughout interstellar medium; Abundances of r process elements in old stars show consistent pattern for Z > 47, but variations in elements with Z ≤ 47, implying at least 2 sites End States of Stellar Evolution: White Dwarves and Neutron Stars

White Dwarf: Stellar cinder left after typical and low-mass stars (M < 8 M) exhaust core H and He fuel: composed mainly of C, O, Ne; M ~ 0.6 M, R ~ 6000 km; supported by electron degeneracy pressure

Neutron Star: End state of massive stars (8 M ≤ M ≤ 10 M) formed during supernova explosions: composed mainly of free neutrons, exotic nuclei; M ~ 1.5 M, R ~ 10 km; supported by neutron degeneracy pressure Novae

Accretion of H- & He-rich matter from low-mass main sequence star onto surface of white dwarf via disk When accreted layer is thick enough, temperature and pressure at base sufficient to initiate thermonuclear runaway H in accreted layer is “burnt” via nuclear reactions Layer ejected, enriching ISM with nucleosynthetic products Repeats nearly ad infinitum w/ recurrence time ~ 104-5 yr

Recoil Mass Separator Radiative Capture Experiments at DRAGON

R = 2.0 m Angle = 20° Gap = 100 mm V = ± 200 kV R = 1.0 m Angle = 50° Gap = 100 mm B = 0.6 T

R = 0.813 m Angle = 75° Gap = 120 mm B = 0.8 T

R = 2.5 m Angle = 35° Gap = 100 mm V = ± 160 kV Beam Suppression

S. Engel et al., NIM A 553 (2005) 491 192 D.A. Hutcheon et al. / Nuclear Instruments and Methods in Physics Research A 498 (2003) 190–210

facility. Here follows a brief description of each Gamma Detector Assembly part of DRAGON, to be expanded on in later

sections. s = 57.8 mm The heavy ion beam enters the target gas cell (Fig. 2) through a series of differentially pumped 66.75 mm tubes. The gas pressure in the cell is regulated to be in the range from 0.2 to 10 Torr; and the gas o/ 56 mm density is uniform over most of the 11 cm between Housing of aluminum the innermost apertures. The downstream gas pressure is reduced by differential pumping Build-in voltage divider through a second set of tubes until it reaches À6 Aluminum can with 10 Torr at the entrance to the first magnetic internal magnetic shield element of the separator, 1 m downstream of the target cell. The gas target cell also contains a solid- o/ 51 mm photomultiplier state detector which measures the rate of elastic ETL - 9214 285 mm

scattering by detecting hydrogen or helium recoil Optical interface ions. Epoxy seal The -detector array is comprised of 30 BGO g Reflector (Bismuth Germanate) scintillation crystals of BGO-crystal 91 mm = x hexagonal cross section (Fig. 3) which are stacked 2.5 mm s 55.8 76 mm height in a close-packed array surrounding the gas target Aluminum - 0.5 mm thick (Fig. 4). Monte Carlo simulations [2] predict that Fig. 3. One of the g-ray scintillation detector composed of a the g-ray detection efficiency of the array varies BGO crystal coupled to a 51 mm diameter photomultiplier from 45% to 60% for 1–10 MeV g-rays over the tube. 11 cm target length. Confirmation of these simula- tions by efficiency measurements are in progress BGO Scintillator Lead Shielding using standard g sources [3]. Among the 30 Photomultiplier Tube detectors the g energy resolution at 6:13 MeV averages 7% full-width half-maximum (FWHM). The heavy-ion recoil leaves the target parallel to the beam and DRAGON accepts recoils within Windowless Gas Target Collimator H /He gas cell 2 insert

Gas Target Box Beam and Recoils

Aluminum Collimators 5cm

Elastic monitor Fig. 4. The DRAGON BGO g array, composed of 30 BGO detectors units, surrounding the gas target region.

Fill tube from 720 mrad or less. The smaller the g-ray energy, recycling Feedthru the closer the recoil trajectory follows the beam connectors direction. The maximum recoil opening angle Fig. 2. Schematic representation of the inner components of varies from reaction to reaction, depending on theD.A. DRAGON Hutcheon windowless et al. gas, NIM target A system. 498, 190 (2003) the masses and Q-values of the capture reaction DRAGON Gamma Ray Detector Array

30 BGO γ ray detectors surrounding gas target

Geometric efficiency of 89-92% ARTICLE IN PRESS

C. Vockenhuber et al. / Nuclear Instruments and Methods in Physics Research A 603 (2009) 372–378 373

particles. This has the advantage of enabling an additional MCP0 has already been used in some previous experiments to measurement (usually a partial or total energy measurement). improve the time resolution of the slow IC [8]. Due to its location The resolution of the timing detectors is to the first order close to the focus, it is the smaller of the two MCPs and is based on independent of the ion energy; thus, at lower energies the flight a Quantar 3394A MCP/REA sensor (diameter of MCP 40 mm). time of the particles is longer, resulting in a better separation Carbon foil diameters between 15 and 40 mm can be used. between different particles. Three wire planes are in the path of the beam; a fourth one is in Here we describe the setup of the DRAGON local time-of-flight front of the MCP detector. The wire planes are made of 20 mm (TOF) system. We refer to ‘local’ meaning the recoil detectors gold-plated tungsten wires with a line spacing of 1 mm. The located after the separator, as opposed to TOF through the entire voltages are optimized for good timing resolution and high separator where the start signal comes from deexcitation gamma efficiency of the MCP detector. MCP0 is equipped with a resistive rays from the reaction detected in the BGO array. The performance encoded anode (REA) which gives position information on the during the commissioning runs with stable 23Na, 24Mg and 27Al particles. beams is described in the second part of the paper. MCP1 is about twice the size of MCP0 in order to collect all recoils with a large divergence emitted in certain experiments (usually reactions with low mass, low energy and high Q-value). 2. Setup The foil has a diameter of 70 mm, the MCP detector has 75 mm (Burle APD 3075 MA). The wire plane configuration is similar to The DRAGON local TOF system is based on time measurement MCP0. The performance of both MCP detectors is similar, except between two timing detectors, following by a multi-anode IC for a slightly higher dark count rate of the larger MCP. or a double-sided silicon strip detector (DSSSD) for an energy The production of large, flat carbon foils is challenging. We use measurement (Fig. 1). Each timing detector consists of a thin diamond-like carbon (DLC) foils produced by Advanced Applied carbon foil through which the particles pass generating secondary Physics Solutions (AAPS) Inc. located at TRIUMF. Very homo- electrons on either side of the foil; an electrostatic mirror which geneous and pinhole-free DLC foils with a thickness of accelerates and deflects the electrons perpendicular to the beam 4–5 mg=cm2 have been produced by laser ablation of carbon and axis; and a micro-channel plate (MCP) which generates a fast were floated onto Ni-plated support meshes with high transmis- timing signal. The first timing detector (MCP0) is located about sion (98% and 95%). The thickness is a compromise between 10 cm upstream of a set of slits which are located at the number of electrons produced per particle and minimal energy- achromatic focus at the end of the separator; the second one loss and angular straggling. (MCP1) is further downstream in front of the energy detector with The detector electronics consists of a fast timing discriminator a flight path between the two foils of 59 0:5 cm. To maximize (Ortec 9327 1-GHz Amplifier and Timing Discriminator) which Æ the flight path, MCP0 detects electrons from the downstream side uses a signal picked off from the high voltage feed in case of MCP0 of the foil whereas MCP1 is mounted backwards detecting the and the anode signal in case of MCP1. The fast timing signals are electrons from the upstream side. Motor-driven actuators allow fed into a time-to-amplitude converter (TAC, Ortec 567) starting Focalremoval of both detectors Plane without breaking theDetectors: vacuum during with the signal from MCP1Local and stopping with theTime- delayed signal beam tuning into a Faraday cup located right after the slits and in from MCP0. The delay depends on the velocity of the ions and is in experiments without local TOF measurements. The vacuum in the the range of 30–100 ns. Separate timing signals from the fast 7 box is usually in the low 10À Torr range, but can rise by one timing discriminator are used to generate trigger signals for both order of magnitude when the gas-filled IC is operated at higher MCPs and a 100 ns coincidence signal indicating a valid local TOF pressures. of-Flighttrigger System signal (MCP-TOF). The MCP coincidence trigger is delayed

MCP0 REA MCP

DLC foil wire planes

multi-anode IC MCP0 FC X/Y slit MCP1

Fig. 1. Schematic setup of the DRAGON end detector comprises two MCP based timing detectors and a multi-anode IC as an energy detector (which can be easily exchanged Twowith a DSSSD). C Thefoils inset shows separated the details of MCP0. by 59 cm generate secondary electrons detected by MCPs; 400 ps FWHM timing resolution Followed by Ionization Chamber or DSSD ARTICLE IN PRESS

ParticleC. Vockenhuber et al. / Nuclear Instruments Identification and Methods in Physics Research A 603 (2009) 372–378 377

1400

1200 24Mg

1000

MCP-TOF (channel) MCP-TOF 800

25Al 600

1000 1200 1400 1600 1800 2000 2200 2400 IC energy (channel)

24 25 Fig. 6. IC-energy vs. MCP-TOF spectrum of the Mg(p; g) Al reaction at Ecm 214 keV. Small green dots are all events reaching the end detectors, larger black dots 25 24 25 ¼ indicate events with BGO coincidences. The region of Al isMg(p, marked. (Forγ) interpretationAl at E ofrel the = references 214 to keV colour in this figure legend, the reader is referred to the web version of this article.) C. Vockenhuber et al., NIM A 603, 372-378 (2009)

1400

27 1200 Al

1000

MCP-TOF (channel) MCP-TOF 800

28Si

600

1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 IC energy (channel)

27 28 Fig. 7. IC-energy vs. MCP-TOF spectrum of the Al(p; g) Si reaction at Ecm 196 keV. Small green dots are all events reaching the end detectors, larger black dots indicate ¼ events with BGO coincidences. The region of 28Si is marked. Note, due to the nature of the scatter plot the tails of the 27Al peak are overemphasized. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

literature value. In addition, in a short test measurement it was upgrade, the machine shop for the fabrication of the new parts, possible to clearly identify 28Si recoils from the very weak Grant Sheffer and Sabaratnam Sooriyakumaran for help with the resonance at 196 keV in the 27Al(p; g)28Si reaction. production of the wire planes, Stefan K. Zeisler and Vinder Jaggi The simultaneous use of the MCP-TOF detector with the IC for supply of carbon foils and fruitful discussions and Bruno allows further to optimize the IC for separation of isobaric Gasbarri, Bruce Keeley, Robert Openshaw and Marielle L. Goyette contamination. This will be important for the upcoming for help during the installation. 23Mg(p; g)24Al experiment where we have a mixed 23Na/23Mg This work was supported in part by a grant from the Natural beam. Therefore, the use of the IC is additionally necessary to Sciences and Engineering Research Council of Canada. The Color- separate 24Al recoils from 24Mg recoils from the 23Na (p; g)24Mg ado School of Mines group is funded by the U.S. Department of reaction. Energy.

Acknowledgments References

The work presented here would not have been possible [1] D.A. Hutcheon, S. Bishop, L. Buchmann, M.L. Chatterjee, A.A. Chen, J.M. D’Auria, S. Engel, D. Gigliotti, U. Greife, D. Hunter, A. Hussein, C. Jewett, without the help of a great number of people at TRIUMF, N. Khan, A. Lamey, W. Liu, A. Olin, D. Ottewell, J.G. Rogers, G. Roy, H. Sprenger, especially Daniel Rowbotham for the detailed design of the C. Wrede, Nucl. Phys. A 718 (2003) 515. 22Na formation: NeNaMg cycle

INTEGRAL

22Mg 23Mg 24Mg

3.8 s 11.3 s

21Na 22Na 23Na

22.5 s 2.6 y 20Ne 21Ne 22Ne 1.275 MeV

22Na not observed by COMPTEL or INTEGRAL Measurement of 21Na(p,γ)22Mg 21Na beam on hydrogen target Scanned over each resonance in small energy steps Detected recoils alone or in coincidence with prompt γ rays

22Mg recoils in DSSSD Excitation function

(singles) ER=738 keV for ER=821 keV

22Mg 21Na 21Na(p,γ)22Mg resonance strengths

21Na beam up to 2 × 109 per second Determined resonance strengths for 7 states in 22Mg between 200 and 1103 keV DRAGON operations: - used DSSSD as focal plane detector - used beta activity, FC and elastics for flux - used BGO detection despite high γ background D’Auria et al., PRC 69, 065803 (2004) Estimated reaction rate for 21Na(p,γ)22Mg based on DRAGON data

The lowest measured state at 5.714 MeV (Ecm = 206 keV) dominates for all nova temperatures and up to about 1.1 GK

Updated nova models showed that 22Na production occurs earlier than previously thought while the envelope is still hot and dense enough for the 22Na to be destroyed, resulting in lower final abundance of 22Na

Reaction not significant for X-ray bursts 26Al in the Milky Way

Radioactive decay with mean lifetime 1 My: 1.8 MeV γ ray Galactic inventory ~ 3 solar masses Is 26Al formed in novae as well as massive stars? Must measure rates of nuclear reactions that create and destroy 26Al in novae to find out 26Al + p → 27Si + γ Average 26Al beam intensity of 3.4 billion s-1 10 µs Measured cross section of 184 keV resonance suggests novae are not dominant source of galactic 26Al Separator Time-of-flight Ruiz et al., PRL 96, 252501 (2006) DSSD Energy (MeV) 18F(p,γ)19Ne Measurement

Measured at 665 keV resonance Previously only upper limit from Rehm et al., PRC 55, 566 (1997) Resonance strength ~ 10 meV, not an important contributor