Study of the 10 B(p,α) 7 Be Reaction through the Indirect Trojan Horse Method

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1 CARPATHIAN SUMMER SCHOOL OF PHYSICS 2014 Exoti Nulei an Nulear/Partile Astrophysis (V) "From nulei to stars" July 13-26, Sinaia, Romania Stuy of the 10 B(p,α) 7 Be Reation through the Iniret Trojan Horse Metho NELLY PUGLIA LNS-INFN & Centro Siiliano i Fisia Nuleare e Struttura ella

2 Outline Light Elements in the Universe an their Astrophysial Relevane Importane of the 10 B(p,α) 7 Be reation in astrophysis Stuy of the reation via the Trojan Horse Metho (THM) The experimental proeure Results

3 Light Elements in the Universe H,D, He, Li, Be B Main proution site: Spallation proesses on ISM; BBN (mainly for lithium an probably beryllium). Neutrino nuleosynthesis in Supernovae (only 7 Li an 11 B) (Aners e Grevesse (1996) ) Solar System abunanes DEPLETION OF THE LIGHT ELEMENTS Chemial evolution of the Galaxy; Li Be B Primorial Nuleosyntesis & Spallation proesses on ISM; Stellar evolution These elements, though being so rare, play a relevant role for solving several astrophysial problems

4 Depletion of Light Elements Main Destrution Sites: Stellar interior Burning (p,α) hannel as the main ontribution to their estrution Li Be B K K K Nulear reations 6 Li(p,α) 3 He (Tumino A. et al.,prc 67, 2003) 7 Li(p,α) 4 He 9 Be(p,α) 6 Li (Lattuaa M. et al.: Ap. J. 562, 2001) (Wen et al. 2008) 10 B(p,α) 7 Be 11 B(p,α) 8 Be (Lamia L. et al. 2012) Alreay been stuie via THM

5 10 B(p,α) 7 Be By onsiering the typial temperatures of some 10 6 K at whih burning (p,α) reations typially our for boron isotopes in stellar environments, the Gamow peak is at about Presene of a resonane 10 kev E 0 =1.22(Z 2 xz 2 yμt 62 ) 1/3 kev 10 kev E 10B-p =10keV E* 11C =8.7MeV E Gamow peak EXTRAPOLATION Aim stuy the energy region orresponing to the Gamow peak

6 Iniret stuy of the 10 B(p,) 7 Be reation through 2 H( 10 B, 7 Be)n by means of the THM Stuy of the 10 B(p,) 7 Be reation (Q= 1.14 MeV) through 2 H( 10 B, 7 Be)n 3- oy reation (Q=-1.08MeV, Eoul=1.23 MeV); 2 H 10 B p n 7 Be α The euteron is use like Trojan Horse nuleus. Deuteron nuleus has a simpler luster struture =p +n with bining energy B p-n =2.2MeV The momentum istribution of interluster motion insie the euteron is known an has maximum at p s =0 MeV/. [Zaro et al.(1989)] Coulomb barrier 10 B- 2 H = 1.80 MeV

7 Experimental Setup The experiment was performe at LNS-INFN (Catania, Italy) E beam ( 10 B)=24.4 MeV & I beam ( 10 B)=1 na 10 B CD 2 E qf = E Bp B p-n E qf 10 kev E Bp beam energy in the B-p.m.s. B p-n p-n bining energy = 2.22 MeV Beam energy = 24.4 MeV Target thikness CD µg/m 2 ; Displaement of the etetors aroun the whole QF-angular range. Two kins of events were triggere by using a TAC A- B an A-C oinienes 7 Be α

8 E Be (MeV) ΔE (Channels) Three-boy 2 H( 10 B,α 7 Be)n hannel ientifiation After alibration, Be isotopes were selete by using stanar DE-E tehnique. Experimental Q-value reation with the assumption of mass 1 for the 3 r unetete partile: agreement between theoretial an experimental one (Q THM =-1.07 MeV, Q THEORETICAL = MeV) B Be Li He H Kinematial lous E 2 (Channels) 2 H( 10 B,α MeV 8 E α (MeV)

9 Stuy of the relative energies Different states of intermeiate nulei an be populate in the 3-boy hannel. A neessary hek for the further appliation of the metho onsist to unerstan if that levels are populate via Sequential Deay or Quasi-Free mehanism Sequential mehanisms oming from exite states of 11 C, 5 He, 8 Be

10 Seletion of the QF-mehanism: Experimental Momentum Distribution Presene of quasi-free mehanism experimental neutron momentum istribution. E 3 KF ps 2 p S 2 3 E KF N HOES N Comparison between the experimental ata (blak points) an the theoretial Hulthén wave funtion (blak line) an a DWBA alulation (re ashe line)

11 Stuy of 10 kev resonane 11 C levels E (MeV) J π E m (kev) Г m (kev) Г tot (experimental) (kev) 2) / ± 3 3) / < 5 34± 2 4) / ±1 40± 2

12 Two-boy ross setion By using the PWIA it is possible to extrat the nulear part of the 2-boy ross setion for the 10 B(p, α ) 7 Be reation See Prof.Spitaleri talk E 3 KF ps 2 HOES In orer to ompare the THM ata with the iret ones an l=0 penetrability funtion was introue. σ N Ω 3 σ Ω α Ω 7Be E m KF Φ(Ps) 2 P l (k 10b-p R)= kr F l2 (k 10b-p R)+ G l2 (k 10b-p R)

13 Astrophysial fator S(E): Results Spitaleri, Lamia, Puglia submitte to PRC THM S(E)-fator infinite resolution EXTRAPOLATION E R =0.010 ±0.002 MeV N ER =1315± 79 MeV/b σ=0.016 ±0.002 MeV A 0 =236± 59MeVb A 1 =-2320± 614 MeV b χ 2 =0.6 S(10keV) THM = 3127± 583 (MeV b) S(10keV) EXTR = 2870± 500 (MeV b) Angulo et al. (1993)

14 Remarks an Conlusions: 10 B(p,α) 7 Be Reation The iniret stuy of the 10 B(p,) 7 Be reation was performe from 1 MeV own to the astrophysial region by means of the Trojan Horse Metho Strong quasi-free ontribution in the three-boy hannel aroun E s =0 has been ientifie: neee for THM The Resonane at E m =10 kev(gamow energy) orresponing to the 11 C*(8.70 MeV) level has been reproue Measurement of ross-setion at the Gamow Energy S(E)-fator in agreement with iret ata BUT it is a FIRST measurements below 20 kev where is present the Gamow Peak

15 C. Spitaleri, L. Lamia, S.M.R. Puglia, S. Romano, M. La Cognata, V. Cruilla`, R.G. Pizzone, G.G. Rapisara, M.L. Sergi, an A. Tumino INFN, Laboratori Nazionali el Su, Catania, Italy Dipartimento i Fisia e Astronomia, Universit a i Catania, Catania, Italy M. Gimenez Del Santo, N. Carlin, M. G. Munhoz, F.A.Souza, an A.Szanto e Toleo Departamento e Fisia Nulear, Universitae e Sao Paulo, Sao Paulo, Brasil B. Irgaziev GIK Institute of Engineering Sienes an Tehnology, Topi, Distriti Swabi, N.W. P.Pakistan A. Mukhamezhanov an G. Tabaaru Cylotron Institute, Texas A&M University, College Station, TX 77843, USA V. Burjan, V. Kroha, Z. Hons, an J. Mrazek Nulear Physis Institute of ASCR, Rez, Czeh Republi Chengbo Li, Qungang Wen, an Shu-Hua Zhou China Institute of Atomi Energy, Beijing, China Y. Wakabayashi an H. Yamaguhi Center for Nulear Stuy, University of Tokyo, RIKEN Campus,Wako, Japan E. Somorjai Atomki, Debreen, Hungary

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17 Diret S(E)-fator Diret S(E)-fator. The lines represent the R-matrix alulation with the resonane parameters from the litterature, for bare (ashe line) an sreene (full line). Data are in the Nare ompilation Resonane parameters use in R-matrix alulation present in literature Angulo et al.1999 Wiesher et al Kelley et al. 2012

18 Stuy of 10 kev resonane 11 C levels E (MeV) J π E m (kev) Г m (kev) Г tot (experime ntal) (kev) F (E) = bw(e) + bw(e) + p(e) unres. (2) (3) 2) / ± 3 3) / < 5 34± 2 4) / ±1 40± 2

19 COMPARISON WITH DIRECT DATA BLU LINE: the THM S(E)- fator at infinite resolution togheter with its upper an lower limit in omparison with iret ata (blak point)

20 Errors bars Value of the S(E) at infinite resolution an at THM energy resolution 34 kev. Aition soure of error are the effet of the hange of the interation raius r 0 on the penetration fator 2% an the normalizzation error 11%

21 ELECTRON SCREENING Blu line: The bare nuleus THM S(E) fator at infinite resolution togheter with the upper an lower values (ashe blue line) Re Line: the low energy ata fitte leaving U e as the only free parameter leaing to U e =310± 200 ev

22 Exitation funtion By using the PWIA it is possible to extrat the nulear part of the 2-boy ross setion for the 10 B(p, α ) 7 Be reation 3 σ Ω α Ω 7Be E m σ N KF Φ(P s ) 2 Ω σ N Ω 3 σ Ω α Ω 7Be E m KF Φ(Ps) 2

23 At astrophysial energies the presene of eletron lous must be taken into aount in laboratory experiments 3 He(,p) 4 He Enhanement in the astrophysial S b (E)-fator S s E S b Ef lab Diretly measure Obtaine by extrapolation f lab E S s E S b E exp U e E 1 Eletron sreening potential To extrat from iret (shiele) measurements the bare astrophysial S b (E) -fator, neessary for astrophysis EXTRAPOLATION were performe at higher energy

24 Trojan Horse Metho Basi iea: it is possible to extrat the ross setion of the a + b + G.Baur: Phys. Lett.B178,(1986),135 two-boy reation from the quasi-free ontribution of an appropriate three-boy reation a + x + + s x QF Break-up s x= b s lusters only b interat with a b s is onsiere to be spetator to the virtual reation a + b + a virtual reation a + b + The reation b(a,) is at energy E m =E - Q 2boy Impulse Approximation

25 The Trojan Horse Metho The THM allows to stuy the astrophysially relevant two-boy reation x(a,c) at Gamow energies, from quasi-free ontribution of an appropriate three-boy reation a(a,cs), inue at energies higher than the Coulomb barrier. a= x s lusters only x interat with A s is onsiere to be spetator to the virtual reation A + x + C Impulse Approximation The reation x(a,c) is at energy E m =E C - Q 2boy QF Break-up 3 2 KF ( p ) E S C Kinemati fator C s impulse istribution insie the nuleus a N virtual reation A + x + C off-energy-shell ross setion for the virtual reation at the E m energy

26 PWIA x a b s The projetile a oes not interat with both the onstituents of the luster struture (b an s) at the same time The interation of the inient partile with the luster b in the target is the same as if the luster were alone E 3 2 p ) KF ( s ab E m Kinemati fator it is a funtion of the masses, momenta an angles of the outgoing partiles s momentum istribution insie the nuleus x ross setion for the virtual reation at the energy E m = E - Q 2-boy

27 Measure Calulate FROM THREE-BODY CROSS SECTION TO INDIRECT TWO-BODY CROSS SECTION 2 3 S N p KF E N S p KF E 2 3 x a b s a b

28 THM: ENERGY PRESCRIPTION 1- In the quasi-free kinematial onition, the inoming Trojan horse partile x is aelerate at energies E x above the Coulomb barrier energy (B xa ) Coul.Bar E x > (B xa ) Coul.Bar 2- The nuleus x an be brought into nulear fiel of nuleus a an the luster b inues the reation a + b + x a b s E m = E ab < B ab

29 Uner proper kinematial onition E C-D = Q 2B x b s E m = 0 a E m = E C-D - Q 2B Q 2b is the two-boy Q-value of the a + b + reation E C-D is the relative energy between the outgoing partiles C an D Overoming the problem of the Coulomb barrier in the ross setion measurements in reations between harge partiles to astrophysial energies No Coulomb effets No eletron sreening

30 relative probability Nulear reation at astrophysial energies Maxwell-Boltzmann istribution exp(-e/kt) tunnelling through Coulomb barrier E /E exp(- G ) Main problem: presene of the Coulomb barrier between the interating nulei Gamow peak E 0 kt E 0 energy The Coulomb barrier E oul, usually of the orer of MeV, is muh higher than energy E kin ~ kev 10-9 :10-12 barn!!! exponential erease of the ross setion INDIRECT METHODS Extrapolation from the higher energies by using the THM ASTROPHYSICAL FACTOR S(E) = (E) E exp(2πη)