Study of Study of 1717O(p,O(p,αα))1414N reaction N reaction

via the Trojan Horse Method for via the Trojan Horse Method for

application to application to 1717O O NucleosynthesisNucleosynthesis

Maria Letizia Maria Letizia SergiSergi

LNS-INFN, LNS-INFN, CataniaCatania

53-esimo Congresso della Societa' Astronomica Italiana (SAIt)

“L'Universo quattro secoli dopo Galileo”

4 - 8 Maggio 2009, PISA

1) It is one of the very few isotopes whose nucleosynthetic origin can be attributed to Novae, stellar explosion occurring in close binary system that contain White Dwarf (WD) as a compact object and a companion star. In novae, 17O is produced in one of

the two paths of CNO cycles leading to 18F production which is of special interest for gamma ray astronomy.

2) The relative abundances of the oxygen isotopes

Giant (RG) stars.

Red Giant Mira

have been observed at the surface of some Red

Role of 17O: astrophysical scenarios

The change in the surface composition offers an opportunity to probe the “history” of the stellar interior.

Nova Cygni 1992

γ-ray line fluxes measurement would shed light into the physical processes that occur in the early phases of the explosion.

In nova 17O is produced starting with the 16O isotope found at the surface of the WD progenitor.

CNO2 cycle HCNO2 cycle

16O nuclei can be processed in a two different competing cycles:

17O production & destruction

16O(p,)17F(+)17O(p,α)14N(p,)15O(+)15N(p,)16O 16O(p,)17F(+)17O(p,)18F(p,α)15O(+)15N(p,)16O

Production:

16O(p,)17F : reaction rate well known in literature

Destruction:

17O(p,)18F: important for 18F production in novae

17O(p,)14N : dominant channel for 17O destructionStellar temperatures of primary importance for nucleosynthesis:

T=0.01-0.1 GK for red giant, AGB, and massive stars;

T=0.01- 0.4 GK for classical nova explosion (peak temperatures of 0.35 GK can be easily achieved in explosion hosting very massive white dwarfs.)

C. Iliadis, Nuclear physics of Stars, 2007

(NACRE)

T=0.01-0.4 GK: 17O(p,α)14N and 17O(p,γ)18F reaction cross section have to be precisely known in the center-of-mass energy range Ec.m.=0.017-0.37 MeV.

In this energetic region, two resonant levels of 18F are important for 17O(p,α)14N reaction:

Ec.m. = 65.0 keV Jπ = 1-

Ec.m. = 183.3 keV Jπ = 2-

corresponding to Ex = 5.673 MeV and Ex = 5.786 MeV respectively..

Two sub-threshold levels at

EX(Jπ)=5.605 MeV (1−) and EX(Jπ)=5.603 MeV (1+)

could also play a significant role in the reaction rate through the high-energy tail of the levels.

Possible interference effects between 5.673 MeV level and 5.605 MeV level

Energetic Region of astrophysical interest for the 17O(p,α)14N reaction

The first direct measurement of the 17O(p,α)14N at low energyLARGE UNCERTAINTIES !!

In the last years several efforts to measure the cross section for the 17O(p,α)14N at astrophysical energies were made in order to reduce the indetermination on reaction rate.

Status of the Art

J.C. Blackmon et al., Phys. Rev. Lett. 74, 2642, (1995)

INDIRECT MEASUREMENT

65.0 keV

183.3 keV

To reduce the uncertainties

A. Chafa et al., Phys. Rev. C 75, 035810, (2007)

Experimental Set-up

L.N.S - Catania

14N

n

17O

2H

α

break-up diretto

p

17O+d 14N+ α +n

17O+p 14N+ α

Trojan Horse Method

Detectors Detectors ThicknessThickness[μm][μm]

θθ[deg][deg]

rr[mm][mm]

ΔθΔθ[deg][deg]

PSD1 500 8.0 ± 0.1 470 5.1

PSD2 500 17.4 ± 0.1 372 7.7

PSD3 500 27.8 ± 0.1 392 6.8

PSD4 500 8.0 ± 0.1 470 5.1

PSD5 500 17.4 ± 0.1 372 7.7

PSD6 500 27.8 ± 0.1 392 6.8

17O

CD2

12

3

4

6

5

Ebeam = 41 MeVTarget Thickness ~ 150 μg/cm2

Two ionization chambers filled with 60 mbar of isobuthan gas as ΔE detector were in front of PSD1 and PSD4 detector

Selection of the 2H(17O, α14N)n reaction channel

N particles were selected with the standard ΔE-E technique in both telescopes 1 and 4

The loci events in E1 vs E5 and E4 vs E2 for the 2H(17O, α14N)n reaction were deduced

Good agreement with the theoretical value -1.033 MeV

Good detector calibration procedure!!

Good reaction channel selection!!

Study of the presence of SD mechanism

The clear horizontal loci in E14N-α represent an evidence for the formation of the 18F excited

states.

E14

N-α

(MeV

)E

14N

-n (M

eV) E14N-n(MeV)

Eα-n(MeV)

The 14N+α+n exit channel can be fed through different reaction mechanism: or Quasi-Free mechanism

(QF).Sequential Decay (SD)

Study of relative energy spectra:

An observable which turns out to be more sensitive to the reaction mechanism is the shape of the experimental momentum distribution

An observable which turns out to be more sensitive to the reaction mechanism is the shape of the experimental momentum distribution

Selection of the Quasi-Free mechanism: experimental momentum distribution

|Pn| < 30 MeV/c

In a energy windows of 100 keV d/dconst. dividing the resulting three-body coincidence yield by the kinematic factor, the p-n momentum distribution in arbitrary units is obtained

|(ks)|2=

2s

22s

22 pb

1

pa

1

)ba(

)ba(ab

2

1N: normalization parameter

a=0.2317 fm-1

b=1.202 fm-1

The extracted experimental momentum distribution is compared with the theoretical one, given by the Hulthén wave function in momentum space:

The extracted experimental momentum distribution is compared with the theoretical one, given by the Hulthén wave function in momentum space:

)()( KFΩdΩddE

σdkΦ

cCC

32

s

Ec.m.=183±50 keV

17O(p,α)14N cross section & angular distributions

Extraction of nuclear part of the two body cross section by using the PWIA approach

d3σ

KF · |Φ(Ps)|2

dΩα dΩ14NdEcmdσN

dΩ∝ THM data

THM dataChafa 07

Legendre polinomyal fit of direct data reported in Chafa et al., 2007 Wc.m.

(θc.m.)=a1+a2P2(cosθc.m.)

Theoretical calculation based on Blatt (1952) theory

Trojan Horse cross section: horizontal error bar refers to the integration bin while the vertical one arise for the statistics (25%)

Trojan Horse cross section: horizontal error bar refers to the integration bin while the vertical one arise for the statistics (25%)

In order to separate the different contributions on this cross section, a fit of the nuclear cross section has been performed.

Extraction of:

Resonance energies: ER1=65±5 keV and ER2=183±5 keV.

Peak value of the two resonances: N1=0.170±0.025 and N2=0.220±0.031, used to derive the resonance strengths ωγ (case of narrow resonances).

Trojan Horse Cross section

The extracted two-body differential cross section has been integrated in the whole angular range, assuming that in the region where no experimental angular distribution are available, their trend is given by the fit of the obtained experimental angular distribution.

The extracted two-body differential cross section has been integrated in the whole angular range, assuming that in the region where no experimental angular distribution are available, their trend is given by the fit of the obtained experimental angular distribution.

σNT

HM

(a

rb. u

n.)

Ec.m. (MeV)

New a

pproach

12

where Mi(E) is the direct transfer reaction amplitude for the binary reaction 17O+d->18F*+s populating the resonant state 18F* with the resonance energy ERi;

σNT

HM

(a

rb. u

n.)

Ec.m. (MeV)

The strength of the resonance at 65 keV is given from the ratio between the peak value N1 and N2 through the relation:

22

12

R1

2

R2

Rp

Rp

2

11 ωγ

NN

EM

EM

EΓ

EΓ

ωω

ωγ1

2

22

11 )()(

)(

)(

)()(

Reaction rate determination

STRENGTH OF THE RESONANCE:

KEY PARAMETER:

We focussed on the 0-0.3 MeV energy region and in particular on both Ec.m.=65 keV and Ec.m.=183 keV, obtaining the strength of the resonance at Ec.m.=65 keV by using the available information in literature on the well measured Ec.m.=183 keV resonance.

We focussed on the 0-0.3 MeV energy region and in particular on both Ec.m.=65 keV and Ec.m.=183 keV, obtaining the strength of the resonance at Ec.m.=65 keV by using the available information in literature on the well measured Ec.m.=183 keV resonance.

La Cognata et al., PRL 101, 152501, (2008)

This two values are in agreement

each other;

with the value 5.5+1.8-1.0 ·10-

9 eV adopted in NACRE;

with the (4.7±0.8)·10-9 eV

calculated by using the value of Γα and Γp reported in Chafa’07.

ωγ RESULTS:

NACRE: C. Angulo et al., Nucl. Phys. A 656, 3-183 (1999)

Moazen’07: B.H. Moazen et al., Phys. Rev. C 75, 065801, (2007)

Reaction rate determination II

TOTAL REACTION RATE:

Ratio of the THM reaction rate to the NACRE one (blu line).

The THM reaction rate was calculated by considering the value of ωγ=(4.4±1.1)x10-9 eV for the 65 keV resonance.

Ratio between the reaction rate evaluated by Chafa’07 and NACRE.

NACRE adopted reaction rate.

THM

keV65A

07Chafa

keV65A

07Chafa

totA

THM

totA vσNvσNvσNvσN ''

This two values are in agreement

each other;

with the value 5.5+1.8-1.0 ·10-9

eV adopted in NACRE;

with the (4.7±0.8)·10-9 eV

calculated by using the value of Γα and Γp reported in Chafa’07.

ωγ RESULTS:

NACRE: C. Angulo et al., Nucl. Phys. A 656, 3-183 (1999)

Moazen’07: B.H. Moazen et al., Phys. Rev. C 75, 065801, (2007)

Reaction rate determination II

TOTAL REACTION RATE:THM

keV65A

07Chafa

keV65A

07Chafa

totA

THM

totA vσNvσNvσNvσN ''

T=0.02-0.1 GK: the difference between the rate adopted in literature and the total rate calculated, if one considers the NA<σv>65

THM extracted as explained before, are smaller than 10%.

Agreement between the two sets of data

Conclusions1. A clear evidence of both levels at Ec.m.=65 and 183 keV is present

in the excitation function.

Main results:

2. Extraction of angular distributions for both levels at Ec.m.=65 (for the first time!!) and 183 keV and comparison with theoretical calculation and direct measurement (only for Ec.m.=183 keV).

3. The 17O(p,α)14N reaction rate was extracted and compared with that one reported in Chafa’07, giving a difference of less than 10%.

A deeper analysis of contribution of sub-threshold level is needed

Our results are affected by a statistical error of 25%.

A further experiment was performed at Physics Department of Notre Dame University (Indiana, USA) in November 2008 by using the same experimental apparatus adopted in the previous one.

Data analysis in progress

… in progress:

ALTRE DIAPOSITIVE

Roche Model

Assumptions:

1.the third mass must be infinitesimal mass;

2.The two large masses must be in circular orbit.

Solution of restricted three body problem

L1,L2… L5 Lagrange points: points where there was not net force exerted on the third mass.

Roche surface: equipotential surface where the sum of the rotational and gravitational potential energy is constant.

Roche surface through L1: consists of two Roche lobes and form the inner critical potential. If one star completely fills its Roche lobe then it may loss matter to its companion star through L1.

Roche surface through L2: it defines the outer critical potential. If a star has a potential greater than the outer critical potential mass may be transferred out of the system

Kopal Classification

Comparison between the star potential and the inner critical potential.

Detached system: neither star completely fill the Roche lobe. The stars evolve separately.

Semi-detached system: only one of the two stars completely fills its Roche lobe. Mass transfer (NOVA EXPLOSION).

Contact system: both stars have the potentials greater than the inner critical potential but less than the outer critical potential. Both componetes of the binary fill their Roche lobe and a common envolope surrounds both stars.

Hydrogen-rich matter is tansferred via Roche lobe from a low-mass main sequence star to surface of WD. For effect of the high gravitational field created from WD, it draws on itself the matter that is in the envelope of the companion star. This transferred matter is accumulated in an accretion disc surrounding the WD with a accretion rates amount to ∼ 10 -10−10−9M⊙ per year.

A fraction of this matter spirals inward and accumulates on the WD surface, where is heated and compressed by the strong surface gravity. At some point the bottom layers of the WD become electronic degenerate. Hydrogen starts to fuse to helium via the p-p chains during the accretion phase and the temperature increases gradually. The electron degeneracy prevents an expansion of the envelope and eventually a thermonuclear runaway occurs near the base of the accreted layers [Iliadis07]. At this stage the nuclear burning is dominated by explosive hydrogen burning via the CNO cycle. Both the compressional heating and the energy released from the nuclear burning heat the accreted material until an explosion occurs.

A nova is a cataclysmic nuclear explosion caused by the accretion of hydrogen onto the surface of a white dwarf star.

L’altezza del picco della i-esima risonanza è legata la rapporto tra Γαi e Γitot(ERi)

della risonanza attraverso il quadrato dell’elemento di matrice che descrive il polo di break-up SiMi

2(ERi):

con Si fattore spettroscopico dell’i-esimo stato dell’ 18F

)E(Γ

)E(Γ)E(Γω=

)E(Γ

)E(Γ)E(Γ

)1+J2)(1+J2(

1+J2=)ωγ(

i

iiii

i

iiii

17

18

Ritot

RαRpi

Ritot

RαRp

pO

Fi

i

• Strength della resonanza:

Sostituendo:

)E(MS

N=

)E(Γ

)E(Γ

ii

ii

R2ii

i

Ritot

Rα

)E(M

N)E(Γ=)E(

M

N

S

)E(Γ=)ωγ(

i

iii

ii

R2i

iRspR2

i

i

i

Rpi

)E(Γ=S

)E(Γii

ii

Rspi

Rpcon “single particle width” ottenuta con calcoli di ANC

M. La Cognata at al. PRL, in press

arXiv:0806.1274

σ(E

) TH

M (

arb

. un.)

Ec.m. (MeV)

)E(M

N)E(Γ=)ωγ(

1

11R

21

1Rsp1

)E(M

N)E(Γ=)ωγ(

2

22R

22

2Rsp2

Quindi:

1

2

Dividendo membro a membro:

Rapporto dei parametri “model dependent”

Calcolo “model independent” !!

σ(E

) TH

M (

arb

. un.)

Ec.m. (MeV)

Some details on used Blatt theoretical calculationConsider the reaction

A+X->Y+b

NOTATION

Before collision:

-channel index α (defines the type of incoming particles and the state of struck nucleus)

-channel spin s (total spin angular momentum in the channel; it is the vector sum of intrinsic spin i of the incoming particle and the spin I of the struck nucleus)

-orbital angular momentum l

After collision:

-channel index α’ (defines the type of outgoing particles and quantum state of the residual nucleus)

-channel spin s’ (it is the vector sum of intrinsic spin i of the outgoing particle and the spin I of the residual nucleus)

-outgoing orbital momentum l’

If the reaction A+X->Y+b procedes via a definite resonance level of the compound nucleus, with angular momentum J0 and parity Π0, the cross section for the α->α’ reaction is given by

Ωd)θ(cosP)sα;'s'α(R)1I2)(1i2(

σd L

L

0L

'i'I

|'i'I|'sL

iI

|iI|s

2α

α,'α

max

where

'sJ

|'sJ|l

'sJ

|'sJ|l

sJ

|sJ|l

sJ

|sJ|l220

s's

L

0

0'2

0

0'1

0

02

0

01)Γ21

()EE(4

)()sα;'s'α(R

'2'121 l's'αl's'αslαslα0'20'10201 gggg)L's,JlJl(Z)sL,JlJl(Zx

'2'121 l'αl'αlαlα ξξξξcosx

If the reaction A+X->Y+b procedes via a definite resonance level of the compound nucleus, with angular momentum J0 and parity Π0, the cross section for the α->α’ reaction is given by

where

Ωd)θ(cosP)sα;'s'α(R)1I2)(1i2(

σd L

L

0L

'i'I

|'i'I|'sL

iI

|iI|s

2α

α,'α

max

'sJ

|'sJ|l

'sJ

|'sJ|l

sJ

|sJ|l

sJ

|sJ|l220

s's

L

0

0'2

0

0'1

0

02

0

01)Γ21

()EE(4

)()sα;'s'α(R

'2'121 l's'αl's'αslαslα0'20'10201 gggg)L's,JlJl(Z)sL,JlJl(Zx

'2'121 l'αl'αlαlα ξξξξcosx

PL are the Legendre polynomials

'sJ

|'sJ|l

'sJ

|'sJ|l

sJ

|sJ|l

sJ

|sJ|l220

s's

L

0

0'2

0

0'1

0

02

0

01])Γ21

()EE[(4

)()sα;'s'α(R

'2'121 ''''0'20'10201 )',(),( lslsslsl ggggLsJlJlZsLJlJlZx

'2'121 l'αl'αlαlα ξξξξcosx

NOTATION

)0Lll|00ll)(sL,JlJl(Wx

)1J2()1l2()1l2(i)sL,JlJl(Z

21210201

021

221

1llL

020121

where W is the Racah coefficients defined in Racah 1942

'sJ

|'sJ|l

'sJ

|'sJ|l

sJ

|sJ|l

sJ

|sJ|l220

s's

L

0

0'2

0

0'1

0

02

0

01)Γ21

()EE(4

)()sα;'s'α(R

'2'121 l's'αl's'αslαslα0'20'10201 gggg)L's,JlJl(Z)sL,JlJl(Zx

'2'121 l'αl'αlαlα ξξξξcosx

NOTATION

21

slαslα )Γ(g , where Γαsl is the partial widths of the resonant level.

'sJ

|'sJ|l

'sJ

|'sJ|l

sJ

|sJ|l

sJ

|sJ|l220

s's

L

0

0'2

0

0'1

0

02

0

01)Γ21

()EE(4

)()sα;'s'α(R

'2'121 l's'αl's'αslαslα0'20'10201 gggg)L's,JlJl(Z)sL,JlJl(Zx

'2'121 l'αl'αlαlα ξξξξcosx

NOTATION

21

slαslα )Γ(g , where Γαsl is the partial widths of the resonant level.

ξl is the phase shifts for the potential scattering, in the hard sphere approximation, defined by equation

)R(iF)R(G

)R(iF)R(G)σi2exp()ξi2exp(

ll

llll

where Fl(R) and Gl(R) are the regular and irregular Coulomb wave function (R is the channel radius and σl is the phase shift for Coulomb scattering from an impenetrable sphere of radius R)

First consideration

PSD1-PSD6 and PSD4-PSD3 coincidences:

PSD3 and PSD6 were placed in the scattering chamber to have an investigation of the whole kinematical locus reaction channel even if far away from the astrophysically relevant energy range.

Ec.m.>500 keV

ps> 30 MeV/c

E (MeV)Run 86 Run 79 Run 56

PSD1The same for PSD4

Not possible to use coincidence 1-4 !!

E1 and E4 obtained by kinematical calculation!

Reaction Rate

Cross section is necessary input to know the stellar reaction rate:

For an isolated and narrow resonance:

where σBW is the Breit-Wigner cross section

Statistical factor depending by nuclear spin of compound nucleus JC*, target JX and projectile Ja

The product of the statistical factor ω and the width ratio γ=Γ1Γ2/Γ is referred as the strength of the resonance:

Г1 and Г2 represent the partial widths describing the formation and the decay of the compound nucleus.

Г= Г1+Г2 is the total width

Reaction Rate

Cross section is necessary input to know the stellar reaction rate:

For an isolated and narrow resonance:

where σBW is the Breit-Wigner cross section

Statistical factor depending by nuclear spin of compound nucleus JC*, target JX and projectile Ja

The product of the statistical factor ω and the width ratio γ=Γ1Γ2/Γ is referred as the strength of the resonance:

KEY PARAMETER FOR NUCLEAR RATE DETERMINATION!!

Consideration on the extraction of the ωγ parameter for the 65 keV resonant level

The first step of the reaction rate calculation is to evaluate the strengths of the resonances

We focussed on the 0-0.3 MeV energy region and in particular on both Ec.m.=65 keV and Ec.m.=183 keV, obtaining the strength of the resonance at Ec.m.=65 KeV by using the available information in literature on the well measured Ec.m.=183 keV resonance.

We focussed on the 0-0.3 MeV energy region and in particular on both Ec.m.=65 keV and Ec.m.=183 keV, obtaining the strength of the resonance at Ec.m.=65 KeV by using the available information in literature on the well measured Ec.m.=183 keV resonance.

To this aim, the extracted two-body differential cross section has been integrated in the whole angular range, assuming that in the region where no experimental angular distribution are available, their trend is given by the fit of the obtained experimental angular distribution.

To this aim, the extracted two-body differential cross section has been integrated in the whole angular range, assuming that in the region where no experimental angular distribution are available, their trend is given by the fit of the obtained experimental angular distribution.

Reaction Rate calculation I

In the narrow resonance approximation, the reaction rate is deduced by relation

where NA<σv>R is expressed in cm3 mol-1 sec-1, ER and ωγ in MeV and S(O) in MeV b.

Z1 and Z2 are the projectile and the target atomic number respectively.

In the calculation of the 17O(p,α)14N reaction rate, we followed the same procedure adopted in Chafa’07 by using for the resonance at Ec.m.=65 keV the two value of ωγ extracted as explained before.

New approach to extract the ωγ parameter for a resonance I

The THM cross section for the A+a(x+s)->c+C+s reaction proceeding through a resonance Fi in the subsystem F=A+x=C+c is:

where

Mi(E) is the direct transfer reaction amplitude for the binary reaction A+a->Fi+s populating the resonant state Fi with the resonance energy ERi;

Γcci(E) is the partial resonance width for the decay Fi -> C+c;

Γi is the total resonance width of Fi.The appearence of the transfer reaction amplitude Mi(E) instead of the entry channel partial resonance width Γ(Ax)i(E) is the main difference between the THM cross section and the cross section for the resonant binary sub-reaction A+x->C+c

A. M. Mukhamedzhanov et al., J. Phys. G: Nucl. Part. Phys. 35 (2008) 014016

The peak TH cross section taken at the resonance ERi energy for the (p,α) reaction A+x->C+c is given by

New approach to extract the ωγ parameter for a resonance II

Γi/2-Γi/2 ERi

σ(E)

)(

|)(|)()(

i

iii

iR

R2

i

2RiRα

iEEsCc

2

EΓ

EMEΓ4N

ΩddEσd

Ni

)(

|)(|)(

1

111

R2

1

2R1Rα

1 EΓ

EMEΓ4N

)(

|)(|)(

2

222

R2

2

2R2Rα

2 EΓ

EMEΓ4N

In our case, we have two resonances:

12

Strength of resonance 2 (Ec.m.=183 keV) well measured in two recent works !!

12

If Г1<<Гris and Г2<<Гris

Г1 ~ 130 eV

Г2 ~ 7 eV

Гris ~ 20 keV

Г1=Гris

Г2=Гris

2R2

2R1

Rα

Rα

2

1

2

1

22

11

EM

EM

EΓ

EΓ

NN

|)(|

|)(|

)(

)(

,)()(

)(ris

RpRα11 Γ

EΓEΓωωγ 1111

ris

RpRα22 Γ

EΓEΓωωγ 2222

)()()(

But

)(

)(

)(

)(

)(

)(

22

11

22

11

Rp

Rp

Rα

Rα

2

1

2

1

EΓ

EΓ

EΓ

EΓ

ωω

ωγωγ

The strength of the resonance at 65 keV is given from the ratio between the peak value N1 and N2 through the relation:

22

12

R1

2

R2

Rp

Rp

2

11 ωγ

NN

EM

EM

EΓ

EΓ

ωω

ωγ1

2

22

11 )()(

)(

)(

)()(