Post on 12-Jan-2016
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 )()(
)(
)(
)()(