LABORATÓRIO ABERTO DE FÍSICA...
Transcript of LABORATÓRIO ABERTO DE FÍSICA...
N°
Proposta de Experimento
Período : segundo semestre de 2012
Título: Estudo da reação 12C+12C em energias de interesse astrofísico utilizando o Método do Cavalo de Tróia
Responsável: Marcelo Gimenez Del Santo
e-mail: [email protected] / [email protected]
Participantes: A. A. P. Suaide, R. A. N. Oliveira, M. G. Del Santo, N. Carlin, M. M.
de Moura, M. G. Munhoz, F. A. Souza, E. M. Szanto, A. Szanto de Toledo, R. Liguori Neto, E. Crema, R. F. Simões, R. Cyburt, C. Spitaleri, S. Romano, X. Tang
Porta Voz: Alexandre A. P. Suaide
e-mail: [email protected]
Número de dias solicitados: 18 Datas preferidas: 01/10/2012 – 1/12/2012 Datas realmente impossíveis:
Canalização: 15B
Feixe Est. Carga Imínima (alvo) Vmin Vmax Pulsado? 16O +4,+5 500 nA 4.95 5.94 Sim
16O +4,+5 500 nA 4.28 5.14 Sim
Alvos: 12C 100g/cm2, 197Au 100g/cm2, CD2 200g/cm2
Pastilhas: Óxido de Titânio
Características de Feixe Pulsado: Continuação da Experiência já Aprovada N°:
Outras informações: O feixe pulsado é necessário apenas para uma das três reações propostas, não impossibilitando a realização do experimento.
LABORATÓRIO ABERTO
DE FÍSICA NUCLEAR
Study of the 12
C+12
C fusion reaction at the Gamow energy
through the Trojan Horse Method
R. A. N. Oliveira, N. Carlin, R. Liguori Neto, M. M. de Moura,
M. G. Munhoz, E. M. Szanto, A. Szanto de Toledo,
A. A. P. Suaide, E. Crema, R. F. Simões
Instituto de Física, Universidade de São Paulo,
CEP 05315-970, São Paulo, SP, Brasil
F. A. Souza
Instituto de Pesquisas Energéticas e Nucleares, IPEN - CNEN/SP,
CEP 05508-000, São Paulo, SP, Brasil
M. G. Del Santo, R. Cyburt
Michigan State University, National Superconducting Cyclotron Laboratory,
East Lansing, MI, 48824, USA
C. Spitaleri, S. Romano
Laboratori Nazionali del Sud, INFN, Catania, Italy
X. Tang
University of Notre Dame, Dept. of Physics, Notre Dame, IN 46556, USA
ABSTRACT
The main goal of the proposed experiment is to extract the cross sections and therefore the
astrophysical S(E)-factors of the reactions 12
C(12
C,p)23
Na, 12
C(12
C,)20
Ne and 12
C(12
C,n)23
Mg
through the indirect Trojan Horse Method using the 12
C(16
O, p23
Na), 12
C(16
O, 20
Ne)and 12
C(16
O, n23
Mg) three body reactions respectively. The implications of the current uncertainty
in these rates affect many astrophysical scenarios, including super-AGB stars, super bursts in X-
ray binary systems and type Ia supernovae.
1. Introduction
The fusion reactions 12
C(12
C,p)23
Na (Q = 2.24 MeV), 12
C(12
C,)20
Ne (Q = 4.62 MeV) and 12
C(12
C,n)23
Mg (Q = -2.60 MeV) are referred to as carbon burning in stars, following the
hydrogen and helium burning stages. These reactions represent key processes in nuclear
astrophysics since they influence not only the nucleosynthesis of the 20
Ne and 23
Na but also the
subsequent evolution of a star, e.g., whether a star evolves into a carbon detonation supernova or
not [1]. Moreover, strong evidence [1a,1b] shows that a large amount of 12
C produced during the
helium burning stage of a star is not completely converted to 16
O, suggesting the presence of
other mechanisms promoting the 12
C burning. Reactions involving 12
C+12
C are possible channels
for the 12
C burning in massive stars (M > 8 MSun) and their reaction rates represent important
inputs for astrophysical network calculations.
The implications of the current uncertainty in this rate affect many astrophysical scenarios,
including super-AGB stars, super bursts in x-ray bursts models and type Ia supernovae [9,9b].
These reactions take place at temperatures from 5×108 K to 1.2×10
9 K and the lowest
temperature corresponds to a Gamow energy of EG = 1.5 ± 0.3 MeV. Previous direct experiments
obtained useful data over a wide range of energies down to the center of mass energy E = 2.5
MeV using charged particle or -ray spectroscopy [2-8]. However, below E = 3.0 MeV the
reported cross sections disagree and are rather uncertain, because at these energies the presence
of 1H and
2H contamination in the C targets hampered the measurement of the
12C+
12C process
both in particle and gamma ray studies.
In a more recent study [9], the astrophysical S(E) factor exhibits new resonances at E < 3.0
MeV, in particular, a strong resonance at E = 2.14 MeV, which lies at the high-energy tail of the
Gamow peak. This resonance increases the present nonresonant reaction rate of the channel by
a factor of 5 near T = 8×108 K. On the other hand, it has been proposed that a sub-barrier fusion
hindrance effect might drastically reduce the reaction rate at astrophysical energies. Moreover, it
has recently been proposed that a hypothetical resonance at 1.5 MeV could help alleviate the
problem of the unexpectedly short recurrence times of X-ray superburts [9a]. In standard stellar
models, the 12
C+12
C fusion reaction is one of the key factors differentiating between the
evolutionary paths leading to either white-dwarfs or heavy element burning stages. In fact it is
the uncertainty in this rate that is responsible for the present uncertainty in the cut off mass (~ 8
MSUN) separating these two paths [9].
The reaction rate that is used in astrophysical models at the moment is based on the value
S(E) = 3×1016
exp(-0.46E) MeV∙b as quoted in reference [13] from the evaluation of three data
sets [2,3,7]. The reference, however, does not quote any uncertainty. This is not a surprise
considering the difficulty of extrapolating from the existing data down to astrophysical energies.
Clearly some resonances contributions (or indeed their absence) in the lower energy region could
significantly change existing predictions. A better understanding of the 12
C+12
C fusion reaction
is extremely needed for a wide range of astrophysical models. In particular, accurate cross
section data in the low energy range is required to base astrophysical implications on firmer
ground.
Because of the resonance structure, extrapolation from high energies to the Gamow energy
EG = 1.5 MeV is quite uncertain and the cross sections for direct measurements become too
small. The indirect Trojan Horse Method (THM) [10-12] can overcome these difficulties and can
provide the astrophysical S(E)-factor of charged particle induced reactions across the entire
Gamow energy range without the need of extrapolation.
2. The Trojan Horse Method theory
The main idea of the Trojan Horse Method is to extract the cross section of an astrophysical
two body reaction A + x → C + c using a suitable three body reaction A + a → C + c + s. The
trojan horse nucleus a should have a strong x + s structure with a well know momentum
distribution. From the three body to the two body process we are interested in a process that is
characterized as a transfer reaction to the continuous, where the Trojan horse nucleus a breaks-
up into a nucleus x that is transferred and into a nucleus s that acts as a spectator to the sub-
reaction. This mechanism dominates the cross section in a region of the three body phase space
where the transferred momentum to the spectator s is small, e.g., for quasi free (QF) scattering
conditions. In the theoretical description of such mechanism using the impulse approximation
(IA) [14] in the framework of the Plane Wave Impulse Approximation (PWIA) the three body
cross section can be factorized into three terms [15] by the relation (2.1):
(2.1)
where KF is a kinematical factor containing the final state phase-space factor, | is the
Fourier transform of the radial wave function for the x-s inter-cluster relative motion and the
term (dd)CM is the off-energy shell differential two body cross section at the center of mass
energy ECM given in post-collision prescription by ECM = Eax = ECc – Q2Body. The variable ECM is
the relative energy between the outgoing particles and Q2Body is the Q-value of the virtual two
body reaction.
The binding energy of the cluster compensates the energy of the incoming nucleus that can
be chosen high enough to overcome the Coulomb barrier in the entrance channel of the three
body reaction. The break-up of the Trojan horse nucleus occurs in the nuclear field and both
Coulomb barrier penetration and electron screening effects are negligible.
The momentum distribution | can be calculated by solving the time-independent
Schrodinger equation, using a simple potential model description of the 12
C+alpha system. The
potential strength is fixed by reproducing the 16
O binding energy and accommodating the Fermi
repulsion of nucleons by admitting 2 nodes in the wave-function solution. The radius is fixed by
reproducing the 16
O rms-charge radius. For small momentum transfers < 100 MeV/c, the derived
momentum distributions should be largely insensitive to the adopted shape of the potential. A
test of this systematic can be performed to ascertain the induced error in the cross section
extraction.
A more complete description of the Trojan Horse Method can be found in references [10,11].
2.1 Previous experiments using the Trojan Horse Method
In the last decade, the method has been applied to several nuclear reactions involved in
different astrophysical scenarios such as primordial nucleosynthesis, the LiBeB depletion
problem, CNO cycle and the fluorine problem in AGB stars. The method was applied as well
into nuclear physics problems such the p-p elastic scattering below the Coulomb barrier where
the Coulomb amplitude is expected to interfere with the nuclear field. Also the method can be
applied to produce virtual neutron beams using deuterons. The reactions that were already
investigated using the Trojan Horse Method are reported in table I together with the
corresponding three-body reaction (more details and references can be found in [12]).
Table I: Reactions investigated by means of the Trojan horse Method
In particular, the reactions 10
B(p,)7Be and
11B(p,)
8Be were studied in details by our group
through the indirect Trojan Horse Method using the 2H(
10B,
7Be)n and
2H(
11B,
8Be)n three
body reactions respectively [17]. The experimental setup and the results for the 2H(
10B,
7Be)n
are described bellow to give an example of the equipment that is needed.
In the astrophysical environment the 10
B(p,)7Be reaction takes place at a temperature of
5×108 K and the Gamow energy is EG = 10 keV. Figure 2.2 shows the S(E)-factor for the
10B(p,)
7Be reaction comparing the indirect data (black points) with the direct data [16]. The
solid line is a fit in the indirect data and the dashed line represents a fit in the direct data
extrapolated to low energies according to reference [16]. Previous experiments obtained data
down to the center of mass energy E = 20 keV and the extrapolation down to lower energies was
hampered by electron screening effects. The result confirmed the behavior of the S(E) factor at
high energies (ECM > 40 keV) but at the Gamow energy the S(E = 10 keV) is 2 times less
compared with the extrapolation curve of the direct data [16]. This result confirms the power of
the Trojan Horse Method to reach the low energy region usually not reached through direct
experiments.
Fig. 2.1: Picture of a typical experimental setup used in Trojan Horse Method experiments [17]. On
the left side, the telescope system made up of an ionization chamber and a position sensitive silicon
detector (PSD). On the right, two PSDs placed on the opposite side with respect to the beam
direction.
Fig. 2.2: S(E)-factor for the
10B(p,)
7Be reaction [17]. The indirect data extracted using the Trojan
Horse Method (black points) compared with three sets of direct data [16]. The current result confirms
the behavior of the S(E)-factor at high energies (ECM > 40 keV) but at the Gamow energy the S(E =
10keV) is 2 times less compared with the extrapolation curve (dashed line) of the direct data [16].
3. Study of the 12
C+12
C fusion reaction
The main goal of the proposed experiment is to extract the cross section and therefore the
astrophysical S(E)-factor of the reactions 12
C(12
C,p)23
Na, 12
C(12
C,)20
Ne and 12
C(12
C,n)23
Mg
through the indirect Trojan Horse Method using the 12
C(16
O, p23
Na)12
C(16
O, 20
Ne) and 12
C(16
O, n23
Mg) three body reactions respectively.
This experiment will provide data in the energy range ECM ~ 2.5 MeV - 5 MeV where
various sets of data from previous experiments disagree in orders of magnitude [2-8] and also
will provide new data below 2.5 MeV where other experiments could not reach due to the
difficulties in performing direct experiments at low energies. The study will be done in two
stages covering different ranges in the center of mass energy of the 12
C+12
C system (Table I).
The overlap between the two energy regions is needed for the normalization procedure.
16
O beam
energy
Interval of energies covered in the 12
C+12
C
center of mass
First stage 29.8 MeV 2.5 – 5.0 MeV
Second stage 25.8 MeV 1.0 – 3.5 MeV
Table I: Beam energies and 12
C+12
C center of mass energies for the two stages of the experiment.
3.1 Monte Carlo simulations
Following are the results of a Monte Carlo simulation for the three body reaction 12
C(16
O, p23
Na) (29.8 MeV 16
O beam). Figure 3.1 shows the angular distribution of the particles
in the exit channel. The points in blue/gray correspond to the events where the QF contribution is
dominant, e.g., where the momentum of the spectator |p| < 40 MeV/c. The dashed lines delimit
the angular region covered by the detectors. The detectors designated to measure the 23
Na will
cover the angular region 4o – 12
o and the detectors to measure the p will cover the angular region
-30o – -100
o (the negative sign indicates that the detector is placed on the opposite side with
respect to the beam direction).
Figure 3.2 is the “butterfly diagram” that shows the 12
C+12
C center of mass energy ECM as a
function of the spectator momentum p (MeV/c). The horizontal dashed lines delimit the region
of astrophysical interest from 2.5 to 5.0 MeV that will be covered in the first stage of the
experiment. The QF mechanism is dominant in this region of interest and is delimited by the
vertical solid lines. The ECM = 4 MeV in the 12
C+12
C system correspond to the 16
O beam energy
of 29.8 MeV in the laboratory system. Simulations for the other two 12
C+12
C channels were
performed demonstrating that will be possible to study the other channels simultaneously using
the same angular regions covered by the detectors.
Fig. 3.1: Monte Carlo simulation for the three body reaction
12C(
16O, p
23Na) (29.8 MeV
16O beam).
The points in blue/gray correspond to the events where the QF contribution is dominant and the dashed
lines delimit the angular region covered by the detectors.
Fig. 3.2: “Butterfly diagram” showing the behavior of the
12C+
12C center of mass energy ECM (MeV)
as a function of the spectator momentum p (MeV/c). The horizontal dashed lines delimit the region of
astrophysical interest from 2.5 to 5.0 MeV that will be covered in the first stage of the experiment. The
QF mechanism is dominant in this region of interest and is delimited by the vertical solid lines.
3.2 Experimental Setup
The experiment will be performed at the LAFN and the detection system will be mounted in
the large scattering chamber in line 15B. The Pelletron accelerator will provide a 500 nA 16
O
beam with energies of 29.8 and 25.8 MeV for the first and second stages of the experiment. A
carbon target of 100 g/cm2 will be used for the experiment and also a 100 g/cm
2 Au target and
a 200 g/cm2
CD2 (self-supported deuterated polyethylene) target for energy calibration. The
detection setup consists of six 5x1 cm position sensitive silicon detectors (PSDs) with energy
resolution of 5% at 5 MeV and position resolution of 0.3 mm. The particle identification will rely
on the well-known E-E method, the PSDs will work together with ionization chambers (IC)
filled with isobutene gas and a control system to monitor the pressure during the experiment.
Figure 3.3 shows a schematic representation of the experimental setup.
The displacement of the detectors is chosen after a Monte Carlo simulation in order to
maximize the quasi-free (QF) contribution, covering the angles where the momentum of the
spectator ranges from 0 to 40 Mev/c. The uncertainty in the center of mass energy in the system 12
C+12
C is mainly determined by the angular resolution of the detectors. To obtain the center of
mass energy with resolution of ~ 30 keV the angular resolution required for the detector
measuring the outgoing particles is ~ 0.1o. To achieve this resolution the PSD must be placed at a
distance greater than 20 cm from the target.
At forward angles, the rate of the elastic scattering can be an issue and overload the detectors,
to overcome this problem one can use a velocity filter after the target to deflect and filter the
particles of interest, for instance the 23
Na that will have angles in the range -3o - 12
o in the
laboratory coordinate system according to Monte Carlo simulations (Figure 3.1). Figure 3.5
shows a preliminary simulation of 16
O and 23
Na trajectories after the target passing through the
velocity filter with a 55 KV applied. Figure 3.6 shows the image in the PSD detector plane
placed at 50 cm from the target. 16
O and 23
Na have very different vertical deflections allowing
the PSDs to be placed out of the reaction plane in a way to detect only the particles of interest, 23
Na for instance
The large-area position-sensitive neutron wall detector [18] will be used to detect neutrons in
coincidence with 23
Mg for the 12
C(12
C,n)23
Mg reaction studied through the 12
C(16
O,
n23
Mg)three body reaction. The energy of the neutron is calculated using the x-y position
information and the time of flight from the target.
Fig. 3.3: Schematic representation (not in scale) of the experimental setup proposed.
Fig. 3.4: Photo of the large scattering chamber located at line 15B in the LAFN experimental area.
Fig 3.3: 16
O and 23
Na trajectories passing through
the velocity filter after the target.
Fig. 3.4: Image in the detector plane at 50 cm from
the target. The PSDs will be placed out of the
reaction plane to detect only the particles of
interest, 23
Na for instance.
3.3 The Pelletron Accelerator
During the last three years, the Pelletron accelerator of the LAFN (Laboratório Aberto de
Física Nuclear) was undergoing a series of maintenances and repairs and is now back in regular
operation since the first semester of 2011. The accelerator is equipped with a MC-SNICS ion
source (Multicathode Source of Negative Ions by Cesium Sputtering) able to produce 16
O beams
with intensities up to 1A. The target laboratory on site uses evaporation techniques (Electron
Bombardment, Sputtering and Lamination) to produce 12
C targets with the thickness required for
the experiment. The voltage in the terminal required for the experiment is around 6.5 MV that is
bellow the present limit of the accelerator that is 7 MV. Therefore, this proposal is feasible from
the technical point of view in the LAFN.
In addition, we are interested in exploring the possibility of using this method with
radioactive beams in the future with FRIB at Michigan State University. The proposed
experimental activity is a great step to develop the method at LAFN and to draw in part of the
low energy community working on this method.
3.4 Beam time request
To calculate the beam time request we considered a 16
O beam intensity of 500 nA (4.4 ×1011
pps for a charge state of 7+) that is reasonable to get enough statistics and at the same time not
overload or damage the detectors. A typical three-body cross section for reactions involving 16
O
break-up is, in the worst case, of about 1 mbarn/sr and we can also empirically estimate a QF
channel contribution to this cross section of about 10%. Assuming a beam intensity of 4.4×1011
pps impinging on a 100 g/cm2 C target would therefore yield 66 pps/sr. The trigger PSD placed
at 30 cm from the target will have a solid angle of 0.0005 sr and a counting rate of 0.033 pps. In
order to get a statistical error smaller than 10% for 10 keV bins, about 25000 events are required
to get good statistics in the overall 2.5 - 5.0 MeV energy range (first stage of the experiment).
The 16
O stable beam time needed is about 210 hours (~ 9 days) to perform each stage of the
experiment. Table II shows a summary of the technical specifications for this proposal.
Beam 16
O, 500nA
Beam energy – first and second stage 29.8 and 25.8 MeV
Terminal voltage – first and second stage 4.95 – 5.94 MV and 4.28 – 5.14 MV
Detectors 6 position sensitive silicon detectors (PSDs)
Neutron wall detector
Devices Velocity filter
Beam time requested – first stage 9 days
Beam time requested – second stage 9 days
Beam time request – Total 18 days Table II: Technical specifications for this proposal.
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