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: mgdsanto@gmail.com / delsanto@nscl.msu.edu

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: suaide@if.usp.br

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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