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**Marina Barbui Trento, Italy, April 7-11, 2014**

Exploring the alpha cluster structure of nuclei using the thick target inverse kinematics technique for multiple alpha decays. The 24Mg case Marina Barbui Trento, Italy, April 7-11, 2014

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**Alpha clustering in Astrophysics**

Estimated limit N = 10a for self-conjugate nuclei(Yamada PRC 69, ) mass Many theoretical works have brought to the picture of alpha cluster nuclei described as a diluted gas of alphas in the lowest S state. (PRL 87, ; PRC 75, ). Many experimental works have explored the 8Be and 12C cases, fewer are available on the heavier systems. Excitation energy We have investigated the 24Mg case with 20Ne+α at 2.9 and 9.7 AMeV using the Thick Target Inverse kinematics Technique (K. Artemov et al., Sov. J. Nucl. Phys. 52, 406 (1990))

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**The Thick target inverse kinematics technique**

Allows covering a large range of incident energies in the same experiment. In the inverse kinematics, the reaction products are focused at forward angles. Allows measuring reaction products emitted at 0o. This Method (K. Artemov et al., Sov. J. Nucl. Phys. 52, 406 (1990)) has been used several times to measure the resonant elastic scattering (Eur. Phys. J. A (2011) 47: 73; Eur. Phys. J. A (2011) 47: 96; AIP Conf. Proc. 1213, 137 (2010) ) and is used here for the first time to detect multiple alpha decays.

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**Experimental setup 20Ne beam from the K150 cyclotron at TAMU**

@ 3.7 AMeV, 2.9 AMeV after the window @ 11 AMeV, 9.7 AMeV after the window 48 cm Reaction chamber filled with 4He gas at a pressure sufficient to stop the beam before the detectors 10.3 PSI with 20Ne AMeV and 50 PSI with 20Ne AMeV Measured quantities: -Energy signals from every detector pad. -Time from the cyclotron radiofrequency.

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**Preliminary analysis Energy calibration. Time calibration.**

Identification of the alpha particles with gates on DE-E and E-Time. Selection of the events with alpha multiplicity 1, 2 and 3 for further analysis. Reconstruction of the interaction point in the gas using the kinematics, the measured alpha energies and the energy loss tables from SRIM (double check with the measured time). Reconstruction of the excitation energy of the 24Mg.

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**Events with Alpha Multiplicity 1**

Ne 2.9 AMeV Threshold for 6a decay Nice energy resolution (about 30 keV at 0o) worsening as we move to larger angles Possibility to measure the whole excitation function in the same experiment. Comparison with the excitation function measured in keV energy steps in normal kinematics at 168o in the center of mass By R. Abegg and C.A. Davis PRC 43(1991)2523

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**Events with alpha multiplicity 2**

9.7 AMeV, 2a in the telescope at about 0 deg Estimate of the uncorrelated events -PRC 63(2001)034317 PRC 57 (1998) 1277 This work Threshold for 6a decay After subtraction of the uncorrelated 24Mg* 8Be 16O

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**Events with alpha multiplicity 3**

9.7 AMeV, 3a Telescope1 24Mg* 12C1 12C2 a if 12C2 is in the ground state Ex(12C) [MeV] Hoyle state 3- state -PRC 63(2001)034317 PRC 57 (1998) 1277 This work

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We can do better Improve the statistics by considering events with 2 alphas in the Telescope 1 and the third elsewhere 7.6 MeV (0+) 2 12C in the Hoyle state we detect mixed alphas 9.6 MeV (3-) 11.8 MeV (2-) 12.7 MeV (1+) 10.8 MeV (1-)

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For each state Relative energy of the three couples of alpha particles -> Tells us if the decay is proceeding through the 8Be ground state. Dalitz Plot and Sphericity/Coplanatity Plot -> Information about the energy and momentum of the emitted alpha particles. Tell us about the shape of the decaying 12C Excitation energy of the 24Mg

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**With selection of events decaying through the 8Begs or not**

Erelative<220keV through 8Begs Erelative>220keV not through 8Begs With subtraction of uncorrelated events 7.6 MeV (0+) 9.6 MeV (3-) 11.8 MeV (2-) 12.7 MeV (1+) Energy [MeV] Through 8Begs No 8Begs 7.65 9.64 11.8 12.7

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**Energy Dalitz Plots Ideal to describe 3 body decays**

Based on Viviani’s theorem saying that for any point P in an equilateral triangle the sum of the distances of the point from the sides of the triangle is a constant independent of P 𝑦=𝑥 3 𝐸 1 + 𝐸 2 + 𝐸 3 =𝑐𝑜𝑛𝑠𝑡= 𝐸 𝑡𝑜𝑡 P= (𝑃 𝑥 , 𝑃 𝑦 ) 𝑃 𝑥 = 𝐸 1 +2 𝐸 2 𝐸 𝑚𝑎𝑥 − 3 2 E2/Emax P E3/Emax 𝑃 𝑦 = 𝐸 1 𝐸 𝑚𝑎𝑥 E1/Emax If the decay proceeds through the formation of a 8Be 𝐸 𝑚𝑎𝑥 = 2 3 𝐸 𝑡𝑜𝑡 Events inside the circle conserve both energy and momentum The center of the circle is at P=(0.5, 0.5)

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**Sphericity/Coplanarity study**

Use Energy flow matrix defined as in the references: Physics Letters 110 B (1982) 185 Physics Letters B 240 (1990) 28 PRL 64(1990) 2246 PRL 78 (1997) 2084 pi (n) are the momentum components of the particle n, mn is the mass of the particle n li are the eigenvalues of the matrix in ascending order l1 ≤ l2 ≤ l3 Disk shape Rod shape

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**7.6 MeV (0+) Hoyle State mostly decays through 8Begs**

Consistent with the description of the Hoyle state by other authors Less than 1.6 % of the events (depending on the cut) decay directly into 3 alphas

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**9.6 MeV (3-) decays through 8Begs**

JoP Conference series 111 (2008)012017

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**Dalitz Plot (2- at 11.8 MeV) not decaying through 8Begs Comapred with Fynbo’s predictions**

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**Dalitz Plot (1+ at 12.7 MeV) not decaying through 8Begs Comapred with Fynbo’s predictions**

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**Simple Monte-Carlo decay simulation to understand something more about the shape of 12C**

-Conservation of energy and momentum -Classical kinematics -Energy and width of the resonances -In case of decay through 8Be Q 1) Q has a flat distribution 2) Q is optimized in order to match the experimental energy distribution and sphericity/coplanarity plot

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Experimental Hoyle state Q optimized (gaussian distribution centered at p/3 with sigma p/6 and Q>p/9) Q has a flat distribution

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Experimental (3-) state Q optimized (gaussian distribution centered at p/2 with sigma p/8) Q has a flat distribution

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Experimental (1+) state at 12.7 MeV decaying through the 8Be excited state (Ex = 2.9 MeV, G=1 MeV ) Q optimized (gaussian distribution centered at p/6 with sigma p/12) Q has a flat distribution

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**E*(12C1) = 11.83 MeV (2-) Decay without 8Be**

Through the 8Be excited state E=2.9 MeV, G=1 MeV Experimental Data Decay without 8Be

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Ex 24Mg

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**Explanation of the peak at 8.6 MeV**

We see the peak only selecting the events decaying through the ground state of 8Be No peak for the other selection. Might be due to 24Mg splitting into 2 carbons each in the Hoyle state (reasonable because the Hoyle state is the most populated and mostly decays through the 8Be gs) If so, there should be a systematic effect if we look at the average kinetic energy along the beam axis (the high energy alpha particle in the center of mass is always connected to the less energetic one in the laboratory framework) If we look at the center of mass velocity in the x direction for the known states this has a symmetric distribution around zero The 8.6 MeV peak does not. Simple Monte-Carlo simulation to show that this is what actually occurs

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**Velocities on the beam direction**

(3- ) 9.6 MeV state -> Symmetric Hoyle State -> Symmetric (2- )11.8 MeV state -> Symmetric 8.6 MeV peak -> NOT Symmetric = Something is wrong (1+) 12.7 MeV-> Symmetric

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**Simple simulation ingredients:**

Using the previous simulation for the 12C decay Conservation of energy and momentum for the decay of 24Mg Inputs: E* (24Mg), E*(12C1) , E*(12C2), width of the states Angular distribution of the carbons proportional to Pl(cos q)2 E* (24Mg) = 33.2 MeV (this is found to decay in 2 carbons) First calculation:

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**If we mix 2 alphas from C1 and one alpha from C2**

The peak at 8.6 MeV appears. There is also a bump at about 10 MeV that we need to take into account Experimental 8.6 MeV peak The x component of the velocity in the center of mass shows an asymmetric shape as for the measured 8.6 MeV peak

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**How we reconstruct those events**

In the laboratory we see two alphas from C1 (va1, va2) and one from C2 (va3) va3<va1≈va2 In case of the Hoyle state the standard deviation of the 3 alphas energies is very small => the average of v1 and v2 is very close to the velocity of C1, v3 represents the velocity of C2 (overestimated). C1 and C2 are in the Hoyle state and emit 3 alphas va3 va2 va1 In the lab We can calculate the relative energy between C1 and C2 E*24Mg = 𝐸 𝑟𝑒 𝑙 𝐶1−𝐶2 + E*C1+ E*C 𝐸 𝑟𝑒 𝑙 𝐶1−𝐶2 = 1 2 𝜇 𝑣 𝑟𝑒𝑙 2 E*C1= E*C2 = 7.65 MeV Q(24Mg->2 12C) = MeV

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Conclusions We observed several resonant states in 24Mg with excitation energy up to 38 MeV, well above the threshold for decaying in 6 alpha particles We did not observe any direct decay into 6 alphas The observed states show alpha cluster properties. Depending on the energy they can decay in 20Ne+a, 16O +8Be, 12C+12C->3a, 12C->3a+12C->3a. Several 12C excited states decaying into 3 a particles were identified and analyzed in detail to obtain information about the decay mode and the shape of the 3 a configuration.

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**Thank you for your attention!**

M. Barbui1, V.Z. Goldberg1, E-J. Kim1, K. Hagel1, G.Rapisarda1, S. Wuenschel1, X. Liu1,2, H. Zheng1, G. Giuliani1, and J.B. Natowitz1 1 Cyclotron Institute, Texas A&M University, MS3366 College Station, TX 2 Institute of modern physics, Chinese Academy of Sciences, Lanzhou, China

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