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

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Alpha clustering in Astrophysics Estimated limit N = 10 for self-conjugate nuclei( Yamada PRC 69, ) 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 8 Be and 12 C cases, fewer are available on the heavier systems. We have investigated the 24 Mg case with 20 Ne+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)) mass Excitation energy

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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 0 o. 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 0o0o 6.6 o 11 o 9.6 o 14 o 3o3o 20 Ne beam from the K150 cyclotron at 3.7 AMeV, 2.9 AMeV after the 11 AMeV, 9.7 AMeV after the window Reaction chamber filled with 4 He gas at a pressure sufficient to stop the beam before the detectors 10.3 PSI with 20 Ne AMeV and 50 PSI with 20 Ne AMeV Measured quantities: -Energy signals from every detector pad. -Time from the cyclotron radiofrequency. 48 cm

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Preliminary analysis Energy calibration. Time calibration. Identification of the alpha particles with gates on E-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 24 Mg.

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Events with Alpha Multiplicity 1 -Nice energy resolution (about 30 keV at 0 o ) 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 168 o in the center of mass By R. Abegg and C.A. Davis PRC 43(1991) Ne 2.9 AMeV Threshold for 6 decay

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

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Events with alpha multiplicity 3 24 Mg* 12 C 1 12 C 2 Ex( 12 C) [MeV] Hoyle state 3- state if 12 C 2 is in the ground state -PRC 63(2001) PRC 57 (1998) This work AMeV, 3 Telescope1

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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 12 C 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 8 Be 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 12 C Excitation energy of the 24 Mg

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With selection of events decaying through the 8 Be gs or not E relative <220keV through 8 Be gs E relative >220keV not through 8 Be gs With subtraction of uncorrelated events 7.6 MeV (0+) 9.6 MeV (3-) 11.8 MeV (2-) 12.7 MeV (1+) Energy [MeV] Through 8 Be gs No 8 Be gs

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Energy Dalitz Plots E 1 /E max E 3 /E max E 2 /E max P If the decay proceeds through the formation of a 8 Be Events inside the circle conserve both energy and momentum The center of the circle is at P=(0.5, 0.5) 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

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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 p i (n) are the momentum components of the particle n, m n is the mass of the particle n i are the eigenvalues of the matrix in ascending order 1 ≤ 2 ≤ 3 Disk shape Rod shape

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7.6 MeV (0+) Hoyle State mostly decays through 8 Be gs 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 8 Be gs JoP Conference series 111 (2008)012017

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

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

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Simple Monte-Carlo decay simulation to understand something more about the shape of 12 C -Conservation of energy and momentum -Classical kinematics -Energy and width of the resonances -In case of decay through 8 Be 1) has a flat distribution 2) is optimized in order to match the experimental energy distribution and sphericity/coplanarity plot

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

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

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

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E*( 12 C 1 ) = MeV (2-) Through the 8 Be excited state E=2.9 MeV, =1 MeV Decay without 8 Be Experimental Data

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Ex 24 Mg

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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 8 Be No peak for the other selection. Might be due to 24 Mg splitting into 2 carbons each in the Hoyle state (reasonable because the Hoyle state is the most populated and mostly decays through the 8 Be 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 Hoyle State -> Symmetric (3- ) 9.6 MeV state -> Symmetric (2- )11.8 MeV state -> Symmetric (1+) 12.7 MeV-> Symmetric 8.6 MeV peak -> NOT Symmetric = Something is wrong

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Simple simulation ingredients: Using the previous simulation for the 12 C decay Conservation of energy and momentum for the decay of 24 Mg Inputs: E* ( 24 Mg), E*( 12 C 1 ), E*( 12 C 2 ), width of the states Angular distribution of the carbons proportional to P l (cos ) 2 E* ( 24 Mg) = 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 The x component of the velocity in the center of mass shows an asymmetric shape as for the measured 8.6 MeV peak Experimental 8.6 MeV peak

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How we reconstruct those events We can calculate the relative energy between C1 and C2 va3 va2 va1 C1 C2 C1 and C2 are in the Hoyle state and emit 3 alphas In the laboratory we see two alphas from C1 (va1, va2) and one from C2 (va3) va3

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Conclusions We observed several resonant states in 24 Mg 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 20 Ne+ , 16 O + 8 Be, 12 C+ 12 C->3 , 12 C->3 12 C->3 Several 12 C excited states decaying into 3 particles were identified and analyzed in detail to obtain information about the decay mode and the shape of the 3 configuration.

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Thank you for your attention! M. Barbui 1, V.Z. Goldberg 1, E-J. Kim 1, K. Hagel 1, G.Rapisarda 1, S. Wuenschel 1, X. Liu 1,2, H. Zheng 1, G. Giuliani 1, and J.B. Natowitz 1 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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