1. 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

2. 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))

3. 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.

4. 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.

5. 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.

6. 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

7. 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

8. 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

9. 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-)

10. 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

11. 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

12. 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)

13. 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

14. 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

15. 9.6 MeV (3-) decays through 8Begs
JoP Conference series 111 (2008)012017

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

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

18. 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

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

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

21. 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

22. 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

23. Ex 24Mg

24. 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

25. 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

26. 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:

27. 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

28. 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

29. 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.

30. 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