5.3 Results for the one-proton transfer reaction (d, 3 He)
5.3.1 Excitation Energy
Figure 5.8: ∆E-E identification plots in the zero degree plastic by. The orange cut selects the kinematically constraints 8He coming from the 9Li(d,3He). The black dot are event in coincidence with3He, the blue dot are event in coincidence with3He and presenting an excitation energy be- tween -2 MeV and 2 MeV.
Figure 5.9: ∆E-E identification plots in the zero degree plastic by. The orange cut selects the non kinematically constraints
8He coming from the 11Li(d,3He)10He.
The black dot are event in coincidence with3He, the blue dot are event in coinci- dence with 3He and presenting an excita- tion energy between -2 MeV and 4 MeV.
The associated energy spectra are presented in Fig.5.13 for8He. The presented fit gives a position of 2.7±196 keV, giving a good agreement with the expected position of the ground state. The absence of background and the compatibility of the width and the position of the signal with the simulations, confer confidence in the analysis.
The position of the first resonant state was left as free parameter. Fig.5.14 shows the obtained spectrum and the fit of the data, giving a first resonant state ER= 1.4±0.3 MeV above the 8He+n+n threshold taken as reference. No evidence for a narrow resonance just above the threshold as predicted by Aoyama [Aoy03] is found, in agreement with previous experimental studies.
Resonances are presenting a specific shape due to their short live time. G.
Breit and E. Wigner showed how a resonance can be described using distribution, nowadays called Breit-Wigner, and which density of probability f(E) is given by:
f(E) = 1
π · Γ/2
(ER−E)2+ (Γ/2)2 (5.21)
where Γ is the width of the resonance and ER its position. The experimental res- olution broadens the resonance shape. The resulting signal can be modeled by the convolution of the Breit-Wigner and a Gaussian function, an example of such con- volution is shown in Fig.5.12.
5.3 Results for the one-proton transfer reaction (d,3He) 101
(deg) θLab 0 5 10 15 20 25 30 35 40 45 50
(MeV)LabE
0 5 10 15 20 25 30
Figure 5.10: Kinematical plot from the
9Li(d,3He) data, the blue line is the the- oretical line of the ground state of 8He.
(deg) θLab 0 5 10 15 20 25 30 35 40 45 50
(MeV)LabE
0 5 10 15 20 25 30
Figure 5.11: Kinematical plot from the
11Li(d,3He) data, the blue line is the the- oretical line of a 1.2 MeV state of 10He.
The green line indicate the 8He+n+n threshold.
The10He was fitted using such convolutions. However, the fit procedure lead to Γ = 0 MeV. This observation is understood as a consequence of the energy resolution of the set-up around 1 MeV (σ) that forbids the determination of the natural width of the state.
E
-10 -8 -6 -4 -2 0 2 4 6 8 10
density of probability (a.u.)
0 0.2 0.4 0.6 0.8
1 Gaussian
Breit-Wigner Convolution
Figure 5.12: Convolution (black) of a Breit-Wigner (green) of Γ = 1 MeV with a Gaussian function (red) of σ= 1 MeV.
(MeV)
8He
E
-10 -5 0 5 10
counts / 600 keV
0 2 4 6 8 10 12
Figure 5.13: Energy spectrum obtained for the 9Li(d,3He)8He reaction.The black line is a fit of fixed 818 keV width that gives Egs= 2.7±196 keV.
(MeV)
10He
E
-8 -6 -4 -2 0 2 4 6 8 10
counts / 750 keV
0 2 4 6 8 10
Figure 5.14: Energy spectrum obtained for the 11Li(d,3He)10He reaction.The black line is a fit of fixed 1050 keV width that gives ER= 1.4±0.3 MeV.
Carbon background
The data accumulated using the carbon target with 9Li beam gives almost no contribution, demonstrating the quality of the identification of both 3He and 8He.
As explained above, the mixing of 8He and 6He leads to an important background contribution in the 10He case, as shown in Fig.5.15.
The Carbon background was estimated using data accumulated with a 1 mg/cm2 thickness for both beams. Spectra were extracted using the exactly same gates as for the CD2 target. The number of events in a bin of excitation energy is given by :
NC =Ndetected(C)· NBeam(C)
NBeam(CD2)· eC
e0CD2 (5.22)
For the 9Li beam, only one event was measured in the high excitation energy region. More counts have been measured with 11Li beam but statistics is quite low as can be seen in fog.5.15. The superposition of the normalized spectrum on Carbon target and the 10He spectrum is presented in Fig.5.16. Clearly the contribution of the Carbon from the CD2 target does not explain the observed structure.
Once normalized, the two spectra can be superimposed to get an idea of the contribution. However, the statistics in the original spectra is rather low and the statistical error bars large (see Fig.5.15), therefore the shape of the distribution is strongly influenced by the statistics and the two histograms can not be subtracted.
However a quantitative study can be performed dividing the spectra in three region of interest (cf Fig.5.16), where the density of count for the CD2 and 12C could
5.3 Results for the one-proton transfer reaction (d,3He) 103
(MeV)
10He
E
-8 -6 -4 -2 0 2 4 6 8 10
counts / 750 keV
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
Figure 5.15: Excitation energy contri- bution to the 10He spectra obtained using data accumulated with a carbon target be- fore normalization.
(MeV)
10He
E
-8 -6 -4 -2 0 2 4 6 8 10
counts / 750 keV
0 2 4 6 8
10 A B C
Figure 5.16: The 10He excitation spec- tra and the normalized carbon contri- bution (gray histogram after normaliza- tion). The spectra can be divided in three area, (A) the negative energies region, (B) the region of interest and (C) the high energies region.
be extracted. The obtained results after normalization are shown in Table 5.1.
The obtained value show clearly that the number of count in the A region are compatible with a carbon contribution while the B region present an increase of statistic explained only by reaction on the deuterium.
A B C
CD2 4(1) 6(1) 4(1)
12C 5(1) 2(1) 2(1) CD2/12C 1(1) 3(1) 2(1)
Table 5.1: Number of counts per MeV for the three region defined in Fig.5.16 Moreover, the angular distributions associate with the different regions, and presented in Fig.5.3.1, shown different trend for A and B region. This indicate that the observed count are not coming from the same physical process.
Figure 5.17: The angular distributions obtained for the three regions described in Fig.5.16. The angular distributions has been multiply by 1, 10, and 100 for re- spectively A, B and C region in order to clarify the figure. The trend of the angu- lar distribution associate with region A is very different, especially at small angle, of the one of region B.
(deg) θCM
0 5 10 15 20 25 30
(mb/sr)Ω/dσd
10-2
10-1
1 10 102
A B (x10) C (x100)