exotic nuclei structure and reaction noyaux exotiques ... - IPN - IN2P3

(E ex =7.654 MeV) and to the complex excited region
of 12 C around E ex 9.64-10.3 MeV. To have a
first indication on the extent to which these states
may be considered candidates for α-particle
condensation, it is mandatory to see whether the
decay is simultaneous or if it proceeds partially via
8 Be. To do this, we plot with blue points the correlation
function obtained with partial event mixing
(i.e. the uncorrelated yield spectrum is built by selecting
two alpha-particles from the same event
and the third one from a different event). As one
may see, the two peaks survive, but while the second
peak is almost unchanged, the magnitude of
the first one is diminished, which signs the presence
of 8 Be for a part of those events.
For sure this part of information is not sufficient to
conclude that those states represent α-particle
Figure 3: Three-α higher order correlation
Figure 2: Three-α correlation functions (total kinetic
energy). See text for the different spectra
larity at forward angles.
Invariant v par -v per plots clearly show the binary character
of collisions with the formation of two emitting
sources, a quasi-target (QT) and a quasiprojectile
(QP), which may be easily separated
according to whether the velocity of a certain reaction
product is smaller or larger than v proj /2. After a
first event filtering according to total α multiplicity
(m α ≥ 3) and total detected charge we have focused
exclusively on QP decays with m α (QP) =3.
Correlation functions and α-particle condensate
nature of the Hoyle state
Various correlation functions have been used: two
particle correlation functions to first judge the quality
of energy calibrations and multi-particle correlation
functions to identify possible α-particle
condensation states and define their de-excitation
characteristics. For example,two- or multipleparticle
correlation functions, with one variable X
are defined as: 1+R(X) = Y corr (X) / Y uncorr (X) where
the role of the generic variable X may be equivalently
played by the total kinetic energy of the particles
of interest in their center-of-mass frame E tot or
by the excitation energy of their emitting source
state, E ex =E tot -Q. Ycorr, the correlated yield spectrum,
is constructed with the considered particles
in the same event and Yuncorr stands for the uncorrelated
yield spectrum constructed by taking
particles in different events. Figure 1 illustrates the
quality of the calibration despite the complexity of
the apparatus. The α-α correlation function shows
a narrow peak centered around 70 keV which
corresponds to the ground state of 8 Be. Figure 2
shows the 3-α correlation function with standard
event mixing for building the uncorrelated yield
spectrum (i.e. each particle belongs to a different
event, (red points). Two peaks are observed,
which correspond respectively to the Hoyle state
condensation. A major step forward is to show that
the emitted particles have the same (low) kinetic
energy. To do that a higher-order intra-event correlation
method is used [6]:
1+R(σ Eα ,)=Y corr (σ Eα ,)/Y uncorr (σ Eα ,).
Here, for a given α multiplicity, the numerator is the
yield of events with given average kinetic energy of
α particles, , and given root mean square
σ(E α ). Figure 3 shows the intra-event correlation
function corresponding to 3-α decays. It is remarkable
to notice the peak localized around
=110 keV and σ(E α ) ≤ 25 keV. Those values
correspond, within our energy calibration uncertainties,
to an equal sharing of the available energy
of the Hoyle state among the three αs. So we
consider that the α-particle condensate nature of
the Hoyle state is demonstrated. The peak localized
around =110-130 keV and σ(E α ) around
90 keV corresponds to the sharing of the available
energy between the 8 Be (two αs of 94 keV) and the
remaining α of 191 keV.
References
[1] K. B. Davis et al., Phys. Rev. Lett. 75, 3969, 1995.
{2] A. Tohsaki et al., Phys. Rev. Lett. 87, 192501, 2001.
[3] T. Yamada and P. Schuck, Phys. Rev. C 69, 024309, 2004.
[4] B. Borderie and M. F. Rivet, Prog. Part. Nucl, Phys. 61, 551,
2008.
[5] A. Pagano et al., Nucl. Phys. A734 , 504, 2004.
[6] B. Borderie and P. Désesquelles, Eur. Phys. J. A30, 243,
2006.
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