text:
\section{Introduction}
\label{sec:1}

In the last decades, one of the greatest challenges in nuclear science is the understanding
of the clustered structure of nuclei from both the experimental and theoretical perspectives
~\cite{Greiner95,Brenner,Cluster1,Cluster2,Cluster3,Delion,Funaki15}. Our knowledge on
physics of nuclear molecules has increased considerably and nuclear clustering
remains one of the most fruitful domains of nuclear physics,
facing some of the greatest challenges and opportunities in the years ahead.
Besides the well known series of Cluster Conferences~\cite{Nara,Stratford,Debrecen},
a series of workshops on the state of the art in nuclear
cluster physics was started. The first one  was held in
Strasbourg in 2008~\cite{Strasbourg}, the second one in
Brussels~\cite{Brussels} in 2010 and
the last one in Yokohama~\cite{Yokohama} in 2014.
Figure 1 (taken from the cover of
Ref.~\cite{Yokohama}) summarizes the different types of clustering
discussed during the last two or three decades~\cite{Catford13,Beck15}.
Most of these structures were investigated in an experimental
context by using either some new approaches or
developments of older methods~\cite{Papka12}.
Starting in the 1960s the search for resonant structures in the excitation functions for
various combinations of light $\alpha$-cluster ($N$=$Z$) nuclei in the energy regime
from the Coulomb barrier up to regions with excitation energies of $E_{x}$=20$-$50~MeV
remains a subject of contemporary
debate~\cite{Greiner95}. These
resonances  have been interpreted in terms of nuclear molecules~\cite{Greiner95}.

\begin{figure}[th]
\centerline{\psfig{figure=IJMPE_Fig1.eps,width=13.2cm,height=8.4cm}}
\caption{\label{fig1}
Different types of clustering
behaviour identified in nuclei, from small clusters outside a
closed shell, to complete condensation into $\alpha$
particles, to halo nucleons outside of a normal core,
have been discussed the last two or three
decades~\cite{Catford13,Beck15}. This figure was adapted
from Ref.~\cite{Yokohama,Catford13}
courtesy from W. Catford.}
\vspace*{-10pt}
\end{figure}

The question of how quasimolecular resonances may reflect continuous transitions
from scattering states in the ion-ion potential to true cluster states in the
compound systems was still unresolved in the 1990s \cite{Greiner95}. In many
cases, these resonant structures have been associated with strongly-deformed
shapes and with $\alpha$-clustering phenomena
\cite{Freer03,Freer07,Horiuchi10}, predicted from the
Nilsson-Strutinsky approach, the cranked $\alpha$-cluster
model~\cite{Freer03,Freer07}, or
other mean-field calculations~\cite{Horiuchi10,Gupta10}. In light $\alpha$-like
nuclei clustering is observed as a general phenomenon at high excitation energy
close to the $\alpha$-decay thresholds \cite{Freer03,Freer07,Oertzen06}. This exotic
behavior has been perfectly illustrated by the famous ''Ikeda-diagram" for $N$=$Z$
nuclei in 1968 \cite{Ikeda}, which has been recently modified and extended by von Oertzen
\cite{Oertzen01,Oertzen03} for neutron-rich nuclei, as shown in the
left panel of Fig.2. Despite the early inception of cluster studies, it is only
recently that radioactive ion beams experiments, with great helps from advanced
theoretical works, enabled new generation of studies, in which data with
variable excess neutron numbers or decay thresholds are compared to predictions
with least or no assumptions of cluster cores. Some of the predicted but elusive
phenomena, such as molecular orbitals or linear chain structures, are now
gradually coming to light.

\begin{figure}[th]
\centerline{\psfig{figure=IJMPE_Fig2.eps,width=12.9cm,height=9.9cm}}
\vspace*{8pt}
\caption{\label{fig2} Schematic illustration of the structures of molecular
shape isomers in light neutron-rich isotopes of nuclei consisting
of $\alpha$-particles, $^{16}$O- and $^{14}$C-clusters plus some
covalently bound neutrons (Xn means X neutrons) \cite{Milin14}. The so called
"Extended Ikeda-Diagram" with $\alpha$-particles (left panel) and
$^{16}$O-cores (middle panel) can be generalized to $^{14}$C-cluster cores
(right panel. The lowest line of each configuration corresponds to parts
of the original Ikeda diagram. However, because of its deformation,
the $^{12}$C nucleus is not included, as it was earlier. The numbers represent
the threshold energy dissociating the ground state into the respective cluster
configuration. Threshold energies are given in MeV. This
figure has been adapted courtesy from W. von Oertzen \cite{Milin14}.}
\end{figure}

Clustering is a general feature \cite{Milin14} not only observed in light
neutron-rich nuclei \cite{Orr03,Kanada03,Kanada10,Ito14}, but also in
halo nuclei  \cite{Tanihata03,Nunes03} such as $^{11}$Li
\cite{Ikeda10} or $^{14}$Be \cite{Nakamura12}, for instance. The problem of
cluster formation has also been treated extensively for very heavy systems by
R.G. Gupta \cite{Gupta10}, by D. Poenaru, V. Zagrebaev and W. Greiner
\cite{Poenaru10,Zagrebaev10} and
by C. Simenel \cite{Simenel14} where giant molecules and collinear ternary
fission may co-exist \cite{Kamanin14}. Finally, signatures of alpha
clustering have also been predicted and/or discovered in light nuclei
surviving from intermediate-energy \cite{Borderie16} to
ultrarelativistic-energy  \cite{Zarubin14,Broniowski14}
nuclear collisions. The topic of clustering in nuclei benefits of intense
theoretical activity where new experimental information has come to light
very recently. Several status reports were already given in conferences and
their written contributions can be found in their proceedings
\cite{Beck15,Beck13a,Beck16}.

In this short review article, only few selected topics
will be presented, I will limit myself first to the light $^{12}$C, $^{16}$O, $^{20}$Ne
and $^{24}$Mg $\alpha$-like nuclei in Section 2, then to alpha clustering,
nuclear molecules and large deformations for heavier light nuclei in Section 3.
The search for electromagnetic transitions and alpha condensates in heavier
$\alpha$-like nuclei will be discussed in Sections 4 and 5, respectively, and,
finally, clustering effects in light neutron-rich nuclei (oxygen isotopes) will
be presented in Section 6 before the summary, conclusions and outlook of Section
7 are briefly proposed.

\section{Renewed interest in the spectroscopy of $^{12}$C,
$^{16}$O, $^{20}$Ne and $^{24}$Mg $\alpha$-like nuclei}
\label{sec:2}

The ground state of $^8$Be is the most simple and convincing example
of $\alpha$-clustering in light nuclei as suggested by several theoretical
models and appears naturally in {\it ab initio} calculations \cite{Navratil00,Wiringa00}.
The picture of the $^8$Be nucleus prediced by the No Core Shell model \cite{Navratil00}
as being a dumbbell-shaped configuration of two alpha particles closely resembles
the superdeformed (SD) shapes known to arise in heavier nuclei in the actinide
mass region. This dumbbell-like structure gives rise to a rotational band,
from which the moment of inertia is found to be commensurate with an axial deformation
of 2:1. The possible of large deformation of light $\alpha$-conjugate nuclei with
SD, hyperdeformed (HD) and linear-chain configurations will be discussed in
following Sections.

\subsection{ $^{12}$C nucleus "Hoyle" state}

The renewed interest in $^{12}$C was mainly focused to a better understanding
of the nature of the so called "Hoyle" state \cite{Hoyle54,Cook57,Freer14},
the excited 0$^+$ state at 7.654 MeV that can be described in terms of a bosonic
condensate, a cluster state and/or a $\alpha$-particle gas
\cite{Tohsaki01,Oertzen10a,Yamada12}. The resonant "Hoyle" state \cite{Hoyle54}
(without it carbon would not exist as proved in 1957 by an experimental group at
Caltech \cite{Cook57}) is regarded as the prototypical alpha-cluster state whose
existence is of great importance for the nucleosynthesis of  $^{12}$C within stars.
The structure of this state has been thoroughly investigated with theoretically
modelled with both {\it ab initio}
\cite{Navratil00,Wiringa00,Chernykh07,Chernykh10,Epelbaum11,Epelbaum12,Epelbaum13,Dreyfuss13}
and cluster models \cite{Fukuoka13,Ishikawa14,Funaki15b}. Much experimental
progress has been achieved recently as far as the spectroscopy of  $^{12}$C
near and above the $\alpha$-decay threshold is
concerned~\cite{Itoh04,Freer11,Zimmerman13,Kokalova13a,Marin14,Jenkins15}. More
particularly, the 2$^{+}_{2}$ "Hoyle" rotational excitation in  $^{12}$C has been observed
by several experimental groups \cite{Itoh04,Zimmerman13}.

The most convincing experimental result comes from measurements of
the $^{12}$C($\gamma$,$\alpha$)$^8$Be reaction performed at the HIGS facility
\cite{Zimmerman13}. The measured angular distributions of the
alpha particles are consistent with an $L$=2 pattern including a dominant 2$^+$
component. This 2$^{+}_{2}$ state that appears at around 10 MeV is considered
to be the 2$^+$ excitation of the "Hoyle" state (in
agreement with the previous experimental investigation of Itoh et
al.~\cite{Itoh04}) according to the $\alpha$
cluster \cite{Uegaki} and $\alpha$ condensation models
\cite{Tohsaki01}.  On the other hand, the experiment
$^{12}$C($\alpha$,$\alpha$)$^{12}$C$^*$ carried out at the
Birmingham cyclotron~\cite{Marin14}, UK, populates a new state compatible with an
equilateral triangle configuration of three $\alpha$ particles.
Still, the structure of the "Hoyle" state remains controversial
as experimental results of its direct decay into three
$\alpha$ particles are found to be in disagreement
~\cite{Freer94,Raduta11,Manfredi12,Kirsebom12,Rana13,Itoh14,Morelli16}.

\subsection{ $^{16}$O nucleus}

In the study of Bose-Einstein Condensation (BEC), that will be presented in more detail
in Section 5, the $\alpha$-particle states in light $N$=$Z$ nuclei
\cite{Tohsaki01,Oertzen10a,Yamada12},
are of great importance. At present, the search for an experimental signature of
BEC in $^{16}$O is of highest priority. Furthermore, {\it ab initio}
calculations \cite{Epelbaum14} predict that nucleons are arranged in
a tetrahedral configuration of alpha clusters.
A state with the structure of the ''Hoyle" state \cite{Hoyle54} in
$^{12}$C coupled to an $\alpha$ particle is
predicted in  $^{16}$O at about 15.1 MeV (the 0$^{+}_{6}$ state), the
energy of which is $\approx$ 700 keV above the 4$\alpha$-particle
breakup threshold \cite{Funaki08}. However, any state in
$^{16}$O equivalent
to the ''Hoyle" state \cite{Hoyle54} in $^{12}$C is most certainly
going to decay exclusively by particle emission with very small
$\gamma$-decay branches, thus, very efficient
particle-$\gamma$ coincidence techniques will
have to be used in the near future to search for them. BEC states are expected to
decay by alpha emission to the ''Hoyle" state and could be found among the
resonances in $\alpha$-particle inelastic scattering on $^{12}$C decaying to
that state.
In 1967 Chevallier et al.
\cite{Chevallier67} could excite these states in the $\alpha$-particle
transfer channel leading to the
$^{8}$Be--$^{8}$Be final state and proposed that a
structure corresponding to a rigidly rotating linear
arrangement of four alpha particles may exist in $^{16}$O. At this time
this experimental observation was considered as the equivalent of the
three alpha chain states postulated by Morinaga for the $^{12}$C nucleus
\cite{Morinaga}. However, very recently, a more sophisticated experimental
setup was used at Notre Dame \cite{Curtis13}: although the excitation function
is generally in good agreement with the previous results \cite{Chevallier67}
a phase shift analysis of the angular distributions does
not provide evidence to support the reported
hypothesis of a 4$\alpha$-chain state configuration.

\subsection{$^{20}$Ne and $^{24}$Mg nuclei}

Experimental investigations are still underway to
understand the nuclear structure of high spin states of
both $^{16}$O and
$^{20}$Ne nuclei for instance at Notre Dame
and/or
iThemba Labs \cite{Papka14} facilities.
Another possibility might be to perform Coulomb
excitation measurements with intense $^{16}$O and
$^{20}$Ne beams at intermediate energies.
The nucleus viewed as a collection of $\alpha$-particles
has been discussed all over the mass table since a long
time and it was only recently shown that clear
deviations from statistical models in the decay of excited
 $^{24}$Mg exist  \cite{Borderie16,Baiocco13,Morelli14a,Morelli14b}.
As far as the theory is concerned, a diversity of cluster/symmetry
models (cluster models, {\it ab initio} calculations, BEC etc ...)
which make concrete predictions in terms of alpha clustering
in light nuclei is available on the market. What is presently
missing is a clearly defined procedure for relating these abstract predictions
to the observed level schemes and clear criteria for what constitutes
discriminating evidence for a particuliar model. A more detailed
discussion of BEC will be proposed in one of the forthcoming section (Section 5).

The search for exotic chain-like structures in light $\alpha$-conjugate
nuclei remains an exciting prospect. Experiments reporting tentative
evidence of $\alpha$-chains in $^{12}$C \cite{Morinaga}. $^{16}$O
\cite{Chevallier67,Curtis13,Papka14}, $^{20}$Ne \cite{Papka14} and
$^{24}$Mg \cite{Wuosmaa} have been largely unsubstantiated, and the view
is that such structure have not yet been definitively observed experimentally.

\section{Alpha clustering, nuclear molecules and large deformations}
\label{sec:3}

The real link between superdeformation/hyperdemormation (SD/HD), nuclear molecules
and alpha clustering \cite{Horiuchi10,Beck04a,Cseh09} is of particular interest,
since nuclear shapes with major-to-minor axis ratios of 2:1 have the typical
ellipsoidal elongation for light nuclei i.e. with quadrupole deformation
parameter $\beta_2$ $\approx$ 0.6. Furthermore, the structure of possible
octupole-unstable 3:1 nuclear shapes - hyperdeformation with $\beta_2$
$\approx$ 1.0 - has also been discussed for actinide
nuclei \cite{Cseh09} in
terms of clustering phenomena. Typical examples for possible relationship
between quasimolecular bands and extremely deformed (SD/HD) shapes have been
widely discussed in the literature for $A = 20-60$ $\alpha$-conjugate
$N$=$Z$ nuclei, such as $^{28}$Si
\cite{Taniguchi09,Ichikawa11,Jenkins12,Jenkins16,Jenkins14,Darai12},
$^{32}$S \cite{Horiuchi10,Ichikawa11,Kimura04,Lonnroth10,Chandana10},
$^{36}$Ar \cite{Cseh09,Beck08a,Svensson00,Sciani09,Beck09,Beck11,Beck13},
$^{40}$Ca \cite{Ideguchi01,Rousseau02,Taniguchi07,Norrby10,Benjamim13},
$^{44}$Ti  \cite{Horiuchi10,Leary00,Fukada09},
$^{48}$Cr \cite{Salsac08,Vardaci16} and $^{56}$Ni
\cite{Nouicer99,Rudolph99,Beck01,Bhattacharya02}.

\begin{figure}[th]
\centerline{\psfig{figure=IJMPE_Fig3.eps,width=11.9cm,height=8.0cm}}
\vspace*{8pt}
\caption{\label{fig3}Rotational bands and deformed shapes in $^{36}$Ar.
Excitation energies
	of the ground state (spherical shape) and SD (ellipsoidal shape)
	bands~\cite{Svensson00}, respectively, and the energies of HD (dinuclear
	shape) band from
	the quasimolecular resonances observed in the $^{12}$C+$^{24}$Mg
	(open rectangles) \cite{Sciani09,Cindro79,Mermaz84,Pocanic85} and
	$^{16}$O+$^{20}$Ne (full rectangles)
	\cite{Shimizu82,Gai84} reactions
	are plotted as a function of J(J+1). This figure
	has been adapted from
	Refs.~\cite{Beck08a,Sciani09,Beck13}.}
\end{figure}

Excitation functions have been measured over a wide range
energies for many reactions. Norrby discussed a study of $^{32}$S
via the $^{28}$Si+$\alpha$ reaction \cite{Lonnroth10} that
revealed 30 new level assignements spanning 132 resonances
in total.

In fact, highly deformed shapes and SD rotational bands have been
discovered in several light $\alpha$-conjugate nuclei, such as $^{36}$Ar
and $^{40}$Ca by using $\gamma$-ray spectroscopy techniques
\cite{Beck08a,Svensson00,Ideguchi01}. In particular, the extremely deformed rotational
bands in $^{36}$Ar (shown as crosses in Fig.~3) might be
comparable in shape to the quasimolecular bands observed in both $^{12}$C+$^{24}$Mg
(shown as open triangles)
and $^{16}$O+$^{20}$Ne (shown as full rectangles) reactions.
These resonances belong to a rotational band, with a moment of inertia close to
that of a HD band provided by both the cranked $\alpha$-cluster model \cite{Freer07}
and the Nilsson-Strutinsky calculations. The fact that similar
quasi-molecular states observed in the two reactions fall on the same rotational
band gives further support to our interpretation of the $^{36}$Ar composite system
resonances. An identical conclusion was reached for the $^{40}$Ca composite system
where SD bands have been discovered \cite{Beck08a}. Therefore, similar
investigations are underway for heavier $\alpha$-like composite systems such as
$^{44}$Ti
\cite{Horiuchi10}, $^{48}$Cr \cite{Salsac08} and $^{56}$Ni
\cite{Nouicer99,Bhattacharya02}.

Ternary clusterizations in light $\alpha$-like composite systems are also
predicted theoretically, but were not found experimentally in $^{36}$Ar so far
\cite{Beck08a}. On the other hand, ternary fission of $^{56}$Ni -- related to
its HD shapes -- was identified from out-of-plane angular correlations
measured in the $^{32}$S+$^{24}$Mg reaction with the Binary Reaction
Spectrometer (BRS) at the {\sc Vivitron} Tandem facility of the IPHC, Strasbourg
\cite{Oertzen08}. This finding \cite{Oertzen08} is not limited to light
$N$=$Z$ compound nuclei, true ternary fission \cite{Zagrebaev10,Kamanin14,Pyatkov10}
can also occur for very heavy \cite{Kamanin14,Pyatkov10} and superheavy
\cite{Zagrebaev10b} nuclei.

\section{Electromagnetic transitions as a probe of quasimolecular states
and clustering in light nuclei}

Clustering in light nuclei is traditionally explored through reaction studies,
but observation of electromagnetic transitions can be of high value in
establishing, for example, that highly-excited states with candidate cluster
structure do indeed form rotational sequences.

\subsection{$^{16}$O nucleus}

There is a renewed interest in the spectroscopy of the $^{16}$O nucleus at high
excitation energy \cite{Beck08a,Beck09}. Exclusive data were collected on $^{16}$O
in the inverse kinematics reaction $^{24}$Mg$+^{12}$C studied at E$_{lab}$($^{24}$Mg)
= 130 MeV with the BRS in coincidence with the {\sc Euroball IV} installed at
the {\sc Vivitron} facility \cite{Beck08a,Beck09}. From the $\alpha$-transfer reactions
(both direct transfer and deep-inelastic orbiting collisions \cite{Sanders99}), new
information has been deduced on branching ratios of the decay of the 3$^{+}$ state
of $^{16}$O at 11.085~MeV $\pm$ 3 keV. The high-energy level scheme of $^{16}$O shown
in Ref.~\cite{Beck08a,Beck09} indicated that this state does not $\alpha$-decay
because of its non-natural parity  (in contrast to the two neighbouring 4$^{+}$ states
at 10.36~MeV and 11.10~MeV), but it $\gamma$ decays to the 2$^{+}$ state at 6.92~MeV
(54.6 $\pm$ 2 $\%$) and to the 3$^-$ state at 6.13~MeV (45.4\%).
By considering all the four possible transition types of the decay of the 3$^{+}$
state (\textit{i.e.} E$1$ and M$2$ for the 3$^{+}$ $\rightarrow$ 3$^{-}$ transition and,
M$1$ and E$2$ for the 3$^{+}$ $\rightarrow$ 2$^{+}$ transition), our
calculations yield the conclusion that $\Gamma_{3^+}<0.23$~eV, a value
fifty times lower than known previously, which is an important result for
the well studied $^{16}$O nucleus \cite{Beck08a,Beck09}.
Clustering effects in the light neutron-rich
oxygen isotopes $^{17,18,19,20}$O will also be discussed in Section 5.

Alpha clustering plays an important role in the description of the ground
state and excited states of light nuclei in the $p$ shell. For heavier nuclei,
in the $sd$-shell, cluster configurations may be based on heavier substructures
like $^{12}$C, $^{14}$C and $^{16}$O as shown by the ''Extended Ikeda-diagram"
proposed in Fig.~2. This was already well discussed to appear in
$^{24}$Mg($^{12}$C-$^{12}$C) and $^{28}$Si($^{12}$C-$^{16}$O) both theoretically
and experimentally.

\subsection{$^{28}$Si nucleus}

\begin{figure}[th]
\centerline{\psfig{figure=IJMPE_Fig4.eps,width=10.3cm,height=11.9cm}}
\caption{\label{fig4} Subset of positive-parity levels in $^{28}$Si derived
from the analysis of a Gammasphere experiment. Excited states and transitions
energies are labeled with their energy in keV, while the width of the arrows
corresponds to the relatve intensity of the observed transitions. The
different structures are labeled according to previous assignements as oblate,
prolate (ND), vibrational and with different K values. This
figure has been adapted from Ref.~\cite{Jenkins12} courtesy from D.G. Jenkins.}
\end{figure}

The case of the mid-$sd$-shell nucleus $^{28}$Si is of
particular interest as it shows the coexistence of deformed and cluster states
at rather low energies \cite{Jenkins12,Jenkins16}. Its ground state is oblate, with a
partial $\alpha$-$^{24}$Mg structure, two prolate normal deformed bands are found, one
built on the ${0}^{+}_{2}$ state at 4.98 MeV and on the ${0}^{+}_{3}$ state
at 6.69 MeV. The SD band candidate with a pronounced $\alpha$-$^{24}$Mg structure
is suggested \cite{Jenkins12}. In this band, the 2$^+$ (9.8 MeV), 4$^+$ and 6$^+$
members are well identified as can be clearly observed in Fig.~4.

In the following we will briefly discuss a resonant cluster band which is
predicted to start close to the Coulomb barrier of the $^{12}$C+$^{16}$O collision,
i.e. around 25 MeV excitation energy in $^{28}$Si. We have
studied the $^{12}$C($^{16}$O,$\gamma$)$^{28}$Si radiative capture reaction at
five resonant energies around the Coulomb barrier by using the zero degree
DRAGON spectrometer installed at Triumf, Vancouver \cite{Lebhertz12,Goasduff14}.
Details about the setup, that has been optimized for the
$^{12}$C($^{12}$C,$\gamma$)$^{24}$Mg radiative capture reaction in our of previous
DRAGON experiments, can be found in Ref.~\cite{Jenkins07}.
The $^{12}$C($^{16}$O,$\gamma$)$^{28}$Si data clearly show \cite{Lebhertz12,Goasduff14}
the direct feeding of the prolate 4$^{+}_{3}$ state at 9.16 MeV and the octupole
deformed 3$^-$ at 6.88 MeV.
This state is the band head of an octupole band which mainly decays to the
$^{28}$Si oblate ground state with a strong E$_3$ transition. Our results are
very similar to what has been measured for the $^{12}$C+$^{12}$C radiative capture
reaction above the Coulomb barrier in the first DRAGON experiment
\cite{Jenkins07} where the enhanced feeding of the $^{24}$Mg prolate band has
been measured for a 4$^+$-2$^+$ resonance at E$_{c.m.}$ = 8.0 MeV near the
Coulomb barrier.

At the lowest energy of $^{12}$C+$^{16}$O radiative capture reaction, an enhanced
feeding from the resonance J$^{\pi}$ = 2$^+$ and 1$^+$ T=1 states around 11 MeV
is observed in $^{28}$Si. Again this is consistent with $^{12}$C+$^{12}$O radiative capture
reaction data where J$^{\pi}$ = 2$^+$ has been assigned to the entrance resonance
and an enhanced decay has been measured via intermediate 1$^+$ T=1 states around
11 MeV in $^{24}$Mg. A definitive scenario for the decay of the resonances at these
low bombarding energies in both systems will come from the measurement of the
$\gamma$ decay spectra with a $\gamma$-spectrometer with better resolution than BGO
but still rather good efficiency such as LaBr$_3$ (lanthanum) crystals (see also
the forthcoming Subsection).

\subsection{$^{12}$C+$^{12}$C resonances}

\begin{figure}[th]
\centerline{\psfig{figure=IJMPE_Fig5.eps,width=10.9cm,height=11.9cm}}
\caption{\label{fig5} Reaction Q-value of the
$^{12}$C($^{12}$C,$^{12}$C)$^{12}$C) reaction at E$_{lab}$
= 32.9 MeV versus $\gamma$-ray energies. The spectrum has
been obtained with fragment-fragment-$\gamma$ coincidence
condition and a $\gamma$ multiplicity M = 1 as explained in
the text (see also Ref.~\cite{Elanique} for more details).
This figure has been adapted from Ref. ~\cite{Elanique}.}
\end{figure}

A further area where electromagnetic transitions would be of great interest in
support of cluster models is in the case of the quasi-molecular resonances
observed in the $^{12}$C+$^{12}$C reaction \cite{Greiner95}. The width of these
resonances were $\approx$ 100 keV, indicating the formation of a $^{24}$Mg
intermediate system with a lifetime significantly longer than the nuclear
crossing time. These resonances were subsequently interpreted as $^{12}$C+$^{12}$C
cluster states.

There has been only one valient attempt to directly observe transitions in this
reaction by Haas et al. \cite{Elanique} focussing on transitions between
10$^{+}$ and 8$^{+}$ resonant states at a bombarding energy E($^{12}$C) = 32 MeV
chosen to populate a known and isolated 10$^+$ resonance. Position Sensitive
Detectors (PSD) were mounted on either side of the beam axis at the center of
the Chateau de Cristal array of 74 barium fluoride detectors. Triple
$\gamma$-$^{12}$C-$^{12}$C coincidences were recorded and it was possible to
observe a few events in the expected energy window corresponding to the
10$^+$ $\rightarrow$ 8$^+$ transitions as shown by Fig. 5. However, the data
were not sufficiently clean to rule out these events as due to the experimental
background. The measurement reported only an upper limit (for the radiative
partial width of 1.2 $\pm$ 10$^{-5}$) given the extreme challenges of
eliminating all background displayed in Fig. 5.

It will be very interesting to revisit this earlier experiment taking advantage
of new experimental techniques and developments in detector technology for the
detection of gamma rays and/or fragments. For example, novel scintillator materials
like lanthanum bromide offer superior resolution for the gamma ray of interest
while improved silicon detector performance and solid angle coverage could lead
to significant improvements both in sensitivity and in statistics.

\begin{figure}[th]
\centerline{\psfig{figure=IJMPE_Fig6.eps,width=8.3cm,height=8.3cm}}
\caption{\label{fig6} Schematic illustration of the
clustering arrangement of five alpha particles in the
nucleus $^{20}$Ne.}
\end{figure}

\section {Condensation of $\alpha$ clusters in light nuclei}

In principle the nucleus is a quasi-homogeneus collection of protons and
neutrons, which adopts a spherical configuration i.e. a spherical droplet
of nuclear matter. For light nuclei the nucleons are capable to arrange
themselves into clusters of a bosonic character. The very stable
$\alpha$-particle is the most favorable light nucleus for quarteting -
$\alpha$ clustering - to occur in dense nuclear matter. These cluster
structures have indeed a crucial role in the synthesis of elements in stars.
The so called ''Hoyle" state~\cite{Hoyle54,Freer14}, the main
portal through which $^{12}$C is created in nucleosynthesis with a
pronounced three-$\alpha$-cluster structure, is the best exemple of
$\alpha$ clustering in light nuclei.
In $\alpha$ clustering a geometric picture can be proposed in the framework
of point group symmetries \cite{Broniowski14}. For instance, in $^{8}$Be the
two $\alpha$ clusters are separated by as much as $\approx$ 2fm, $^{12}$C
exhibits a triangle arrangement of the three $\alpha$ particles $\approx$ 3fm
apart, $^{16}$O forms a tetrahedron, etc. Evidence for tetrahedral symmetries in
$^{16}O$ was given by the algebraic cluster model \cite{Iachello14}.
Such kind of symmetries are rather well illustrated by the
schematic picture of the $^{20}$Ne nucleus proposed in
Fig.~6. More realistic is the
density plot for $^{20}$Ne nucleus calculated as an arrangement of
two $\alpha$ particles with a  $^{12}$C core which is displayed in
Fig.~7 to illustrate the enhancement of the symmetries of the $\alpha$
clustering.

In the study of the Bose-Einstein Condensation (BEC) the
$\alpha$-particle states were first described for $^{12}$C and $^{16}$O
\cite{Tohsaki01,Suhara14} and later on generalized to heavier light $N$=$Z$ nuclei
\cite{Oertzen10a,Yamada12,Ebran12,Girod13}. The structure of the ``Hoyle"
state and the properties of its assumed rotational band have been studied
very carefully from measurements of the $^{12}$C($\gamma$,3$\alpha$) reaction
performed at the HIGS facility, TUNL~\cite{Zimmerman13}.
At present, the search for an experimental signature of BEC in $^{16}$O is
of highest priority. A state with the structure of the ''Hoyle" state
in $^{12}$C coupled to an $\alpha$ particle is predicted
in $^{16}$O at about 15.1 MeV (the 0$^{+}_{6}$ state), the energy of which
is $\approx$ 700 keV above the 4$\alpha$-particle breakup threshold
\cite{Funaki08,Dufour13,Kanada14}: in other words, this 0$^{+}_{6}$ state
might be a good candidate for the dilute 4$\alpha$ gas state.
However, any state in $^{16}$O equivalent to the ''Hoyle"
state in $^{12}$C is most certainly going to decay by particle emission with
very small, probably un-measurable, $\gamma$-decay branches, thus, very
efficient particle-detection techniques will have to be used in the near
future to search for them.

\begin{figure}[th]
\centerline{\psfig{figure=IJMPE_Fig7.eps,width=11.7cm,height=8.3cm}}
\vspace*{8pt}
\caption{\label{Fig7} Self-consistent ground-state densities of the nucleus $^{20}$Ne
as calculated with EDF (see text for details). Densities (in units of fm$^{-3}$) are
plotted in the intrinsic frame of reference that coincides with the principal axes of
the nucleus. This figure has been adapted from Ref.~\cite{Ebran12} courtesy from
E. Kahn and J.-P. Ebran.}
\end{figure}

BEC states are expected to decay by $\alpha$ emission to the ''Hoyle" state
and could be found among the resonances in $\alpha$-particle inelastic
scattering on $^{12}$C decaying to that state or could be observed in an
$\alpha$-particle transfer channel leading to the $^{8}$Be--$^{8}$Be final
state. The attempts to excite these states by $\alpha$ inelastic
scattering~\cite{Itoh04} was confirmed recently~\cite{Freer12}.
Another possibility, that has not been yet explored, might be to perform
Coulomb excitation measurements with intense $^{16}$O beams at intermediate
energies.

Clustering of $^{20}$Ne has also been described within the energy density functional
theory~\cite{Ebran12} (EDF) as illustrated by Fig.~7 that displays axially and
reflection symmetric self-consistent equilibrium nucleon density distributions.
We note the well known quasimolecular $\alpha$-$^{12}$C-$\alpha$ structure
although clustering effects are less pronounced than the ones (schematically
displayed in Fig.~5) predicted by
Nilsson-Strutinsky calculations and
even by mean-field calculations (including Hartree-Fock and/or
Hartree-Fock-Bogoliubov calculations) \cite{Freer07,Horiuchi10,Gupta10,Girod13}.

The most recent work of Girod and Schuck \cite{Girod13} validates several
possible scenarios for the influence of clustering effects as a function of
the neutron richness that will trigger more experimental works. We describe
in the following (i.e. in Section 6) recent experimental investigations on the Oxygen
isotopes chain.

\section{Clustering in light neutron-rich nuclei}
\label{sec:2}

As discussed previously, clustering is a general phenomenon observed also in
nuclei with extra neutrons as it is presented in an ''Extended Ikeda-diagram"
\cite{Ikeda} proposed by von Oertzen \cite{Oertzen01} (see the left panel of
Fig.~2). With additional neutrons, specific molecular structures
appear with binding effects based on covalent molecular neutron orbitals. In
these diagrams $\alpha$-clusters and $^{16}$O-clusters (as shown by the middle
panel of the diagram of Fig.~2) are the main ingredients. Actually, the $^{14}$C
nucleus may play similar role in clusterization as the $^{16}$O one since it has similar
properties as a cluster: i) it has closed neutron p-shells,
ii) first excited states are well above E$^{*}$ = 6 MeV, and
iii) it has high binding energies for $\alpha$-particles.

The possibility of extending molecular structures from dimers (berylium
isotopes) \cite{Oertzen96} to trimers \cite{Oertzen97} has been
investigated in detail for carbon isotopes
\cite{Milin02,Bohlen03,Oertzen04}.
Here the neutrons would be exchanged between the three centers
(alpha particles). It is possible that the three $\alpha$-particle
configuration can align themselves in a linar fashion, or alternative
collapse into a triangle arragment - in either case the neutrons being
localised across the three centers. At present experimental evidence
for such structures have been found in $^{13}$C
\cite{Milin02} and $^{14}$C \cite{Oertzen04}. Possibly
the best case for the linear arrangement - from a theoretical
perspective \cite{Itagaki01,Maruhn10} - is $^{16}$C \cite{Bohlen03}.

A general picture of clustering and molecular configurations in light nuclei
can also be drawn from a detailed investigation of the light oxygen isotopes with
A $\geq$ 17. Here we will only present recent results on the even-even
oxygen isotopes: $^{18}$O \cite{Oertzen10b} and $^{20}$O \cite{Oertzen09}.
But very striking cluster states have also been found in odd-even oxygen
isotopes such as: $^{17}$O \cite{Milin09} and $^{19}$O \cite{Oertzen11}.

Figs. 8 and 9 give an overview of all bands in $^{18}$O
and  $^{20}$O, respectively, as plots of excitation energies
as a function of J(J+1) together with their respective moments of inertia. In the
assignment of the bands both the dependence of excitation energies on J(J+1)
and the dependence of measured cross sections on 2J+1 \cite{Oertzen09}
were considered. Slope parameters obtained in
a linear fit to the excitation energies \cite{Oertzen09} indicate the moment
of inertia of the rotational bands given in the respective
figures. The intrinsic structure
of the cluster bands is reflection asymmetric, the parity projection gives an
energy splitting between the partner bands.
The assignments of the experimental molecular bands of $^{18}$O are
supported by both the
Generator-Coordinate-Method \cite{Descouvemont} and the Antisymmetrized Molecular
Dynamics (AMD) calculations \cite{Furutachi08}.

\begin{figure}[th]
\centerline{\psfig{figure=IJMPE_Fig8.eps,width=8.3cm,height=8.3cm}}
\vspace*{8pt}
\caption{\label{fig8}Overview of six rotational band structures observed in
	$^{18}$O. Excitation energy systematics for the members of the rotational
	bands forming inversion doublets with K=0 are plotted as a function
	of J(J+1). The curves are drawn to guide the eye for the slopes. The
	indicated slope parameters contain information on
	the moments of inertia. Square symbols correspond to cluster bands,
	whereas diamonds symbols correspond to molecular
	bands. This figure has been adapted from Ref.
	\cite{Oertzen10b} courtesy from W. von Oertzen.}
\end{figure}

\begin{figure}[th]
\centerline{\psfig{figure=IJMPE_Fig9.eps,width=8.3cm,height=8.3cm}}
\vspace*{8pt}
\caption{\label{fig9}Overview of four rotational band structures observed in
        $^{20}$O. Excitation energy systematics for the members of the rotational
	bands forming inversion doublets with K=0 are plotted as a function
	of J(J+1). The curves are drawn to guide the eye for the slopes. The
	indicated slope parameters contain information on
	the moments of inertia. Square and triangle symbols correspond to cluster bands,
	whereas diamonds symbols correspond to molecular
	bands. This figure has been adapted from Ref.
	\cite{Oertzen09} courtesy from W. von Oertzen.}
\end{figure}

We can compare the bands of $^{20}$O \cite{Oertzen09}
shown in  Fig.~9 with the ones of $^{18}$O in  Fig.~8.  The
first doublet (K=0$^{\pm}_{2}$) has a slightly larger moment of
inertia (smaller slope parameter) in $^{20}$O, which is consistent
with its interpretation as $^{14}$C--$^{6}$He or $^{16}$C--$^{4}$He
molecular structures (they start well below the thresholds of 16.8 MeV and
12.32 MeV, respectively). The second band, for which the negative parity
partner is yet to be determined, has a slope parameter slightly smaller
than in $^{18}$O. This is consistent with the study of the bands in
$^{20}$O by Furutachi et al. \cite{Furutachi08}, which clearly establishes
parity inversion doublets predicted by AMD calculations for the
$^{14}$C--$^6$He cluster and $^{14}$C-2n-$\alpha$ molecular structures.
The corresponding moments of inertia given in Fig.~5 are
strongly suggesting large deformations for the cluster structures. We may
conclude that the  reduction of the moments of inertia of the lowest
bands of $^{20}$O is consistent with the assumption that the strongly bound $^{14}$C
nucleus having equivalent properties to $^{16}$O, has a similar role
as $^{16}$O in relevant, less neutron rich nuclei. Therefore, the Ikeda-diagram
\cite{Ikeda} and the "extended Ikeda-diagram" consisting of $^{16}$O cluster
cores with covalently bound neutrons \cite{Oertzen01} must be further extended to
include also the $^{14}$C cluster cores as illustrated in Fig.~2.

\section{Summary, conclusions and outlook}

The link of alpha clustering, quasimolecular resonances, orbiting
phenomena and extreme deformations (SD, HD, ...) has been discussed in this
review article. Several examples emphasize the general
connexion between molecular structure and deformation
effects within the shell model, or rather the Nilsson
model. However, we have also presented the BEC picture of light
(and medium-light) $\alpha$-like nuclei that
appears to be an alternate way of understanding most of properties of nuclear clusters.
New results regarding cluster
and molecular states in neutron-rich oxygen isotopes in agreement with AMD
predictions are finally summarized. Consequently, the ''Extended Ikeda-diagram"
has been further modified for light neutron-rich nuclei by inclusion of the $^{14}$C
cluster, similarly to the $^{16}$O one. Of particular interest is the
quest for the  4$\alpha$ states of $^{16}$O near the $^{8}$Be+$^{8}$Be and
$^{12}$C+$\alpha$ decay thresholds, which correspond to the so-called ''Hoyle"
state. The search for extremely elongated configurations (HD) in rapidly rotating
medium-mass nuclei, which has been pursued by $\gamma$-ray spectroscopy measurements,
will have to be performed in conjunction with charged-particle techniques in the
near future since such states are most certainly  going to decay by particle emission
(see \cite{Papka12,Oertzen08}).
Marked progress has been made in many traditional and novels subjects of nuclear
cluster physics. The developments in these subjects show the importance of
clustering among the basic modes of motion of nuclear many-body systems.
All these open questions will require precise coincidence measurements
\cite{Papka12} coupled with state-of-the-art theory.

\section{Dedication and acknowledments}

This review article is dedicated to the memory of my friends Alex Szanto de Toledo
and Valery Zagrebaev who unexpectelly passed away in early 2015. I am very pleased
to first acknowledge Walter Greiner (who celebrated his 80th birthday on October
29th, 2015) for his continuous support of the cluster physics
\cite{Greiner95,Strasbourg,Zagrebaev10,Poenaru10,Greiner08}.
I would like also to
thank Christian Caron (Springer)
for initiating in 2008 the series of the three volumes of \emph{Lecture Notes
in Physics} entitled "Clusters in Nuclei" and edited between 2010 and 2014
\cite{Cluster1,Cluster2,Cluster3}.
All the authors of the 19 chapters of these volumes are warmly thanked for their
fruitfull collaboration during the course of the project which is still in
progress.

\newpage

\begin{center}

redpajama_set_name: RedPajamaArXiv


Nicky Brett won the International Bowls Open to become world number one.
Yaxley's Nicky Brett claimed his third world ranking title with a masterful display in the International Bowls Open in Blackpool today (March 6).
The win means Brett, who works as a plumber in Yaxley, is now ranked world number one.
Third seed Brett beat six-time world champion Alex Marshall MBE 12-4, 9-8 in the final to win this particular title for the first time. He had to survive a tense final bowl from Marshall who missed a golden opportunity to take the three shots he needed to take the final into a tie-break set.
Brett had kept his nerve to claim two shots on the penultimate end of the second set to go 9-7 ahead.
Brett was described as the 'Ginger Ninja' at the presentation ceremony. He performed a cartwheel to celebrate a terrific win and his new position as the world's best player.
"I'm quite pleased to say the least," Brett said. "I've now found a way to win when I've not been playing sensational bowls when in the past I've found a way to lose when playing well.
Brett started the tournament as world number three and looked on course for an easy win against Dawes when taking the first set 10-1 and then strolling into a 5-1 lead in the second set, but Dawes scored eight shots without reply to take the match into a tie break.
Dawes took the first end, but Brett hit back with successive singles to sneak through.
Brett beat Damien Doubler (9-7, 10-5) and his regular doubles partner and City of Ely clubmate Greg Harlow (9-5, 6-6) on his way to the title.