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The ternary cluster decay of heavy nuclei has been observed in several experiments with binary coincidences between two fragments using detector telescopes (the FOBOS-detectors, JINR, Dubna) placed on the opposite sides from the source of fissioning nuclei. The binary coincidences at a relative angle of 180$^0$ deg. correspond to binary fission or to the decay into three cluster fragments by registration of two nuclei with different masses (e.g.$^{132}$Sn,$^{52-48}$Ca,$^{68-72}$Ni). This marks a new step in the physics of fission-phenomena of heavy nuclei. These experimental results for the collinear cluster tripartition (CCT), refer to the decay into three clusters of comparable masses. In the present work we discuss the various aspects of this ternary fission (FFF) mode. The question of collinearity is analysed on the basis of recent publications. Further insight into the possible decay modes is obtained by the discussion of the path towards larger deformation, towards hyper-deformation and by inspecting details of the potential energy surfaces (PES). In the path towards the extremely deformed states leading to ternary fission, the concept of deformed shells is most important. At the scission configuration the phase space determined by the PES's leads to the final mass distributions. The possibility of formation of fragments of almost equal size ($Z_i$ = 32, 34, 32, for $Z$=98) and the observation of several other fission modes in the same system can be predicted by the PES. The PES's show pronounced minima and valleys, namely for several mass/charge combinations of ternary fragments, which correspond to a variety of collinear ternary fission (multi-modal) decays. The case of the decay of $^{252}$Cf(sf,fff) turns out to be unique due to the presence of deformed shells in the total system and of closed shells in all three nuclei in the decay., Comment: 22 pages, 38 figures

We consider the collinear ternary fission which is a sequential ternary decay with a very short time between the ruptures of two necks connecting the middle cluster of the ternary nuclear system and outer fragments. In particular, we consider the case where the Coulomb field of the first massive fragment separated during the first step of the fission produces a lower pre-scission barrier in the second step of the residual part of the ternary system. In this case, we obtain a probability of about $10^{-3}$ for the yield of massive clusters such as \nuclide[70]{Ni}, \nuclide[80-82]{Ge}, \nuclide[86]{Se}, and \nuclide[94]{Kr} in the ternary fission of \nuclide[252]{Cf}. These products appear together with the clusters having mass numbers of $A = 132$--$140$. The results show that the yield of a heavy cluster such as \nuclide[68-70]{Ni} would be followed by a product of $A = 138$--$148$ with a large probability as observed in the experimental data obtained with the FOBOS spectrometer at the Joint Institute for Nuclear Research. The third product is not observed. The landscape of the potential energy surface shows that the configuration of the Ni + Ca + Sn decay channel is lower about 12 MeV than that of the Ca + Ni + Sn channel. This leads to the fact, that the yield of Ni and Sn is large. The analysis on the dependence of the velocity of the middle fragment on mass numbers of the outer products leads to the conclusion that, in the collinear tripartition channel of \nuclide[252]{Cf}, the middle cluster has a very small velocity, which does not allow it to be found in experiments., Comment: 11 pages, 9 figures

A possibility of formation of the three reaction products having comparable masses at the spontaneous fission of $^{252}$Cf is theoretically explored. This work is aimed to study the mechanism leading to observation of the reaction products with masses $M_1=$136---140 and $M_2=$68---72 in coincidence by the FOBOS group in JINR. The same type of ternary fission decay has been observed in the reaction $^{235}$U(n$_{\rm th}$,fff). The potential energy surface for the ternary system forming a collinear nuclear chain is calculated for the wide range of mass and charge numbers of constituent nuclei. The results of the PES for the tripartition of $^{252}$Cf(sf,fff) shows, that we have favorable dynamical conditions for the formation of fragments with mass combinations of clusters $^{68-70}$Ni with $^{130-132}$Sn and with missing cluster $^{48-52}$Ca., Comment: 13 pages, 9 figures, Contribution of the International conference on "75 Years of Nuclear Fission: Present Status and future perspectives", May 8-10, 2014, Bhabha Atomic Research Centre, Mumbai, INDIA. Accepted to the Journal of Physics Pramana of Indian Academy of Science

The existence of a new type of cluster decay called "collinear cluster tri-partition" (CCT) is discussed by an analysis of the landscape of the potential energy surface (PES). The total energy of the ternary system is found as a sum the binding energies of fragments and nucleus-nucleus interaction between them. The pre-scission state of the ternary system is assumed to be arranged as a chain of the three fragments along a straight line. Minima and valleys of the PES are determined by variation of the proton and neutron distributions between them. Pre-scission prompt emission of neutrons is assumed and PES is calculated for the cases of emission of 2---4 neutrons. The presence of the valley corresponding to the formation of the isotopes of Sn with masses $A$=130---136 is inherent for all PES calculated for CCT for spontaneous fission of $^{252}$Cf and fission induced by neutrons of $^{235}$U. There are local minima indicating the formation of Ca, Fe, Ni, Ge and Se isotopes having magic proton or/and neutron numbers, such as 20, 28, and 50. The analysis shows that the experimentally observed $^{68}$Ni is formed as the edge fragment of the ternary system connecting to Sn by Si and Ca isotopes at fission of $^{236}$U and $^{252}$Cf, respectively., Comment: 13 pages, 6 figures

We investigate the existence of weakly coupled gas-like states comprised of three $\alpha$ particles around an $^{16}$O core in $^{28}$Si. We calculate the excited states in $^{28}$Si using the multi-configuration mixing method based on the $^{16}$O + 3$\alpha$ cluster model. We also include the $^{16}$O + $^{12}$C and $^{24}$Mg + $\alpha$ basis wave functions prepared by the generator coordinate method. To identify the gas-like states, we calculate the isoscalar monopole transition strengths and the overlap of the obtained states with the geometrical cluster wave function and the Tohsaki-Horiuchi-Schuck-R\"{o}pke (THSR) wave function. The results show that the obtained fourth and twelfth states significantly overlap with the THSR wave function. These two states clearly coexist with the $^{16}$O + $^{12}$C cluster states, emerging at similar energies. The calculated isoscalar monopole strengths between those two states are significantly large, indicating that the states are members of the excitation mode. Furthermore, the calculated root-mean-squared (RMS) radii for these states also suggest that a layer of gas-like three $\alpha$ particles could exist around the surface of the $^{16}$O core, which can be described as a "two-dimensional gas" in the intermediate state before the Hoyle-like three $\alpha$ states emerge., Comment: 5 pages, 3 figures

We have studied gas-like states of $\alpha$ clusters around an $^{16}$O core in $^{24}$Mg based on a microscopic $\alpha$-cluster model. This study was performed by introducing a Monte Carlo technique for the description of the THSR (Tohsaki Horiuchi Schuck R\"{o}pke) wave function, and the coupling effect to other low-lying cluster states was taken into account. A large isoscalar monopole ($E0$) transition strength from the ground to the gas-like state is discussed. The gas-like state of two $\alpha$ clusters in $^{24}$Mg around the $^{16}$O core appears slightly below the 2$\alpha$-threshold e, Comment: submitted to Phys. Rev. C

A great deal of research work has been undertaken in the alpha-clustering study since the pioneering discovery, half a century ago, of 12C+12C molecular resonances. Our knowledge of the field of the 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. In this work, the occurence of "exotic" shapes in light N=Z alpha-like nuclei is investigated. Various approaches of superdeformed and hyperdeformed bands associated with quasimolecular resonant structures are presented. Results on clustering aspects are also discussed for light neutron-rich Oxygen isotopes., Comment: 12 pages, 5 figures. Invited Talk presented by C. Beck at the Zakopane Conference on Nuclear Physics "Extremes of the Nuclear Landscape" XLV in the series of Zakopane Schools of Physics - International Symposium - Zakopane, Poland, August 30 - September 5, 2010.To be publihed in Acta Physica Polonica B42 no 3, March 2011

Certain aspects of the recently proposed antisymmetrised alpha particle product state wave function, or THSR alpha cluster wave function, for the description of the ground state in 8Be, the Hoyle state in 12C, and analogous states in heavier nuclei, are elaborated in detail. For instance, the influence of antisymmetrisation in the Hoyle state on the bosonic character of the alpha particles is studied carefully. It is shown to be weak, so that bosonic aspects are predominant. The de Broglie wave length of alpha particles in the Hoyle state is shown to be much larger than the inter-alpha distance. It is pointed out that the bosonic features of low density alpha gas states have measurable consequences, one of which, that is enhanced multi-alpha decay properties, likely already have been detected. Consistent with experiment, the width of the proposed analogue to the Hoyle state in 16O at the excitation energy of E_x=15.1 MeV is estimated to be very small (34 keV), lending credit to the existence of heavier Hoyle-like states. The intrinsic single boson density matrix of a self-bound Bose system can, under physically desirable boundary conditions, be defined unambiguously. One eigenvalue then separates out, being close to the number of alpha's in the system. Differences between Brink and THSR alpha cluster wave functions are worked out. No cluster model of the Brink type can describe the Hoyle state with a single configuration. On the contrary, many superpositions of the Brink type are necessary, implying delocalisation towards an alpha product state. It is shown that single alpha particle orbits in condensates of different nuclei are almost the same. It is thus argued that alpha particle antisymmetrised product states of the THSR type are a very promising novel and useful concept in nuclear physics., Comment: 16 pages, 14 figures, to appear in PRC

Charged particle and gamma decays in 24Mg* are investigated for excitation energies where quasimolecular resonances appear in 12C+12C collisions. Various theoretical predictions for the occurence of superdeformed and hyperdeformed bands associated with resonance structures with low spin are discussed within the measured 24Mg* excitation energy region. The inverse kinematics reaction 24Mg+12C is studied at E_lab(24Mg) = 130 MeV, an energy which enables the population of 24Mg states decaying into 12C+12C resonant break-up states. Exclusive data were collected with the Binary Reaction Spectrometer in coincidence with EUROBALL IV installed at the VIVITRON Tandem facility at Strasbourg. Specific structures with large deformation were selectively populated in binary reactions and their associated gamma decays studied. Coincident events associated with inelastic and alpha-transfer channels have been selected by choosing the excitation energy or the entry point via the two-body Q-values. The analysis of the binary reaction channels is presented with a particular emphasis on 24Mg-gamma, 20Ne-gamma and 16O-gamma coincidences. New information (spin and branching ratios) is deduced on high-energy states in 24Mg and 16O, respectively., Comment: 27 pages, 8 figures, 1 table

The occurence of "exotic" shapes in light N=Z alpha-like nuclei is investigated for 24Mg+12C and 32S+24Mg. Various approaches of superdeformed and hyperdeformed bands associated with quasimolecular resonant structures with low spin are presented. For both reactions, exclusive data were collected with the Binary Reaction Spectrometer in coincidence with EUROBALL IV installed at the VIVITRON Tandem facility of Strasbourg. Specific structures with large deformation were selectively populated in binary reactions and their associated $\gamma$-decays studied. The analysis of the binary and ternary reaction channels is discussed., Comment: 7 pages, 4 figures, Paper presented at the Fusion08 International Conference on New Aspects of Heavy Ion Collisions Near the Coulomb Barrier, Chicago. Proceedings to be published by AIP Conference Proceedings Illinois, USA, September 22-26, 2008

Using a unique two-arm detector system for heavy ions (the BRS, binary reaction spectrometer) coincident fission events have been measured from the decay of $^{60}$Zn compound nuclei formed at 88MeV excitation energy in the reactions with $^{36}$Ar beams on a $^{24}$Mg target at $E_{lab}(^{36}$Ar) = 195 MeV. The detectors consisted of two large area position sensitive (x,y) gas telescopes with Bragg-ionization chambers. From the binary coincidences in the two detectors inclusive and exclusive cross sections for fission channels with differing losses of charge were obtained. Narrow out-of-plane correlations corresponding to coplanar decay are observed for two fragments emitted in binary events, and in the data for ternary decay with missing charges from 4 up to 8. After subtraction of broad components these narrow correlations are interpreted as a ternary fission process at high angular momentum through an elongated shape. The lighter mass in the neck region consists dominantly of two or three-particles. Differential cross sections for the different mass splits for binary and ternary fission are presented. The relative yields of the binary and ternary events are explained using the statistical model based on the extended Hauser-Feshbach formalism for compound nucleus decay. The ternary fission process can be described by the decay of hyper-deformed states with angular momentum around 45-52 $hbar$., Comment: 23 pages, 25 figures

A previously derived semi-microscopic analysis based on the Double Folding Model, for alpha-particle elastic scattering on A~100 nuclei at energies below 32 MeV, is extended to medium mass A ~ 50-120 nuclei and energies from ~13 to 50 MeV. The energy-dependent phenomenological imaginary part for this semi-microscopic optical model potential was obtained including the dispersive correction to the microscopic real potential, and used within a concurrent phenomenological analysis of the same data basis. A regional parameter set for low-energy alpha-particles entirely based on elastic-scattering data analysis was also obtained for nuclei within the above-mentioned mass and energy ranges. Then, an ultimate assessment of (alpha,gamma), (alpha,n) and (alpha,p) reaction cross sections concerned target nuclei from 45Sc to 118Sn and incident energies below ~12 MeV. The former diffuseness of the real part of optical potential as well as the surface imaginary-potential depth have been found responsible for the actual difficulties in the description of these data, and modified in order to obtain an optical potential which describe equally well both the low energy elastic-scattering and induced-reaction data of alpha-particles., Comment: 46 pages, 16 figures. n_TOF Collaboration Annual Meeting, Bari, Italy, 28-30 November 2007 (http://www.cern.ch/ntof/Documents/bari_nov07/bari_slides.php); revised version accepted for publication in ADNDT

In a recent paper, arXiv0712.1191 [nucl-th], Zinner and Jensen (ZJ) expressed strong doubts about the concept of alpha-particle condensation in finite nuclei. In this article we give a reply which, essentially, is point by point (but not in the order)., Comment: 9 pages, 4 figures; section IV simplified

Elastic scattering of alpha-particle and some tightly-bound light nuclei has shown the pattern of rainbow scattering at medium energies, which is due to the refraction of the incident wave by a strongly attractive nucleus-nucleus potential. This review gives an introduction to the physics of the nuclear rainbow based essentially on the optical model description of the elastic scattering. Since the realistic nucleus-nucleus optical potential (OP) is the key to explore this interesting process, an overview of the main methods used to determine the nucleus-nucleus OP is presented. The refractive rainbow-like structures observed in other quasi-elastic scattering reactions have also been discussed. Some evidences for the refractive effect in the elastic scattering of unstable nuclei are presented and perspectives for the future studies are discussed., Comment: 66 pages, 43 figures, Topical Review to appear in J. Phys. G

Large-angle elastic scattering of alpha-particle and strongly-bound light nuclei at a few tens MeV/nucleon has shown the pattern of rainbow scattering. This interesting process was shown to involve a significant overlap of the two colliding nuclei, with the total nuclear density well above the saturation density of normal nuclear matter (NM). For a microscopic calculation of the nucleus-nucleus potential within the folding model, we have developed a density dependent nucleon-nucleon (NN) interaction based on the G-matrix interaction M3Y. Our folding analysis of the refractive 4He, 12C, and 16O elastic scattering shows consistently that the NM incompressibility K should be around 250 MeV which implies a rather soft nuclear Equation of State (EOS). To probe the symmetry part of the nuclear EOS, we have used the isovector coupling to link the isospin dependence of the proton optical potential to the cross section of (p,n) charge-exchange reactions exciting the isobaric analog states in nuclei of different mass regions. With the isospin dependence of the NN interaction fine tuned to reproduce the charge exchange data, a realistic estimate of the NM symmetry energy has been made., Comment: 6 pages, 6 figures; Plenary Talk given at Asia Pacific Forum on Frontiers of Basic Science, Hanoi, September 27-29, 2005, organized by Osaka University and Vietnam National University

The data of inelastic 16O+16O scattering to the lowest 2+ and 3- excited states of 16O have been measured at Elab = 250, 350, 480, 704 and 1120 MeV and analyzed consistently in the distorted wave Born approximation (DWBA), using the semi- microscopic optical potentials and inelastic form factors given by the folding model, to reveal possible refractive structure of the nuclear rainbow that was identified earlier in the elastic 16O+16O scattering channel at the same energies. Given the known transition strengths of the 2+ and 3- states of 16O well determined from the (e,e') data, the DWBA description of the inelastic data over the whole angular range was possible only if the absorption in the exit channels is significantly increased (especially, for the 16O+16O(2+) exit channel). Although the refractive pattern of the inelastic 16O+16O scattering was found to be less pronounced compared to that observed in the elastic scattering channel, a clear remnant of the main rainbow maximum could still be seen in the inelastic cross section at Elab = 350 - 704 MeV., Comment: 26 pages, 10 figures, Accepted for publication in Nucl. Phys. A

Elastic $^{6}$He+$^4$He data measured at $E_{\rm c.m.}=11.6,$ 15.9, and 60.3 MeV have been analyzed within the coupled reaction channels (CRC) formalism, with the elastic-scattering and two-neutron ($2n$) transfer amplitudes coherently included. Contributions from the direct (one-step) and sequential (two-step) $2n$-transfers were treated explicitly based on a realistic assumption for the $2n$-transfer form factor. The oscillatory pattern observed in $^4$He($^6$He,$^6$He)$^4$He angular distribution at low energies was found to be due to an interference between the elastic scattering and $2n$-transfer amplitudes. Our CRC analysis shows consistently that the direct $2n$-transfer strongly dominates over the sequential transfer and thus confirms the dominance of 2$n-^4$He configuration over the $n-^5$He one in the $^6$He wave function. This result suggests a strong clusterization of the two valence neutrons and allows, therefore, a reliable estimate for the \emph{di-neutron} spectroscopic amplitude., Comment: Accepted for publication in Phys. Lett. B

The gamma-decay properties of 24Mg excited states are investigated in the inverse reaction 24Mg+12C at E(24Mg) = 130 MeV. At this energy the direct inelastic scattering populates a 24Mg* energy region where 12C+12C breakup resonances can occur. Very exclusive data were collected with the Binary Reaction Spectrometer (BRS) in coincidence with EUROBALL installed at the VIVITRON Tandem facility of the IReS at Strasbourg. The experimental detection system is decribed and preliminary results of binary reaction coincid data are presented., Comment: 4 pages, 2 figures included; paper presented at the Nucleus-Nucleus Conference, Moscow, June 2003, and submitted to Nucl. Phys. A

The elastic scattering $^{16}$O$+^{12}$C angular distributions at $^{16}$O bombarding energies of 100.0, 115.9 and 124.0 MeV and their optical model description including the $\alpha$-particle exchange contribution calculated in the Coupled Reaction Channel approach are presented. The angular distributions show not only the usual diffraction pattern but also, at larger angles, intermediate structure of refractive origin on which finer oscillations are superimposed. The large angle features can be consistently described including explicitly the elastic $\alpha$-transfer process and using a refractive optical potential with a deep real part and a weakly absorptive imaginary part., Comment: 3 pages, 2 figures, accepted in Eur.Phys.J A (Short note)

The use of radioactive ion beams is shown to offer the possibility to study collective pairing states at high excitation energy, which are not usually accessible with stable projectiles because of large energy mismatch. In the case of two-neutron stripping reactions induced by 6He, we predict a population of the Giant Pairing Vibration in 208Pb or 116Sn with cross sections of the order of a millibarn, dominating over the mismatched transition to the ground state., Comment: 6 pages, 4 figures

Using particle-$\gamma$ coincidences we have studied the population of final states after the emission of 2 $\alpha$-particles and of $^{8}$Be in nuclei formed in $^{32}$S+$^{24}$Mg reactions at an energy of $\textrm{E}_{\rm L}(^{32}\textrm{S}) = 130 {\rm MeV}$. The data were obtained in a setup consisting of the GASP $\gamma$-ray detection array and the multidetector array ISIS. Particle identification is obtained from the $\Delta$E and E signals of the ISIS silicon detector telescopes, the $^{8}$Be being identified by the instantaneous pile up of the $\Delta$E and E pulses. $\gamma$-ray decays of the $^{48}$Cr nucleus are identified with coincidences set on 2 $\alpha$-particles and on $^{8}$Be. Some transitions of the side-band with $K^\pi=4^{-}$ show stronger population for $^{8}$Be emission relative to that of 2 $\alpha$-particles (by a factor $1.5-1.8$). This observation is interpreted as due to an enhanced emission of $^{8}$Be into a more deformed nucleus. Calculations based on the extended Hauser-Feshbach compound decay formalism confirm this observation quantitatively., Comment: 17 pages, 9 figures accepted for publication in J. Phys. G