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Inclusive Υ(1S) and Υ(2S) production have been measured in Pb-Pb collisions at the centre-of-mass energy per nucleon-nucleon pair sNN−−−√=5.02 TeV, using the ALICE detector at the CERN LHC. The Υ mesons are reconstructed in the centre-of-mass rapidity interval 2.5<y<4 and in the transverse-momentum range pT<15 GeV/c, via their decays to muon pairs. In this Letter, we present results on the inclusive Υ(1S) nuclear modification factor RAA as a function of collision centrality, transverse momentum and rapidity. The Υ(1S) and Υ(2S) RAA, integrated over the centrality range 0-90%, are 0.37±0.02(stat)±0.03(syst) and 0.10±0.04(stat)±0.02(syst), respectively, leading to a ratio RΥ(2S)AA/RΥ(1S)AA of 0.28±0.12(stat)±0.06(syst). The observed Υ(1S) suppression increases with the centrality of the collision and no significant variation is observed as a function of transverse momentum and rapidity.
ϕ meson measurements provide insight into strangeness production, which is one of the key observables for the hot medium formed in high-energy heavy-ion collisions. ALICE measured ϕ production through its decay in muon pairs in Pb-Pb collisions at sNN−−−√ = 2.76 TeV in the intermediate transverse momentum range 2<pT<5 GeV/c and in the rapidity interval 2.5<y<4. The ϕ yield was measured as a function of the transverse momentum and collision centrality. The nuclear modification factor was obtained as a function of the average number of participating nucleons. Results were compared with the ones obtained via the kaon decay channel in the same pT range at midrapidity. The values of the nuclear modification factor in the two rapidity regions are in agreement within uncertainties.
A measurement of the production of prompt +c baryons in Pb–Pb collisions at √sNN = 5.02 TeV with the ALICE detector at the LHC is reported. The +c and − c were reconstructed at midrapidity (|y| < 0.5) via the hadronic decay channel +c → pK0 S (and charge conjugate) in the transverse momentum and centrality intervals 6 < pT < 12 GeV/c and 0–80%. The +c /D0 ratio, which is sensitive to the charm quark hadronisation mechanisms in the medium, is measured and found to be larger than the ratio measured in minimum-bias pp collisions at √s = 7 TeV and in p–Pb collisions at √sNN = 5.02 TeV. In particular, the values in p–Pb and Pb–Pb collisions differ by about two standard deviations of the combined statistical and systematic uncertainties in the common pT interval covered by the measurements in the two collision systems. The + c /D0 ratio is also compared with model calculations including different implementations of charm quark hadronisation. The measured ratio is reproduced by models implementing a pure coalescence scenario, while adding a fragmentation contribution leads to an underestimation. The + c nuclear modification factor, RAA, is also presented. The measured values of the RAA of + c , D+ s and non-strange D mesons are compatible within the combined statistical and systematic uncertainties. They show, however, a hint of a hierarchy (RD0 AA < RD+ s AA < R+ c AA ), conceivable with a contribution from coalescence mechanisms to charm hadron formation in the medium.
A measurement of the production of prompt Λ+c baryons in Pb-Pb collisions at sNN−−−√=5.02 TeV with the ALICE detector at the LHC is reported. The Λ+c and Λ¯¯¯¯−c were reconstructed at midrapidity (|y|<0.5) via the hadronic decay channel Λ+c→pK0S (and charge conjugate) in the transverse momentum and centrality intervals 6<pT<12 GeV/c and 0-80%. The Λ+c/D0 ratio, which is sensitive to the charm quark hadronisation mechanisms in the medium, is measured and found to be larger than the ratio measured in minimum-bias pp collisions at s√=7 TeV and in p-Pb collisions at sNN−−−√=5.02 TeV. In particular, the values in p-Pb and Pb-Pb collisions differ by about two standard deviations of the combined statistical and systematic uncertainties in the common pT interval covered by the measurements in the two collision system. The Λ+c/D0 ratio is also compared with model calculations including different implementations of charm quark hadronisation. The measured ratio is reproduced by models implementing a pure coalescence scenario, while adding a fragmentation contribution leads to an underestimation. The Λ+c nuclear modification factor, RAA, is also presented. The measured values of the RAA of Λ+c, Ds and non-strange D mesons are compatible within the combined statistical and systematic uncertainties. They show, however, a hint of a hierarchy (RD0AA<RDsAA<RΛ+cAA), conceivable with a contribution of recombination mechanisms to charm hadron formation in the medium.
We study the Wigner function for massive spin-1/2 fermions in electromagnetic fields. The Wigner function is analytically solved in five cases when electromagnetic fields are constants. For a general space-time dependent field configuration, we use the method of semi-classical expansion and solved the Wigner function at linear order in the Planck's constant. At the same order, we obtained a generalized Boltzmann equation for particle distribution, and a generalized BMT equation for spin polarization. Using the Wigner function, we calculated some physical quantities in a thermal equilibrium system.
Behavior is characterized by sequences of goal oriented conducts, such as food uptake, socializing and resting. Classically, one would define for each task a corresponding satisfaction level, with the agent engaging, at a given time, in the activity having the lowest satisfaction level. Alternatively, one may consider that the agent follows the overarching objective to generate sequences of distinct activities. To achieve a balanced distribution of activities would then be the primary goal, and not to master a specific task. In this setting the agent would show two types of behaviors, task-oriented and task-searching phases, with the latter interseeding the former. We study the emergence of autonomous task switching for the case of a simulated robot arm. Grasping one of several moving objects corresponds in this setting to a specific activity. Overall, the arm should follow a given object temporarily and then move away, in order to search for a new target and reengage. We show that this behavior can be generated robustly when modeling the arm as an adaptive dynamical system. The dissipation function is in this approach time dependent. The arm is in a dissipative state when searching for a nearby object, dissipating energy on approach. Once close, the dissipation function starts to increase, with the eventual sign change implying that the arm will take up energy and wander off. The resulting explorative state ends when the dissipation function becomes again negative and the arm selects a new target. We believe that our approach may be generalized to generate self-organized sequences of activities in general.
This article reports measurements characterizing the Underlying Event (UE) associated with hard scatterings at midrapidity (|η|<0.8) in pp collisions at s√ = 13 TeV. The hard scatterings are identified by the leading particle, the charged particle with the highest transverse momentum (pleadingT) in the event. Charged-particle numbers and summed transverse-momentum densities are measured in different azimuthal regions defined with respect to the leading particle direction: Toward, Transverse, and Away. The Toward and Away regions contain the fragmentation products of the hard scatterings in addition to the UE contribution, whereas particles in the Transverse region are expected to originate predominantly from the UE. The study is performed as a function of pleadingT with three different pT thresholds for the associated particles, ptrackT> 0.15, 0.5, and 1.0 GeV/c. The charged-particle density in the Transverse region rises steeply for low values of pleadingT and reaches a plateau. The results confirm the trend observed at lower collision energies that the charged-particle density in the Transverse region shows a stronger increase with s√ than the inclusive charged-particle density at midrapidity. The plateau in the Transverse region (5<pleadingT<40 GeV/c) is further characterized by the probability distribution of its charged-particle multiplicity normalized to its average value (relative transverse activity, RT) and the mean transverse momentum as a function of RT. Experimental results are compared to model calculations obtained using PYTHIA 8 and EPOS LHC. The overall agreement between models and data is within 30%. These measurements provide new insights on the interplay between hard scatterings and the associated UE in pp collisions.
To gain a better understanding of complex mechanisms in biological systems, simultaneous control over multiple processes is key. To this purpose selective photouncaging has been developed. Photo-uncaging is an experimental scheme in which a molecule of interest has been inactivated synthetically and is activated by light. Usually a bond is cleaved and a leaving group is set free. The molecule which inactivates the molecule of interest and sets the leaving group free is called (photo-)cage. In a selective photo-uncaging scheme a number of leaving groups can be released independently, usually by irradiation with light of different wavelengths. This approach is, however, seriously limited in its applicability due to the properties of the involved cages and irradiation schemes. A major drawback is the usually quite broad UV-Vis absorption of the cages. This makes a selective activation by light difficult and limits the maximal number of independent cages severely.
Therefore, the aim of this thesis is to introduce the Vibrationally Promoted Electronic Resonance (VIPER) 2D-IR pulse sequence in a alternative selective uncaging scheme.
The VIPER 2D-IR pulse sequence is a spectroscopic tool which allows to generate 2D-IR signals whose lifetime are independent of the vibrational relaxation lifetime. It has been first used to monitor chemical exchange. It consists of a narrowband infared pump pulse, a subsequent UV-Vis pump pulse and a broadband infrared probe pulse. The UV-Vis pump pulse is off-resonant with regard to the UV-Vis absorption band. Electronic excitation becomes only possible, if the infrared pump pulse modulates the UV-Vis transition of the IR-excited molecule. This modulation brings the UV-Vis transition in resonance with the UV-Vis pump pulse. Thereby, only the molecules which were pre-excited with the infrared pulse can be excited into the electronically excited state. A computational prediction of the modulation was carried out by Jan von Cosel in the Burghardt group.
The narrowband infrared pump pulse can be used to selectively excite a subensemble of molecules in a mixture into an electronically excited state even if the UV-Vis spectra of all molecules are virtually identical. For this the sub-ensemble needs to exhibit an identifiable infrared spectrum. Combined with the introduction of isotope labels, which lead to changes in the infrared absorption spectra, the larger selectivity in the infrared region can be exploited for an alternative selective uncaging approach. In VIPER uncaging the infrared pump pulse selects the species and the subsequent UV-Vis pulse provides the energy needed for electronic excitation upon which the photo cleavage can occur.
After an introduction of the principle idea of uncaging and VIPER spectroscopy, the concept of VIPER uncaging is introduced and its limits and requirements are discussed. Some examples for possible VIPER cages are reviewed.
A coumarin molecule (7-diethylamino coumarin) which can release an azide group was chosen as a first test molecule for VIPER uncaging. Its isotopomers were characterized to determine suitable spectroscopic markers for successful uncaging and to find fitting experimental conditions. The chosen coumarin cage has an UV-Vis absorption band at approximately 380 nm and a steep flank on the high wavelength side of the band. The quantum yield for the azide compound is between 10-20 % depending on the solvent’s water content. The release was found to be on a picosecond timescale which is among the fastest known photo reactions, but the photo reaction mechanism has proven to be not straightforward. For the VIPER experiment on the mixture two isotopomers were chosen with a 13C atom at different positions. In one species a ring mode of the coumarin is changed by the 13C atom. In the other isotopomer the carbonyl stretching mode is influenced. The change in the ring mode region allows to select one species or the other with the infrared pre-excitation. Because of experimental difficulties only isotopomers with the same leaving group could be used. The successful selective electronic excitation of the individual isotopomers in a mixture was monitored by probing the carbonyl region.
As a second VIPER cage, para-hydroxyphenacyl (pHP) was chosen. A thiocyanate group was selected as leaving group. pHP cages have their electronic transition in the UV, with a maximum absorption at 290 nm. The shape of the spectrum is suitable and the quantum yield is very high, with values in the literature of up to 90 %. Also the photo reaction is well studied and the expected byproducts are well characterized. The chosen isotopologues were characterized spectroscopically. The resulting data on the photo reaction were in agreement with the mechanism proposed in the literature. The mixture for the VIPER experiment consisted of two isotopologues, where for one species all the C atoms in the ring were labelled and for the other the C-atom in the thiocyanate leaving group was labelled. Here the release of the different leaving groups, labelled and unlabelled thiocyanate, could be monitored selectively. This shows that it is possible to selectively release a molecule in a mixture of caged molecules by applying the VIPER pulse sequence.
The samples were synthesized by Matiss Reinfelds from the Heckel group and the VIPER experiments were done together with Carsten Neumann and with support
of the Bredenbeck group.
The leaving groups were chosen because of their infrared absorption which allowed to directly monitor the successful cleavage by spectroscopy. This was needed for the proof-of-concept experiment and to allow direct optimization of the experimental parameters but is not necessarily a requirement for VIPER uncaging.
Concerning the selectivity of the VIPER uncaging, the approach is at the moment mainly limited by the infrared pulse energy. The selective VIPER excitation is competing with unselective excitation directly by just the UV-Vis pulse. A more intense infrared pump pulse would increase only the selective VIPER excitation and thereby improve the contrast to the unspecific background.
To address this issue, the first steps towards an alternative infrared light generation are undertaken. In this alternative approach the infrared light for preexcitation is directly generated by difference frequency generation of the laser output, i.e. the high energy 800 nm fundamental, and the output of a non-collinear optical parametric amplifier (NOPA). To achieve a narrowband pump pulse the pulses are chirped before mixing. In the scope of this thesis a NOPA has been installed and the mixing has been tested with available test crystal medium. While infrared wavelength region and power were not in the aspired range with this alternative crystal the feasibility of mixing between a NOPA output and the fundamental could be shown.
Other possibilities to increase the contrast to the unspecific background excitation by the UV-Vis pump pulse are discussed. For most applications of selective VIPER uncaging the detection by fs-laser spectroscopy will not be needed and could be replaced by other methods e.g. chromatography. This will allow the experimental parameters of the VIPER pulse sequence to be changed in a way which reduces unspecific excitation i.e. reducing the UV-Vis-pump energy and result in much better contrast.
In conclusion, the experimental data in this thesis shows the VIPER pulse sequence to be applicable to selective uncaging schemes and indicates measures to arrive at the specificity necessary for uncaging applications. This thesis was focused on uncaging photo reactions with isotopomers and isotopologues, but other types of photo reactions could in principle be controlled in the same way. It should be possible to address different isomers in mixtures or different ground states of proteins selectively. The discussed experiments are a significant step towards control over photo reactions in mixtures.
We present measurements of two-particle differential number correlation functions R2 and transverse momentum correlation functions P2, obtained from p-Pb collisions at 5.02 TeV and Pb-Pb collisions at 2.76 TeV. The results are obtained using charged particles in the pseudorapidity range |η|< 1.0, and transverse momentum range 0.2<pT<2.0 GeV/c as a function of pair separation in pseudorapidity, |Δη|, azimuthal angle, Δφ, and for several charged-particle multiplicity classes. Measurements are carried out for like-sign and unlike-sign charged-particle pairs separately and combined to obtain charge-independent and charge-dependent correlation functions. We study the evolution of the width of the near-side peak of these correlation functions with collision centrality. Additionally, we study Fourier decompositions of the correlators in Δφ as a function of the pair separation |Δη|. Significant differences in the dependence of their harmonic coefficients on multiplicity classes are found. These differences can be exploited, in theoretical models, to obtain further insight into charged-particle production and transport in heavy-ion collisions. Moreover, an upper limit of non-flow contributions to flow coefficients vn measured in Pb-Pb collisions based on the relative strength of Fourier coefficients measured in p-Pb interactions is estimated.
We present measurements of two-particle differential number correlation functions R2 and transverse momentum correlation functions P2, obtained from p-Pb collisions at 5.02 TeV and Pb-Pb collisions at 2.76 TeV. The results are obtained using charged particles in the pseudorapidity range |η|< 1.0, and transverse momentum range 0.2<pT<2.0 GeV/c as a function of pair separation in pseudorapidity, |Δη|, azimuthal angle, Δφ, and for several charged-particle multiplicity classes. Measurements are carried out for like-sign and unlike-sign charged-particle pairs separately and combined to obtain charge-independent and charge-dependent correlation functions. We study the evolution of the width of the near-side peak of these correlation functions with collision centrality. Additionally, we study Fourier decompositions of the correlators in Δφ as a function of the pair separation |Δη|. Significant differences in the dependence of their harmonic coefficients on multiplicity classes are found. These differences can be exploited, in theoretical models, to obtain further insight into charged-particle production and transport in heavy-ion collisions. Moreover, an upper limit of non-flow contributions to flow coefficients vn measured in Pb-Pb collisions based on the relative strength of Fourier coefficients measured in p-Pb interactions is estimated.
Transverse momentum (pT) spectra of charged particles at mid-pseudorapidity in Xe-Xe collisions at sNN−−−√ = 5.44 TeV measured with the ALICE apparatus at the Large Hadron Collider are reported. The kinematic range 0.15<pT<50 GeV/c and |η|<0.8 is covered. Results are presented in nine classes of collision centrality in the 0-80% range. For comparison, a pp reference at the collision energy of s√ = 5.44 TeV is obtained by interpolating between existing \pp measurements at s√ = 5.02 and 7 TeV. The nuclear modification factors in central Xe-Xe collisions and Pb-Pb collisions at a similar center-of-mass energy of sNN−−−√ = 5.02 TeV, and in addition at 2.76 TeV, at analogous ranges of charged particle multiplicity density ⟨dNch/dη⟩ show a remarkable similarity at pT>10 GeV/c. The centrality dependence of the ratio of the average transverse momentum ⟨pT⟩ in Xe-Xe collisions over Pb-Pb collision at s√ = 5.02 TeV is compared to hydrodynamical model calculations.
In this work we provided additional insights into our understanding of bulk QCD matter through the study of the transport coeffcients which govern the non-equilibrium microscopical processes of statistical ensembles. Specically, we focused on the low energy regime corresponding to the hadron gas, as the properties of this region of the phase diagram are still relatively unknown, and existing calculations for the transport coeffcients are either scarce, contradictory, or somewhat limited in scope; this thesis' main goal was thus to shed some light on this by providing new independent calculations of these quantities.
We subsequently presented two formalisms which can be used to calculate transport coeffcients. The first one (which also was the main tool we used in the following chapters to produce our results) relies on the development of so-called Green-Kubo formulas, which relate non-equilibrium dissipative fluctuations with transport coeffcients; notably, the off-diagonal components of the energy-momentum tensor are shown to be related to the shear viscosity, its diagonal components to the bulk viscosity and fluctuations in the electric current can be related to the electric conductivity. We additionally introduced two new conductivities, namely the baryon-electric and strange electric conductivities, which we dubbed, together with the already known electric one, the "cross-conductivity", which encodes information about how electric fluctuations are correlated to changes in electric, baryonic or strange currents, or vice-versa. The second way of calculating transport coeffcient which we discussed consists in linearizing the collision term of the Boltzmann equation through the Chapman-Enskog formalism. While in principle providing direct semi-analytical results for the transport coeffcients, this approach is complicated to implement when more than a few species are considered, and as such was then mostly used as a tool to calibrate our Green-Kubo calculations.
The hadron gas model that we used for all calculations, namely the transport approach SMASH, was then presented. The main features of the model were explained, such as the collision criterion, the considered degrees of freedom and the specific way in which they microscopically interact with each other. It was verified that SMASH does reproduce analytical results of the Boltzmann equation in an expanding universe scenario, thus showing the equivalence of this transport approach and the associated kinetic theory results. A special care was taken to detail the ways in which a state of thermal and chemical equilibrium (which is necessary for Green-Kubo relations to be valid) can be reached and described using SMASH.
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ALICE (A Large Ion Collider Experiment) is preparing for a major upgrade of the detector, readout and computing systemsfor LHC Run 3. A new facility called O2 (Online-Offline) will play a major role in data compression and event processing. To efficiently operate the experiment, we are designing a monitoring subsystem, which will provide a complete overview of the O2 overall health, detect performance degradation and component failures. The monitoring subsystem will receive and collect up to 600 kHz of performance metrics. It consists of a custom monitoring library and a server-side, distributed software covering five main functional tasks: parameter collection and processing, storage, visualisation and alarms. To select the most appropriate tools for these tasks, we evaluated three options: “Modular Stack”, Zabbix and the currently used ALICE Grid monitoring tool called MonALISA. The former one consists of a toolkit including collectd, Apache Flume, Apache Spark, InfluxDB, Grafana and Riemann. This paper describes the monitoring subsystem functional architecture. It goes through a complete evaluation of the three considered options, the selection process, risk assessment and justification for the final decision. The in-depth comparison includes functional features and throughput measurement to ensure the required processing and storage performance.
HADES (High Acceptance DiElectron Spectrometer), located at GSI, is a versatile detector for precise spectroscopy of e+ e- pairs and charged hadrons produced on a fixed target in a 1 to 3.5 AGeV kinetic beam energy region. The main experimental goal is to investigate properties of dense nuclear matter created in heavy ion collisions and learn about in-medium hadron properties.
In the HADES set-up 24 Mini Drift Chambers (MDC) allow for track reconstruction and determining the particle momentum by exploiting charged particle deflection in a magnetic field. In addition, the drift chambers contribute to particle identification by measuring the energy loss. The read-out concept foresees each sensing wire to be equipped with a preamplifier, analog pulse shaper and discriminator. In the current front-end electronics, the ASD-8 ASIC comprises the above modules. Due to limitations of the current on-board time to digital converters (TDC), especially regarding higher reaction rates expected at the future FAIR facility (HADES at SIS-100), the electronics need to be replaced by new board featuring multi-hit TDCs. Whereas ASD-8 chips cannot be procured anymore, a promising replacement candidate is the PASTTREC ASIC, developed by JU Krakow, which was tested w.r.t. suitability for MDC read-out in a variety of set-ups and, where possible, in direct comparison to ASD-8.
The timing precision, being the most crucial performance parameter of the joint system of detector and read-out electronics, was assessed in two different set-ups, i.e. a cosmic muon tracking set-up and a beam test at the COSY accelerator at Juelich using a minimum ionizing proton beam.
The beam test results were reproduced and can thus be quantitatively explained in a three dimensional GARFIELD simulation of a HADES MDC drift cell. In particular, the simulation is able to describe the characteristic dependence of the time precision on the track position within the cell.
A circuit simulation (SPICE) was used to closely model the time development of a raw drift chamber pulse, measured as a response to X-rays from a 55 Fe source. The insights gained from this model were used for attributing realistic charge values to the time over threshold values measured with the read-out ASICs in a charge calibration set-up. Furthermore, a high-level circuit simulation of the PASTTREC shaper is implemented to serve as a demonstration of the effect of the individual shaping and tail cancellation stages which are present in both ASICs.
Charmonia with different transverse momentum pT usually comes from different mechanisms in the relativistic heavy ion collisions. This work tries to review the theoretical studies on quarkonium evolutions in the deconfined medium produced in p-Pb and Pb-Pb collisions. The charmonia with high pT are mainly from the initial hadronic collisions, and therefore sensitive to the initial energy density of the bulk medium. For those charmonia within 0.1 < pT < 5 GeV/c at the energies of Large Hadron Collisions (LHC), They are mainly produced by the recombination of charm and anti-charm quarks in the medium. In the extremely low pT ∼ 1/RA (RA is the nuclear radius), additional contribution from the coherent interactions between electromagnetic fields generated by one nucleus and the target nucleus plays a non-negligible role in the J/ψ production even in semi-central Pb-Pb collisions.
The Projectile Spectator Detector (PSD) of the CBM experiment at the future FAIR facility is a compensating lead-scintillator calorimeter designed to measure the energy distribution of the forward going projectile nucleons and nuclei fragments (reaction spectators) produced close to the beam rapidity. The detector performance for the centrality and reaction plane determination is reviewed based on Monte-Carlo simulations of gold-gold collisions by means of four different heavy-ion event generators. The PSD energy resolution and the linearity of the response measured at CERN PS for the PSD supermodule consisting of 9 modules are presented. Predictions of the calorimeter radiation conditions at CBM and response measurement of one PSD module equipped with neutron irradiated MPPCs used for the light read out are discussed.
In high multiplicity nucleus-nucleus collisions baryon-antibaryon annihilation and regeneration occur during the final hadronic expansion phase, thus distorting the initial equilibrium multiplicity ratios. We quantify the modifications employing the hybrid UrQMD transport model and apply them to the grand canonical partition functions of the Statistical Hadronization Model(SHM). We analyze minimum bias and central Pb+Pb collision data at SPS and LHC energy. We explain the Pion to Proton ratio puzzle. We also reproduce the deuteron to proton ratio at LHC energy by the SHM, and by UrQMD after attaching a phase space coalescence process. We discuss the resulting (T,μB) diagram.
We present the first measurement of the proton–Ω correlation function in heavy-ion collisions for the central (0–40%) and peripheral (40–80%) Au + Au collisions at √sNN = 200 GeV by the STAR experiment at the Relativistic Heavy-Ion Collider (RHIC). Predictions for the ratio of peripheral collisions to central collisions for the proton–Ω correlation function are sensitive to the presence of a nucleon– bound state. These predictions are based on the proton– interaction extracted from (2 + 1)-flavor lattice QCD calculations at the physical point. The measured ratio of the proton–Ω correlation function between the peripheral (small system) and central (large system) collisions is less than unity for relative momentum smaller than 40 MeV/c. Comparison of our measured correlation ratio with theoretical calculation slightly favors a proton– bound system with a binding energy of ∼ 27 MeV.
We investigate the role of the Pauli Exclusion Principle (PEP) for light nuclei, at the examples of 12C and 16O. We show that ignoring the PEP does lead not only to a too dense spectrum at low energy but also to a wrong grouping into bands. Using a geometrical mapping, a triangular structure for 12C and a tetrahedral structure in 16O in the ground state is obtained by using the indistinguishably of the α-particles.