Maximum Angular Momentum Research Articles

Weak cosmic censorship and the rotating quantum BTZ black hole

Tests of the weak cosmic censorship conjecture examine the possibility of the breakdown of predictivity of the gravitational theory considered, by checking if curvature singularities typically present in black hole spacetimes are concealed within an event horizon at all times. A possible method to perform such tests was proposed by Wald and consists in trying to overspin an extremal rotating black hole by throwing at it a test particle with large angular momentum. In this paper, we analyze the effects of dropping a test particle into an extremal quantum rotating BTZ black hole, whose three-dimensional metric captures the exact backreaction from strongly coupled quantum conformal fields. Our analysis reveals that, despite the inclusion of quantum effects, and akin to the classical scenario, these attempts to destroy the black hole are doomed to be unsuccessful. Particles carrying the maximum angular momentum and still falling into an extremal quantum BTZ black hole can, at most, leave it extremal. Nevertheless, we found numerical evidence that large backreaction of the quantum fields tends to disfavor violations of cosmic censorship.

Long-Lived Circular Rydberg Qubits of Alkaline-Earth Atoms in Optical Tweezers

Coherence time and gate fidelities in Rydberg atom quantum simulators and computers are fundamentally limited by the Rydberg state lifetime. Circular Rydberg states are highly promising candidates to overcome this limitation by orders of magnitude, as they can be effectively protected from decay due to their maximum angular momentum. We report the first realization of alkaline-earth circular Rydberg atoms trapped in optical tweezers, which provide unique and novel control possibilities due to the optically active ionic core. Specifically, we demonstrate creation of very high-n (n=79) circular states of Sr88. We measure lifetimes as long as 2.55 ms at room temperature, which are achieved via cavity-assisted suppression of black-body radiation. We show coherent control of a microwave qubit encoded in circular states of nearby manifolds, and characterize the qubit coherence time via Ramsey and spin-echo spectroscopy. Finally, circular-state tweezer trapping exploiting the Sr+ core polarizability is quantified via measurements of the trap-induced light shift on the qubit. Our work opens routes for quantum simulations with circular Rydberg states of divalent atoms, exploiting the emergent toolbox associated with the optically active core ion. Published by the American Physical Society 2024

Spin angular momentum of Gaussian beams with several polarization singularities

We study a paraxial vector Gaussian beam with several polarization singularities located on a circle. Such a beam is superposition of a cylindrically polarized Laguerre-Gaussian beam and a linearly polarized Gaussian beam. It is found that although polarization in the initial plane is linear, alternating regions with the different-sign spin angular momentum density are generated upon free-space propagation, showing that a spin Hall effect arises. For an arbitrary transverse plane, it is shown that the spin angular momentum magnitude is maximal on a certain-radius circle. We obtain an approximate expression for the distance to the transverse plane where the spin angular momentum density is maximal. Besides, we derive an optimal radius of the singularity-containing circle in the initial plane for which the maximal spin angular momentum density can be achieved upon propagation. It is revealed that in this case, the energies of the Laguerre-Gaussian beam and the Gaussian beam are equal to each other. We also obtain an expression for the orbital angular momentum density and find it to be defined by the spin angular momentum density, multiplied by –m/2, with m being the upper index of the Laguerre-Gaussian beam, equal to the number of the polarization singularities. An analogy with plane waves reveals that the spin Hall effect arises due to different divergence rates of the linearly polarized Gaussian beam and the cylindrically polarized Laguerre-Gaussian beam.

Fallback onto kicked neutron stars and its effect on spin-kick alignment

ABSTRACT Fallback in core-collapse supernova explosions is potentially of significant importance for the birth spins of neutron stars and black holes. It has recently been pointed out that the angular momentum imparted onto a compact remnant by fallback material is subtly intertwined with its kick because fallback onto a moving neutron star or black hole will preferentially come for a conical region around its direction of travel. We show that contrary to earlier expectations such one-sided fallback accretion onto a neutron star will tend to produce spin-kick misalignment. Since the baroclinic driving term in the vorticity equation is perpendicular to the nearly radial pressure gradient, convective eddies in the progenitor as well as Rayleigh–Taylor plumes growing during the explosion primarily carry angular momentum perpendicular to the radial direction. Fallback material from the accretion volume of a moving neutron star therefore carries substantial angular momentum perpendicular to the kick velocity. We estimate the seed angular momentum fluctuations from convective motions in core-collapse supernova progenitors and argue that accreted fallback material will almost invariably be accreted with the maximum permissible specific angular momentum for reaching the Alfvén radius. This imposes a limit of ${\sim }10^{-2}\, \mathrm{M}_\odot$ of fallback accretion for fast-spinning young neutron stars with periods of ${\sim }20\, \mathrm{ms}$ and less for longer birth spin periods.

HCl, DCl and TCl diatomic molecules in their ground state: predicting Born–Oppenheimer rovibrational spectra

The analytic Born–Oppenheimer (B-O) potential curve for the ground state of the molecule (H,D,T)Cl is constructed for the whole range of internuclear distances with an accuracy of 3–5 significant figures in comparison with the Rydberg–Klein–Rees-style potential curve derived from available experimental data on vibrational energies. With an accuracy of 3–4 significant figures, energy predictions are made for HCl (DCl, TCl) for the 836 (1625, 2366) B-O rovibrational bound states with maximal vibrational number and maximal angular momentum , including 24 (46, 63) weakly-bound states (close to the dissociation limit) with energies Hartree. The insufficiency of existing experimental data is indicated, and predictions for the bulk of the missing rovibrational states are made for all HCl, DCl, and TCl molecules.

Helicity and vorticity in heavy-ion collisions at energies available at the JINR Nuclotron-based Ion Collider facility

Heavy-ion collisions at center-of-mass nucleon collision energies 4.5--11.5 GeV are analyzed within the parton-hadron-string dynamics (PHSD) transport model. Spectator nucleons are separated, and the transfer of the initial angular momentum of colliding nuclei to the fireball formed by participants is studied. The maximal angular momentum is carried by the fireball in gold-gold collisions with the impact parameter about 5 fm corresponding to centrality class 10--20%. The obtained participant distributions were fluidized and the energy and baryon number densities, temperature, and velocity fields are obtained in the Landau frame. It is shown that the velocity field has dominantly Hubble-like transversal and longitudinal expansion with the vortical motion being only a small correction on top of it. The vorticity field is calculated and illustrated in detail. The formation of two oppositely rotating vortex rings moving in opposite directions along the $z$ axis is demonstrated. Other characteristics of the vortical motion such as the Lamb vector field and the kinematic vorticity number are considered. The magnitude of the latter one is found to be smaller than that for the Poiseuille flow and close to the pure shear deformation corresponding to just a flattening of fluid cells. The field of hydrodynamic helicity, which is responsible for the axial vortex effect, is calculated. The separation of positive and negative helicities localized in upper and lower semiplanes with respect to the reaction plane is shown. It is proved that the areas with various helicity signs can be probed by the selection of $\mathrm{\ensuremath{\Lambda}}$ hyperons with positive and negative projections of their momenta orthogonal to the reaction plane.

Inelastic Neutron Scattering Measurement of the Ground State Tunneling Gap in Tb and Ho Analogues of a Dy Field-Induced Single-Molecule Magnet.

Recent advances in single-molecule magnet (SMM) research have placed great value on interpretation of inelastic neutron scattering (INS) data for rare earth (RE)-containing SMMs. Here, we present the synthesis of several rare earth complexes where combined magnetic and INS studies have been performed, supported by ab initio calculations. The reaction of rare earth nitrate salts with 2,2'-bipyridine (2,2'-bpy) and tetrahalocatecholate (X4Cat2-, X = Br, Cl) ligands in methanol (MeOH) afforded two new families of compounds [RE(2,2'-bpy)2(X4Cat)(X4CatH)(MeOH)] (X = Br and RE = Y, Eu, Gd, Tb, Dy, Ho, Yb for 1-RE; X = Cl and RE = Y, Tb, Dy, Ho, and Yb for 2-RE). Addition of triethylamine (Et3N) to the reaction mixture delivered Et3NH[RE(2,2'-bpy)2(Br4Cat)2] (3-RE, RE = Er and Yb). Interestingly, cerium behaves differently to the rest of the series, generating (2,2'-bpyH)2[Ce(Br4Cat)3(2,2'-bpy)] (4-Ce) with tetravalent Ce(IV) in contrast to the trivalent metal ions in 1-3. The static magnetic properties of 1-RE (RE = Gd, Tb, Dy and Ho) were investigated in conjunction with INS measurements on 1-Y, 1-Tb, and 1-Ho to probe their ground state properties and any crystal field excitations. To facilitate interpretation of the INS spectra and provide insight into the magnetic behavior, ab initio calculations were performed using the single-crystal X-ray diffraction structural data of 1-RE (RE = Tb, Dy and Ho). The ab initio calculations indicate ground doublets dominated by the maximal angular momentum projection states of Kramers type for 1-Dy and Ising type for 1-Tb and 1-Ho. Dynamic magnetic susceptibility measurements indicate that 1-Dy exhibits slow magnetic relaxation in the presence of a small applied magnetic field mainly through Raman pathways. Inelastic neutron scattering spectra exhibit distinct transitions corresponding to crystal field-induced tunneling gaps between the pseudo-doublet ground state components for 1-Tb and 1-Ho, which is one of the first direct experimental measurements with INS of such tunneling transitions in a molecular nanomagnet. The power of high-resolution INS is demonstrated with evidence of two distinct tunneling gaps measurable for the two crystallographically unique Tb coordination environments observed in the single crystal X-ray structure.

Triggering single-molecule qubit spin dynamics via non-Abelian geometric phase effects.

We illustrate how macroscopic rotations can be utilised to trigger and control a spin dynamics within the ground doublet of both Kramers and non-Kramers-type molecular nanomagnets via the non-Abelian character of the time-evolution operator. For Kramers magnets, we show how this effect can be harnessed to realise single-qubit quantum gates and give the explicit example of a recently reported CoCl2(tu)4 single-molecule magnet (SMM). We demonstrate that gating operations could be performed on this magnet in as fast as 10 ps before the breakdown of adiabaticity, much faster than typical spin-lattice relaxation times. Based on this effect, we also suggest CoCl2(tu)4 as a quantum gyroscope for sensing yaw-axis rotations. For integer spin nanomagnets where non-axial crystal field interactions often lift ground state degeneracy, we show how spin dynamics from the non-Abelian geometric propagator can be recovered using non-adiabatic macroscopic rotations not-necessarily resonant with the tunnel splitting gap. Using the well-known TbPc2 single-ion magnet as a further example, we identify an experimentally plausible non-adiabatic rotation that induces a coherent superposition of tunnelling ground states, tantamount to preparing each member of a TbPc2 ensemble in the maximal angular momentum state |mJ = 6〉. The detection of an ensuing coherent oscillation of the macroscopic magnetisation polarised along the TbPc2 principal magnetic axis after the completed rotation could then proceed via time-resolved magnetisation measurements.

Chirality-assisted spin Hall effect of light in the vicinity of the quasi-antidual symmetry mode of a chiral sphere

The spin Hall shift (SHS) refers to a transverse shift in the scattering plane during the spin-orbit interaction (SOI). SHS is considerably small when light is scattered by a sphere due to the absence of unidirectional scattering. This work shows that the chiral property of a sphere can offer a platform to optimize the SOI by achieving nearly zero forward scattering with significant backward scattering. As a result, a polarization transformation takes place and the scattered field transfers its maximum spin angular momentum to orbital angular momentum. Consequently, an enhanced transversal shift is observed due to the momentum conservation of the scattered field. The results reveal that the shift strongly depends on the handedness of the chiral sphere and the helicity of the incident beam. Thus, offering an alternative paradigm for the quantitative measurement of chirality parameters of a single chiral nanoparticle. We hope that these results will potentially shed new light on the SOI of various forms that can find potential applications such as optical sensing, chiral resolution of single nanoparticles, precision measurements, and the manipulation of subwavelength nanoparticles.

Reaching the Maximal Unquenched Orbital Angular Momentum L = 3 in Mononuclear Transition-Metal Complexes: Where, When and How?

The conditions for achieving the maximal unquenched orbital angular momentum L = 3 and the highest magnetic anisotropy in mononuclear 3d complexes with axial coordination symmetry are examined in terms of the ligand field theory. It is shown that, apart from the known linear two-coordinate 3d7 complex CoII(C(SiMe2ONaph)3)2 characterized by record magnetic anisotropy and single-molecule magnet (SMM) performance (with the largest known spin-reversal barrier Ueff = 450 cm−1), the maximal orbital angular momentum L = 3 can also be obtained in linear two-coordinate 3d2 complexes (V3+, Cr4+) and in trigonal-prismatic 3d3 (Cr3+, Mn4+) and 3d8 (Co+, Ni2+) complexes. A comparative assessment of the SMM performance of the 3d2, 3d3 and 3d8 complexes indicates that they are unlikely to compete with the record linear complex CoII(C(SiMe2ONaph)3)2, whose magnetic anisotropy is close to the physical limit for a 3d metal.

A theoretical study on the impact of centrifugal potential and fragment identification in the decay of compound nuclei (ACN = 60&100)

Decay analysis of compound nuclei such as [Formula: see text] and [Formula: see text] formed in [Formula: see text]Ca and [Formula: see text]Ni reactions, respectively, is studied using two theoretical frameworks, dynamical cluster-decay model (DCM) and PACE4. To explore the decay dynamics in a relatively lighter mass region [Formula: see text], two more reactions are picked (i) [Formula: see text]Mg forming the [Formula: see text] compound nucleus, (ii) another one involving the odd mass projectile, [Formula: see text]. In DCM, the fusion excitation functions are calculated using sticking [Formula: see text] and nonsticking [Formula: see text] limits of the moment of inertia. For the chosen reactions, fusion cross-sections are equivalent to evaporation residue (ER) cross-sections [Formula: see text] as fission cross-sections are negligible. A lower magnitude of maximum angular momentum [Formula: see text] is obtained via the [Formula: see text] approach in comparison to the [Formula: see text] approach and the angular momentum obtained via the [Formula: see text] approach is closer to the experimental observations. The structure and magnitude of fragmentation potential and preformation probability [Formula: see text] depend on the choice of moment of inertia and the magnitude of angular momentum involved. Besides this, PACE4 is employed to address the fusion cross-section of chosen reactions. The most probable decay channel is identified using both DCM and PACE4 approaches.

Explicitly Correlated Double-Hybrid DFT: A Comprehensive Analysis of the Basis Set Convergence on the GMTKN55 Database.

Double-hybrid density functional theory (DHDFT) offers a pathway to accuracy approaching composite wavefunction approaches such as G4 theory. However, the Görling–Levy second-order perturbation theory (GLPT2) term causes them to partially inherit the slow ∝L–3 (with L the maximum angular momentum) basis set convergence of correlated wavefunction methods. This could potentially be remedied by introducing F12 explicit correlation: we investigate the basis set convergence of both DHDFT and DHDFT-F12 (where GLPT2 is replaced by GLPT2-F12) for the large and chemically diverse general main-group thermochemistry, kinetics, and noncovalent interactions (GMTKN55) benchmark suite. The B2GP-PLYP-D3(BJ) and revDSD-PBEP86-D4 DHDFs are investigated as test cases, together with orbital basis sets as large as aug-cc-pV5Z and F12 basis sets as large as cc-pVQZ-F12. We show that F12 greatly accelerates basis set convergence of DHDFs, to the point that even the modest cc-pVDZ-F12 basis set is closer to the basis set limit than cc-pV(Q+d)Z or def2-QZVPPD in orbital-based approaches, and in fact comparable in quality to cc-pV(5+d)Z. Somewhat surprisingly, aug-cc-pVDZ-F12 is not required even for the anionic subsets. In conclusion, DHDF-F12/VDZ-F12 eliminates concerns about basis set convergence in both the development and applications of double-hybrid functionals. Mass storage and I/O bottlenecks for larger systems can be circumvented by localized pair natural orbital approximations, which also exhibit much gentler system size scaling.

HF, DF, TF: approximating potential curves, calculating rovibrational states

A simple analytical expression for the potential energy curve for the ground state X 1Σ+ of the hydrogen fluoride molecule HF obtained in the framework of the Born–Oppenheimer approximation is proposed. This analytical expression for the potential energy curve is based in the two point Padé approximation, which correctly reproduces the asymptotic behavior at small R → 0 and large R → ∞ internuclear distances, and position and depth of potential well, leading to the accuracy of 4–5 decimal digits when compared with experimental data. The rovibrational spectra of the diatomic molecule HF is calculated by solving the Schrödinger equation for nuclear motion using the Lagrange-mesh method. The ground state X 1Σ+ contains 21 vibrational states (ν, 0) and 724 rovibrational states (ν, L) with maximal angular momentum equal to 55. The change of reduced mass in the Schrödinger equation for nuclear motion allows us to obtain the rovibrational spectrum of the ground state potential curve of the deuterium fluoride DF (contains 29 vibrational states (ν, 0) and 1377 rovibrational states (ν, L)) and tritium fluoride TF (contains 35 vibrational states (ν, 0) and 1967 rovibrational states (ν, L)) with maximal angular momenta 76 and 92, respectively. Entire rovibrational spectra is presented for the HF molecule and its two isotopologues DF and TF.

Angular-Momentum-Based Sizing of Control Moment Gyro Cluster for an Agile Spacecraft

The sizing of a control moment gyro (CMG) cluster is covered sparsely in literature, but it is of considerable interest to a practicing engineer. In this paper, the sizing of a cluster of four control moment gyros is investigated based on the mission angular momentum requirement of a typical agile spacecraft. The CMG skew angle and individual CMG angular momentum are determined as part of the sizing. The work focuses on the sizing of a minimally redundant cluster of four CMGs in a pyramid and roof-type arrangement considering their external angular momentum surfaces. Two approaches are discussed: the first considers maximum angular momentum about individual axis separately, and the second considers the momentum requirement about two axes simultaneously. The internal momentum surfaces of the CMG clusters are analyzed. Gimbal angle desaturation and the fuel consumed for it by the roof-type and pyramid configurations are also examined. Both the four CMG clusters are able to meet the maximum nonspherical angular momentum demanded by a typical mission about each axes. However, using method 1, the cluster is able to generate only 88% of the two-axis mission demand. The clusters meet the mission demand completely with method 2 using 20% more angular momentum per CMG and an increase in skew angle by compared to method 1. The 20% increase in momentum increases power consumption by 11%. For a typical gimbal angle desaturation, the roof-type cluster uses 8.5% more fuel than the pyramid arrangement. However, the former has only one major internal singular surface in contrast with seven for the latter. This makes the roof-type arrangement very desirable to keep the singularity avoidance algorithm simple and amenable with the CMGs operating within the momentum capability, and achieve the required spacecraft agility.

ClF diatomic molecule: Rovibrational spectra

Following the first principles the analytic Born–Oppenheimer (BO) potential curve for the ground state X1Σ+ of the molecule ClF is proposed for whole range of internuclear distances R∈[0,∞). It is based on matching the perturbation theory at small internuclear distances R and multipole expansion at large distances R, it has the form of two-point Pade approximant and provides 3–4 figures in rovibrational energies. It supports 5719 rovibrational states with maximal vibrational number νmax=47 and maximal angular momentum Lmax=210 including 36 weakly-bound states close to threshold (to dissociation limit) with the energies ≲10-4hartree. The van der Waals constant C6(ClF)∼29.3a.u. is predicted.

Calculation of double differential cross sections of electron–atom bremsstrahlung by the relativistic partial-wave method at electron energies greater than 3 MeV

This work describes an extension of the relativistic partial-wave (PW) method for calculation of the double differential cross sections (DDCS) of electron–atom bremsstrahlung at incident electron energies (T1) of the order of 10 MeV. The PW method is extended to higher energies by replacing some of the radial matrix elements with interpolated values, and by extrapolating the truncated PW series to a sufficiently high value of the maximum total angular momentum of the electron (jmax). Although the current analysis has been mostly limited to the cases with the outgoing electron energy T2≤10MeV and all values of Z from 1 to 100, this method allows to obtain accurate values of the DDCS even when T2>20MeV, using a relatively small number of partial waves (jmax<300), as demonstrated by a case study described in the present work (Z=1, T1=30MeV, T2=24MeV).

São Paulo potential version 2 (SPP2) and Brazilian nuclear potential (BNP)

The REGINA code calculates the São Paulo potential version 2 (SPP2) and the Brazilian nuclear potential (BNP). The code also provides nuclear densities obtained from the Dirac-Hartree-Bogoliubov model, which are used to calculate the nuclear potentials. Elastic scattering cross sections are obtained within the context of the optical model, with different options for the real and imaginary parts of the optical potential. In this manuscript, we provide a summary of the theoretical framework and information about the use of the code. Program summaryProgram Title: REGINA.fCPC Library link to program files:https://doi.org/10.17632/vfkkjb8dv7.1Licensing provisions: GPLv3Programming language: Fortran-77Nature of problem: We provide a code to calculate the nuclear potential between two nuclei according to two different models: the São Paulo potential version 2 (SPP2), that includes a dependence on the relative velocity between the nuclei, and the velocity independent Brazilian nuclear potential (BNP). These potentials assume the effective nuclear interactions proposed in [1,2], and are obtained within the double-folding approach with nuclear densities calculated through the Dirac-Hartree-Bogoliubov model [3].Solution method: The code involves two files containing previously calculated results for theoretical neutron and proton distributions and also experimental charge densities obtained from electron scattering experiments. These results are used to obtain matter densities through convolution using Fourier transforms. The Fourier transform method is also employed to obtain the double-folding potentials. Integration of the Schrödinger equation with a complex optical potential is performed using the Cowell method [4,5]. With this, for a given system and energy, we obtain the S-matrix and the elastic scattering cross sections.Additional comments including restrictions and unusual features: The maximum angular momentum supported in the optical model calculations is 2000.

Large angle maneuver and high accuracy attitude pointing steering law for variable speed control momentum gyroscopes

In the variable speed control momentum gyroscopes (VSCMG), the output torque of the VSCMG can be supported by the gyroscopic torque by a large margin with low resolution. The output torque of the VSCMG can be only supported by the reaction torque of the flywheels with high resolution when the gimbals are locking. Consequently, the torque error that is determined by the low spin rate fluctuation or servo tracking error of the gimbals can be vanished, and the VSCMG can be suitable for large maneuver and high accuracy attitude pointing as the actuator. Unfortunately, the singularity of the flywheel torque co-plane may be encountered. In this paper, the singularity of the flywheel torque co-plane is visualized based on geometry method. The singularity can be effectively avoided by locking gimbals. The locking gimbals positions are optimized with the maximum angular momentum. The steering laws with two phases are proposed to operate the task of the large angle maneuver and high accuracy control for a spacecraft. In the phase 1, a large margin torque can be achieved by the new designed steering law, and the gimbals can be steered to the optimization gimbals positions at the final stage of the phase 1. In the phase 2, the high precision torque can be achieved by only steering the flywheels and the locking the gimbals. Consequently, the torque error that is caused by the spin rate fluctuation or servo tracking error of the gimbals can be effectively eliminated.

Application of Complex Functional of Quality in Optimal Control of Spacecraft Motion

The problem of optimal control of the reorientation of a spacecraft as a solid body from an arbitrary initial ‎position into a prescribed final angular position is considered and solved. The case is ‎studied in detail when the ‎minimized index combines, in a given proportion, the integral of modulus of angular momentum and duration of ‎maneuver. It is proved that the accepted optimality ‎criterion guarantees the motion of a spacecraft with modulus of ‎angular momentum not exceeding the required value. Formalized equations and expressions for the synthesis of ‎the optimal rotation program are obtained using quaternion models. It is shown that the optimal solution corresponds to the strategy “acceleration - rotation with constant modulus of angular momentum-‎braking”, the ‎angular momentum and the controling moment are perpendicular during optimal rotation between acceleration and ‎braking. On the basis of necessary optimality conditions, the ‎main properties, laws, and key characteristics ‎‎(parameters, constants, integrals of motion) of the ‎optimal solution of the control problem, including the turn time ‎and the maximum angular momentum for the optimal motion, are determined. An estimation of the influence of the ‎bounded ‎controling moment on the character of the optimal motion and on the indicators of quality is ‎made. The ‎construction of an optimal control program of rotation is based on the quaternion variables and Pontryagin’s ‎maximum principle. The value of maximal angular momentum magnitude is calculated by condition of ‎transversality. The designed method is universal and invariant ‎relative to the moments of inertia. For dynamically ‎symmetric spacecraft, a complete solution of ‎the reorientation problem in closed form is presented. An example ‎and results of mathematical ‎modeling of the motion of a spacecraft under optimal control are presented, ‎demonstrating the ‎practical feasibility of the method for controlling spacecraft's spatial orientation.

Biomechanical agreement between different imitation jumps and hill jumps in ski jumping.

Even though the take-off in ski jumping is decisive, athletes only have a very limited number of training trials on the actual ski jump to practice under real ski jump conditions. Hence, various imitation jumps aiming to mimic the hill jump are performed during daily training. These imitation jumps should therefore mimic the kinematic pattern of hill jumps appropriately. This study aimed to identify imitation jumps that resemble hill jumps regarding four performance-related biomechanical criteria: maximal vertical take-off velocity, maximal knee extension velocity, maximal forward-directed angular momentum and anterior shift of the center of mass. Therefore, a three-dimensional analysis of the take-off during six different modalities of imitation jumps as well as hill jumps for validation was carried out in nine professional ski jumpers. Imitation jumps from a rolling platform show better agreement than stationary jumps and three out of the four parameters were best resembled via an imitation jump that included ski jumping boots. Thus, non-hill take-off training should be performed with complex imitation jumps to mimic the actual ski jump. Except for the vertical take-off velocity, we could identify one imitation jump type that is not statistically different to the hill. Consequently, the individual deficiencies of the athletes can be addressed and specifically trained using the appropriate imitation jump. These information about the similarity between imitation jumps and real hill jumps are highly relevant for trainers and athletes in order to effectively design their training programs.