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The differential cross sections for alpha-particle emission at an angle of 0 $${}^{\circ}$$ in the reactions induced by a 6-MeV/nucleon $${}^{56}$$ Fe beams incident to $${}^{238}$$ U and $${}^{181}$$ Ta targets were measured versus the alpha-particle energy by means of a high-resolution magnetic analyzer (MAVR setup). The resulting spectra were found to contain fast alpha particles of energy corresponding to the two- and three-body exit reaction channels, including alpha particles of energy close to the two-body kinematical limit. The data obtained in this experiment were analyzed on the basis of the moving-source model. The emission of nonequilibrium alpha particles in the forward direction from the heavier target nucleus upon the complete or incomplete fusion of nuclei was revealed within the time-dependent quantum approach.

Within the study of the time-of-flight method, an appropriate system has been created and the first test data have been obtained that fully demonstrate the efficient operation of the equipment. An MCP detector is used as the start detector. During the experiment at this facility, the time resolution, depending on parameters of the reaction products (mass, charge, and energy), has been measured. The characteristics of the detector operating at the IC-100 accelerator (FLNR, JINR) have been measured. The results demonstrate a high time resolution for charged particles in a wide mass range.

Non-relativistic ionization energies 3He2+μ−e− and 4He2+μ−e− of helium-muonic atoms are calculated for ground states. The calculations are based on the variational method of the exponential expansion. Convergence of the variational energies is studied by an increasing of a number of the basis functions N. This allows to claim that the obtained energy values have 26 significant digits for ground states. With the obtained results we calculate hyperfine splitting of the muonic helium atoms.

International audience; Secondary beams (6Li,7Be,8B) obtained by separation of fragmentation products of 15N beam (50 A MeV) impinging on a Be target using COMBAS spectrometer. The secondary products will be detected by a telescope consisting of five Si-detectors (dE) and CsI(Tl) detector (Er). By the dE-E method, the telescope allowed us to achieve unambiguous particle identification originating from incident secondary beams as well as theirs reaction products resulting from reactions with one of Si detectors chosen as the target. Accordingly, break-up reactions of 6Li, 7Be and 8B were studied in this experiment.

HD$^+$ hydrogen molecular ion is of metrological interest due to possibility of precise theoretical evaluation of its spectrum and of external-field-induced shifts. In present work, the rates of laser-induced electric quadrupole transitions are calculated for a wide range of rovibrational transitionsin particular for L0-L’2, L1-L’3, L2-L’4 (v=(0-10)-v’=(0-3)). Results are presented with six significant digits.

High-precision variational calculations of the operators for the relativistic corrections in the leading $m{\ensuremath{\alpha}}^{4}$ order are presented. The rovibrational states in the range of the total orbital angular momentum $L=0--4$ and vibrational quantum number $v=0--10$ for the ${\text{H}}_{2}{\phantom{\rule{0.16em}{0ex}}}^{+}$ and ${\text{HD}}^{+}$ molecular ions are considered. We estimate that about 10 significant digits are obtained. This high precision is required for making theoretical predictions for transition frequencies at the level of ${10}^{\ensuremath{-}12}$ relative uncertainty.

We use the exponential explicitly correlated variational basis set of the type exp(-αnR - βnr1 - γnr2) to calculate systematically the nonrelativistic bound-state energies for the hydrogen molecular ion H2+ and HD+. We perform calculations for the states of the total angular momentum L=0-4 with the complete set of vibrational numbers v=0-10.

We numerically investigate the following two-body stationary Schrodinger equation (SE): \(\left\{ { - \frac{{{{\rlap{--} h}^2}}}{{2m}}\frac{\partial }{{x_1^2}} - \frac{{{{\rlap{--} h}^2}}}{{2m}}\frac{\partial }{{x_2^2}} + V\left( {{x_2}} \right) + g\partial \left( {{x_1} - {x_2}} \right)} \right\}x\Psi \left( {{x_1},{x_2}} \right) = E\Psi \left( {{x_1},{x_2}} \right),\) where \({x_1},{x_2} \in \mathbb{R},V\left( {{x_1}} \right) = {V_0}{\sin ^2}\left( {{k_x}{x_i}} \right)\) is the potential describing the interaction of atoms with a trap and gδ(x1–x2) is the interatomic potential. Previously, a similar problem has been solved analytically for the harmonic interaction \({V_h}\left( {{x_i}} \right) = \frac{1}{2}m\omega x_i^2\) with the trap, which leads to the separation of coordinates \(y = \frac{{{x_1} + {x_2}}}{{\sqrt 2 }},{\kern 1pt} x = \frac{{{x_1} - {x_2}}}{{\sqrt 2 }}\) for the center-of-mass and relative motion. The anharmonicity of the trap couples these motions and, there-fore, the problem becomes significantly more complicated. In previous works, the anharmonicity Va = V–Vh of the trap has been taken into account in the framework of perturbation theory. In this work, the energy level shifts of a two-body atomic system are calculated beyond the perturbation theory for different magnitudes of parameter g of the interatomic interaction. The results are compared to those computed using the perturbation theory.

The nonrelativistic ionization energy levels of a helium atom are calculated for S, P, and D states. The calculations are based on the variational method of “exponential” expansion. The convergence of the calculated energy levels is studied as a function of the number of basis functions (N). This allows us to claim that the obtained energy values (including the values for the states with a nonzero angular momentum) are accurate to 20 significant digits.

We present systematic calculations of the leading order relativistic corrections including the hyperfine splitting (HFS) for a wide range of rotational and vibrational states of the HT+ molecular ion. We also calculate the DC and AC Stark effects for the molecular hydrogen ions \(H_{2}^{+}\) and HD+ in the non-relativistic approximation. The influence of the DC Stark polarizability effect on the hyperfine substates of a ro-vibrational state is carefully analyzed. Our results enable the detailed evaluation of certain systematic shifts of the transition frequencies for the purpose of ultra-high-precision optical, microwave, or radio-frequency spectroscopy of the hydrogen molecular ions in a trap.

The static dipole polarizability for the hydrogen molecular ions H$_2^+$, HD$^+$, and D$_2^+$ are calculated. These new data for polarizability takes into account the leading order relativistic corrections to the wave function of the three-body system resulted from the Breit-Pauli Hamiltonian of $m\alpha^4$ order. Our study covers a wide range of rotational ($L=0-5$) and vibrational ($v=0-10$) states, which are of practical interest for precision spectroscopy of the hydrogen molecular ions.

The static dipole polarizability of metastable states in pionic helium atoms is studied. We use the complex coordinate rotation method to properly take account of the resonant nature of the states. Our calculation shows that the (17, 14) states both in 3He and 4He are not stable due to strong collisional quenching. This explains the absence of signal in the PiHe experiment at the Paul Scherer Institute, Switzerland while studying the (16, 15) (17, 14) transition.