Yu. M. Belousov

Theoretical description of the muon spin depolarization in the crystalline phase of 3He

We present a theoretical description of the behavior of a positive muon stopped in a solid helium target that allows the results of experiments for the crystalline phase of 3He to be explained. The forming linear (He2μ)+ molecular ion is shown to have time to be thermalized in the muon lifetime and to be in a state with the rotational quantum numbers K = 1 and K = 0 for ions with the total nuclear spins I = 1 and I = 0, respectively. The thermalization mechanism is attributable to the interaction between the electric quadrupole moment of the ion and the helium lattice. This interaction removes the three-fold angular momentum component degeneracy and there is no spin-rotation interaction. We derive the Hamiltonian of the spin-phonon interaction between the helium ion nuclei and the lattice. Depolarization is observed only for the ion with I = 1 and is attributable to the spin-exchange interaction between the lattice nuclei and the 3He nuclei bound with the muon with the emission of phonons in the lattice deformed by the strong Coulomb field of the positively charged ion.

Theory of muon spin depolarization in crystalline phases of 3He

As is obvious from the energetic point of view, positive muons must form the molecular ion ( He_2μ)+ in condensed phases of helium. A theory of positive muon spin depolarization in crystalline phase of 3He in this model is devised. The theory explains experimental results. It is shown that the abrupt temperature dependence of the muon spin depolarization rate at T < 2 K which is observed in experiments is explained by spin–phonon interaction. This interaction mechanism arises due to a modulation of the exchange interaction between host atoms of the 3He‐lattice.

Dynamics of charge carriers at the place of the formation of a muonic atom in diamond and silicon

The space-time distribution of charge carriers at the place of the location of a muonic atom formed when a negative muon is captured by an atom of the lattice has been numerically simulated taking into account the self-consistent electric field. The results of μSR experiments with negative muons in diamond crystals have been explained and reasons for the difference in the behavior of the spin polarization of the negative muon in boron-doped diamond and in silicon have been revealed. The condition of the validity of the analytical solution of this problem has been obtained. It has been shown that the muonic atom in diamond, in contrast to silicon, does not form a neutral acceptor center in the paramagnetic state during the muon experiment and remains in the diamagnetic state of a positive ion.

Laser-induced conductivity of semiconductors at low temperatures

We consider the negative conductivity of electrons in semiconductors excited by a picosecond laser pulse at low temperatures, due to the inelastic electron-phonon collisions. For the first time, the dependence of the deformation potential on the phonon wave number is taken into account. This dependence significantly changes the region of negative electron conductivity as a function of the phonon temperature.

The theory of muon spin depolarization in the crystalline phase of 3He

Abstract Peculiarities of a muon spin diamagnetic component behavior in condensed phases of 3He are considered. It is shown that the experimentally observed relaxation of a diamagnetic component in solid 3He could be explained theoretically if μ+ forms a molecular ion with a 3He atom. In this case the relaxation of the muon spin polarization is determined by a spin–phonon interaction at T⩽1 K . In the temperature range T⩾1 K a hyperfine interaction in a molecular ion is not effective and the relaxation is determined by a direct interaction of muon magnetic moment with fluctuating local magnetic fields in the crystal lattice.

Theory of muon spin depolarization in condensed phases of hydrogen isotopes

A theory of muon spin depolarization in the molecular ion ( H2μ)+(( D_2μ)) formed in a crystalline phase of hydrogen isotopes is presented. It is shown that the molecular ion ( H_2μ)+ has no time to thermalize during the muon lifetime, but after \tau\ll \tau_μ has time to transit to the lowest energy levels of the vibration‐rotation spectrum. The depolarization of the muon spin is determined by the interaction of the ion’s electric dipole moment with the lattice and by spin‐rotation interactions VLS in the ion. This mechanism is analogous to that of “muonium”, replacing the hyperfine interaction by VLS. The results can explain the experimental data and in particular the absence of a strong isotopic effect.

Excited states of the molecular ion (H2μ)

The rotation-vibration spectrum of (H2μ)+ is computed. Radiative lifetimes of the excited states are of order 10−4 s or more. These times can be considered infinite compared to the lifetime ofμ+. For the ion in a crystal the lifetimes are significantly decreased by interaction with polarized molecules of the lattice. Transition rates to the ground state are calculated for (H2μ)+ in a hydrogen crystal. The results make it possible to interpret the experimental data from μSR investigations of hydrogen, deuterium and hydrogen-deuterium mixtures.

Time evolution of a pair of distinguishable interacting spins subjected to controllable and noisy magnetic fields

Abstract The quantum dynamics of a J ˆ 2 = ( j ˆ 1 + j ˆ 2 ) 2 -conserving Hamiltonian model describing two coupled spins j ˆ 1 and j ˆ 2 under controllable and fluctuating time-dependent magnetic fields is investigated. Each eigenspace of J ˆ 2 is dynamically invariant and the Hamiltonian of the total system restricted to any one of such ( j 1 + j 2 ) − | j 1 − j 2 | + 1 eigenspaces, possesses the SU(2) structure of the Hamiltonian of a single fictitious spin acted upon by the total magnetic field. We show that such a reducibility holds regardless of the time dependence of the externally applied field as well as of the statistical properties of the noise, here represented as a classical fluctuating magnetic field. The time evolution of the joint transition probabilities of the two spins j ˆ 1 and j ˆ 2 between two prefixed factorized states is examined, bringing to light peculiar dynamical properties of the system under scrutiny. When the noise-induced non-unitary dynamics of the two coupled spins is properly taken into account, analytical expressions for the joint Landau–Zener transition probabilities are reported. The possibility of extending the applicability of our results to other time-dependent spin models is pointed out.

Process of negative-muon-induced formation of an ionized acceptor center (μA)– in crystals with the diamond structure

The formation of an ionized acceptor center by a negative muon in crystals with the diamond structure is considered. The negative muon entering a target is captured by a nucleus, forming a muonic atom μA coupled to a lattice. The appearing radiation-induced defect has a significant electric dipole moment because of the violation of the local symmetry of the lattice and changes the phonon spectrum of the crystal. The ionized acceptor center is formed owing to the capture of an electron interacting with the electric dipole moment of the defect and with the radiation of a deformation-induced local-mode phonon. Upper and lower bounds of the formation rate of the ionized acceptor center in diamond, silicon, and germanium crystals are estimated. It is shown that the kinetics of the formation of the acceptor center should be taken into account when processing μSR experimental data.

Quasi-elastic and inelastic approximations in the description of the charge carrier dynamics in diamond

The differences between the quasi-elastic and inelastic approximations in calculating the carrier mobility in diamond is numerically estimated for the spatially uniform and one-dimensional cases. Data on the steady-state mobility at 20 K in the quasi-elastic and inelastic approximations differ by a factor of about 6. In the one-dimensional case for a time-constant carrier source located deep inside the sample, the data on the heavy-hole mobility in the quasi-elastic and inelastic approximations nearly coincide. When the initial distribution function is located at the sample edge, the time dependences of the carrier mobility in the quasi-elastic and inelastic approximations are markedly different. The results obtained are of importance for the interpretation of electrophysical experiments with diamond.