Spin Density Matrix Research Articles

Spin interference in the spin density matrix of a compound nucleus in reactions of nuclear fission by cold polarized neutrons

Spin density matrices of neutron resonance states of a compound nucleus formed in the reaction of capture of a polarized neutron by a non-oriented target nucleus for different directions of neutron polarization vector are constructed within the quantum fission theory. The obtained spin matrices are used to calculate T-odd asymmetries in differential cross sections of ternary nuclear fission with the emission of different third particles. It is demonstrated that the expressions for T-odd asymmetries in the cases of neutron polarization direction \(\vec p_n\) along the x and y axes in the laboratory reference frame differ by the values of the unified correlator of the form \(\left( {\vec p_n ,\left[ {\vec k_{LF} ,\vec k_3 } \right]} \right)\) (where \(\vec k_{LF}\) and \(\vec k_3\) are the wave vectors of a light fission fragment and the third particle, respectively), and are transformed into one another if the laboratory reference frame in which \(\vec p_n\) is directed along the x axis is rotated to a laboratory reference frame in which \(\vec p_n\) is directed along the y axis. It is shown that T-odd TRI and ROT asymmetries are associated, respectively, with the odd and even components of the amplitudes of the angular distribution of third particles perturbed by the collective rotation of a polarized fissile nucleus, and each of these amplitudes can be considerably amplified (or suppressed) relative to one another due to the interference from fission amplitudes of pairs of neutron resonances sJs and s′Js′.

Preparation of new polarization experiment SPASCHARM at IHEP

A new experiment SPASCHARM devoted to a systematic study of polarization phenomena in hadron-hadron interactions in the energy range 10-70 GeV is under preparation at IHEP (Protvino). The physical observables will be single-spin asymmetries, hyperon polarizations and spin-density matrix elements. A universal setup will detect and identify various neutral and charge particles in the full azimuthal angle and a wide polar angle range. A polarized target is used to measure the SSA. The SPASCHARM sub-detectors are being designed and constructed now. The possibility of obtaining a polarized proton beam for the SPASCHARM experiment from Lambda decays is under study.

Reaction operators for spin-selective chemical reactions of radical pairs

Spin-selective reactions of radical pairs have traditionally been modelled theoretically by adding phenomenological rate equations to the quantum mechanical equation of motion of the radical pair spin density matrix. More recently an alternative set of rate expressions, based on a quantum measurement approach, has been suggested. Here we show how these two reaction operators can be seen as limiting cases of a more general reaction scheme.

Effect of periodically time-dependent magnetic fields on a population of spin states of radical pairs

The time dependences for a population of radical pair spin states and the amplitudes of the transitions between them are calculated for magnetic fields of complex configuration. The abovementioned values are derived directly from the solution to the Liouville equation for the components of a spin density matrix for a radical pair. The oscillating mechanism of the relaxation of partial populations of spin levels upon the monotonous reduction of the full population was established in the course of our calculations.

A heuristic model of damped quantum rotation effects in nuclear magnetic resonance spectra

The damped quantum rotation (DQR) theory describes temperature effects in NMR spectra of hindered molecular rotators composed of identical atoms arranged in regular N-gons. In the standard approach, the relevant coherent dynamics are described quantum mechanically and the stochastic, thermally activated motions classically. The DQR theory is consistent. In place of random jumps over one, two, etc., maxima of the hindering potential, here one has damping processes of certain long-lived coherences between spin-space correlated eigenstates of the rotator. The damping-rate constants outnumber the classical jump-rate constants. The jump picture is recovered when the former cluster appropriately around only as many values as the number of the latter. The DQR theory was confirmed experimentally for hindered methyl groups in solids and even in liquids above 170 K. In this paper it is shown that for three-, four-, and sixfold rotators, the Liouville space equations of NMR line shapes, derived previously with the use of the quantum mechanical reduced density matrix approach, can be be given a heuristic justification. It is based on an equation of motion for the effective spin density matrix, where the relevant spin hamiltonian contains randomly fluctuating terms. The occurrence of the latter can be rationalized in terms of fluctuations of the tunneling splittings between the torsional sublevels of the rotator, including momentary liftings of the Kramers degeneracies. The question whether such degeneracy liftings are physical or virtual is discussed. The random terms in the effective hamiltonian can be Monte Carlo modeled as piecewise constant in time, which affords the stochastic equation of motion to be solved numerically in the Hilbert spin space. For sixfold rotators, this way of calculating the spectra can be useful in the instances where the Liouville space formalism of the original DQR theory is numerically unstable.

A general approach for prediction of motional EPR spectra from Molecular Dynamics (MD) simulations: application to spin labelled protein

A general approach for the prediction of EPR spectra directly and completely from single dynamical trajectories generated from Molecular Dynamics (MD) simulations is described. The approach is applicable to an arbitrary system of electron and nuclear spins described by a general form of the spin-Hamiltonian for the entire motional range. It is shown that for a reliable simulation of motional EPR spectra only a single truncated dynamical trajectory generated until the point when correlation functions of rotational dynamics are completely relaxed is required. The simulation algorithm is based on a combination of the propagation of the spin density matrix in the Liouville space for this initial time interval and the use of well defined parameters calculated entirely from the dynamical trajectory for prediction of the evolution of the spin density matrix at longer times. A new approach is illustrated with the application to a nitroxide spin label MTSL attached to the protein sperm whale myoglobin. It is shown that simulation of the EPR spectrum, which is in excellent agreement with experiment, can be achieved from a single MD trajectory. Calculations reveal the complex nature of the dynamics of a spin label which is a superposition of the fast librational motions within dihedral states, of slow rotameric dynamics among different conformational states of the nitroxide tether and of the slow rotational diffusion of the protein itself. The significance of the slow rotameric dynamics of the nitroxide tether on the overall shape of the EPR spectrum is analysed and discussed.

T>0ensemble-state density functional theory via Legendre transform

A logical foundation of equilibrium state density functional theory in a Kohn-Sham-type formulation is presented on the basis of Mermin's treatment of the grand canonical state by exploiting functional Legendre transforms. It is simpler and more satisfactory compared to the usual derivation of the ground-state theory and free of most remaining open points of the latter. The existence of the functional derivative of the corresponding density functional $F[n]$ at all densities of grand canonical equilibrium states is proved even in the spin-density matrix version of the theory. It may, in particular, be relevant with respect to cases of spontaneous symmetry breaking such as noncollinear magnetism and orbital order.

Two-dimensional surface charge transport in topological insulators

We construct a theory of charge transport by the surface states of topological insulators in three dimensions. The focus is on the experimentally relevant case when the Fermi energy ${\ensuremath{\epsilon}}_{F}$ and transport scattering time $\ensuremath{\tau}$ satisfy ${\ensuremath{\epsilon}}_{F}\ensuremath{\tau}/\ensuremath{\hbar}⪢1$ but ${\ensuremath{\epsilon}}_{F}$ lies below the bottom of the conduction band. Our theory is based on the spin density matrix and takes the quantum Liouville equation as its starting point. The scattering term is determined to linear order in the impurity density ${n}_{i}$ and explicitly accounts for the absence of backscattering while screening is included in the random-phase approximation. The main contribution to the conductivity is $\ensuremath{\propto}{n}_{i}^{\ensuremath{-}1}$ and has different carrier density dependencies for different forms of scattering while an additional contribution is independent of ${n}_{i}$. The dominant scattering angles can be inferred by studying the ratio of the transport time to the Bloch lifetime as a function of the Wigner-Seitz radius ${r}_{s}$. The current generates a spin polarization that could provide a smoking-gun signature of surface state transport. We also discuss the effect on the surface states of adding metallic contacts.

A study of the relationships between unpaired electron density, spin-density and cumulant matrices

This work describes the derivation of simple relationships between the density matrix of effectively unpaired electrons and the spin-density matrix in N-electron systems. The link between both devices turns out to be the one-electron matrix arising from the diagonal contraction of the cumulant matrix corresponding to the second-order reduced density matrix. We study some features of this contracted matrix, showing its usefulness to describe the electronic correlation. Numerical determinations performed in selected systems with different spin symmetries confirm the theoretical predictions.

Measurement of spin-density matrix elements forϕ-meson photoproduction from protons and deuterons near threshold

The LEPS/SPring-8 experiment made a comprehensive measurement of the spin-density matrix elements for $\gamma p \to \phi p$, $\gamma d \to \phi p n$ and $\gamma d \to \phi d$ at forward production angles. A linearly polarized photon beam at $E_{\gamma}$=1.6-2.4 GeV was used for the production of $\phi$ mesons. The natural-parity Pomeron exchange processes remains dominant nearthreshold. The unnatural-parity processes of pseudoscalar exchange is visible in the production from nucleons but is greatly reduced in the coherent production from deuterons. There is no strong $E_{\gamma}$-dependence, but some dependence on momentum-transfer. A small but finite value of the spin-density matrix elements reflecting helicity-nonconserving amplitudes in the $t$-channel is observed.

EPR detected polarization transfer between Gd3+ and protons at low temperature and 3.3 T: The first step of dynamic nuclear polarization

Electron-electron double resonance pulsed electron paramagnetic resonance (EPR) at 95 GHz (3.3 T) is used to follow the dynamics of the electron spin polarization during the first stages of dynamic nuclear polarization in solids. The experiments were performed on a frozen solution of Gd(+3) (S=7/2) in water/glycerol. Focusing on the central vector -1/2 --> vector +1/2 transition we measured the polarization transfer from the Gd(3+) electron spin to the adjacent (1)H protons. The dependence of the echo detected EPR signal on the length of the microwave irradiation at the EPR "forbidden" transition corresponding to an electron and a proton spin flip is measured for different powers, showing dynamics on the microsecond to millisecond time scales. A theoretical model based on the spin density matrix formalism is suggested to account for this dynamics. The central transition of the Gd(3+) ion is considered as an effective S = 1/2 system and is coupled to (1)H (I = 1/2) nuclei. Simulations based on a single electron-single nucleus four level system are shown to deviate from the experimental results and an alternative approach taking into account the more realistic multinuclei picture is shown to agree qualitatively with the experiments.

Production and polarization of J/ψ mesons at HERA versus k t -factorization approach

In the framework of k f -factorization approach, inclusive production of J/ψ mesons at HERA is considered. The differential cross sections and spin-density matrix elements are calculated. Theoretical predictions are compared with recent H1 experimental data.

Diffractive electroproduction of ρ and ϕ mesons at HERA

Diffractive electroproduction of ρ and ϕ mesons is measured at HERA with the H1 detector in the elastic and proton dissociative channels. The data correspond to an integrated luminosity of 51 pb−1. About 10500 ρ and 2000 φ events are analysed in the kinematic range of squared photon virtuality 2.5 ≤ Q 2 ≤ 60 GeV2, photon-proton centre of mass energy 35 ≤ W ≤ 180 GeV and squared four-momentum transfer to the proton |t| ≤ 3 GeV2. The total, longitudinal and transverse cross sections are measured as a function of Q 2, W and |t|. The measurements show a transition to a dominantly “hard” behaviour, typical of high gluon densities and small $$ q\overline q $$ dipoles, for Q 2 larger than 10 to 20 GeV2. They support flavour independence of the diffractive exchange, expressed in terms of the scaling variable (Q 2+M 2 V )/4, and proton vertex factorisation. The spin density matrix elements are measured as a function of kinematic variables. The ratio of the longitudinal to transverse cross sections, the ratio of the helicity amplitudes and their relative phases are extracted. Several of these measurements have not been performed before and bring new information on the dynamics of diffraction in a QCD framework. The measurements are discussed in the context of models using generalised parton distributions or universal dipole cross sections.

Spin-selective reactions of radical pairs act as quantum measurements

Since the 1970s, spin-selective reactions of radical pairs have been modelled theoretically by adding phenomenological rate equations to the quantum mechanical equation of motion of the radical pair spin density matrix. Here, using a quantum measurement approach, we derive an alternative set of rate expressions which predict a faster decay of coherent superpositions of the singlet and triplet radical pair states. The difference between the two results, however, is not dramatic and would probably be difficult to distinguish experimentally from decoherence arising from other sources.

Relationships between Cumulant and Spin-Density Matrices: Application to the Decomposition of Spin

This paper reports the derivation of a relationship between some elements of the cumulant matrix of the second-order reduced density matrix and the elements of the spin-density matrix. This relationship turns out to be very useful to determine local spins through the partitioning of the spin expectation value <S(2)> of an N-electron system. The procedure enables expression of both one- and two-center contributions only in terms of one-electron matrix elements, the elements of the spin-density matrix. We report numerical determinations of local spins in the Hilbert space of atomic orbitals in selected molecules and radicals in triplet and doublet states.

Probing scalar particle and unparticle couplings in $e^{+}e^{-}\to t\bar{t}$ with transversely polarized beams

In searching for indications of new physics scalar particle and unparticle couplings in e^+ e^- \to t\bar t, we consider the role of transversely polarized initial beams at e^+ e^- colliders. By using a general relativistic spin density matrix formalism for describing the particles spin states, we find analytical expressions for the squared amplitude of the process with t or \bar t polarization measured, including the anomalous coupling contributions. Thanks to the transversely polarized initial beams these contributions are first order anomalous coupling corrections to the Standard Model (SM) contributions. We present and analyse the main features of the SM and anomalous coupling contributions. We show how differences between SM and anomalous coupling contributions provide means to search for anomalous coupling manifestations at future e^+ e^- linear colliders.

An all-proton spin quantum gate in semiconductor spin magnetic resonance force system

We report on a kind of all-proton spin quantum gate realized by fabric silicon cantilever in a semiconductor spin magnetic resonance microscopy system. In the paper, the Rf pulse sequence control and the spin rotate frame system are adopted according to spin-lattice and spin-spin relaxation times,and the small resonance force, the sensitivity and the spin density matrix are studied. The results show that all-proton spin quantum gates have high Q controlling and detecting sensitivity, and gain the effective force oscillating through the resonance slice and fiber interferometer. The system has advantages of MRI and AFM characteristics. In addition, the calculation indicates that it is powerful tool of magnetic resonance force technology and useful way to achieve quantum computation and quantum information.

Polarization of J/ ψ mesons at HERA in the [formula omitted]-factorization approach

In the framework of k t -factorization approach, inclusive production of J/ψ mesons at HERA is considered. The spin density matrix elements are calculated. Theoretical predictions are compared with H1 experimental data.

Differential cross sections and spin density matrix elements for the reactionγp→pω

High-statistics differential cross sections and spin density matrix elements for the reaction gamma p -> p omega have been measured using the CLAS at Jefferson Lab for center-of-mass (CM) energies from threshold up to 2.84 GeV. Results are reported in 112 10-MeV wide CM energy bins, each subdivided into cos(theta_CM) bins of width 0.1. These are the most precise and extensive omega photoproduction measurements to date. A number of prominent structures are clearly present in the data. Many of these have not previously been observed due to limited statistics in earlier measurements.

Partial wave analysis of the reactionγp→pωand the search for nucleon resonances

An event-based partial wave analysis (PWA) of the reaction gamma p -> p omega has been performed on a high-statistics dataset obtained using the CLAS at Jefferson Lab for center-of-mass energies from threshold up to 2.4 GeV. This analysis benefits from access to the world's first high precision spin density matrix element measurements, available to the event-based PWA through the decay distribution of omega-> pi+ pi - pi0. The data confirm the dominance of the t-channel pi0 exchange amplitude in the forward direction. The dominant resonance contributions are consistent with the previously identified states F[15](1680) and D[13](1700) near threshold, as well as the G[17](2190) at higher energies. Suggestive evidence for the presence of a J(P)=5/2(+) state around 2 GeV, a "missing" state, has also been found. Evidence for other states is inconclusive.