Set Of Matrix Elements Research Articles

Extending the drug discovery pipeline to simultaneously-applied chemical agents, and extending the study of evolution to simultaneous mutations, through an ab initio model that relates changes in phenotype to changes in molecular binding interactions

Abstract An ab initio model is proposed for extending the search for medicinal drugs to simultaneously-applied chemical agents and extending the study of evolution to simultaneous mutations, through relating the phenotype to molecular binding interaction types. In the case of drug discovery, evaluation of drug candidates for simultaneous use is enabled by incorporating, as design criteria, the effects of coupling between phenotypic properties and binding interactions. This discovery pipeline may yield lead candidates whose collective ability to treat a medical condition exceeds that of independently-applied chemical agents. The pipeline also enables the design of structural adjustments to existing drugs for their simultaneous use, to minimize detrimental side-effects or maximize beneficial side-effects. In the case of evolution, binding interaction types may be identified for simultaneous modification or implementation, by inherited gene mutation, to study transitions from one type of organism to another. Both findings are based on an ab initio model – a multivariate first-principles approach that relates changes in the molecular properties of binding complexes to changes in phenotypic properties, in prokaryotes or eukaryotes. That relationship is a network of binding interaction types whose level of interdependence or coupling is determined through a set of matrix elements. The matrix elements are to be determined for each type of binding interaction using a small set of chemical agents or mutations, and then applied to arbitrary chemical agents or mutations.

Deformation and mixing of coexisting shapes in neutron-deficient polonium isotopes

Coulomb-excitation experiments are performed with postaccelerated beams of neutron-deficient Po-196,Po-198,Po-200,Po-202 isotopes at the REX-ISOLDE facility. A set of matrix elements, coupling the low-lying states in these isotopes, is extracted. In the two heaviest isotopes, Po-196,Po-198, the transitional and diagonal matrix elements of the 2(1)(+) state are determined. In Po-196,Po-198 multistep Coulomb excitation is observed, populating the 4(1)(+), 0(2)(+), and 2(2)(+) states. The experimental results are compared to the results from the measurement of mean-square charge radii in polonium isotopes, confirming the onset of deformation from Po-196 onwards. Three model descriptions are used to compare to the data. Calculations with the beyond-mean-field model, the interacting boson model, and the general Bohr Hamiltonian model show partial agreement with the experimental data. Finally, calculations with a phenomenological two-level mixing model hint at the mixing of a spherical structure with a weakly deformed rotational structure.

6+isomers in neutron-rich Sn isotopes beyondN=82and effective interactions

Recent observation of the 6$^+$ seniority isomers and measurements of the B${(E2)}$ values in the $^{134-138}$Sn isotopes lying close to the neutron drip line have raised some questions about the validity of the currently used effective interactions in the neutron-rich region. Simpson $\it{et}$ $\it{al.}$ [Phys. Rev. Lett. $\textbf{113}$, 132502 (2014)] had to modify the diagonal and non-diagonal ${\nu}f_{7/2}^2$ two body matrix elements of the "${Vlk}$" interaction by ${\sim150}$ keV in their shell model calculations in order to explain the data of $^{136}$Sn. In contrast, we are able to explain the observed energy levels and the B${(E2)}$ values after marginal reduction of the same set of matrix elements by ${25}$ keV in the "RCDB" (Renormalized CD-Bonn) interaction. The observed mismatch in reproducing the data of $^{136}$Sn is due to the seniority mixing. Further, we do not find it necessary to consider the core excitations, and the "RCDB" interaction seems better suited to explain the data beyond N$=82$ magic number.

Low-frequency phonons of few-layer graphene within a tight-binding model

Few-layer graphene is a layered carbon material with covalent bonding in the layers and weak van der Waals interactions between the layers. The interlayer energy is more than two orders of magnitude smaller than the intralayer one, which hinders the description of the static and dynamic properties within parameter-free electron band structure models. We overcome this difficulty by introducing two sets of matrix elements - one set for the covalent bonds in the graphene layers and another one for the van der Waals interactions between adjacent graphene layers in a tight-binding model of the band structure. Both sets of matrix elements are derived from an ab-initio study on carbon dimers. The matrix elements are then applied in the calculation of the phonon dispersion of graphite and few-layer graphene with AB and ABC layer stacking. The results for AB stacking agree well with the available experimental data, which justifies the application of the matrix elements to other layered carbon structures with van der Waals interactions such as few-layer graphene nanoribbons, multiwall carbon nanotubes, and carbon onions.

Sub-barrier Coulomb excitation of 107Sn

A Coulomb excitation experiment in inverse kinematics has been carried out at the REX-ISOLDE facility in order to study the properties of low-lying excited states in 107Sn. The measured γ ray spectrum has been compared with predicted γ ray spectra from a combined shell-model and GOSIA analysis. In this approach, a set of matrix elements, generated within the shell-model framework, based on a realistic nucleon-nucleon interaction and a set of single-particle energies relative to 100Sn, is used as input. Comparison between the calculated and predicted spectra can be used to help identify the placement of the single-neutron states in 101Sn. In particular, the results can potentially provide clues on the ordering of the two lowest-lying orbits; the g7/2 and d5/2 states.

Selective and Efficient Estimation of Parameters for Quantum Process Tomography

We present a new method for quantum process tomography enabling the efficient estimation, with fixed precision, of any of the parameters characterizing a quantum channel. The estimation strategy depends upon the set of matrix elements one selects to estimate. Furthermore, we describe a way to efficiently gather all the information required to efficiently estimate any average survival probability of the channel (i.e., to measure any diagonal element of its chi matrix).

NUCLEON SPIN AND ITS GAUGE INVARIANCE AND CANONICAL COMMUTATION RELATION

The nucleon spin structure has been shown to be described by a dynamical constituent quark model with ~85% q3 and [Formula: see text] Fock components. As a QCD system there is no gauge invariance and canonical commutation relation simultaneously satisfied decomposition of the nucleon spin operator. To keep gauge invariance but give up the canonical commutation relation of the angular momentum operator will ruin the multiple moments expansion and the partial wave decomposition. A weak gauge invariant condition is proposed where the canonical commutation relation of angular momentum operator is intact and the gauge invariance is only true for special sets of matrix elements instead of the operators.

The origin of the spin–orbit splitting in some light nuclei using a modified interaction

The spin–orbit splittings in the spectra of nuclei with A = 5, 15, and 17 have been restudied, with a new set of matrix elements, within the framework of the shell model with core excitations. Investigated are the dependences of these splittings on core-excitation and on some of the different components of the nucleon- nucleon interaction. Our work confirms that the two-body spin–orbit interaction has a major effect whose magnitude depends on the size of the model space that is used. The effect of the tensor interaction is again seen to be considerably less important.

COULOMB EXCITATION OF 150Nd

The nucleus 150 Nd was Coulomb excited using 14 N , 58 Ni and 92 Mo beams. The overall result of the experiments performed consists of 780 measured gamma yields, which combined with available spectroscopic data gave about 800 data points to overdetermine the set of matrix elements needed to describe the observed processes. A number of E1, E2 and E3 matrix elements coupling the low-lying states has been determined in a model-independent way. In addition, an influence of E4 moments, competing with double E2 excitations, was tested with the low energy 14 N beam. Possible interpretations of the unusual electromagnetic structure found experimentally may pose the challenge to the theorists.

Matrix elements for photoionization in xenon derived from coincidence electron spectrometry

The magnitudes and relative phases of the matrix elements pertaining to photoionization in xenon at 132.2 eV photon energy have been derived from observables in an angle-resolved electron spectrometry experiment. The observables in question are the partial cross section, the angular distribution parameter of the photoelectron, the alignment parameter of the photoion, and the angular correlation between the photoelectron and the coincident Auger electron. Difficulties in extracting the desired matrix elements from these observables are discussed. Despite these difficulties, a set of matrix elements and relative phases could be extracted which is in good agreement with all experimental observables and also fulfils the constraint that spin - orbit effects in the photoelectron's partial waves be negligible. This data set differs significantly from theoretical predictions from relativistic random-phase calculations.

Quantum beats in excitons in Cu2O

A theoretical study is carried out of quantum beats (QB) in the time-dependent intensities of absorption of a test pulse and of spontaneous luminescence in a Cu2O crystal under conditions of double optical resonance. It is assumed that pumping is effected by a CO2-laser pulse which dynamically couples the exciton levels 1s(Γ5+) and 2p(Γ4−,Γ5−,Γ3−Γ2−) and splits them into two or three pairs of quasi-energy levels. The frequency of the test pulse is in resonance with the frequency Γ5+ of the exciton. The corresponding intensities for various directions of the electric vector of the pump field EL, the polarization vector ξ, and the wave vector q of the test pulse are obtained. The frequency of the quantum beats is twice the Rabi frequency, which for different values of EL, ξ and q contains different sets of matrix elements of the dipole transitions between the levels 1s(Γ5+) and 2p(Γ4−,Γ5−,Γ3−Γ2−). Thus, by measuring the period of the quantum beats it is possible to determine the unknown matrix elements of the indicated transitions.

Quantum Beats of Excitons in Cu2O at Double Optical Resonance

The quantum beats (QB) in the time-dependent absorption intensity of the probe pulse and the spontaneous luminescence one in Cu2O crystal at the condition of double optical resonance are studied theoretically. It is assumed that the pump is performed by the CO2 laser pulse, which couples dynamically the 1s (Γ 5 + ) and 2p (Γ 4 - , Γ 5 - , Γ 3 - , Γ 2 - ) excitonic states and leads to their splitting into two or three quasienergy levels. The frequency of the probe pulse is in the region of the Γ 5 + exciton resonance. The respective intensities for different directions of the electric field E L of the pump, the polarization ξ of the probe pulse, and the observation q are obtained. The QB take place with the doubled Raby frequency, which at different E L , ξ, and q includes different sets of matrix elements of dipole transitions between 1s (Γ 5 + ) and 2p (Γ 4 - , Γ 5 - , Γ 3 - , Γ 2 - ) levels. These unknown matrix elements can be obtained, measuring the period of the QB.

Toroidal coupling of ideal magnetohydrodynamic instabilities in tokamak plasmas

A theoretical framework is developed to describe the ideal magnetohydrodynamic (MHD) stability properties of axisymmetric toroidal plasmas. The mode structure is described by a set of poloidal harmonics in configuration space. The energy functional, δW, is then determined by a set of matrix elements that are computed from the interaction integrals between these harmonics. In particular, the formalism may be used to study the stability of finite-n ballooning modes. Using for illustration the s-α equilibrium, salient features of the n■∞ stability boundary can be deduced from an appropriate choice of test function for these harmonics. The analysis can be extended to include the toroidal coupling of a free-boundary kink eigenfunction to the finite-n ideal ballooning mode. A unified stability condition is derived that describes the external kink mode, a finite-n ballooning mode, and their interaction. The interaction term plays a destabilizing role that lowers the instability threshold of the toroidally coupled mode. These modes may play a role in understanding plasma edge phenomena, L–H physics and edge localized modes (ELMs).

Quark-like fractional parentage for the atomic f shell

The states of the atomic f shell are constructed by coupling together four quark-like objects belonging to the eight-dimensional spinor irreducible representation (irrep) (1/2 1/2 1/2) of SO(7). Two parity labels are also required. Transformations among the eight components of each quark lead to the groups U(8) and SO(8), which can be used to augment the labels provided by the groups SO(7) and G2 that Racah (1943,1949) used in his classic analysis. Coefficients of fractional parentage (CFP) have been calculated for the quark configurations q2, q3 and q4. To allow for the automorphisms of SO(8), the groups SO(7)' and SO(7)" of Labarthe (1980) are used as alternative intermediaries to SO(7) between SO(8) and G2. Parallel tables of CFP are provided. As an example of the usefulness of the quark model, a correspondence is established between a three-electron operator t4 used in configuration-interaction studies and a two-quark operator. Some matrix elements of the latter in q4 are calculated by means of the quark CFP, thereby giving the corresponding matrix elements of t4 in the electronic configurations f6 and f7. By using the irreps of SO(7)', an unexpected proportionality between the sets of matrix elements can be accounted for.

Coherent contributions of charge-dependent forces to the spreading width of the analog of 49Ca.

We report on a microscopic calculation of the spreading width GAMMA/sub A//sup arrow-down/ of the isobaric analog state in /sup 49/Sc of the ground state of /sup 49/Ca. In calculating the coupling of the isobaric analog state to hallway states we included (1) first and second order Coulomb coupling, (2) a charge-dependent but charge-symmetric interaction from the mass difference between charged and neutral pions, and (3) a charge-asymmetric interaction fitted to the Coulomb displacement anomaly in /sup 41/Sc-/sup 41/Ca. The second order Coulomb terms arise from mixing with the T = (7/2) component of a giant isovector monopole. The different sets of matrix elements are found to add coherently to give GAMMA/sub A//sup arrow-down/ = 5--7 keV, in excellent agreement with the value of GAMMA/sub A//sup arrow-down/ = 5.3 keV which we obtain from a strength function analysis of the high resolution data on /sup 48/Ca(p,p). The coherent charge-symmetric--charge-dependent contribution gives approximately one-half of GAMMA/sub A//sup arrow-down/. The result for GAMMA/sub A//sup arrow-down/ also includes a charge-asymmetric reduction of about 1 keV, but this is too small to confirm its presence in view of the uncertainty in the value of GAMMA/sub A//sup arrow-down/. .AE

An approximate analytical treatment of the T⊗(ε⊕τ2) Jahn-Teller effect

The octahedral Jahn-Teller system T(X)( epsilon g(+) tau 2g) is considered, in which the epsilon g and tau 2g modes correspond to the same frequency and are equally coupled to the electronic state T. A correspondence is drawn between the energy matrix for the J=1 states of this system and the energy matrix for the m=0 states of a three-dimensional harmonic oscillator displaced along the z axis. It is shown that the two sets of matrix elements become asymptotically proportional to each other as one proceeds towards the far interior of each infinite matrix. This permits a perturbation procedure to be set up for the Jahn-Teller system. Orthonormal basis states are established and a number of relations involving Laguerre polynomials are exploited to calculate to first order the energies of the J=1 levels, the Ham reduction factors and the intensities for the vibronic structure of the transition s to p. Analytic expressions are obtained for these quantities as a function of the coupling strength, and good agreement is obtained with the numerical calculations that are available at present.

Gauge invariance of radiative transitions of atoms (I). perturbation theory

The gauge invariance (GI) of the S-matrix element describing the radiative emission or absorption of a single photon by a many-electron atom is explicitly demonstrated in an arbitrary gauge, first when the non-radiative part of the problem is assumed to have been solved exactly, and subsequently when its solutions are available only in perturbation theory in the electron-electron interaction. The perturbation theory proof of GI leads to a calculational prescription which allows one to specify the set of matrix elements which must be calculated to obtain a GI expression order by order. The transition amplitude which one might have naively assumed to be sufficient for such a calculation is only one element of this set.

Shell-model calculations with an adjusted surface-delta interaction (I) application to spectroscopic factors inA=24?28 nuclei

Shell-model calculations have been performed for positive-parity levels of theA=24–28,T≦3/2 nuclei in a 1d5/22s1/21d3/2 configuration space. The space, for each (A, J, T) set, was restricted such that only mixing of less than about 300 low-lying pure configurations was allowed. An effective interaction (MSDI) was used of which the parameters have been determined by a fit of the calculated energies to the experimental values. This resulted in an averaged deviation of 0.52 MeV for 67 fitted levels. Spectroscopic factors have been calculated with the derived wave functions. In order to obtain better agreement for the energies, all of the 63 two-body matrix elements and three single-particle energies were adjusted systematically. The wave functions derived from this adjusted set of matrix elements denoted by ASDI yield considerably better spectroscopic factors. For comparison, the spectroscopic factors have also been calculated in a 1d5/22s1/2 model space. The omission of the 1d3/2 subshell was found to result in a substantially poorer agreement for the spectroscopic factors for 1d5/2 and 2s1/2 transfer.

Spectroscopy of 42Ca from 41Ca(d, p)

Energy levels in 42Ca up to 7.8 MeV have been studied in the neutron capture reaction 41Ca(d, p) 42Ca with 12 MeV bombarding energy. Ninety-four excited states have been identified and angular distributions have been measured in the interval from 5° to 110° by means of a broad-range magnetic spectrograph. The angular distributions together with DW calculations have been used to determine I n values and spectroscopic factors. The f 7 2 strength sum agrees with shell-model expectations if the f 7 2 spectroscopic factors are renormalized by 1 0.75 , in line with other f 7 2 . transfer experiments on 40Ca and 41Ca. A similar renormalization of the l n = 1 spectroscopic factors brings this strength sum in accordance with the shell-model calculations. The effective ( f 7 2 2 ) matrix elements for 42Ca are compared with the corresponding matrix elements of 42Sc and 48Sc. The differences between the three sets of matrix elements are of the order of a few hundred keV or less. The monopole centroid energy of the ( f 7 2 ) 2 multiplet is shifted downwards in the mass-42 nuclei compared to 48Sc, possibly indicating the importance of the monopole pairing force near 40Ca.

Exact phonon Green function for Kirkwood's model of polyethylene

The matrix elements of the lattice Green function for Kirkwood's model (describing the in-plane skeletal vibrations of an extended polyethylene chain) have been calculated exactly as a smooth function of frequency, using a semianalytic approach based on complex integration. The infinite set of matrix elements has been reduced to 12 basic real quantities from which any matrix element of the Green function in space-energy representation (including symmetry states) is obtained by linear combinations. Analytic expressions for these basic quantities are derived containing as parameter the solutions of a cubic equation. In principle, they could be evaluated on a desk calculator. Experimentally accessible frequencies are plotted as a function of the model parameters from which a graphical fit of the model can be easily found. The asymptotic behaviour of the Green function near these critical frequencies is studied in detail. As examples of straightforward applications, the density of states, the incoherent neutron scattering cross section and the localized modes due to an isotopic mass defect are plotted.