Singlet Part Research Articles

Triplet character of 2D-fermion dimers arising from $s$-wave attraction via spin-orbit coupling and Zeeman splitting

We theoretically study spin-1/2 fermions confined to two spatial dimensions and experiencing isotropic short-range attraction in the presence of both spin-orbit coupling and Zeeman spin splitting -- a prototypical system for developing topological superfluidity in the many-body sector. Exact solutions for two-particle bound states are found to have a triplet contribution that dominates over the singlet part in an extended region of parameter space where the combined Zeeman- and center-of-mass-motion-induced spin-splitting energy is large. The triplet character of dimers is purest in the regime of weak s-wave interaction strength. Center-of-mass momentum is one of the parameters determining the existence of bound states, which we map out for both two- and one-dimensional types of spin-orbit coupling. Distinctive features emerging in the orbital part of the bound-state wave function, including but not limited to its p-wave character, provide observable signatures of unconventional pairing.

Three-body model for K(1460) resonance

The three-body $KK\bar K$ model for the $K(1460)$ resonance is developed on the basis of the Faddeev equations in configuration space. A single-channel approach is using with taking into account the difference of masses of neutral and charged kaons. It is demonstrated that a splitting the mass of the $K(1460)$ resonance takes a place around 1460 MeV according to $K^0K^0{\bar K}^0$, $K^0K^+K^-$ and $K^+K^0{\bar K}^0$, $ K^+K^+K^-$ neutral and charged particle configurations, respectively. The calculations are performed with two sets of $KK$ and $K\bar K$ phenomenological potentials, where the latter interaction is considered the same for the isospin singlet and triplet states. The effect of repulsion of the $KK$ interaction on the mass of the $KK\bar K$ system is studied and the effect of the mass polarization is evaluated. The first time the Coulomb interaction for description of the $K(1460)$ resonance is considered. The mass splitting in the $K$(1460) resonances is evaluated to be in range of 10 MeV with taking into account the Coulomb force. The three-body model with the $K\bar K$ potential, which has the different strength of the isospin singlet and triplet parts that are related by the condition of obtaining a quasi-bound three-body state is also considered. Our results are in reasonable agreement with the experimental mass of the $K(1460)$ resonance.

The Interaction Potential between an Atom and a Conductive Wall

In this work, the interaction potential between an atom (with definite Static Polarizability) and a perfect neutral conductive wall is evaluated in two approaches. First, using, the explicit form of the singlet and doublet parts of the vacuum vector potential operator in atomic quadratic stark shift formula and taking the expectation value in vacuum state. Second, writing, the quadratic stark shift formula in terms of electric field correlation function, relating the correlation function to the imaginary parts of the vector potential Green function tensor components (via fluctuation dissipation theorem in statistical mechanics) and the evaluation of the required vector potential Green function tensor components. The consistency of the two methods is shown.

Extension of frozen natural orbital approximation to open-shell references: Theory, implementation, and application to single-molecule magnets.

Natural orbitals are often used to achieve a more compact representation of correlated wave-functions. Using natural orbitals computed as eigenstates of the virtual-virtual block of the state density matrix instead of the canonical Hartree-Fock orbitals results in smaller errors when the same fraction of virtual space is frozen. This strategy, termed frozen natural orbital (FNO) approach, is effective in reducing the cost of regular coupled-cluster (CC) calculations and some multistate methods, such as EOM-IP-CC (equation-of-motion CC for ionization potentials). This contribution extends the FNO approach to the EOM-SF-CC ansatz (EOM-CC with spin-flip). In contrast to EOM-IP-CCSD, EOM-SF-CCSD relies on high-spin open-shell references. Using FNOs computed for an open-shell reference leads to an erratic behavior of the EOM-SF-CC energies and properties due to an inconsistent truncation of the α and β orbital spaces. A general solution to problems arising in the EOM-CC calculations utilizing open-shell references, termed OSFNO (open-shell FNO), is proposed. By means of singular value decomposition (SVD) of the overlap matrix of the α and β orbitals, the OSFNO algorithm identifies the corresponding orbitals and determines virtual orbitals corresponding to the singly occupied space. This is followed by SVD of the singlet part of the state density matrix in the remaining virtual orbital subspace. The so-computed FNOs preserve the spin purity of the open-shell orbital subspace to the extent allowed by the original reference, thus facilitating a safe truncation of the virtual space. The performance of OSFNO is benchmarked for selected diradicals and triradicals.

Time resolved mechanism of the isotope selectivity in the ultrafast light induced dissociation in N2.

The time evolution of a vacuum ultraviolet excited N2 molecule is followed all the way from an ultrafast excitation to dissociation by a quantum mechanical simulation. The primary aim is to discern the role of the excitation by a pulse short compared to the vibrational period, to discern the different coupling mechanisms between different electronic states, nonadiabatic, spin orbit, and to analyze the origin of any isotopic effect. We compare the picture in the time and energy domains. The initial ultrafast excitation pumps the molecule to a coherent electronic wave packet to which several singlet bound electronic states contribute. The total nonstationary wave function is given as a coherent sum of nuclear wave packets on each electronic state times the stationary electronic wave function. When the wave packets on different electronic states overlap, they are coupled in a mass-dependent manner whether one uses an adiabatic or a diabatic electronic basis. A weak spin-orbit coupling acts as a bottleneck between the bound singlet part of phase space and the triplet manifold of states in which dissociation takes place. To describe the spin-orbit perturbation that is ongoing in time, an energy-resolved eigenstate representation appears to be more intuitive. In the eigenstate basis, the singlet-to-triplet population transfer is large only between those vibronic eigenstates that are quasiresonant in energy. The states in resonance are different for different excitation energy ranges. The resonances are mass dependent, which explains the control of the isotope effect through the profile of the pulse.

Quark and gluon form factors in four loop QCD: The Nf2 and NqγNf contributions

We calculate the four-loop massless QCD corrections with two closed quark lines to quark and gluon form factors. The results for the gluon form factor and the singlet part of the quark form factor are given for the first time. From our analytic expressions for the form factors, we determine the corresponding cusp anomalous dimensions. The relevant Feynman integrals are obtained with novel integral reduction techniques and direct integration methods.

Geminal perturbation theory based on the unrestricted Hartree–Fock wavefunction

A perturbative correction exploiting natural orbitals and the pair function structure of the unrestricted Hartree-Fock (UHF) wavefunction is devised. The method offers a simple framework for describing multireference systems where static correlation is captured by UHF. The UHF wavefunction is built of two-electron fragments (geminals), involving both singlet and triplet (ms = 0) parts. At order zero of the perturbative treatment, configuration interaction coefficients of UHF geminals are relaxed. The zero order Hamiltonian is of the Dyall-type, including explicit two-electron interaction within geminals and leading to a formal 6th power scaling. Adopting an effective one-electron zero order Hamiltonian term for the subset of virtual orbitals reduces scaling of the correction step to 4th power. Formal properties of the proposed schemes are discussed. Energetic data and natural occupation numbers of illustrative test systems are used to assess the new approach. The cases where the wavefunction becomes essentially spin pure at the level of reference show good performance. Spin contamination remaining at order zero is found to undermine the perturbative correction.

Precision measurement of the forbidden 21S0 – 23S1 transition frequency in a helium atom

We demonstrate the possibility of measuring the forbidden 21S0 – 23S1 transition frequency (λ = 1557 nm) of a helium atom by the method of stimulated Raman scattering through the intermediate 23P1 level. Singlet (21S0) and triplet (23S1) states have long lifetimes of 20 ms and 8000 s, respectively. The transition is important for the spectroscopy of the helium atom because it relates the singlet and triplet parts of the spectrum.

SO(10) grand unified theories with dynamical Yukawa couplings

Renormalizable SO(10) grand unified theories (GUTs), extended by $O(N_g)_F$ family gauge symmetry, generate minimal supersymmetric Standard Model flavour structure dynamically via vacuum expectation values of "Yukawon" Higgs multiplets. For concrete illustration and calculability, we work with the fully realistic minimal supersymmetric GUTs based on the $\bf{210 \oplus {\overline{126}}\oplus 126} $ GUT Higgs system - which were already parameter counting minimal relative to other realistic models. $SO(10)$ fermion Higgs channels $\bf{{\overline{126}},10}$($\mathbf{120}$) extend to symmetric(antisymmetric) representations of $O(N_g)_F$, while $\mathbf{210,126}$ are symmetric. $N_g=3$ dynamical Yukawa generation reduces the matter fermion Yukawas from 15 to 3 (21 to 5) without (with) the $\bf{120}$ Higgs. Yukawon GUTs are thus ultraminimal in parameter counting terms. Consistent symmetry breaking is ensured by a hidden sector Bajc-Melfo(BM) superpotential with a pair of symmetric $O(N_g)$ multiplets $\phi,S $, of which the latter's singlet part $S_s$ breaks supersymmetry and the traceless part $\hat S $ furnishes flat directions to cancel the $O(N_g)$ D-term contributions of the visible sector. Novel dark matter candidates linked to flavour symmetry arise from both the BM sector and GUT sector minimal supersymmetric Standard Model singlet pseudo-Goldstones. These relics may be viable light($< 50 $ GeV) cold dark matter as reported by DAMA/LIBRA. In contrast to the new minimal supersymmetric SO(10) grand unified theory (NMSGUT) even sterile neutrinos can appear in certain branches of the flavour symmetry breaking without the tuning of couplings.

Adler function, sum rules and Crewther relation of order [formula omitted]: The singlet case

The analytic result for the singlet part of the Adler function of the vector current in a general gauge theory is presented in five-loop approximation. Comparing this result with the corresponding singlet part of the Gross-Llewellyn Smith sum rule (Baikov et al., 2010 [1]), we successfully demonstrate the validity of the generalized Crewther relation for the singlet part. This provides a non-trivial test of both our calculations and the generalized Crewther relation. Combining the result with the already available non-singlet part of the Adler function (Baikov et al., 2008 [2], Baikov et al., 2010 [3]) we arrive at the complete O(αs4) expression for the Adler function and, as a direct consequence, at the complete O(αs4) correction to the e+e− annihilation into hadrons in a general gauge theory.

Erratum: Polarized structure of nucleon in the valon representation

We have utilized the concept of valon model to calculate the spin structure functions of proton, neutron and deuteron. The valon structure itself is universal and arises from the perturbative dressing of the valence quark in QCD. Our results agree rather well with all the relevant experimental data on $g_{1}^{p, n, d}$ and $g_{A}/g_{v}$, and suggests that the sea quark contribution to the spin of proton is consistent with zero. It also reveals that while the total quark contribution to the spin of valon is almost constant at $Q^{2}>=1$ the gluon contribution grows with the increase of $Q^2$ and hence requiring a sizable negative orbital angular momentum component $L_z$. This component along with the singlet and non-singlet parts are calculated in the Next-to-Leading order in QCD. We speculate that gluon contribution to the spin content of the proton is about 60% for all $Q^2$ values. Finally, we show that the size of gluon polarization and hence, $L_{z}$, is sensitive to the initial scale$Q_{0}^{2}$.

Adler Function, DIS sum rules and Crewther Relations

The current status of the Adler function and two closely related Deep Inelastic Scattering (DIS) sum rules, namely, the Bjorken sum rule for polarized DIS and the Gross-Llewellyn Smith sum rule are briefly reviewed. A new result is presented: an analytical calculation of the coefficient function of the latter sum rule in a generic gauge theory in order O(alpha_s^4). It is demonstrated that the corresponding Crewther relation allows to fix two of three colour structures in the O(alpha_s^4) contribution to the singlet part of the Adler function.

Triplet contribution to the Josephson current in the nonequilibrium superconductor/ferromagnet/superconductor junction

The Josephson current through a long s-wave superconductor/weak ferromagnet/s-wave superconductor weak link is studied theoretically in the regime of nonequilibrium spin-dependent occupation of electron states in the ferromagnetic intelayer. While under the considered nonequilibrium condition the standard supercurrent, carried by the singlet part of current-carrying density of states, is not modified, the additional supercurrent flowing via the triplet part of the current-carrying density of states appears. Depending on voltage, controlling the particular form of spin-dependent nonequilibrium in the interlayer, this additional current can enhance or reduce the usual current of the singlet component and also switch the junction between 0- and $\pi$-states.

Angle-differential Stokes parameters for spin-polarized electron-impact excitation of the Hg6s6p3P1state at25-eV scattering energy

Results of spin-resolved angle-differential Stokes parameters from electron-photon coincidence studies of electron-impact excitation of the 6s6p {sup 3}P{sub 1} state of mercury, resulting in 254 nm radiation, are presented. Due to the intermediate-coupling nature of the excited state, the wave function of this state has a small singlet part. With increasing scattering energy, the influence of exchange scattering decreases, so that direct scattering via the singlet part can become relevant. Recent angle-integrated Stokes-parameter measurements indicated that exchange is still important for the 254 nm line (6s6p {sup 3}P{sub 1}->6s{sup 2} {sup 1}S{sub 0}) up to at least 50 eV incident energy [Juettemann et al., Phys. Rev. A 79, 042712 (2009)]. At energies above 15 eV, however, cascade effects complicate a detailed comparison of these angle-integrated results with theoretical calculations. The angle-differential Stokes parameters presented here are unaffected by cascade effects due to the coincidence technique and thus allow for an analysis of the discrepancies observed by Juettemann et al. and also by Srivastava et al. [Phys. Rev. A 80, 022718 (2009)]. Comparison of the experimental data with theoretical predictions reveals that the description of the initial target state and the excited state in intermediate coupling have a significant influence onmore » the overall agreement.« less

Triplet Cooper Pair Formation by Anomalous Spin Fluctuations in Non-centrosymmetric Superconductors

A microscopic theory for the spin triplet Cooper pairing in non-centrosymmetric superconductors like CePt_3Si and CeTSi_3 (T=Rh, Ir) is presented. The lack of inversion symmetry leads to new anomalous spin fluctuations which stabilize the triplet part in addition to the singlet part originating from the centrosymmetric spin fluctuations. It is shown that both parts have similar nontrivial momentum dependence of A_1 type. Therefore the mixed singlet-triplet gap function has accidental line nodes on both Fermi surface sheets which are stable as function of temperature. This gap function explains the salient features of CePt_3Si and CeTSi_3 superconductors.

Polarized structure of nucleon in the valon representation

We have utilized the concept of valon model to calculate the spin structure functions of proton, neutron, and deuteron. The valon structure itself is universal and arises from the perturbative dressing of the valence quark in QCD. Our results agree rather well with all of the relevant experimental data on g1p,n,d and gA/gV, and suggests that the sea quark contribution to the spin of proton is consistent with zero. It also reveals that while the total quark contribution to the spin of a valon, ΔΣvalon, is almost constant at Q2 ≥ 1 the gluon contribution grows with the increase of Q2 and hence requiring a sizable negative orbital angular momentum component Lz. This component along with the singlet and non-singlet parts are calculated in the Next-to-Leading order in QCD . We speculate that gluon contribution to the spin content of the proton is about 60% for all Q2 values. Finally, we show that the size of gluon polarization and hence, Lz, is sensitive to the initial scale Q02.

A systematic study of QCD coupling constant from deep-inelastic measurements

We reanalyze deep-inelastic scattering data of the BCDMS Collaboration by including proper cuts of ranges with large systematic errors. We also perform the fits of high-statistic deep-inelastic scattering data of the BCDMS, SLAC, NM, and BFP Collaborations taking the data separately and in a combined way and find good agreement between these analyses. We extract the values of both the QCD coupling constant α s(M Z 2 ) up to the NLO level and of the power corrections to the structure function F 2. The fits of the combined data for the nonsinglet part of the structure function F 2 predict the coupling constant value α s(M Z 2 ) = 0.1174 ± 0.0007 (stat.) ± 0.0019 (syst.) ± 0.0010 (norm.) (or QCD parameter $$\Lambda \tfrac{{(5)}}{{MS}} = 204 \pm 25$$ (total experimental error) MeV). The fits of the combined data for both the nonsinglet part and the singlet part lead to the values α s(M Z 2 ) = 0.1177 ± 0.0007 (stat.) ± 0.0021 (syst.) ± 0.0009 (norm.) (or QCD parameter $$\Lambda \tfrac{{(5)}}{{MS}}$$ =(208±27 (total experimental error)MeV). The above values are in very good agreement with each other. We estimate theoretical uncertainties for α s(M Z 2 ) at +0.0047 and −0.0057 from fits of the combined data when complete singlet and nonsinglet Q 2 evolution is taken into account.

Evolution of the gluon density in $x$ with a running coupling constant

We describe the calculation of the evolution of the gluon density in $x$ from an initial value $x=x_{0}=0.01$ to smaller values, up to $x=10^{-8}$ in the hard pomeron formalism with a running coupling introduced on the basis of the bootstrap equation. The obtained gluon density is used to calculate the singlet part of the proton structure function. Comparison with experiment and the results following from the fixed coupling evolutio n is made.

Evolution of the gluon density in

This is a draft describing the calculation of the evolution of the gluon density in $x$ from an initial value $x=x_{0}=0.01$ to smaller values, up to $x=10^{-8}$ in the hard pomeron formalism with a running coupling introduced on the basis of the bootstrap equation. The obtained gluon density is used to calculate the singlet part of the proton structure function. Comparison with experiment and the results following from the fixed coupling evolution is made.

Theory of small x deep inelastic scattering: NLO evaluations, and low Q2 analysis

We calculate structure functions at small x both under the assumption of a hard singularity (essentially, a power behaviour χ − λ , A positive, for x → 0) and that of a soft-pomeron dominated behaviour, also called double scaling limit, for the singlet component. A full next to leading order (NLO) analysis is carried out for the functions F 2, F Glue and the longitudinal one F L in ep scattering, and for χF 3 in neutrino scattering. The results of the calculations are compared with experimental data, particularly the recent ones from HERA, in the range x ⩽ 0.032, 10 GeV 2 Q2 ⩽ 1500 GeV 2. We get reasonable fits, with a chi-squared per degree of freedom around two units, with only three-four parameters in both cases. However, none of the assumptions is by itself able to give a fully satisfactory description of the data. The results improve substantially when combining a soft and a hard component; in this case it is even possible to extend the analysis, phenomenologically, to small values of Q 2, 0.31 GeV 2 ⩽ Q 2 ⩽ 8.5 GeV 2, and in the x range 6 × 10 −6 ⪅ x ⪅ 0.04, with the same hard plus soft pomeron hypothesis by assuming a saturating expression for the strong coupling, α s (Q2) = 4π / β 0 log[ (Q2 + Γ eff 2) / Γ eff 2 1. The formulation for low Q2 implies self-consistent values for the parameters in the exponents of x both for singlet and non-singlet components. One has to have, for the Regge intercepts, α ϱ (0) = 0.48 and α ϱ (0) = 1.470 [ λ = 0.470], in uncanny agreement with other determinations of these parameters, and in particular the results of the large Q 2 fits. The fit to data is so good that we may look (at large Q 2) for signals of a “triple pomeron” vertex, for which some evidence is found. The quality of the calculations of F 2, and of the predictions for F Glue, F L is only marred by the very large size of the NLO corrections for the singlet part of F 2. This, in particular, forbids a truly reliable determination of the QCD parameter, A.