Pairing Force Research Articles

Rotational states and masses of heavy and superheavy nuclei

The macroscopic-microscopic model with the Lublin-Strasbourg drop, the Strutinsky shell-correction method, and the BCS approach for pairing correlations is used with the cranking model to describe nuclear masses and rotational bands in even-even Ra to Cn isotopes of actinide and transactinide nuclei. The single-particle levels and potential-energy surfaces are calculated with the Yukawa-folded single-particle potential using the “modified funny hills” (c, h) shape parametrization. A monopole pairing force is used in our calculations. At equilibrium deformation the pairing strength is adjusted for every nucleus so as to reproduce the experimentally known rotational E2+ state within the cranking model. The pairing strength obtained in this way is used to predict the masses and rotational states in superheavy No to Cn nuclei. It is also shown that the rotational states with L 10 in Ra to No nuclei evaluated using a simple rotational formula agree quite well with the data. We propose a simple mechanism which takes into account a dynamical coupling of rotation with the pairing field that then allows one to obtain an excellent agreement with the data up to the states with the largest angular momenta (L 30) measured in this mass region.

Covariant description of shape evolution and shape coexistence in neutron-rich nuclei at

The shape evolution and shape coexistence phenomena in neutron-rich nuclei at N≈60, including Kr, Sr, Zr, and Mo isotopes, are studied in the covariant density functional theory (DFT) with the new parameter set PC-PK1. Pairing correlations are treated using the BCS approximation with a separable pairing force. Sharp rising in the charge radii of Sr and Zr isotopes at N=60 is observed and shown to be related to the rapid changing in nuclear shapes. The shape evolution is moderate in neighboring Kr and Mo isotopes. Similar as the results of previous Hartree–Fock–Bogoliubov (HFB) calculations with the Gogny force, triaxiality is observed in Mo isotopes and shown to be essential to reproduce quantitatively the corresponding charge radii. In addition, the coexistence of prolate and oblate shapes is found in both Sr98 and Zr100. The observed oblate and prolate minima are related to the low single-particle energy level density around the Fermi surfaces of neutron and proton respectively. Furthermore, the 5-dimensional (5D) collective Hamiltonian determined by the calculations of the PC-PK1 energy functional is solved for Sr98 and Zr100. The resultant excitation energy of 02+ state and E0 transition strength ρ2(E0;02+→01+) are in rather good agreement with the data. It is found that the lower barrier height separating the two competing minima along the γ deformation in Zr100 gives rise to the larger ρ2(E0;02+→01+) than that in Sr98.

Thomas-Fermi approximation to pairing in finite Fermi systems. The weak coupling regime

We present a new semiclassical theory for describing pairing in finite Fermi systems. It is based on taking the ℏ → 0, i.e. Thomas-Fermi, limit of the gap equation written in the basis of the mean field (weak coupling). In addition to the position dependence of the Fermi momentum, the size dependence of the pairing force is also taken into account in this theory. Along isotopic chains the Thomas-Fermi gaps average the well known arch structure shown by the quantal gaps. This structure can be almost recovered in our formalism if some shell fluctuations are included in the level density. We point out that at the drip line nuclear pairing is strongly reduced. This fact is illustrated with the behaviour of the gap in the inner crust of neutron stars.

Study on Dynamic Characteristics of Wind Turbine Planetary Gear System Coupled with Bearing at Varying Wind Speed

The sparse least squares support vector machines (SL-SVM) is used to simulate wind speed of real wind field, and time-varying wind load caused by stochastic wind speed is then obtained. A coupling gear-bearing dynamical model of planetary gear transmission system of wind turbine is built using lumped-parameter method, in which the varying wind load, time-vary mesh stiffness of gear pair and time-vary stiffness of rolling element bearing are taken into account. Numerical method is used to simulate the dynamic performance of planetary gear transmission of multibrid technology wind turbine (MTWT) with 1.5MW rated power, the vibration displacement responses of gears and dynamic meshing forces of gear pairs as well as nonlinear bearing forces in the transmission system are obtained, and the influence rules of external varying wind load on the vibration characteristics of transmission system of wind turbine are studied. The research results lay a foundation for dynamic performance optimization and reliability design of gear transmission system of wind turbine.

Microscopic structure of 126Ba in IBM terms

The yrast band of the nonaxially deformed 126Ba nucleus is described by the Hamiltonian of the interaction boson model. Its parameters are calculated on the basis of a microscopic theory within a spherical mean field, and residual interactions that include pairing and multipole factorized forces. Each state of the yrast band is considered independently of others, allowing us to study variations in the superfluid properties of the nucleus and the quasiparticle structure of collective D phonons with spin. The calculations are performed in an expanded configuration space that includes the collective D phonon states, and noncollective states in which an additional phonon of positive parity whose spin assumes values of 0 to 6 is present along with the D phonons. It is shown that the collective Hamiltonian parameters cannot be reproduced without considering the effect of the noncollective states.

Resonance Energy Transfer (RET)-Induced Intermolecular Pairing Force: A Tunable Weak Interaction and Its Application in SWNT Separation

This paper explores evidence of an optically mediated interaction that is active in the separation mechanism of certain selective agents through consideration of the contrasting selective behaviors of two conjugated polymers with distinct optical properties. The involvement of a RET-induced intermolecular pairing force is implied by the different illumination response behaviors. The magnitude of this interaction scales with the external stimulus parameter, the illumination irradiance (I), and thus is tunable. This suggests a facile technique to modify the selectivity of polymers toward specific SWNT species by altering the polymer structure to adjust the corresponding intermolecular interaction. This is the first experimental verification and application of a RET-induced intermolecular pairing force to SWNT separation. With this kind of interaction taken into account, reasonable interpretation of some conflicting data, especially PLE maps, can be easily made. The above conclusion can be applied to other substances as long as they are electrically neutral and there is photon-induced RET between them. The significant magnitude of this interaction makes direct manipulation of molecules/particles possible and is expected to have applications in molecular engineering.

Communication: Shifted forces in molecular dynamics

Simulations involving the Lennard-Jones potential usually employ a cutoff at r = 2.5σ. This communication investigates the possibility of reducing the cutoff. Two different cutoff implementations are compared, the standard shifted potential cutoff and the less commonly used shifted forces cutoff. The first has correct forces below the cutoff, whereas the shifted forces cutoff modifies Newton's equations at all distances. The latter is nevertheless superior; we find that for most purposes realistic simulations may be obtained using a shifted forces cutoff at r = 1.5σ, even though the pair force is here 30 times larger than at r = 2.5σ.

SEMICLASSICAL DESCRIPTION OF AVERAGE PAIRING PROPERTIES IN NUCLEI

We present a new semiclassical theory for describing pairing in finite Fermi systems. It is based on taking the ħ → 0, i.e. Thomas-Fermi, limit of the gap equation written in the basis of the mean field (weak coupling). In addition to the position dependence of the Fermi momentum, the size dependence of the matrix elements of the pairing force is also taken into account in this theory. An example typical for the nuclear situation shows the improvment of this new approach over the standard Local Density Approximation. We also show that if in this approach some shell fluctuations are introduced in the level density, the arch structure displayed by the quantal gaps along isotopic chains is almost recovered. We also point out that in heavy drip line nuclei pairing is strongly reduced.

Structure and total strength of the magnetic dipole resonance in 35Cl nuclei

The γ-decay of the resonance-like structure observed in the 34S(pγ)35Cl reaction in the energy range Ep = 1.0–3.0 MeV of accelerated protons was investigated. The M1 resonance on the ground and excited states of 35Cl with E* = 1219 and 1763 keV was identified. The position of the center of gravity and total strength of the M1 resonance on ground state 35Cl nucleus are determined. The position and total strength of the M1 resonance on the ground state in 35Cl are explained taking into account pairing forces.

Shell-model study for neutron-richsd-shell nuclei

The microscopic structure of neutron-rich $\mathit{sd}$-shell nuclei is investigated by using the spherical-shell model in the $\mathit{sd}$-$\mathit{pf}$ valence space with the extended pairing plus quadrupole-quadrupole forces accompanied by the monopole interaction (EPQQM). The calculation reproduces systematically the known energy levels for even-even and odd-mass nuclei including the recent data for $^{43}\mathrm{S}$, $^{46}\mathrm{S}$, and $^{47}\mathrm{Ar}$. In particular, the erosion of the $N=28$ shell closure in $^{42}\mathrm{Si}$ can be explained. Our EPQQM results are compared with other shell-model calculations with the SDPF-NR and SDPF-U effective interactions.

Observation of a ubiquitous three-dimensional superconducting gap function in optimally doped Ba0.6K0.4Fe2As2

The iron-pnictide superconductors have a layered structureformed by stacks of FeAs planes from which the superconductivity originates. Given the multiband and quasi three-dimensional \cite{3D_SC} (3D) electronic structure of these high-temperature superconductors, knowledge of the quasi-3D superconducting (SC) gap is essential for understanding the superconducting mechanism. By using the \KZ-capability of angle-resolved photoemission, we completely determined the SC gap on all five Fermi surfaces (FSs) in three dimensions on \BKFAOP samples. We found a marked \KZ dispersion of the SC gap, which can derive only from interlayer pairing. Remarkably, the SC energy gaps can be described by a single 3D gap function with two energy scales characterizing the strengths of intralayer $\Delta_1$ and interlayer $\Delta_2$ pairing. The anisotropy ratio $\Delta_2/\Delta_1$, determined from the gap function, is close to the c-axis anisotropy ratio of the magnetic exchange coupling $J_c/J_{ab}$ in the parent compound \cite{NeutronParent}. The ubiquitous gap function for all the 3D FSs reveals that pairing is short-ranged and strongly constrain the possible pairing force in the pnictides. A suitable candidate could arise from short-range antiferromagnetic fluctuations.

Cold Neutrons Trapped in External Fields

The properties of inhomogeneous neutron matter are crucial to the physics of neutron-rich nuclei and the crust of neutron stars. Advances in computational techniques now allow us to accurately determine the binding energies and densities of many neutrons interacting via realistic microscopic interactions and confined in external fields. We perform calculations for different external fields and across several shells to place important constraints on inhomogeneous neutron matter, and hence the large isospin limit of the nuclear energy density functionals that are used to predict properties of heavy nuclei and neutron star crusts. We find important differences between microscopic calculations and current density functionals; in particular, the isovector gradient terms are significantly more repulsive than in traditional models, and the spin-orbit and pairing forces are comparatively weaker.

Blocking of coupling to the 02 + excitation in 154Gd by the [505]11/2- neutron in 155Gd

The concept that the first excited 0+ states in N = 90 nuclei are not a \( \beta\) -vibration but a second vacuum formed by the combination of the quadrupole pairing force and the low density of oblate orbitals near the Fermi surface is supported by the blocking of this collective mode in 154Gd from coupling to the [505]11/2- single-particle quasi-neutron orbital in 155Gd . The coupling of this orbital to the 2+\( \gamma\) -vibration in 154Gd is observed since this coupling is not Pauli-blocked.

A Dynamical Classification of the Range of Pair Interactions

We formalize a classification of pair interactions based on the convergence properties of the forces acting on particles as a function of system size. We do so by considering the behavior of the probability distribution function (PDF) P(F) of the force field F in a particle distribution in the limit that the size of the system is taken to infinity at constant particle density, i.e., in the “usual” thermodynamic limit. For a pair interaction potential V(r) with V(r→∞)∼1/r γ defining a bounded pair force, we show that P(F) converges continuously to a well-defined and rapidly decreasing PDF if and only if the pair force is absolutely integrable, i.e., for γ>d−1, where d is the spatial dimension. We refer to this case as dynamically short-range, because the dominant contribution to the force on a typical particle in this limit arises from particles in a finite neighborhood around it. For the dynamically long-range case, i.e., γ≤d−1, on the other hand, the dominant contribution to the force comes from the mean field due to the bulk, which becomes undefined in this limit. We discuss also how, for γ≤d−1 (and notably, for the case of gravity, γ=d−2) P(F) may, in some cases, be defined in a weaker sense. This involves a regularization of the force summation which is generalization of the procedure employed to define gravitational forces in an infinite static homogeneous universe. We explain that the relevant classification in this context is, however, that which divides pair forces with γ>d−2 (or γ<d−2), for which the PDF of the difference in forces is defined (or not defined) in the infinite system limit, without any regularization. In the former case dynamics can, as for the (marginal) case of gravity, be defined consistently in an infinite uniform system.

Method to circumvent the neutron-gas problem in the BCS treatment for nuclei far from stability

Extending the Kruppa's prescription for the continuum level density, we have recently improved the BCS method with seniority-type pairing force in such a way that the effects of discretized unbound states are properly taken into account for finite depth single-particle potentials. In this paper, it is further shown, by employing the Woods-Saxon potential, that the calculation of spatial observables like nuclear radius converges as increasing the basis size in the harmonic oscillator expansion. Namely the disastrous problem of a "particle gas" surrounding nucleus in the BCS treatment can be circumvented. In spite of its simplicity, the new treatment gives similar results to those by more elaborate Hartree-Fock-Bogoliubov calculations; e.g., it even mimics the pairing anti-halo effect. The obtained results as well as the reason of convergence in the new method are investigated by a variant of the Thomas-Fermi approximation within the limited phase space which corresponds to the harmonic oscillator basis truncation.

Microscopic description of nuclear structure aroundZr80

A new approach for the calculation of angular momentum projected potential energy surfaces (AMPPESs) is proposed which combines the projected shell model with a quadrupole constrained relativistic Hartree-Bogoliubov (RHB) theory in which the NL3 effective interaction is chosen for the relativistic mean-field effective Lagrangian and a separable Gogny D1S interaction for the pairing force (QCRHB-NL3 + separable Gogny D1S force theory). We apply this approach to compute the AMPPESs of 80,82,84 Zr nuclei up to high spins and investigate the spin-induced shape transitions and decay out of the superdeformed (SD) bands in these nuclei. We find that the shape transitions occur in 80 Zr and 84 Zr, which are driven by the rotational alignments of the nucleons in the 1g 9/2 orbitals, and a strong shape mixing happens in 82 Zr. Moreover, it is shown that the barrier separating the SD states and normal deformed (or spherical) states becomes lower and narrower for 82 Zr and 84 Zr at high spins, indicating that the decay out of the SD bands could occur at high spins. For 80 Zr, however, there is no decay out of the SD band because the barrier is so high and thick. Meanwhile, the QCRHB-NL3 + separable Gogny D1S force theory is employed to calculate the ground-state potential energy surfaces and the single-particle levels of these nuclei, which in turn are used to determine and analyze the equilibrium shapes and discuss the shape coexistence of these nuclei. In addition, this theory is compared with other state-of-the-art mean-field theories to justify its use to study the ground-state potential energy surfaces of 80,82,84 Zr.

Effective contact pairing forces from realistic calculations in infinite homogeneous nuclear matter

Non-empirical effective contact pairing forces to be used in self-consistent mean-field calculations are presented. These pairing forces, constructed so as to reproduce exactly any given microscopic pairing gaps in infinite homogeneous nuclear matter for any isospin asymmetry, are given in analytical form. As a by-product, this work provides an analytical solution of the BCS gap equations which could be applied to describe various many-body systems.

Turning limited experimental information into 3D models of RNA

Our understanding of RNA functions in the cell is evolving rapidly. As for proteins, the detailed three-dimensional (3D) structure of RNA is often key to understanding its function. Although crystallography and nuclear magnetic resonance (NMR) can determine the atomic coordinates of some RNA structures, many 3D structures present technical challenges that make these methods difficult to apply. The great flexibility of RNA, its charged backbone, dearth of specific surface features, and propensity for kinetic traps all conspire with its long folding time, to challenge in silico methods for physics-based folding. On the other hand, base-pairing interactions (either in runs to form helices or isolated tertiary contacts) and motifs are often available from relatively low-cost experiments or informatics analyses. We present RNABuilder, a novel code that uses internal coordinate mechanics to satisfy user-specified base pairing and steric forces under chemical constraints. The code recapitulates the topology and characteristic L-shape of tRNA and obtains an accurate noncrystallographic structure of the Tetrahymena ribozyme P4/P6 domain. The algorithm scales nearly linearly with molecule size, opening the door to the modeling of significantly larger structures.

Molecular group dynamics study on slip flow of thin fluid film based on the Hamaker hypotheses

The thin fluid film was assumed to consist of a number of spherical fluid molecular groups and the attractive forces of molecular group pairs were calculated by the derived equation according to the three Hamaker homogeneous material hypotheses. Regarding each molecular group as a dynamics individual, the simulation method for the shearing motion of multilayer fluid molecular groups, which was initiated by two moving walls, was proposed based on the Verlet velocity iterative algorithm. The simulations reveal that the velocities of fluid molecular groups change about their respective mean velocities within a narrow range in steady state. It is also found that the velocity slips occur at the wall boundary and in a certain number of fluid film layers close to the wall. Because the dimension of molecular group and the number of group layers are not restricted, the hypothetical thickness of fluid film model can be enlarged from nanometer to micron by using the proposed simulation method.

3D relativistic Hartree-Bogoliubov model with a separable pairing interaction: Triaxial ground-state shapes

Potential-energy surfaces and pairing energy maps of nuclei with triaxial shapes are studied in the framework of the relativistic Hartree-Bogoliubov (RHB) model. The recently introduced separable pairing force, adjusted in nuclear matter to the pairing gap of the Gogny force, is employed in the pairing channel of the three-dimensional RHB model for triaxial shapes, and the density-dependent meson-exchange effective interaction (DD-ME2) is used in the particle-hole channel. Even-$A$ Pt isotopes with triaxial ground-state shapes and Sm nuclei with $\ensuremath{\gamma}$-soft potential-energy surfaces are analyzed.