Unbound Region Research Articles

Lagrangian descriptor and escape time as tools to investigate the dynamics of laser-driven polar molecules.

We consider the nonlinear dynamics of a diatomic polar molecule under a linearly polarized laser field. We assume a model in which the molecule dipole is coupled with a time-dependent electric field. This system presents a bound energy region where the atoms are bound, and a free-energy region where the atoms are dissociated. Due to the nonalignment between the dipole axis and the laser direction, and the time dependence of the external field, this system presents two and a half degrees of freedom, namely the vibrational degree, the rotation degree, and the time. To investigate the system dynamics, instead of using the Poincaré surface-of-section technique, we propose the use of the Lagrangian descriptor associated with the escape times. The Lagrangian descriptor is a quantity that reveals complex structures in the phase space, whereas the escape times are the time span in which a trajectory is initially in the bound region before escaping to the unbound region. The combination of these two quantities allows us to distinguish between real stability regions from other complex structures, including stickiness regions, and a different formation, which we call escape islands. With the help of these tools, we find that for high-field amplitudes the inclusion of rotation leads to an increase of the stability regions, which implies a decrease of the dissociation in comparison with the one-dimensional case.

Analysis of Stabilization and Extrapolation Methods for Determining Energies and Lifetimes of Metastable Electronic States.

Two methods that make use of standard electronic structure tools, the stabilization and extrapolation methods, are discussed with an eye toward pointing out their relative strengths and weaknesses and for improving their applications. In the former, whether to utilize energy data from only one or from both branches of an avoided crossing between the quasi-bound and pseudo-continuum states is one issue that is focused on. Another is the decision of where along the stabilization plot's branches (i.e., far from or close to the avoided crossing) to create data points for optimal performance given a reasonable (10-5-10-7 eV) precision in the electronic energy. A third issue is how many parameters to use in fitting energy data to the (one or two) branches of the stabilization plot. In extrapolation methods, one uses energy data computed when the metastable state's energy has been rendered stable by the application of an external potential, which thus produces a one-branch function. The main issues in implementing this method are the functional form for how the energy E depends on the strength of the external potential especially as the energy evolves from the bound-state region toward the unbound region and how to choose data points so that energy values of a reasonable precision are capable of determining the parameters in the formula that produces the metastable state's energy E and half-width Γ/2 (inversely related to the state's lifetime). In addition to explaining, critiquing, and comparing these two methods, several suggestions are offered for their further testing and improvements.

Nonlinear photoassociation through exotic orbits.

We investigate the effects of a particular kind of orbits, which we call exotic orbits, on the process of classical molecular photoassociation. As a starting model system, we consider the process described by the Morse potential with a time-dependent perturbation consisting of the interaction of an external laser field with the molecular dipole. When the external perturbation is turned off, the bound molecular states are classically represented by librational motion, whereas the unbound, the collisional states, are represented by unbound motion, and in both cases, the energy is a constant of motion. When the perturbation is turned on, the total energy is no longer a constant of motion and initial conditions in the unbound region can reach the bound region, and vice versa, through chaotic orbits. Alternatively, we have found that the connection between the bound and unbound sectors can be achieved through exotic orbits, which are comprised by librationlike parts, a localized chaotic region, and an unbounded constant-energy part. Thus, if a colliding atomic pair is in an exotic orbit, it penetrates a chaotic region coming from the unbound sector, subsequently performing librationlike motion, during which the molecule with constant bound energy is formed. Afterwards, the molecule returns to the chaotic region and from this region, it can either access a distinct bound energy or dissociate. We call this phenomenon, in which a metastable molecule is formed, intermittent photoassociation. We show that the key for the emergence of exotic orbits is the relatively short range of the dipole as compared to the interacting potential range. In order to further verify our results, we have considered realistic forms for the potentials and dipole functions of several molecules and found the emergence of exotic orbits, and consequently of intermittent photoassociation, for the MgLi and SrLi molecular parameters.

Domain Sorting in Giant Unilamellar Vesicles Adsorbed on Glass.

Giant unilamellar vesicles (GUVs) adsorb to a solid surface and rupture to form a planar bilayer patch. These bilayer patches are used to investigate the properties and functions of biological membranes. Therefore, it is crucial to understand the mechanisms of GUV adsorption. In this study, we investigate the adsorption of phase-separated GUVs on glass using fluorescence microscopy. GUVs containing liquid-ordered (Lo) and liquid-disordered (Ld) phases underwent domain sorting after adsorption. The Ld domain in the unbound region migrated to the highly curved region near the edge of the adsorbed region. Additionally, the Lo phase grew linearly along the edge of the adsorbed region, creating a thin ring-like domain. After the domain sorting event, the GUV ruptured to form a planar bilayer patch with circular-patterned domains in the initially adsorbed area. We found that domain sorting was promoted by increasing the extent of GUV deformation. These results suggest that both the Ld and Lo domains are reorganized for stabilizing the curved bilayer region in adsorbed GUVs.

A tunable mechanism to control photo-dissociation with invariant tori with variable energies

In this work, we investigate the classical dynamics of a polar diatomic molecule under the action of a space and time-dependent laser field. In the absence of laser fields, the phase space consists of a bound and an unbound region divided by a separatrix. When an interacting laser field is present, some surviving invariant tori are deformed. Therefore, the initial conditions in the bound region which are over the surviving tori may visit the unbound region but still undergoing a bounded motion. Based on this analysis, we propose a mechanism to control the photo-dissociation process using the driven Morse oscillator as a model.

The ionized electron return phenomenon of Rydberg atom in crossed-fields

Rydberg atom is highly excited with one valence electron being in a high quantum state, which is very far away from the nucleus. The energy level is similar to that of the hydrogen atom. Introducing externally perpendicular electric and magnetic fields breaks the rotation symmetry and the traditional view is that the ionized electron crosses from the bound into the unbound region and will never return. However, we find that when the field is strong enough, the electron does not move off to infinity and there is a certain possibility of return. Three new periodic orbits are found by the variational method and the physical significance of the phenomenon is also discussed.

Unified studies of structure and reactions in light unstable nuclei

The generalized two-center cluster model (GTCM), which can treat covalent, ionic and atomic configurations in general systems with two inert cores plus valence nucleons, is formulated in the basis of the microscopic cluster model. In this model, the covalent configurations constructed by the molecular orbital (MO) method and the atomic (or ionic) configuration obtained by the valence bonding (VB) method can be described in a consistent manner. GTCM is applied to the light neutron-rich system, 10,12 Be = α + α + XN (X = 2,4), and the unified studies of the structural changes and the reaction problem are performed. In the structure study, the calculated energy levels are characterized in terms of the chemical bonding like structures, such as the covalent MO or ionic VB structures. The chemical bonding structures changes from level to level within a small energy interval. In the unbound region, the structure problem with the total system of α + α + XN and the reaction problem, induced by the collision of an asymptotic VB state of α +6,8 He, are combined by GTCM. The properties of unbound resonant states are discussed in a close connection to the reaction mechanism, and some enhancement factors originated from the properties of the intrinsic states are predicted in the reaction observables. The unified calculation of the structures and the reactions is applied to the Coulomb shift problem in the mirror system, such the 10 Be and 10 C nuclei. The Coulomb displacement energy of the mirror systems are discussed.

α + 15O cluster structures in 19Ne and the α resonant scattering

The rotational bands of α + 15O(1/2−) in 19Ne are calculated by employing a simple potential model. The α−15 O interaction potential is constructed from the scattering calculation of its mirror system, α + 15N. The resonance states are identified by imposing the absorbing boundary condition. The present calculations predict the sequence of the spin-orbit splitting states in the unbound region of 19Ne, which are generated from the higher spin states in the 20Ne nucleus. The excitation function of the α + 15O elastic scattering is also predicted, and the appropriate condition to observe the resonances is also discussed.

Studies of light neutron-excess systems from bound states to continuum

The generalized two-centre cluster model (GTCM), which can handle various single-particle configurations in general two-centre systems, is applied to the light neutron-rich system, 12Be = α+α+4N. We discuss the change of the neutrons' configuration around two α cores as the excitation energy varies. We show that the excess neutrons form various chemical-bonding-like configurations around the two α cores in the unbound region above the α-decay threshold. The possibility of α-cluster formation in a heavier system with neutron excess, 28Ne, is also discussed.

Studies of Light Neutron-Excess Systems from Bounds to Continuum

The generalized two-center cluster model, which can handle various single particle configurations in general two center systems, is applied to the light neutron-rich system, 12Be = α+α+4N. We discuss the change of the neutrons’ configuration around two α-cores as a variation of an excitation energy. We show that the excess neutrons form various chemical-bonding-like configurations around two α cores in the unbound region above the α decay threshold. The possibility of the α cluster formation in the heavier neutron-excess system, 28Ne, is also discussed.

Formations of loose clusters in an unbound region of12Be

The generalized two-center cluster model (GTCM), which can treat covalent and atomic configurations in general two-center systems, is applied to the light neutron-excess system ${}^{12}$Be $=$ $\ensuremath{\alpha}$ $+$ $\ensuremath{\alpha}$ $+$ 4$N$. The changes of the orbits of the neutrons are analyzed by calculating adiabatic energy surfaces with a variation of the $\ensuremath{\alpha}$-$\ensuremath{\alpha}$ distance. The smooth transition from covalent molecular orbits to atomic He-dimer states is realized in the adiabatic energy surfaces. According to this smooth transition, the adiabatic states are divided into two regions, the internal covalent region and the external He-dimer region, by introducing boundaries of the change in structure. The intrinsic structure of the excited energy levels is investigated. We found that, in an unbound region, the He dimers appear as the molecular resonances of $\ensuremath{\alpha}$ + ${}^{8}$He${}_{g.s.}$, ${}^{6}$He${}_{g.s.}$ + ${}^{6}$He${}_{g.s.}$, and ${}^{5}$He${}_{g.s.}$ + ${}^{7}$He${}_{g.s.}$. An exotic superdeformation, which has a hybrid configuration of both the covalent and He-dimer structures, is also realized in the same energy region. These unbound states can be classified into internal and external states, and the excitation degrees of freedom are assigned for the individual states. The level scheme of these unbound states reveals a strong degenerate feature with a considerable mixture of the different configurations. From the result of the level scheme, the ``loose clusters'' are introduced to characterize the unbound states in the neutron-excess system ${}^{12}$Be.

Studies of Light Neutron-Excess Nuclei from Bounds to Continuum

The generalized two-center cluster model, which can handle various single particle configurations in general two center systems, is applied to the light neutron-rich system, 12Be = α+α+4N. We discuss the change of the neutrons’ configuration around two α-cores as a variation of an excitation energy. We show that the excess neutrons form various chemical-bonding-like configurations around two α cores in the unbound region above the α decay threshold. The possibility of the α cluster formation in the heavier neutron-excess system, 28Ne, is also discussed.

Formula omitted]-Nucleus optical potential and possible [formula omitted] bound states

Starting from a recent model of the η′N interaction, we evaluate the η′-nucleus optical potential, including the contribution of lowest order in density, tρ/2mη′, together with the second-order terms accounting for η′ absorption by two nucleons. We also calculate the formation cross section of the η′ bound states from (π+,p) reactions on nuclei. The η′-nucleus potential suffers from uncertainties tied to the poorly known η′N interaction, which can be partially constrained by the experimental modulus of the η′N scattering length and/or the recently measured transparency ratios in η′ nuclear photoproduction. Assuming an attractive interaction and taking the claimed experimental value |aη′N|=0.1 fm, we obtain an η′ optical potential in nuclear matter at saturation density of Vη′=−(8.7+1.8i) MeV, not attractive enough to produce η′ bound states in light nuclei. Larger values of the scattering length give rise to deeper optical potentials, with moderate enough imaginary parts. For a value |aη′N|=0.3 fm, which can still be considered to lie within the uncertainties of the experimental constraints, the spectra of light and medium nuclei show clear structures associated to η′-nuclear bound states and to threshold enhancements in the unbound region.

Studies of light neutron-excess systems from bounds to continuum

The generalized two-center cluster model (GTCM), which can handle various single particle config urations in general two center systems, is applied to the light neutron-rich system, 12 Be= α+α+4N . We discuss the change of the neutrons’ configuratio around two α-cores as a variation of an excitation energy. We show that the covalent, ionic and atomic configuration appear in the unbound region above the α+8 Heg.s. particledecay threshold. The GTCM calculation is also applied to even Be isotopes, and the systematics on the structural changes from bound region to continuum is discussed.

ASYMMETRIC CLUSTERS IN EVEN Be ISOTOPES

The generalized two-center cluster model (GTCM), which can treat various single particle configurations in general two center systems, is applied to light neutron-rich systems, Be isotopes (α+α+ X N). We discuss the change of the neutrons' configuration around two α-cores as a variation of an excitation energy. We show that the asymmetric clusters, which correspond to the atomic or ionic configurations, appear in the unbound region above the α particle-decay threshold systematically.

COVALENT, IONIC, AND ATOMIC STRUCTURES IN 12Be

The generalized two-center cluster model (GTCM), which can treat various single particle configurations in general two center systems, is applied to the light neutron-rich system, 12 Be = α+α+4N. We discuss the change of the neutrons' configuration around two α-cores as a variation of an excitation energy. We show that the covalent, ionic and atomic configurations appear in the unbound region above the α+8 He g.s. particle-decay threshold, and they coexist within a quite small energy interval.

Coexistence of Covalent Superdeformation and Molecular Resonances in an Unbound Region ofBe12

The generalized two-center cluster model, which can treat static structures and dynamical reactions in excited states, is applied to the light neutron-rich system, 12Be=alpha+alpha+4N. We discuss the change of the neutrons' configuration around two alpha cores from the covalent structure to the ionic one. We show that, in the unbound region above particle-decay thresholds, the ionic configurations appear as the molecular resonances of alpha+8He, 6He+6He, and 5He+7He. A new type of superdeformation is possible, and we find here a covalent superdeformation with a hybrid configuration of both the covalent and ionic structures. The excitation of these exotic structures through the two-neutron transfer reaction is also discussed.

Exotic molecular structures in highly-excited states of 12Be

The generalized two-center cluster model (GTCM), which can treat static structures and dynamical reactions in excited states, is applied to the light neutron-rich system, 12Be = α+α+4N. We discuss the change of the neutrons' configuration around two α-cores from the covalent structure to the ionic one. It is shown that, in the unbound region above particle-decay thresholds, the ionic configurations appear as the molecular resonances of α+8He, 6He+6He and 5He+7He. A new type of superdeformation is possible, and we find here the covalent superdeformation which has a hybrid configuration of the covalent and ionic ones. The excitation of these exotic structures through the two neutron transfer reaction is also discussed.

Yersinia pestis YopD 150–287 fragment is partially unfolded in the native state

Yersinia pestis, a human and animal pathogen, uses the type III secretion system (T3SS) for delivering virulence factors and effectors into the host cells. The system is conserved in animal pathogens and is hypothesized to deliver the virulence factors directly from bacterial to mammalian cells through a pore composed of YopB and YopD translocation proteins. The YopB and YopD translocator proteins must be delivered first to form a functional pore in the mammalian cell. The criteria by which Yersinia selects the two proteins for initial delivery are not known and we hypothesized that the extensive binding by the chaperone and partial unfolding of the unbound region may be the criteria for selection. The YopB and YopD translocator proteins, unlike other effectors, have a common chaperone SycD, which binds through multiple regions. Due to the small size of the pore, we hypothesized that many of the transported virulence factors, translocators YopB and YopD included, are delivered in a partially unfolded state stabilized by binding to specific chaperones. The YopD protein binds the chaperone through amino acid (a.a.) 53–149 and a.a. 278–292 regions but biophysical characterization of YopD has not been possible due to the lack of an expression system for soluble, large fragments of the protein. In our present work, we demonstrated that the YopD 150–287 peptide fragment, almost the full soluble C-terminal part, including the non-interacting peptide fragment YopD 150–277, was partially unfolded in its native state by a combination of biophysical methods: circular dichroism, quasi-elastic light scattering, chemical unfolding and 8-anilino-1-naphthalene sulfonate (ANS) binding. The secondary structure of the peptide converted easily between α-helical and random coil states at neutral pH, and the α-helical state was almost fully recovered by lowering the temperature to 263 K. The current results suggest that YopD 150–287 peptide may have the postulated transport-competent state in its native form.

Quarkonia and quark drip lines in a quark-gluon plasma

We extract the $Q\text{\ensuremath{-}}\overline{Q}$ potential by using the thermodynamic quantities obtained in lattice gauge calculations. The potential is tested and found to give spontaneous dissociation temperatures that agree well with those from lattice gauge spectral function analysis. Using such a $Q\text{\ensuremath{-}}\overline{Q}$ potential, we examine the quarkonium states in a quark-gluon plasma and determine the ``quark drip lines'' which separate the region of bound color-singlet $Q\overline{Q}$ states from the unbound region. The characteristics of the quark drip lines severely limit the region of possible bound $Q\overline{Q}$ states with light quarks to temperatures close to the phase transition temperature. Bound quarkonia with light quarks may exist very near the phase transition temperature if their effective quark mass is of the order of 300--400 MeV and higher.