Energy-dependent Term Research Articles

Inverse problem in energy-dependent potentials using semiclassical methods

Wave equations with energy-dependent potentials appear in many areas of physics, ranging from nuclear physics to black hole perturbation theory. In this work, we use the semiclassical Wentzel-Kramers-Brillouin (WKB) method to first revisit the computation of bound states of potential wells and reflection/transmission coefficients in terms of the Bohr-Sommerfeld rule and the Gamow formula. We then discuss the inverse problem, in which the latter observables are used as a starting point to reconstruct the properties of the potentials. By extending known inversion techniques to energy-dependent potentials, we demonstrate that so-called width-equivalent or WKB-equivalent potentials are not isospectral anymore. Instead, we explicitly demonstrate that constructing quasi-isospectral potentials with the inverse techniques is still possible. Those reconstructed, energy-independent potentials share key properties with the width-equivalent potentials. We report that including energy-dependent terms allows for a rich phenomenology, particularly for the energy-independent equivalent potentials. Published by the American Physical Society 2024

Nonlinear Evolution of Fast Collective Neutrino Oscillations in Core-Collapse Supernovae

According to one of the most promising supernova theories, the neutrino-heating mechanism, neutrinos are responsible for transferring the energy released during the gravitational collapse of massive stars to their surroundings. If neutrino flavors are converted fast in the cores, the efficiency of neutrino heating is enhanced and can change the dynamics of the shock wave in supernovae. In this article, we investigate the dynamics of fast neutrino flavor conversions with collisions under energy-dependent treatment in detail. For the first time, we use a realistic initial condition, which is taken from the results of the self-consistent, realistic Boltzmann simulations in two spatial dimensions under axisymmetry. We report that the neutrino flavor conversion will be significantly enhanced if the energy-dependent collision term is considered in the neutrino transport equation which has been ignored in previous studies. We present the preliminary results of our investigation here, which are consistent with other studies which were conducted under simple treatments. It is believed that such findings may have an impact on the explosion mechanism of core-collapse supernovae, nucleosynthesis and neutrino astronomy.

Nonlinear Evolution of Fast Collective Neutrino Oscillations in Core-collapse Supernovae

According to one of the most promising supernova theories, the neutrino-heating mechanism, neutrinos are responsible for transferring the energy released during the gravitational collapse of massive stars to their surroundings. If neutrino flavors are converted fast in the cores, the efficiency of neutrino heating is enhanced and can change the dynamics of the shock wave in supernovae. In this article, we investigate the dynamics of fast neutrino flavor conversions with collisions under energy-dependent treatment in detail. For the first time, we use a realistic initial condition, which is taken from the results of the self-consistent, realistic Boltzmann simulations in two spatial dimensions under axisymmetry. We report that the neutrino flavor conversion will be significantly enhanced if the energy-dependent collision term is considered in the neutrino transport equation which has been ignored in previous studies. We present the preliminary results of our investigation here, which are consistent with other studies which were conducted under simple treatments. It is believed that such findings may have an impact on the explosion mechanism of core-collapse supernovae, \mbox{nucleosynthesis and neutrino astronomy.

Probing neutral triple gauge couplings at the LHC and future hadron colliders

We study probes of neutral triple gauge couplings (nTGCs) at the LHC and the proposed 100TeV $pp$ colliders, and compare their sensitivity reaches with those of the proposed $e^+ e^-$ colliders. The nTGCs provide a unique window to the new physics beyond the Standard Model (SM) because they can arise from SM effective field theory (SMEFT) operators that respect the full electroweak gauge group $SU(2)_L\otimes U(1)_Y$ of the SM only at the level of dimension-8 or higher. We derive the neutral triple gauge vertices (nTGVs) generated by these dimension-8 operators in the broken phase and map them onto a newly generalized form factor formulation, which takes into account only the residual U(1)$_{\rm{em}}$ gauge symmetry. Using this mapping, we derive new relations between the form factors that guarantee a truly consistent form factor formulation of the nTGVs and remove large unphysical energy-dependent terms. We then analyze the sensitivity reaches of the LHC and future 100TeV hadron colliders for probing the nTGCs via both the dimension-8 nTGC operators and the corresponding nTGC form factors in the reactions $ pp(q\bar{q})\to Z\gamma$ with $Z\to\ell^+\ell^-,\nu\bar{\nu}$. We compare their sensitivities with the existing LHC measurements of nTGCs and with those of the high-energy $e^+e^-$ colliders. In general, we find that the prospective LHC sensitivities are comparable to those of an $e^+ e^-$ collider with center-of-mass energy $\leq 1$TeV, whereas an $e^+ e^-$ collider with center-of-mass energy $(3 - 5)$TeV would have greater sensitivities, and a 100TeV $pp$ collider could provide the most sensitive probes of the nTGCs.

Resonant mode coupling approximation for calculation of optical spectra of stacked photonic crystal slabs. Part II

We propose the further development of the resonant mode coupling approximation for the calculation of optical spectra of stacked periodic nanostructures in terms of the scattering matrix. We previously showed that given the resonant input and output vectors as well as background scattering matrices of two subsystems, one can easily calculate those for the combined system comprising two subsystems. It allows us to write a resonant approximation for the combined system and speed up the calculation significantly for typical wave scattering problems. This approach is best suitable for isolated resonances when the approximation of a constant background scattering matrix is reasonable. In this article, we aim at expanding the applicability of the resonant mode coupling approximation by utilizing more complicated approximations for the background matrices. In particular, we show that consideration of energy-dependent correction terms for the background matrices remarkably reduces the calculation error of the resonant parameters. Here we first consider a linear approximation of the background scattering matrices which is subsequently used as a base for a piecewise-linear approximation. We show that the latter allows one to keep the approximation error negligibly small with only a few sample points and to apply the resonant mode coupling approximation within almost arbitrary large energy ranges. Finally, we consider the approximation of background matrices by arbitrary matrix functions and propose a technique to derive resonant poles in this case. The methods described here could be considered an alternative approach for calculating the optical spectra of stacked systems.

Combined analysis of the Zc(3900) and the Zcs(3985) exotic states

We have performed a combined analysis of the BESIII data for both the $Z_c(3900)$ and $Z_{cs}(3985)$ structures, assuming that the latter is an SU(3) flavor partner of the former one. We have improved on the previous analysis of Albaladejo $et$ $al.$ [Phys. Lett. B 755, 337 (2016)] by computing the amplitude for the $D_1\bar{D}D^*$ triangle diagram considering both $D$ and $S$-wave $D_1D^*\pi$ couplings. We have also investigated effects from SU(3) light-flavor violations, which are found to be moderate and of the order of 20%. The successful reproduction of the BESIII spectra, in both the hidden-charm and hidden-charm strange sectors, strongly supports that the $Z_{cs}(3985)$ and $Z_c(3900)$ are SU(3) flavor partners placed in the same octet multiplet. The best results are obtained when an energy-dependent term in the diagonal $D^{(*)}\bar D_{(s)}^{(*)}$ interaction is included, leading to resonances (poles above the thresholds) to describe these exotic states. We have also made predictions for the isovector $Z_{c}^*$ and isodoublet $Z_{cs}^*$, $D^*\bar{D}^*$ and $D^*\bar{D}_{s}^*$ molecules, with $J^{PC}=1^{+-}$ and $J^{P}=1^{+}$, respectively. These states would be heavy-quark spin symmetry partners of the $Z_{c}$ and $Z_{cs}$. Besides the determination of the masses and widths of the $Z_c(3900)$ and $Z_{cs}(3985)$, we also predict those of the $Z_c^*$ and $Z_{cs}^*$ resonances.

Inelastic collisions of fast charged particles with atoms: Bethe asymptotic formulas and shell corrections

The relativistic plane-wave Born approximation is applied to the study of inelastic collisions of charged particles with atoms, by considering atomic wave functions calculated from the independent-electron approximation with the self-consistent Dirac-Hartree-Fock-Slater potential. A database of longitudinal and transverse generalized oscillator strengths (GOSs) has been computed by using accurate numerical methods for all the subshells of the ground-state configurations of the elements with atomic numbers from 1 (hydrogen) to 99 (einsteinium). The calculated GOS do not satisfy the Bethe sum rule; departures from the sum rule are in accordance with previous theoretical estimates. Asymptotic high-energy formulas for the total cross section, the stopping cross section, and the energy-straggling cross section are derived with proper account of the relativistic departure from the Bethe sum rule. The shell correction is calculated as the energy-dependent term that, when added to the asymptotic formula, reproduces the value of the atomic cross section calculated by integrating the energy-loss differential cross section. Shell corrections to the stopping cross section obtained from the present approach are presented and compared with previous estimates.

Probing Quantum Gravity with Imaging Atmospheric Cherenkov Telescopes

High energy photons from astrophysical sources are unique probes for some predictions of candidate theories of Quantum Gravity (QG). In particular, Imaging atmospheric Cherenkov telescope (IACTs) are instruments optimised for astronomical observations in the energy range spanning from a few tens of GeV to ∼100 TeV, which makes them excellent instruments to search for effects of QG. In this article, we will review QG effects which can be tested with IACTs, most notably the Lorentz invariance violation (LIV) and its consequences. It is often represented and modelled with photon dispersion relation modified by introducing energy-dependent terms. We will describe the analysis methods employed in the different studies, allowing for careful discussion and comparison of the results obtained with IACTs for more than two decades. Loosely following historical development of the field, we will observe how the analysis methods were refined and improved over time, and analyse why some studies were more sensitive than others. Finally, we will discuss the future of the field, presenting ideas for improving the analysis sensitivity and directions in which the research could develop.

A new form of pseudopotential for the study of lattice mechanical properties of transition metals

ABSTRACT The study of lattice mechanical properties of transition metals using pseudopotential is burdensome as the presence of d-band in these metals complicates their electronic structure. The use of pseudopotential for the study of physical properties can be justified if it accounts for the effect of d-band. The local form of the pseudopotentials is widely used to study the physical properties of materials due to their computational simplicity, physical transparency, and transferability to other environments. It is a well-established fact that non-local pseudopotentials should be preferred to the local ones. But, non-local pseudopotentials are proven to be at a higher computational cost. Inspired by such requirements, we, in the present communication, propose a pseudopotential comprising of one non-local (energy-dependent) and another local term in q-space. The non-local (energy-dependent) term accounts for s-p interaction, while the other term is used to account for the effect of s-d hybridisation. The Generalized Pseudopotential Theory (GPT) has been used to formulate the pseudopotential. Further, the pseudopotential has been used to study static binding energy, lattice dynamics, lattice mechanical properties and second-order elastic constants in the long-wavelength limit (q→0) for transition metals γ-Fe (fcc), Co and α-Fe (bcc). Computed results are found to be in good agreement with experimental and other theoretical results, which proves that the proposed pseudopotential itself accounts for the effect of d-band without using additional short-ranged Born–Mayer type potential and effective valency.

Cancer cells optimize elasticity for efficient migration.

Cancer progression is associated with alternations in the cytoskeletal architecture of cells and, consequently, their mechanical properties such as stiffness. Changing the mechanics of cells enables cancer cells to migrate and invade to distant organ sites. This process, metastasis, is the main reason for cancer-related mortality. Cell migration is an essential step towards increasing the invasive potential of cells. Although many studies have shown that the migratory speed and the invasion of cells can be inversely correlated to the stiffness of cells, some other investigations indicate opposing results. In the current work, based on the strain energy stored in cells due to the contractile forces, we defined an energy-dependent term, migratory index, to approximate how changes in the mechanical properties of cells influence cell migration required for cancer progression. Cell migration involves both cell deformation and force transmission within cells. The effects of these two parameters can be represented equally by the migratory index. Our mechanical modelling and computational study show that cells depending on their shape, size and other physical parameters have a maximum migratory index taking place at a specific range of cell bulk elasticity, indicating the most favourable conditions for invasive mobility. This approximate model could be used to explain why the stiffness of cells varies during cancer progression. We believe that the stiffness of cancer or malignant cells depending on the stiffness of their normal or non-malignant counterparts is either decreased or increased to reach the critical condition in which the mobility potential of cells is approximated to be maximum.

Mean-field theory for fermion pairs and the ab initio particle-vibration coupling approach

A Dyson Bethe-Salpeter equation (Dyson-BSE) for fermion pairs is presented whose kernel has a static and a one frequency dependent contribution, analogous to the self energy of the single particle Dyson equation with the (static) mean field term and the energy dependent correlation term. The static part of the Dyson-BSE is the self-consistent mean field for the vibrations. At the same time, for the correlated single particle self-energy a full particle-vibration coupling (PVC) scattering equation is established where the vibration is the same as obtained from the Dyson-BSE. Both equations, single particle Dyson equation and Dyson-BSE, are coupled through self-consistency. Numerical results for Lipkin and 1D Hubbard chain are very promising.

Investigation of the energy dependence of the p_{text {T0}} parameter in the Pythia\xa08 Monte Carlo event generator

By using predictions from the Pythia 8 Monte Carlo event generator, we determine the energy-dependent turn-over values (p_{text {T0}}) of the partonic cross section for the simulation of multiparton interactions. Since the observed energy dependence of the p_{text {T0}} values is not well described by a power-law function, we introduce an additional energy-dependent term, to better describe the experimental observations in the energy range sqrt{s} = 0.3-13 , hbox {TeV}. We obtain a similar level of agreement for predictions using various parton densities.

Light bending, static dark energy, and related uniqueness of Schwarzschild–de Sitter spacetime

Since the Schwarzschild-de Sitter spacetime is static inside the cosmological event horizon, if the dark energy state parameter is sufficiently close to $-1$, apparently one could still expect an effectively static geometry, in the attraction dominated region inside the maximum turn around radius, $R_{\rm TA, max}$, of a cosmic structure. We take the first order metric derived recently assuming a static and ideal dark energy fluid with equation of state $P(r)=\alpha\rho(r)$ as a source in Ref. [1], which reproduced the expression for $R_{\rm TA, max}$ found earlier in the cosmological McVittie spacetime. Here we show that the equality originates from the equivalence of geodesic motion in these two backgrounds, in the non-relativistic regime. We extend this metric up to the third order and compute the bending of light using the Rindler-Ishak method. For $ \alpha\neq -1$, a dark energy dependent term appears in the bending equation, unlike the case of the cosmological constant, $\alpha=-1$. Due to this new term in particular, existing data for the light bending at galactic scales yields, $(1+\alpha)\lesssim {\cal O}(10^{-14})$, thereby practically ruling out any such static and inhomogeneous dark energy fluid we started with. Implication of this result pertaining the uniqueness of the Schwarzschild-de Sitter spacetime in such inhomogeneous dark energy background is discussed.

Determination of minimum impact parameter by modified touching spheres schemes for intermediate energy Coulomb excitation experiments

The energy-independent touching spheres schemes commonly used for the determination of the safe minimum value of the impact parameter for Coulomb excitation experiments are modified through the inclusion of an energy-dependent term. The touching spheres+3fm scheme after modification emerges out to be the best one while touching spheres+4fm scheme is found to be better in its unmodified form.

Modified interaction radius and touching spheres schemes for the determination of impact parameter in Coulomb excitation experiments

The parametrization schemes based on interaction radius and touching spheres (ts) commonly used for the determination of minimum value of impact parameter [Formula: see text] in the above barrier Coulomb excitation experiments are modified by incorporating an energy-dependent term. The modification leads to about 13% improvement in the value of [Formula: see text] for a variety of projectile target combinations at above Coulomb barrier incident energies.

Nucleon-antinucleon annihilation at largeNc

Nucleon-antinucleon annihilation in the large $N_c$ limit of QCD in the Witten regime of fixed velocity is considered with a focus on the spin and isospin dependence of the annihilation cross-section. In general, time-reversal and isospin invariance restricts the annihilation cross-section to depend on 6 independent energy-dependent terms. At large $N_c$, a spin-flavor symmetry emerges in the theory that acts to further restrict the dependence of the annihilation cross-section to three of these terms; the other terms amount to $1/N_c$ corrections. Assuming dominance of the leading order terms, several identities are derived that relate annihilation in different spin-isospin channels. A key prediction is that for unpolarized nucleons in Witten kinematics, the proton-antiproton annihilation cross-section should be equal to the proton-antineutron annihilation cross-section up to corrections of relative order $1/N_c$. Unpolarized nucleon-antinucleon annihilation data appears to be consistent with this expectation.

A critical assessment of the angular momentum sum rules

There are now five angular momentum relations or sum rules in the literature: the Jaffe, Manohar relation for a longitudinally polarized nucleon, and the Bakker, Leader, Trueman result for the case of transverse polarization; the Ji relation for longitudinal polarization, and the Leader result for transverse polarization, both involving generalized parton distributions; and a new sum rule due to Ji, Xiong and Yuan dealing with the transverse component of the Pauli–Lubanski vector. I discuss these various relations and examine their precise interpretation in the light of the so-called “angular momentum controversy”. In particular, I show that the claim of Ji, Xiong, Yuan that their Pauli–Lubanski relation is frame or energy independent is incorrect and that they have missed an energy dependent term in their expression.

Relativistic mean field model for nuclear matter with non-linear derivative couplings

We apply the non-linear derivative (NLD) model proposed recently by Gaitanos et al. to investigate the properties of nuclear matter and the mass-radius relation of neutron stars as well. Three cases with different energy-dependent non-linear terms in this model are chosen, in which comparison among the obtained results has been made. It is found that the calculated results are sensitive to the non-linear terms in the NLD model.

Study of Heavy Quarkonium with Energy Dependent Potential

Heavy quark systems (c and b ) have been studied in the nonrelativistic framework using energy dependent interquark potential of the form harmonic oscillator with a small linear term as energy dependent as perturbation plus a inverse square potential. This potential admits exact analytical solution of the Schrodinger equation. Mass spectra, leptonic decay width, root mean square radii (), the expectation value of the radius (r) and have been estimated for different quantum mechanical states for and systems. It is observed that energy dependent term in the potential leads to saturation of the mass spectra and degree of saturation is governed by the magnitude of perturbation. The calculated values of leptonic decay widths for 1s state are in very good agreement with the experimental data both for c and b systems.

Anomalous Small-angle X-ray Scattering Study on Aggregation of a Block Copolymer in a Selective Solvent

Anomalous small-angle X-ray Scattering (ASAXS) analysis for poly(4-vinylphenol)-b-poly(4-bromostyrene) (PVPh-b-PBrS) in N,N,N',N'-tetramethyl ethylene diamine (TMEDA) solution was examined. The ASAXS measurements, executed at three different energies, provided the separation of the scattering of the Br atoms from whole system. The energy-dependent term in the SAXS profile, which is corresponding to the form factor of PBrS domain, sufficiently agree with the SAXS profile calculated for hard sphere with 41 nm radius. Therefore, the PBrS chains assemble into spherical core with 41 nm radius in TMEDA solution.