Centrifugal Barrier Research Articles

Calculation of α-decay half-lives of 186−218Po isotopes and actinide nuclei using a new phenomenological potential

This paper is devoted to the calculations of alpha decay half-lives of [Formula: see text]Po [Formula: see text] isotopes and actinide nuclei between the atomic numbers Z = 90 and Z = 102, using an energy-dependent potential model. The [Formula: see text]-nucleus effective potential employed in this study includes a Coulomb potential, a centrifugal barrier potential, and a nuclear potential. The nuclear potential is chosen to be the energy-dependent singularized harmonic potential, typical of nuclear interactions. The role of the energy-dependent potential is very significant in this study. Indeed, when compared to the experimental data, our results are found to be improved when energy-dependent interaction potential is employed compared to when energy-independent interactions are used, especially for small values of the parameter [Formula: see text] as evidenced by the values of the root mean square deviation.

Structure and dynamics of magneto-inertial, differentially rotating laboratory plasmas

We present a detailed characterization of the structure and evolution of differentially rotating plasmas driven on the MAGPIE pulsed-power generator (1.4 MA peak current, 240 ns rise time). The experiments were designed to simulate physics relevant to accretion discs and jets on laboratory scales. A cylindrical aluminium wire array Z pinch enclosed by return posts with an overall azimuthal off-set angle was driven to produce ablation plasma flows that propagate inwards in a slightly off-radial trajectory, injecting mass, angular momentum and confining ram pressure to a rotating plasma column on the axis. However, the plasma is free to expand axially, forming a collimated, differentially rotating axial jet that propagates at ${\approx }100\,{\rm km}\,{\rm s}^{-1}$ . The density profile of the jet corresponds to a dense shell surrounding a low-density core, which is consistent with the centrifugal barrier effect being sustained along the jet's propagation. We show analytically that, as the rotating plasma accretes mass, conservation of mass and momentum implies plasma radial growth scaling as $r \propto t^{1/3}$ . As the characteristic moment of inertia increases, the rotation velocity is predicted to decrease and settle on a characteristic value ${\approx }20\,{\rm km}\,{\rm s}^{-1}$ . We find that both predictions are in agreement with Thomson scattering and optical self-emission imaging measurements.

Approximate solutions for diatomic molecules under combined potentials in a global monopole and Aharonov–Bohm flux field

AbstractBound state energy eigensolutions of nine different diatomic molecules, specifically, , TiH, , CO, NO, ScH, CrH, HCl and LiH, placed in a point‐like global monopole, have been calculated by solving the time‐independent Schrödinger equation (SE). The molecules are confined by the Aharonov–Bohm (AB) flux field and the interaction potential among the charged particles is governed by the combined screened modified Kratzer potential (SMKP) plus Hulthén potential model. Three other special cases of the interaction potential have also been discussed here. Asymptotic iteration method has been used for the mathematical calculations. It is difficult to solve the SE exactly for any non‐zero values of the azimuthal quantum number due to the presence of the centrifugal barrier term. The well‐known Pekeris approximation technique for the terms and has taken into consideration for the purpose of performing numerical computations connected to an arbitrary state. The outcomes of this study are in reasonable agreement with the results of previous research on SMKP, Kratzer‐Fues potential, and modified Kratzer potential in the Minkowski space. It is observed that the energy spectra of the diatomic molecules suffer considerable change due to the effects of the background AB‐flux field and topological defect parameter.

Noncommutative of Klein–Gordon and Schrödinger equations in the background of the improved Hua plus modified Eckart potential model in 3D-(R/NR)NCQS symmetries: Spectrum and thermodynamic properties

The impact of deformation space on the physical characteristics of diverse physics systems has been thoroughly investigated in research papers. In this work, we study the deformed Klein–Gordon equation (DKGE) in the three-dimensional relativistic non-commutative quantum space (3D-RNCQS) regime by using the improved Hua plus modified Eckart potential (IHPMEP) model. For this consideration, the DKGE in the 3D-RNCQS regime is solved using the standard perturbation theory and the well-known Bopp’s shifts method with the Greene–Aldrich approximation to the centrifugal barrier. The new relativistic energy equation and eigenfunction for the IHPMEP in the presence of deformation space-space for the heterogeneous (CO, HF, and NO) and homogeneous (N2, H2, and Li2) diatomic molecules are obtained to be sensitive to the atomic quantum numbers ([Formula: see text] and [Formula: see text]), the mixed potential depths ([Formula: see text], and [Formula: see text]), the inverse of the screening parameter [Formula: see text], and non-commutativity parameters ([Formula: see text], [Formula: see text], and [Formula: see text]). Analysis is performed on the non-relativistic limit of new energy spectra. By appropriately adjusting the combined potential parameters, we analyze the obtained new bound state eigenvalues of the DKGE and deformed Schrödinger equation with the IHPMEP in 3D-NCQS symmetries and obtain the new modified Eckart potential, the modified Hua potential, the modified Morse potential, and the modified Pöschl–Teller potential. Within the framework of the 3D-NRNCQS regime, the homogeneous and heterogeneous composite systems under IHPMEP models are examined. A thorough investigation is carried out into the impact of space-space deformation on the thermal parameters of the IHPMEP, including the partition function, mean energy, free energy, specific heat, and entropy. This work is of a fundamental absorbability nature and pedagogical interest in atomic and molecular physics.

CH3OH and Its Deuterated Species in the Disk/Envelope System of the Low-mass Protostellar Source B335

Deuterium fractionation in the closest vicinity of a protostar is important in understanding its potential heritage to a planetary system. Here, we have detected the spectral line emission of CH3OH and its three deuterated species, CH2DOH, CHD2OH, and CH3OD, toward the low-mass protostellar source B335 at a resolution of 0.″03 (5 au) with Atacama Large Millimeter/submillimeter Array. They have a ring distribution within the radius of 24 au with the intensity depression at the continuum peak. We derive the column densities and abundance ratios of the above species at six positions in the disk/envelope system as well as the continuum peak. The D/H ratio of CH3OH is ∼[0.03–0.13], which is derived by correcting the statistical weight of 3 for CH2DOH. The [CHD2OH]/[CH2DOH] ratio is derived to be higher ([0.14–0.29]). On the other hand, the [CH2DOH]/[CH3OD] ratio ([4.9–15]) is higher than the statistical ratio of 3 and is comparable to those reported for other low-mass sources. We study the physical structure on a few astronomical unit scales in B335 by analyzing the CH3OH (183,15 − 182,16, A) and HCOOH (120,12 − 110,11) line emission. Velocity structures of these lines are reasonably explained as the infalling-rotating motion. The protostellar mass and the upper limit to the centrifugal barrier are thus derived to be 0.03–0.07 M ⊙ and <7 au, respectively, showing that B335 harbors a young protostar with a tiny disk structure. Such youth of the protostar may be related to the relatively high [CH2DOH]/[CH3OH] ratio.

Enhancement of p-wave dark matter annihilation by quasi-bound states

We scrutinize the Sommerfeld enhancement in dark matter pair annihilation for p-wave and higher-ℓ partial waves. For the Yukawa potential these feature a super-resonant Breit-Wigner peak in their velocity-dependence close to Sommerfeld resonances as well as a universal scaling with velocity for all ℓ ≥ 1 that differs from the s-wave case. We provide a quantum mechanical explanation for these phenomena in terms of quasi-bound states sustained by the centrifugal barrier of the partial-wave potential, and give approximate WKB expressions capturing the main effects. The impact of quasi-bound states is exemplified for wino dark matter and models with light mediators, with a focus on indirect detection signals. We note that quasi-bound states can also explain similar peaks in the bound-state formation and self-scattering cross sections.

Roaming in acetaldehyde.

We investigate roaming in the photodissociation of acetaldehyde (CH3CHO), providing insights into the contrasting roaming dynamics observed for this molecule compared to formaldehyde. We carry out trajectory studies for full-dimensional acetaldehyde, supplemented with an analysis of a two-degree-of-freedom restricted model and obtain evidence for two distinct roaming pathways. Trajectories exhibit roaming at both shorter (9-11.5 au) and larger (14.5-22.9 au) maximum CH3-HCO separations, characterized by differing amounts of HCO rotation. No roaming trajectories were found in the intervening gap region. The roaming dynamics near 14.5-22.9 au are well-reproduced by the restricted model and involve passage through a centrifugal barrier, analogous to formaldehyde roaming. However, the shorter-range 9-11.5 au roaming appears unique to acetaldehyde and is likely facilitated by repulsive interactions absent in the simplified models. Phase space analysis reveals that this additional roaming pathway is inaccessible in the reduced dimensionality system. The findings suggest that acetaldehyde's increased propensity for roaming compared to formaldehyde may arise from the presence of multiple distinct roaming mechanisms rather than solely the higher roaming fragment mass.

High-Resolution Crossed-Beam Dynamics Studies of the D + Para-H2 → HD + H Reaction at 1.21 eV.

Understanding kinetic isotope effects is important in the study of the reaction dynamics of elementary chemical reactions, particularly those involving hydrogen atoms and molecules. As one of the isotopic variants of the hydrogen exchange reaction, the D + para-H2 reaction has attracted much attention. However, experimental studies of this reaction have been limited primarily due to its strong experimental background noise. In this study, by using the velocity map ion imaging method and the near-threshold ionization technique, together with improvements on the vacuum condition in the vicinity of the collision zone, background noise was reduced significantly, and quantum state-resolved differential cross sections (DCSs) for the D + para-H2 reaction at a collision energy of 1.21 eV were acquired in a crossed molecular beams experiment. Interestingly, clear rotational state-dependent angular distributions were noticed in the quantum state-resolved DCSs. The most intense peak's positions for HD (v', j') products shift to different scattering directions as the product's ro-vibrational quantum number increases. Two different microscopic reaction mechanisms are found to be involved in this reaction for HD products in different vibrational states. The results show a direct correlation between the scattering angle and the product's rotational quantum number, revealing that the contributions of impact parameters are strongly influenced by the corresponding centrifugal barrier.

Uniform descriptions of pseudospin symmetries in bound and resonant states

As a continuation of our previous work on the conservation and breaking of the pseudospin symmetry (PSS) in resonant states [Phys. Lett. B 847, 138320 (2023)], in this work, the PSS in nuclear single-particle bound and resonant states are investigated uniformly within a relativistic framework by exploring the poles of the Green's function in spherical Woods-Saxon potentials. As the potential depths increase from zero to finite depths, the PS partners evolve from resonant states to bound states. In this progress, the PSS is broken gradually with energy, width, and density splittings. Specially, the energy and width splittings for the resonant and bound states are directly determined by the ratio of the pseudo spin-orbit potentials between the PS partners. Obvious threshold effect is observed for the energy splitting at a critical potential depth, with which one PS partner has become a quasi-bound state inside the centrifugal barrier while the other one is still a high-energy resonant state outside the centrifugal barrier. The differences in the density distributions of the lower component between the PS partners are manifested in the phase shift for the resonant states and amplitudes for bound states.

A theoretical Fourier-transformation model for the formation of X-ray time lags from black hole accretion discs

ABSTRACT X-ray emission from active galactic nuclei (AGNs) often displays complex and rapid variability, which may provide a glimpse into the detailed thermal and dynamical structure of the accreting gas near the event horizon of the central black hole. The observed variability can be analysed using Fourier transforms of the light curves in multiple energy channels, which can be used to generate Fourier phase lags, corresponding to lags in the time domain. The X-ray time lags may be either soft lags or hard lags, depending on whether the variability in the hard energy channel precedes that in the soft channel or vice versa. The physical explanation for the observed X-ray time lags from AGNs has been puzzling, and several scenarios have been proposed. In this paper, we explore the hypothesis that the X-ray time lags are produced as a result of the reprocessing of iron L-line and K-line seed photons generated via fluorescence, which is driven by a variable incident radiation field. The seed photons are reprocessed by a combination of thermal and bulk Comptonization and spatial reverberation. We assume that the inner region of the accretion flow can be approximated as a hot, geometrically thick ADAF disc. The outer radius of the ADAF region is equal to the shock formation radius, which is located just outside the centrifugal barrier. The time-dependent radiative transfer in the disc is analysed using a Fourier-transformed, vertically averaged transport equation in cylindrical coordinates. We demonstrate that the new model can successfully reproduce the complex X-ray variability data for the Seyfert 1 galaxies 1H 0707–495 and Ark 564.

Enthalpy, mean energy, entropy, and Gibbs free energy of lithium dimer under magnetic field

It is well known that the lithium diatomic molecule has important potential application in engineering, and industry. For this purpose, in this research, the thermal properties of the lithium diatomic molecule are theoretically calculated taking into account both an external magnetic field and Aharonov-Bohm (AB) flux. To this end, the interaction in the diatomic molecule is proposed as an improved Scarf ΙΙ potential model (ISPM). The Schrödinger equation is solved using an appropriate Pekeris-like approximation form for the centrifugal barrier and the energy spectrum and wave functions are obtained. Then, the partition function is obtained to study the thermal properties of the lithium dimer. The calculated thermal properties of 7Li2 (2 3Πg) in this work are mean energy, entropy, specific heat, enthalpy, and Gibbs free energy. Our theoretical results are also compared with the experimental data. The findings show that the obtained results are in good agreement with experimental data. Without considering the magnetic field and AB flux, the deviation of specific heat, Gibbs free energy, and enthalpy are 3.73%, 4.96%, and 5.31%, respectively. By considering the magnetic field and AB flux, we find that the deviation of the aforementioned properties are 1.91%, 2.04%, and 2.32%, respectively. Therefore, it is found that the external magnetic field and AB flux have great influences on the thermal properties of lithium.

On the quantum problem with harmonic, Stark, Coulombian and centrifugal barrier potential terms, and biconfluent Heun functions

&#x0D; &#x0D; &#x0D; We show here that the one dimensional Schro ̈dinger problem with a potential function with harmonic, Stark, Coulombian and centrifugal barrier terms can be described in terms of biconfluent Heun functions, and review some possible solutions of the problem. Considering the algebraic form of the quantum problem, we readily find two new relations between biconfluent Heun functions, which have not been considered before in the literature.&#x0D; &#x0D; &#x0D;

Synthetic Observations of the Infalling Rotating Envelope: Links between the Physical Structure and Observational Features

We performed synthetic observations of the Ulrich, Cassen, and Moosman (UCM) model to understand the relation between the physical structures of the infalling envelope around a protostar and their observational features in molecular lines, adopting L1527 as an example. We also compared the physical structure and synthetic position–velocity (P–V) diagrams of the UCM model and a simple ballistic (SB) model. There are multiple ways to compare synthetic data with observational data. We first calculated the correlation coefficient. The UCM model and the SB model show similarly good correlation with the observational data. While the correlation reflects the overall similarity between the cube datasets, we can alternatively compare specific local features, such as the centrifugal barrier in the SB model or the centrifugal radius in the UCM model. We evaluated systematic uncertainties in these methods. In the case of L1527, the stellar mass values estimated using these methods are all lower than the value derived from previous Keplerian analysis of the disk. This may indicate that the gas infall motion in the envelope is retarded by, e.g., magnetic fields. We also showed analytically that, in the UCM model, the spin-up feature of the P–V diagram is due to the infall velocity rather than the rotation. The line-of-sight velocity V is thus ∝x −0.5, where x is the offset. If the infall is retarded, rotational velocity should dominate so that V is proportional to x −1, as is often observed in the protostellar envelope.

On the stability and deformability of top stars

Topological stars, or top stars for brevity, are smooth horizonless static solutions of Einstein-Maxwell theory in 5-d that reduce to spherically symmetric solutions of Einstein-Maxwell-Dilaton theory in 4-d. We study linear scalar perturbations of top stars and argue for their stability and deformability. We tackle the problem with different techniques including WKB approximation, numerical analysis, Breit-Wigner resonance method and quantum Seiberg-Witten curves. We identify three classes of quasi-normal modes corresponding to prompt-ring down modes, long-lived meta-stable modes and what we dub ‘highly-damped’ modes. All mode frequencies we find have negative imaginary parts, thus suggesting linear stability of top stars. Moreover we determine the tidal Love and dissipation numbers encoding the response to tidal deformations and, similarly to black holes, we find zero value in the static limit but, contrary to black holes, we find non-trivial dynamical Love numbers and vanishing dissipative effects at linear order. For the sake of illustration in a simpler context, we also consider a toy model with a piece-wise constant potential and a centrifugal barrier that captures most of the above features in a qualitative fashion.

Digging into the Interior of Hot Cores with ALMA: Spiral Accretion into the High-mass Protostellar Core G336.01–0.82

We observed the high-mass star-forming core G336.01–0.82 at 1.3 mm and 0.″05 (∼150 au) angular resolution with the Atacama Large Millimeter/submillimeter Array (ALMA) as part of the Digging into the Interior of Hot Cores with ALMA survey. These high-resolution observations reveal two spiral streamers feeding a circumstellar disk at opposite sides in great detail. Molecular line emission from CH3OH shows velocity gradients along the streamers consistent with infall. Similarly, a flattened envelope model with rotation and infall implies a mass larger than 10 M ☉ for the central source and a centrifugal barrier of 300 au. The location of the centrifugal barrier is consistent with local peaks in the continuum emission. We argue that gas brought by the spiral streamers is accumulating at the centrifugal barrier, which can result in future accretion burst events. A total high infall rate of ∼4 × 10−4 M ☉ yr−1 is derived by matching models to the observed velocity gradient along the streamers. Their contribution accounts for 20%–50% the global infall rate of the core, indicating streamers play an important role in the formation of high-mass stars.

5–12 pc resolution ALMA imaging of gas and dust in the obscured compact nucleus of IRAS 17578-0400

AbstractWe here present 0.02–0.04″ resolution ALMA observation of the compact obscured nucleus (CON) of IRAS 17578-0400. A dusty torus within the nucleus, approximately 4 pc in radius, has been uncovered, exhibiting a usually flat spectral index at ALMA band 3, likely due to the millimeter corona emission from the central supermassive black hole (SMBH). The dense gas disk, traced by 13CO(1-0), spans 7 pc in radius and suggests an outflow driven by a disk wind due to its asymmetrical structure along the minor axis. Collimated molecular outflows (CMO), traced by the low-velocity components of the HCN(3-2) and HCO+(3-2) lines, align with the minor axis gas disk. Examination of position-velocity plots of HCN(3-2) and HCO+(3-2) reveals a flared dense gas disk extended a radius of ∼60 pc, infalling and rotating at speeds of about 200 km s−1 and 300 km s−1 respectively. A centrifugal barrier, located around 4 pc from the dynamical center, implies an SMBH mass of approximately 108Mȯ, consistent with millimeter corona emission estimates. The CMO maintains a steady rotation speed of 200 km s−1 over the 100 pc scale along the minor axis. The projected speed of the CMO is about 80 km s−1, corresponding to around ∼500 km s−1, assuming an inclination angle of 80°. Such a kinematics structure of disk-driven collimated rotating molecular outflow with gas supplies from a falling rotating disk indicates that the feedback of the compact obscured nucleus is likely regulated by the momentum transfer of the molecular gas that connects to both the feeding of the nuclear starburst and supermassive black hole.

Well-posed evolution of field theories with anisotropic scaling: the Lifshitz scalar field in a black hole space-time

Partial differential equations exhibiting an anisotropic scaling between space and time — such as those of Hořava-Lifshitz gravity — have a dispersive nature. They contain higher-order spatial derivatives, but remain second order in time. This is inconvenient for performing long-time numerical evolutions, as standard explicit schemes fail to maintain convergence unless the time step is chosen to be very small. In this work, we develop an implicit evolution scheme that does not suffer from this drawback, and which is stable and second-order accurate. As a proof of concept, we study the numerical evolution of a Lifshitz scalar field on top of a spherically symmetric black hole space-time. We explore the evolution of a static pulse and an (approximately) ingoing wave-packet for different strengths of the Lorentz-breaking terms, accounting also for the effect of the angular momentum eigenvalue and the resulting effective centrifugal barrier. Our results indicate that the dispersive terms produce a cascade of modes that accumulate in the region in between the Killing and universal horizons, indicating a possible instability of the latter.

Topological defects on the energy spectra of diatomic molecules embedded with shifted Deng–Fan oscillator potential under AB flux field

AbstractA study on the effect of point like global monopole topological defects on the energy eigenvalues of the diatomic molecules , , , embedded with Shifted Deng–Fan Oscillator Potential under the influence of Aharonov–Bohm flux field has been made here. Asymptotic Iteration Method (AIM) is used to find out the bound state solutions for arbitrary states by solving the non‐relativistic Schrödinger equation. A Pekeris‐type approximation has been used to approximate the centrifugal barrier term. It is observed that, energy levels of the diatomic molecules is significantly affected by the global effects of the point like global monopole, flux field and effective potential field.

Energy eigenvalues and finite-temperature magnetization for the improved Scarf II potential in the presence of external magnetic and Aharonov-Bohm flux fields

In this paper, the bound state solutions of the radial Schrödinger equation are obtained in closed form under an improved Scarf II potential energy function (ISPEF) constrained by external magnetic and Aharonov-Bohm (AB) flux fields. By constructing a suitable Pekeris-like approximation scheme for the centrifugal barrier, approximate analytical expressions for the bound-states and thermal partition function were obtained. With the aid of the partition function, an explicit equation for magnetization at finite temperatures is developed. The obtained equations were then applied to calculate the energy levels and magnetic properties of 7Li2 (2 3Πg), K2 (X 1Σg+), Mg2 (X 1Σg+) and NaBr (X 1Σ+) diatomic molecules. The obtained numerical results of the vibrational energies for these molecules were found to be in good agreement with theoretic and experimental values reported in the existing literature. The results indicated that by turning off the magnetic and AB fields, the energy levels of the diatomic molecules degenerate. The results further revealed that an increase in the temperature of the molecules and the AB field strengths leads to a linear decrease in magnetization.

The Influence of Deformation Space-Space on High and Low Energy Spectra of Fermionic Particles and Spectra of Heavy Quarkonia with Improved Hulthén Plus Hyperbolic Exponential Inversely Quadratic Potential

In this work, the modified approximation to the centrifugal barrier term is applied to find approximate bound-state solutions of the deformed Dirac equation for the spin and pseudospin symmetries in a model with the improved hyperbolic Hulth´en and hyperbolic exponential inversely quadratic potentials (IHHEIQPs) using the parametric method of Bopp’s shift and the standard perturbation theory in the extended relativistic quantum mechanics (ERQM). Our results indicate that the new energy eigenvalues are highly sensitive to the potential parameters (ν1, A) and to the values of quantum atomicnumbers (j, k, l, m,̃︀ l, ̃︀ m, s, ̃︀s), range of the potential ν, and noncommutativity parameters (θ, σ, β). We found that the effect of a space-space deformation gives a correction in the energy spectrum, where the main energy term remains due to the effect of the hyperbolic Hulth´en and hyperbolic exponential inversely quadratic potentials known in the literature. The new nonrelativistic energies are obtained by applying the nonrelativistic limit to the relativistic spin-energy equation in the extended nonrelativistic quantum mechanics (ENRQM). The proposed potential model reduces to the improved Hulth´en and exponential inversely quadratic potentials as special cases in ERQM. The present results are applied for calculating the new mass spectra Mhiqpnc−nl of heavy mesons such as cc, bb, bc, bs, cs, and bq,q = (u, d) in ENRQM. It turns out that the values of masses come from the contribution of the mass spectra Mhiqpnl in NRQM, while the effect of a space-space deformation δMhiqpnc−nl is an infinitesimal correction as compared with Mhiqpnl. Our results seem to be significant and agree perfectly with the ones in the literature.