The Experts below are selected from a list of 40098 Experts worldwide ranked by ideXlab platform
Tomasz Wasak - One of the best experts on this subject based on the ideXlab platform.
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quantum reactive scattering in the long range ion dipole potential
Physical Review A, 2021Co-Authors: Tomasz Wasak, Zbigniew IdziaszekAbstract:An ion and a polar molecule interact by an anisotropic ion-dipole potential scaling as $\ensuremath{-}\ensuremath{\alpha}\phantom{\rule{0.16em}{0ex}}cos(\ensuremath{\theta})/{r}^{2}$ at large distances. Due to its long-range character, it modifies the properties of angular wave functions, which are no longer given by spherical harmonics. In addition, an effective centrifugal potential in the Radial Equation can become attractive for low angular momenta. In this paper, we develop a general framework for an ion-dipole reactive scattering, focusing on the regime of large $\ensuremath{\alpha}$. We introduce modified spherical harmonics as solutions of the angular part of the Schr\"odinger Equation and derive several useful approximations in the limit of large $\ensuremath{\alpha}$. We present a formula for the scattering amplitude expressed in terms of the modified spherical harmonics and we derive expressions for the elastic and reactive collision rates. The solutions of the Radial Equation are given by Bessel functions, and we analyze their behavior in two distinct regimes corresponding, basically, to attractive and repulsive long-range centrifugal potentials. Finally, we study reactive collisions in the universal regime, where the short-range probability of loss or reaction is equal to unity.
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quantum reactive scattering in the long range ion dipole potential
arXiv: Atomic Physics, 2020Co-Authors: Tomasz Wasak, Zbigniew IdziaszekAbstract:An ion and a polar molecule interact by an anisotropic ion-dipole potential scaling as $- \alpha \cos (\theta)/r^2$ at large distances. Due to its long-range character, it modifies the properties of angular wave functions, which are no longer given by spherical harmonics. In addition, an effective centrifugal potential in the Radial Equation can become attractive for low angular momenta. In this paper, we develop a general framework for ion-dipole reactive scattering, focusing on the regime of large $\alpha$. We introduce modified spherical harmonics as solutions of angular part of the Schrodinger Equation and derive several useful approximations in the limit of large $\alpha$. We present the formula for the scattering amplitude expressed in terms of the modified spherical harmonics and we derive expressions for elastic and reactive collision rates. The solutions of the Radial Equation are given by Bessel functions, and we analyse their behaviour in two distinct regimes corresponding, basically, to attractive and repulsive long-range centrifugal potentials. Finally, we study reactive collisions in the universal regime, where the short-range probability of loss or reaction is equal to unity.
Zbigniew Idziaszek - One of the best experts on this subject based on the ideXlab platform.
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quantum reactive scattering in the long range ion dipole potential
Physical Review A, 2021Co-Authors: Tomasz Wasak, Zbigniew IdziaszekAbstract:An ion and a polar molecule interact by an anisotropic ion-dipole potential scaling as $\ensuremath{-}\ensuremath{\alpha}\phantom{\rule{0.16em}{0ex}}cos(\ensuremath{\theta})/{r}^{2}$ at large distances. Due to its long-range character, it modifies the properties of angular wave functions, which are no longer given by spherical harmonics. In addition, an effective centrifugal potential in the Radial Equation can become attractive for low angular momenta. In this paper, we develop a general framework for an ion-dipole reactive scattering, focusing on the regime of large $\ensuremath{\alpha}$. We introduce modified spherical harmonics as solutions of the angular part of the Schr\"odinger Equation and derive several useful approximations in the limit of large $\ensuremath{\alpha}$. We present a formula for the scattering amplitude expressed in terms of the modified spherical harmonics and we derive expressions for the elastic and reactive collision rates. The solutions of the Radial Equation are given by Bessel functions, and we analyze their behavior in two distinct regimes corresponding, basically, to attractive and repulsive long-range centrifugal potentials. Finally, we study reactive collisions in the universal regime, where the short-range probability of loss or reaction is equal to unity.
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quantum reactive scattering in the long range ion dipole potential
arXiv: Atomic Physics, 2020Co-Authors: Tomasz Wasak, Zbigniew IdziaszekAbstract:An ion and a polar molecule interact by an anisotropic ion-dipole potential scaling as $- \alpha \cos (\theta)/r^2$ at large distances. Due to its long-range character, it modifies the properties of angular wave functions, which are no longer given by spherical harmonics. In addition, an effective centrifugal potential in the Radial Equation can become attractive for low angular momenta. In this paper, we develop a general framework for ion-dipole reactive scattering, focusing on the regime of large $\alpha$. We introduce modified spherical harmonics as solutions of angular part of the Schrodinger Equation and derive several useful approximations in the limit of large $\alpha$. We present the formula for the scattering amplitude expressed in terms of the modified spherical harmonics and we derive expressions for elastic and reactive collision rates. The solutions of the Radial Equation are given by Bessel functions, and we analyse their behaviour in two distinct regimes corresponding, basically, to attractive and repulsive long-range centrifugal potentials. Finally, we study reactive collisions in the universal regime, where the short-range probability of loss or reaction is equal to unity.
Mirjam Cvetic - One of the best experts on this subject based on the ideXlab platform.
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an analysis of the wave Equation for the u 1 2 gauged supergravity black hole
Classical and Quantum Gravity, 2015Co-Authors: T Birkandan, Mirjam CveticAbstract:We study the massless Klein–Gordon Equation in the background of the most general rotating dyonic anti-de Sitter black hole in , supergravity in D = 4, originally presented by Chow and Compere (2014 Phys. Rev. D 89 065003). The angular part of the separable wave Equation is of Heun type, while the Radial part is a Fuchsian Equation with five regular singularities. The Radial Equation is further analyzed and written in a specific form, which reveals the pole structure of the horizon Equation, whose residua are expressed in terms of the surface gravities and angular velocities associated with the respective horizons. The near-horizon (near-)extremal limits of the solution are also studied, where the expected hidden conformal symmetry is revealed. Furthermore, we present the retarded Green's functions for these limiting cases. We also comment on the generality of the charge-dependent parts of the metric parameters and address some further examples of limiting cases.
S Shu - One of the best experts on this subject based on the ideXlab platform.
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nucleon anti nucleon intruder state of dirac Equation for nucleon in deep scalar potential well
arXiv: Nuclear Theory, 2017Co-Authors: T T S Kuo, T K Kuo, E Osnes, S ShuAbstract:We solve the Dirac Radial Equation for a nucleon in a scalar Woods-Saxon potential well of depth $V_0$ and radius $r_0$. A sequence of values for the depth and radius are considered. For shallow potentials with $-1000 MeV\lesssim V_0 < 0$ the wave functions for the positive-energy states $\Psi _+(r)$ are dominated by their nucleon component $g(r)$. But for deeper potentials with $V_0 \lesssim -1500 MeV $ the $\Psi_+(r)$s begin to have dominant anti-nucleon component $f(r)$. In particular, a special intruder state enters with wave function $\Psi_{1/2}(r)$ and energy $E_{1/2}$. We have considered several $r_0$ values between 2 and 8 fm. For $V_0 \lesssim -2000 MeV$ and the above $r_0$ values, $\Psi _{1/2}$ is the only bound positive-energy state and has its $g(r)$ closely equal to $-f(r)$, both having a narrow wave-packet shape centered around $r_0$. The $E_{1/2}$ of this state is practically independent of $V_0$ for the above $V_0$ range and obeys closely the relation $E_{1/2}=\frac{\hbar c}{r_0}$.
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nucleon anti nucleon intruder state of dirac Equation for nucleon in deep scalar potential well
International Journal of Modern Physics E-nuclear Physics, 2017Co-Authors: T T S Kuo, T K Kuo, E Osnes, S ShuAbstract:We solve the Dirac Radial Equation for a nucleon in a scalar Woods–Saxon potential well of depth V0 and radius r0. A sequence of values for the depth and radius are considered. For shallow potentials with − 1000MeV ≲ V0 < 0 the wave functions for the positive-energy states Ψ+(r) are dominated by their nucleon component g(r). But for deeper potentials with V0 ≲−1500MeV the Ψ+(r)s begin to have dominant anti-nucleon component f(r). In particular, a special intruder state enters with wave function Ψ1/2(r) and energy E1/2. We have considered several r0 values between 2 and 8fm. For V0 ≲−2000MeV and the above r0 values, Ψ1/2 is the only bound positive-energy state and has its g(r) closely equal to − f(r), both having a narrow wave packet shape centered around r0. The E1/2 of this state is practically independent of V0 for the above V0 range and obeys closely the relation E1/2 = ℏc r0.
Idziaszek Zbigniew - One of the best experts on this subject based on the ideXlab platform.
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Quantum reactive scattering in the long-range ion-dipole potential
'American Physical Society (APS)', 2021Co-Authors: Wasak Tomasz, Idziaszek ZbigniewAbstract:An ion and a polar molecule interact by an anisotropic ion-dipole potential scaling as $- \alpha \cos (\theta)/r^2$ at large distances. Due to its long-range character, it modifies the properties of angular wave functions, which are no longer given by spherical harmonics. In addition, an effective centrifugal potential in the Radial Equation can become attractive for low angular momenta. In this paper, we develop a general framework for an ion-dipole reactive scattering, focusing on the regime of large $\alpha$. We introduce modified spherical harmonics as solutions of the angular part of the Schr\"odinger Equation and derive several useful approximations in the limit of large $\alpha$. We present a formula for the scattering amplitude expressed in terms of the modified spherical harmonics and we derive expressions for the elastic and reactive collision rates. The solutions of the Radial Equation are given by Bessel functions, and we analyse their behaviour in two distinct regimes corresponding, basically, to attractive and repulsive long-range centrifugal potentials. Finally, we study reactive collisions in the universal regime, where the short-range probability of loss or reaction is equal to unity.Comment: 19 pages, 11 figures, 5 appendice
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Quantum reactive scattering in the long-range ion-dipole potential
2020Co-Authors: Wasak Tomasz, Idziaszek ZbigniewAbstract:An ion and a polar molecule interact by an anisotropic ion-dipole potential scaling as $- \alpha \cos (\theta)/r^2$ at large distances. Due to its long-range character, it modifies the properties of angular wave functions, which are no longer given by spherical harmonics. In addition, an effective centrifugal potential in the Radial Equation can become attractive for low angular momenta. In this paper, we develop a general framework for ion-dipole reactive scattering, focusing on the regime of large $\alpha$. We introduce modified spherical harmonics as solutions of angular part of the Schr\"odinger Equation and derive several useful approximations in the limit of large $\alpha$. We present the formula for the scattering amplitude expressed in terms of the modified spherical harmonics and we derive expressions for elastic and reactive collision rates. The solutions of the Radial Equation are given by Bessel functions, and we analyse their behaviour in two distinct regimes corresponding, basically, to attractive and repulsive long-range centrifugal potentials. Finally, we study reactive collisions in the universal regime, where the short-range probability of loss or reaction is equal to unity.Comment: 18 pages, 11 figures, 4 appendice
