Exact solution of the particle-rotor model, angular momentum spread and transition rates

1980 ◽  
Vol 334 (3) ◽  
pp. 486-498 ◽  
Author(s):  
C.G. Andersson ◽  
J. Krumlinde
Keyword(s):  
Exact Solution ◽  
Angular Momentum ◽  
Transition Rates ◽  
Momentum Spread ◽  
Rotor Model

Angular Momentum Dependence of Transition Rates in the Exciton Model

1995 ◽  
Vol 75 (12) ◽  
pp. 2284-2287 ◽  
Author(s):  
Ye. A. Bogila ◽  
V. M. Kolomietz ◽  
A. I. Sanzhur ◽  
S. Shlomo
Keyword(s):  
Angular Momentum ◽  
Momentum Dependence ◽  
Transition Rates ◽  
Exciton Model

scholarly journals Asymmetric hypergeometric laser beams

2019 ◽  
Vol 43 (5) ◽  
pp. 735-740
Author(s):  
V.V. Kotlyar ◽  
A.A. Kovalev ◽  
E.G. Abramochkin
Keyword(s):  
Exact Solution ◽  
Angular Momentum ◽  
Hypergeometric Function ◽  
Orbital Angular Momentum ◽  
Topological Charge ◽  
Optical Axis ◽  
Type Equation ◽  
Laser Beams ◽  
Propagation Equation ◽  
Degenerate Hypergeometric Function

Here we study asymmetric Kummer beams (aK-beams) with their scalar complex amplitude being proportional to the Kummer function (a degenerate hypergeometric function). These beams are an exact solution of the paraxial propagation equation (Schrödinger-type equation) and obtained from the conventional symmetric hypergeometric beams by a complex shift of the transverse coordinates. On propagation, the aK-beams change their intensity weakly and rotate around the optical axis. These beams are an example of vortex laser beams with a fractional orbital angular momentum (OAM), which depends on four parameters: the vortex topological charge, the shift magnitude, the logarithmic axicon parameter and the degree of the radial factor. Changing these parameters, it is possible to control the beam OAM, either continuously increasing or decreasing it.

scholarly journals Exact Solution for Relativistic Trajectories Using Modal Transseries

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1505
Author(s):  
Luis Acedo ◽  
Abraham J. Arenas ◽  
Nicolas De La Espriella
Keyword(s):  
Exact Solution ◽  
Angular Momentum ◽  
High Precision ◽  
Limit Cycles ◽  
Fundamental Problem ◽  
Orbital Plane ◽  
Relativistic Effects ◽  
Geodesic Equation ◽  
Novel Method ◽  
Analytical Expressions

In this article, we design a novel method for finding the exact solution of the geodesic equation in Schwarzschild spacetime, which represents the trajectories of the particles. This is a fundamental problem in astrophysics and astrodynamics if we want to incorporate relativistic effects in high precision calculations. Here, we show that exact analytical expressions can be given, in terms of modal transseries for the spiral orbits as they approach the limit cycles given by the two circular orbits that appear for each angular momentum value. The solution is expressed in terms of transseries generated by transmonomials of the form e−nθ, n=1, 2, …, where θ is the angle measured in the orbital plane. Examples are presented that verify the effect of the solutions.

In search of empirical rule relating E21+ and B(E2; 01+→21+) in asymmetric even–even nuclei of mass region A = 90–120

2013 ◽  
Vol 91 (10) ◽  
pp. 777-782
Author(s):  
Yuvraj Singh ◽  
S.K. Dhiman ◽  
M. Singh ◽  
Chhail Bihari ◽  
A.K. Varshney ◽  
...  
Keyword(s):  
Mass Region ◽  
Quadrupole Deformation ◽  
Nucl Phys ◽  
Yrast Band ◽  
Transition Rates ◽  
Empirical Rule ◽  
Asymmetric Rotor ◽  
The Moment ◽  
Rotor Model ◽  
Static Quadrupole

The quadrupole deformation β are extracted independently from energy and transition rates. The set of asymmetric parameters γ are obtained from energy ratio [Formula: see text]. It is observed that the set of β values evaluated from B(E2) are closer to the values of β extracted from [Formula: see text] on considering the Grodzins empirical rule (Grodzins. Phys. Lett. 2, 88 (1962)) with uncertainty in even Mo, Ru, and Pd nuclei. The moment of inertia [Formula: see text] generating the yrast band in these nuclei is evaluated from [Formula: see text] using the asymmetric rotor model (Davydov and Filippov. Nucl. Phys. 8, 237 (1958)). The β, γ, and I0 values have good correlations with NpNn. In addition, β and I0 are related linearly in general. This systematic relate [Formula: see text] [Formula: see text] and asymmetric deformation γ that enables one to predict [Formula: see text], the static quadrupole moment Q0 and quadrupole deformation β of those nuclei whose only [Formula: see text] is known.

The Expected Performance of an Optical Pumping Light Source, and the Kinetics of Optical Pumping of 23S13He

1971 ◽  
Vol 49 (5) ◽  
pp. 525-538 ◽  
Author(s):  
J. M. Daniels ◽  
R. S. Timsit
Keyword(s):  
Angular Momentum ◽  
Light Source ◽  
Optical Pumping ◽  
Light Flux ◽  
Resonance Radiation ◽  
Transition Rates ◽  
Expected Performance ◽  
Kinetics Of

A practical light source for optical pumping necessarily excites transitions other than those which it is desired should be excited. It is shown that a pumping light source for 23S13He may be characterized by three parameters, which describe the transition rates for Δm = ±1, and 0, transitions under standard conditions. Expressions are derived relating these parameters to the geometry of the light source. The equation which describes the flow of angular momentum into 3He is formulated, using these parameters, the light flux, the lifetime of the metastable atoms, and collisional mixing in the 23P states. This equation is solved to give the polarization which may be attained, and the rate at which the polarization is built up. A modification of this equation is also given, which takes into account moderate trapping of resonance radiation. An expression is also derived which relates the polarization of 3He to the intensity of the scattered pumping light.

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