scholarly journals THEORETICAL COMPLEX ENERGIES OF STARK RESONANCES IN LITHIUM BY OPERATOR PERTURBATION THEORY APPROACH

2021 ◽  
pp. 68-77
Author(s):  
A. Kuznetsova ◽  
A. Glushkov ◽  
E. Plisetskaya
Keyword(s):  
Perturbation Theory ◽  
Lithium Atom ◽  
Potential Method ◽  
Complex Eigenvalue ◽  
Theory Approach ◽  
Atomic Systems ◽  
Rotation Method ◽  
Coordinate Rotation ◽  
Mechanical Procedure ◽  
Distorted Waves

The theoretical complex energies of the Stark resonances in the lithium atom (non-hydrogenic atomic system) in a DC electric are calculated within the operator form of the modified perturbation theory for the non-H atomic systems. The method includes the physically reasonable distorted-waves approximation in the frame of the formally exact quantum-mechanical procedure. The calculated  Stark resonances energies and widths in the lithium atom are calculated and compared with  results of calculations on the basis of the  method of  complex eigenvalue Schrödinger equation by Themelis-Nicolaides, the complex absorbing potential method by Sahoo-Ho and the B-spline-based coordinate rotation method approach  by Hui-Yan Meng et al.    

scholarly journals DECAY RATES OF METASTABLE STATES IN CUBIC POTENTIAL BY VARIATIONAL PERTURBATION THEORY

1996 ◽  
Vol 11 (24) ◽  
pp. 4383-4399 ◽  
Author(s):  
H. KLEINERT ◽  
I. MUSTAPIC
Keyword(s):  
Perturbation Theory ◽  
Decay Rates ◽  
Metastable States ◽  
Energy Eigenvalues ◽  
Variational Perturbation Theory ◽  
Rotation Method ◽  
Complex Eigenvalues ◽  
Coordinate Rotation ◽  
Variational Perturbation ◽  
Wkb Expansion

Variational perturbation theory is used to determine the decay rates of metastable states across a cubic barrier of arbitrary height. For high barriers, a variational resummation procedure is applied to the complex energy eigenvalues obtained from a WKB expansion. For low barriers, the variational resummation procedure converts the non-Borel-summable Rayleigh-Schrödinger expansion into an exponentially fast convergent approximation. The results in the two regimes match each other well and yield very accurate imaginary parts for the energy eigenvalues. This is demonstrated by comparison with the complex eigenvalues obtained from solutions of the Schrödinger equation via the complex-coordinate rotation method.

scholarly journals Perturbation theory approach to predict the covariance matrices of the galaxy power spectrum and bispectrum in redshift space

2020 ◽  
Vol 497 (2) ◽  
pp. 1684-1711 ◽  
Author(s):  
Naonori S Sugiyama ◽  
Shun Saito ◽  
Florian Beutler ◽  
Hee-Jong Seo
Keyword(s):  
Perturbation Theory ◽  
Power Spectrum ◽  
Shot Noise ◽  
Signal To Noise Ratio ◽  
Covariance Matrices ◽  
Theory Approach ◽  
Cross Covariance ◽  
The Galaxy ◽  
The Cross ◽  
Non Gaussian

ABSTRACT In this paper, we predict the covariance matrices of both the power spectrum and the bispectrum, including full non-Gaussian contributions, redshift space distortions, linear bias effects, and shot-noise corrections, using perturbation theory (PT). To quantify the redshift-space distortion effect, we focus mainly on the monopole and quadrupole components of both the power and bispectra. We, for the first time, compute the 5- and 6-point spectra to predict the cross-covariance between the power and bispectra, and the autocovariance of the bispectrum in redshift space. We test the validity of our calculations by comparing them with the covariance matrices measured from the MultiDark-Patchy mock catalogues that are designed to reproduce the galaxy clustering measured from the Baryon Oscillation Spectroscopic Survey Data Release 12. We argue that the simple, leading-order PT works because the shot-noise corrections for the Patchy mocks are more dominant than other higher order terms we ignore. In the meantime, we confirm some discrepancies in the comparison, especially of the cross-covariance. We discuss potential sources of such discrepancies. We also show that our PT model reproduces well the cumulative signal-to-noise ratio of the power spectrum and the bispectrum as a function of maximum wavenumber, implying that our PT model captures successfully essential contributions to the covariance matrices.

scholarly journals Calculations of Resonance Parameters for the Doubly Excited 1P° States in Ps− Using Exponentially Correlated Wave Functions

Atoms ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 1 ◽  
Author(s):  
Sabyasachi Kar ◽  
Yew Kam Ho
Keyword(s):  
Feshbach Resonance ◽  
Wave Functions ◽  
Negative Ion ◽  
Shape Resonance ◽  
Resonance States ◽  
Resonance Parameters ◽  
Rotation Method ◽  
Resonance Energies ◽  
Doubly Excited ◽  
Coordinate Rotation

Recent observations on resonance states of the positronium negative ion (Ps−) in the laboratory created huge interest in terms of the calculation of the resonance parameters of the simple three-lepton system. We calculate the resonance parameters for the doubly excited 1P° states in Ps− using correlated exponential wave functions based on the complex-coordinate rotation method. The resonance energies and widths for the 1P° Feshbach resonance states in Ps− below the N = 2, 3, 4, 5 Ps thresholds are reported. The 1P° shape resonance above the N = 2, 4 Ps thresholds are also reported. Our predications are in agreement with the available results. Few Feshbach resonance parameters below the N = 4 and 5 Ps thresholds have been reported in the literature. Our predictions will provide useful information for future resonance experiments in Ps−.

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