Stripping and excitation in collisions between<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mtext>He</mml:mtext></mml:mrow><mml:mo>+</mml:mo></mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>n</mml:mi><mml:mo>⩽</mml:mo><mml:mn>3</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>calculated by a

Melezhik, Vladimir S.; Cohen, James S.; Hu, Chi-Yu

doi:10.1103/physreva.69.032709

Cited by 29 publications

(30 citation statements)

References 39 publications

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“…It gives us the possibility to perform the diagonalization of the angular part of the kinetic energy operator by using the unitary transformation S jν = λ 1/2 j Y jν defined in the previous section. This has been exploited for developing an efficient algorithm with a computational time scaling proportional to the number N = N θ × N φ of the unknowns in the system of equations ( = 1) [1,19,20,24] …”

Section: Splitting-up Methods For 3d Time-dependent Schrödinger Equationmentioning

confidence: 99%

“…The system of equations (6) arises in the description of pair collisions of the ultracold identical atoms (m 1 = m 2 = m) in optical waiveguides when ω 1 = ω 2 = ω and the center-of-mass of the pair can be separated [1]. For the propagation ψ j (r, t n ) → ψ j (r, t n+1 ) in time t n → t n+1 = t n + Δt we have developed a computational scheme [1,18,20,24] based on the component-by-component split-operator method suggested by G.I. Marchuk in 1971 [28].…”

Section: Splitting-up Methods For 3d Time-dependent Schrödinger Equationmentioning

confidence: 99%

“…To overcome this difficulty, we have suggested [18,19] to use the basis of the orthogonalized combinations of the spherical harmonics on the two-dimensional grid over θ and φ variables. It turned out that this idea was very efficient for the time-dependent Schrödinger equation with three [18][19][20][21][22][23][24] and four [1,4,25,26] nonseparable spatial variables. Especially productive it was for the quantitative description of the ultracold pair atomic collisions in confined geometry of harmonic traps (low-dimensional few-body systems) [1,2,4,9,[25][26][27].…”

Section: Nondirect Product Discrete-variable Representationmentioning

confidence: 99%

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Mathematical Modeling of Ultracold Few-Body Processes in Atomic Traps

Melezhik

2016

EPJ Web of Conferences

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Abstract. We discuss computational aspects of the developed mathematical models for ultracold few-body processes in atomic traps. The key element of the elaborated computational schemes is a nondirect product discrete variable representation (npDVR) we have suggested and applied to the time-dependent and stationary Schrödinger equations with a few spatial variables. It turned out that this approach is very efficient in quantitative analysis of low-dimensional ultracold few-body systems arising in confined geometry of atomic traps. The efficiency of the method is demonstrated here on two examples. A brief review is also given of novel results obtained recently.

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Section: Splitting-up Methods For 3d Time-dependent Schrödinger Equationmentioning

confidence: 99%

Section: Splitting-up Methods For 3d Time-dependent Schrödinger Equationmentioning

confidence: 99%

Section: Nondirect Product Discrete-variable Representationmentioning

confidence: 99%

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Mathematical Modeling of Ultracold Few-Body Processes in Atomic Traps

Melezhik

2016

EPJ Web of Conferences

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“…The injection of negative muons into a mixture of hydrogen isotopes creates repetitive cycles of processes that are nuclear fusion and the release of energy. So far, many studies have been carried out on µ CF [7][8][9][10][11][12][13][14][15][16]. The µ CF allows nuclear fusion to take place at temperatures significantly lower than the temperatures required for thermonuclear fusion.…”

Section: Introductionmentioning

confidence: 99%

“…The formation of muonic molecules of hydrogen isotopes and their nuclear reactions have been the subject of many experimental and theoretical studies [7][8][9][10][11][12] …”

Section: Introductionmentioning

confidence: 99%

Survey of muon stripping in the muon-catalyzed $d-d$ fusion cycle in pure deuterium

Motevalli¹,

Mohammdapourfard²

2015

Turk J Phys

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Muon-catalyzed fusion is a very efficient nuclear fusion method to which a wide variety of experimental and theoretical studies have been devoted in recent years. The mixtures of hydrogen isotopes are the most appropriate particles to do this kind of fusion. The efficiency of muon-catalyzed fusion in mixtures of pure deuterium is due to the abundance of this isotope as compared to other hydrogen isotopes. The most important issue of reducing the efficiency of the muon-catalyzed fusion chain in pure deuterium mixtures is the probability of muons sticking to the helium-3 particle produced after the d − d nuclear fusion reaction. In this investigation, the density dependence of the slowing down, muon stripping, and effective sticking in pure deuterium fuel are presented by considering all possible effective processes and solving a set of coupled differential equations. The results show that our calculated values are in agreement with available experimental and theoretical data.

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Lagrange‐mesh method for quantum‐mechanical problems

Baye

2006

Physica Status Solidi (b)

109

139

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The Lagrange-mesh method is an approximate variational calculation with the simplicity of a mesh calculation because of the use of a consistent Gauss quadrature. The method can be used for quantum-mechanical bound-state and scattering problems with local and non-local interactions or with a semi-relativistic kinetic energy, and for solving the time-dependent Schrödinger equation. No analytical evaluation of matrix elements is needed. The accuracy is exponential in the number of mesh points and is not significantly reduced with respect to the corresponding variational calculations. Lagrange functions can be based on classical or non-classical orthogonal polynomials as well as on trigonometric and sinc functions, as described in examples. Some singularities can be handled with a regularization technique. Applications to three-body systems are discussed for various choices of coordinate systems. The helium atom and hydrogen molecular ion are presented as examples.

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Stripping and excitation in collisions betweenpandHe+(n⩽3)calculated by a

Cited by 29 publications

References 39 publications

Mathematical Modeling of Ultracold Few-Body Processes in Atomic Traps

Mathematical Modeling of Ultracold Few-Body Processes in Atomic Traps

Survey of muon stripping in the muon-catalyzed $d-d$ fusion cycle in pure deuterium

Lagrange‐mesh method for quantum‐mechanical problems

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