scholarly journals Exact Factorization of the Time-Dependent Electron-Nuclear Wave Function

2010 ◽  
Vol 105 (12) ◽  
Author(s):  
Ali Abedi ◽  
Neepa T. Maitra ◽  
E. K. U. Gross
Keyword(s):  
Wave Function ◽  
Time Dependent ◽  
Nuclear Wave Function ◽  
Exact Factorization

scholarly journals A TIME-DEPENDENT MULTI-DETERMINANT APPROACH TO NUCLEAR DYNAMICS

2013 ◽  
Vol 22 (06) ◽  
pp. 1350040 ◽  
Author(s):  
G. PUDDU
Keyword(s):  
Wave Function ◽  
Time Evolution ◽  
Krylov Subspace ◽  
Equations Of Motion ◽  
Strength Function ◽  
Time Dependent ◽  
Nuclear Wave Function ◽  
Nuclear Dynamics ◽  
Hartree Fock

We propose a Time-Dependent Multi-Determinant (TDMD) approach to the description of the time evolution of the nuclear wave functions. We use the Dirac variational principle to derive the equations of motion using as ansatz for the nuclear wave function a linear combination of Slater determinants. We prove explicitly that the norm and the energy of the wave function are conserved during the time evolution. This approach is a generalization of the time-dependent Hartree–Fock method to many Slater determinants. We apply this approach to a case study of 6 Li using the N3LO interaction renormalized to four major harmonic oscillator shells. We solve the TDMD equations of motion using Krylov subspace methods of Lanczos type. As an application, we discuss the isoscalar monopole strength function.

The Two-Nucleon Mechanism for the Neutrinoless Double Beta Decay and the BCS Nuclear Wave Function

1994 ◽  
Vol 21 (4) ◽  
pp. 447-454
Author(s):  
Zhong-Jin Lin ◽  
You-Ping Gan ◽  
De-Ji Fu ◽  
Hui-Fang Wu ◽  
Chong-En Wu
Keyword(s):  
Wave Function ◽  
Beta Decay ◽  
Neutrinoless Double Beta Decay ◽  
Double Beta Decay ◽  
Nuclear Wave Function

scholarly journals Electronic non-adiabatic states: towards a density functional theory beyond the Born–Oppenheimer approximation

2014 ◽  
Vol 372 (2011) ◽  
pp. 20130059 ◽  
Author(s):  
Nikitas I. Gidopoulos ◽  
E. K. U. Gross
Keyword(s):  
Wave Function ◽  
Density Functional ◽  
Adiabatic Approximation ◽  
Complete System ◽  
Wave Functions ◽  
Nuclear Wave Function ◽  
Functional Theory ◽  
Novel Treatment ◽  
Oppenheimer Approximation ◽  
Adiabatic Case

A novel treatment of non-adiabatic couplings is proposed. The derivation is based on a theorem by Hunter stating that the wave function of the complete system of electrons and nuclei can be written, without approximation, as a Born–Oppenheimer (BO)-type product of a nuclear wave function, X ( R ), and an electronic one, Φ R ( r ), which depends parametrically on the nuclear configuration R . From the variational principle, we deduce formally exact equations for Φ R ( r ) and X ( R ). The algebraic structure of the exact nuclear equation coincides with the corresponding one in the adiabatic approximation. The electronic equation, however, contains terms not appearing in the adiabatic case, which couple the electronic and the nuclear wave functions and account for the electron–nuclear correlation beyond the BO level. It is proposed that these terms can be incorporated using an optimized local effective potential.

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