Variational solution of the single-particle Dirac equation in the field of two nuclei using relativistically adapted Slater basis functions

1998 ◽  
Vol 99 (5) ◽  
pp. 351-356 ◽  
Author(s):  
L. LaJohn ◽  
J. D. Talman
Keyword(s):  
Dirac Equation ◽  
Single Particle ◽  
Basis Functions ◽  
Variational Solution ◽  
Slater Basis

Helicity rotation induced by Lorentz boosts

2019 ◽  
Vol 17 (08) ◽  
pp. 1941005
Author(s):  
Massimo Blasone ◽  
Victor A. S. V. Bittencourt ◽  
Alex E. Bernardini
Keyword(s):  
Dirac Equation ◽  
Quantum Entanglement ◽  
Single Particle ◽  
Inertial Frame ◽  
Rotation Angle ◽  
Positive Energy ◽  
Wigner Rotation ◽  
Lorentz Boost ◽  
The One ◽  
Lorentz Boosts

In this paper, we calculate the helicity rotation angle induced by Lorentz boosts. This is relevant for the study of Lorentz boost effects on quantum entanglement encoded in pairs of massive fermions, which are described in terms of positive energy solutions of the Dirac equation with definite helicity. A Lorentz boost describing the change to an inertial frame moving at uniform speed will in general rotate the particle’s helicity. We obtain the coefficients of the helicity superposition in the boosted frame and specialize our results for a perpendicular boost geometry. We verify that the helicity rotation angle can be obtained in terms of the Wigner rotation angle for spin [Formula: see text] states, bridging the framework considered in our previous works to the one of the Wigner rotations. Finally, we calculate the boost-induced spin-parity entanglement for a single particle.

The Two Centre Dirac Equation

1976 ◽  
Vol 31 (1) ◽  
pp. 1-30 ◽  
Author(s):  
Berndt Müller ◽  
Walter Greiner
Keyword(s):  
Dirac Equation ◽  
Heavy Ions ◽  
Nuclear Charge ◽  
Basis Functions ◽  
Wave Functions ◽  
Matrix Elements ◽  
Prolate Spheroidal ◽  
Prolate Spheroidal Coordinates ◽  
Spheroidal Coordinates ◽  
Dirac Hamiltonian

During collisions of heavy ions with heavy targets below the Coulomb barrier, adiabatic molecular orbitals are formed for the inner electrons. Deviations from adiabaticity lead to coupling between various states and can be treated by time-dependent perturbation theory. For high charges ( Z1+Z2 ≧ 60) the molecular electrons are highly relativistic. Therefore, the Dirac equation has to be used to obtain the energies and wave functions. The Dirac Hamiltonian is transformed into the intrinsic rotating coordinate system where prolate spheroidal coordinates are introduced. A set of basis functions is proposed which allows the evaluation of all matrix elements of the Dirac Hamiltonian analytically. The resulting matrix is diagonalized numerically. The finite nuclear charge distribution is also taken into account. Results are presented and discussed for various characteristic systems, e. g. Br-Br, Ni-Ni, I-I, Br-Zr, I-Au, U -U, etc.

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