Potential independence of the solution to the relativistic many-body problem and the role of negative-energy states in heliumlike ions

1999 ◽  
Vol 59 (1) ◽  
pp. 259-266 ◽  
Author(s):  
J. Sapirstein ◽  
K. T. Cheng ◽  
M. H. Chen
Keyword(s):  
Body Problem ◽  
Negative Energy ◽  
Many Body ◽  
Negative Energy States ◽  
Energy States

Relativistic many-body calculations of atomic properties in Pd-like ions

2008 ◽  
Vol 86 (1) ◽  
pp. 131-149 ◽  
Author(s):  
U I Safronova ◽  
R Bista ◽  
R Bruch ◽  
H Merabet
Keyword(s):  
Perturbation Theory ◽  
Negative Energy ◽  
Second Order ◽  
Energy Splitting ◽  
Transition Rates ◽  
Matrix Elements ◽  
Many Body ◽  
Negative Energy States ◽  
Many Body Perturbation Theory ◽  
Energy States

Wavelengths, transition rates, and line strengths are calculated for the 85 possible multipole transitions between the excited 4p6 4d9 4f, 4p6 4d9 5l, 4p5 4d10 4f, and 4p5 4d10 5l states and the ground 4p6 4d10 state in Pd-like ions with the nuclear charges ranging from Z = 47 to 100. Relativistic many-body perturbation theory (RMBPT), including the Breit interaction, is used to evaluate energies and transition rates for multipole transitions in hole–particle systems. This method is based on the relativistic many-body perturbation theory, agrees with MCDF calculations in lowest order, includes all second-order correlation corrections, and includes corrections from negative energy states. The calculations start from a [Zn]4p64d10 Dirac–Fock potential. First-order perturbation theory is used to obtain intermediate-coupling coefficients, and second-order RMBPT is used to determine the matrix elements. The contributions from negative-energy states are included in the second-order multipole matrix elements. The resulting transition energies and transition rates are compared with experimental values and with results from other recent calculations. Trends of the transitions rates for the selected multipole transitions as function of Z are illustrated graphically. The Z dependence of the energy splitting for all triplet terms of the 4p64d9 4f and 4p64d9 5l configurations are shown for Z = 47–100. PACS Nos.: 31.15.Ar, 31.15.Md, 32.70.Cs, 32.30.Rj, 31.25.Jf

E1, E2, M1, and M2 transitions in the nickel isoelectronicsequence

2004 ◽  
Vol 82 (5) ◽  
pp. 331-356 ◽  
Author(s):  
S M Hamasha ◽  
A S Shlyaptseva ◽  
U I Safronova
Keyword(s):  
Perturbation Theory ◽  
Negative Energy ◽  
Second Order ◽  
Oscillator Strengths ◽  
Transition Rates ◽  
Matrix Elements ◽  
Coupling Coefficients ◽  
Many Body ◽  
Negative Energy States ◽  
Energy States

A relativistic many-body method is developed to calculate energy and transition rates for multipole transitions in many-electron ions. This method is based on relativistic many-body perturbation theory (RMBPT), agrees with MCDF calculations in lowest order, includes all second-order correlation corrections, and includes corrections from negative-energy states. Reduced matrix elements, oscillator strengths, and transition rates are calculated for electric-dipole (E1) and electric-quadrupole (E2) transitions, and magnetic-dipole (M1) and magnetic-quadrupole (M2) transitions in Ni-like ions with nuclear charges ranging from Z = 30 to 100. The calculations start from a 1s22s22p63s23p63d10 Dirac–Fock potential. First-order perturbation theory is used to obtain intermediate-coupling coefficients, and second-order RMBPT is used to determine the matrix elements. The contributions from negative-energy states are included in the second-order E1, M1, E2, and M2 matrix elements. The resulting transition energies and transition rates are compared with experimental values and withresults from other recent calculations.PACS Nos.: 32.30.Rj, 32.70.Cs, 32.80.Rm, 34.70.+e

scholarly journals Three-nucleon forces

2014 ◽  
Vol 23 (09) ◽  
pp. 1430015 ◽  
Author(s):  
Peter U. Sauer
Keyword(s):  
Ab Initio Calculations ◽  
Ab Initio ◽  
Body Problem ◽  
Many Body ◽  
Nuclear Systems ◽  
The Difference

In this paper, the role of three-nucleon forces in ab initio calculations of nuclear systems is investigated. The difference between genuine and induced many-nucleon forces is emphasized. Induced forces arise in the process of solving the nuclear many-body problem as technical intermediaries toward calculationally converged results. Genuine forces make up the Hamiltonian. They represent the chosen underlying dynamics. The hierarchy of contributions arising from genuine two-, three- and many-nucleon forces is discussed. Signals for the need of the inclusion of genuine three-nucleon forces are studied in nuclear systems, technically best under control, especially in three-nucleon and four-nucleon systems. Genuine three-nucleon forces are important for details in the description of some observables. Their contributions to observables are small on the scale set by two-nucleon forces.

scholarly journals Negative energy states in the Reissner–Nordström metric

2021 ◽  
pp. 2150120
Author(s):  
O. B. Zaslavskii
Keyword(s):  
Turning Point ◽  
High Energy ◽  
Negative Energy ◽  
Infinite Chain ◽  
White Hole ◽  
Negative Energy States ◽  
Energy Formula ◽  
High Energy Collisions ◽  
Energy States

We consider electrogeodesics on which the energy [Formula: see text] in the Reissner–Nordström metric. It is shown that outside the horizon there is exactly one turning point inside the ergoregion for such particles. This entails that such a particle passes through an infinite chain of black–white hole regions or terminates in the singularity. These properties are relevant for two scenarios of high energy collisions in which the presence of white holes is essential.

THE ROLE OF THE NUCLEAR MATTER COMPRESSION MODULUS IN NEUTRON STARS

2004 ◽  
Vol 13 (07) ◽  
pp. 1519-1524 ◽  
Author(s):  
VERÔNICA A. DEXHEIMER ◽  
CÉSAR A. Z. VASCONCELLOS ◽  
MOISÉS RAZEIRA ◽  
MANFRED DILLIG
Keyword(s):  
Neutron Stars ◽  
Nuclear Matter ◽  
Body Problem ◽  
Mean Field Theory ◽  
Mean Field ◽  
Compression Modulus ◽  
Baryon Number ◽  
Many Body ◽  
Relativistic Mean Field

For the nuclear many body problem at high densities, formulated in the framework of a relativistic mean-field theory, we investigate in detail the compression modulus of nuclear matter as a function of the effective nucleon mass. We include consistently in our modelling chemical equilibrium as well as baryon number and electric charge conservation and investigate properties of neutron stars. Among other predictions we focus on the dependence of the maximum mass of a sequence of neutron stars as a function of the compression modulus and the nucleon effective mass.

scholarly journals The vacuum in Dirac's theory of the positive electron

1934 ◽  
Vol 146 (857) ◽  
pp. 420-441 ◽  
Keyword(s):  
Kinetic Energy ◽  
Infinite Number ◽  
Strong Support ◽  
Negative Energy ◽  
Positive Energy ◽  
Quantum Mechanical ◽  
Normal Density ◽  
Physical Picture ◽  
Negative Energy States ◽  
Energy States

According to a theory proposed by Dirac one has to picture the vacuum as filled with an infinite number of electrons of negative kinetic energy, the electric density of which is, however, unobservable. One can observe only deviations from this "normal" density which either consist of an addition of electrons in states of positive energy or absence of electrons from some of the negative energy states (positive electrons). The discovery of the positive electron and the observed magnitude of the processes involving it give strong support to this view. This theory, as it stands, however, is not complete because it makes use of infinite quantities which are inadmissible in physical equations. It therefore must be understood (and was meant so by Dirac) to be a physical picture showing a way in which the quantum mechanical equations can probably be modified in order to give account of the positive electron and to solve the difficulty connected with the states of negative energy.

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