Intrinsic Quadrupole-Moment Transition Rates and Spectroscopic Factors for the Self-Consistent HFB Shapes of the Ti, Cr, and Fe Isotopes

1970 ◽  
Vol 2 (6) ◽  
pp. 2444-2446 ◽  
Author(s):  
Harish Chandra
Keyword(s):  
Quadrupole Moment ◽  
The Self ◽  
Transition Rates ◽  
Intrinsic Quadrupole Moment ◽  
Fe Isotopes ◽  
Spectroscopic Factors ◽  
Self Consistent

scholarly journals SPECTROSCOPIC FACTORS IN 16O AND NUCLEON ASYMMETRY

2009 ◽  
Vol 24 (11) ◽  
pp. 2060-2068 ◽  
Author(s):  
C. BARBIERI ◽  
W. H. DICKHOFF
Keyword(s):  
Random Phase Approximation ◽  
Green's Functions ◽  
Green’S Functions ◽  
Collective Excitation ◽  
Random Phase ◽  
Heavy Ion ◽  
The Self ◽  
Phase Approximation ◽  
Spectroscopic Factors ◽  
Self Consistent

The self-consistent Green's functions method is employed to study the spectroscopic factors of quasiparticle states around 16,28 O and 40,60 Ca . The Faddeev random phase approximation (FRPA) is used to account for the coupling of particles with collective excitation modes. Results for 16 O are reviewed first. The same approach is applied to isotopes with large proton-neutron asymmetry to estimate its effect on spectroscopic factors. The results, based on the chiral N3LO force, exhibit an asymmetry dependence similar to that observed in heavy-ion knockout experiments but weaker in magnitude.

scholarly journals The relativistic self-consistent field

1935 ◽  
Vol 152 (877) ◽  
pp. 625-649 ◽  
Keyword(s):  
Wave Equation ◽  
Field Equation ◽  
Wave Functions ◽  
The Self ◽  
Magnetic Interactions ◽  
Consistent Field ◽  
Exchange Effects ◽  
Self Consistent ◽  
Self Consistent Field ◽  
Schrödinger's Equation

1—The method of the self-consistent field for determining the wave functions and energy levels of an atom with many electrons was developed by Hartree, and later derived from a variation principle and modified to take account of exchange and of Pauli’s exclusion principle by Slater* and Fock. No attempt was made to consider relativity effects, and the use of “ spin ” wave functions was purely formal. Since, in the solution of Dirac’s equation for a hydrogen-like atom of nuclear charge Z, the difference of the radial wave functions from the solutions of Schrodinger’s equation depends on the ratio Z/137, it appears that for heavy atoms the relativity correction will be of importance; in fact, it may in some cases be of more importance as a modification of Hartree’s original self-nsistent field equation than “ exchange ” effects. The relativistic self-consistent field equation neglecting “ exchange ” terms can be formed from Dirac’s equation by a method completely analogous to Hartree’s original derivation of the non-relativistic self-consistent field equation from Schrodinger’s equation. Here we are concerned with including both relativity and “ exchange ” effects and we show how Slater’s varia-tional method may be extended for this purpose. A difficulty arises in considering the relativistic theory of any problem concerning more than one electron since the correct wave equation for such a system is not known. Formulae have been given for the inter-action energy of two electrons, taking account of magnetic interactions and retardation, by Gaunt, Breit, and others. Since, however, none of these is to be regarded as exact, in the present paper the crude electrostatic expression for the potential energy will be used. The neglect of the magnetic interactions is not likely to lead to any great error for an atom consisting mainly of closed groups, since the magnetic field of a closed group vanishes. Also, since the self-consistent field type of approximation is concerned with the interaction of average distributions of electrons in one-electron wave functions, it seems probable that retardation does not play an important part. These effects are in any case likely to be of less importance than the improvement in the grouping of the wave functions which arises from using a wave equation which involves the spins implicitly.

Sign in / Sign up

Export Citation Format

Share Document