Some Properties of Coupled RPA Equations with Separable Interactions

1997 ◽  
Vol 06 (02) ◽  
pp. 251-258 ◽  
Author(s):  
Hideo Sakamoto
Keyword(s):  
Ground State ◽  
Random Phase Approximation ◽  
Strength Function ◽  
Random Phase ◽  
Transition Strength ◽  
Body System ◽  
Many Body ◽  
Hartree Fock ◽  
Secular Equations ◽  
The Stability

We investigate some properties of coupled eigenvalue equations in the random phase approximation for fundamental modes of motion in a nuclear many-body system undergoing several separable two-body interactions. Based on the Sturm's method, a new algorithm is proposed for solving such coupled secular equations and for testing the stability condition of the Hartree-Fock ground state. A transition strength in general is expressed in a compact form and, in a restricted case, a continuous strength function is constructed by averaging with a Lorentzian distribution function.

scholarly journals Dynamic response of some atoms: Many-body calculations

2005 ◽  
Vol 3 (2) ◽  
pp. 129-140 ◽  
Author(s):  
Aleksandar Tancic ◽  
M. Nikolic
Keyword(s):  
Random Phase Approximation ◽  
Random Phase ◽  
Atomic Interaction ◽  
Correlation Effects ◽  
Many Body ◽  
Hartree Fock ◽  
Many Body Theory ◽  
Correlation Potential ◽  
Body Theory ◽  
True Correlation

The frequency-dependent polarizability in the Hartree-Fock (HF) approximation has been corrected for true correlation effects by means of many-body theory. The polarizability has been computed in the Random Phase Approximation with Exchange (RPAE) for He, Ar Xe, Kr, Li, Ca through the second (and some higher) order in the correlation potential. With this polarizability as input we obtained the values of some atomic interaction constants.

scholarly journals γ-ray strength function for astrophysical applications in the IAEA-CRP

2020 ◽  
Vol 239 ◽  
pp. 07005
Author(s):  
Hiroaki Utsunomiya ◽  
Stephane Goriely ◽  
Therese Renstrøm ◽  
Gry M. Tveten ◽  
Takashi Ari-izumi ◽  
...  
Keyword(s):  
Cross Sections ◽  
Random Phase Approximation ◽  
Function Method ◽  
Strength Function ◽  
Random Phase ◽  
Phase Approximation ◽  
Quasiparticle Random Phase Approximation ◽  
Hartree Fock ◽  
Γ Ray

The γ-ray strength function (γSF) is a nuclear quantity that governs photoabsorption in (γ, n) and photoemission in (n, γ) reactions. Within the framework of the γ-ray strength function method, we use (γ, n) cross sections as experimental constraints on the γSF from the Hartree-Fock-Bogolyubov plus quasiparticle-random phase approximation based on the Gogny D1M interaction for E1 and M1 components. The experimentally constrained γSF is further supplemented with the zero-limit M1 and E1 strengths to construct the downward γSF with which (n, γ) cross sections are calculated. We investigate (n, γ) cross sections in the context of astrophysical applications over the nickel and barium isotopic chains along the s-process path.

scholarly journals Hartree–Fock and random phase approximation theories in a many-fermion solvable model

2015 ◽  
Vol 30 (36) ◽  
pp. 1550196 ◽  
Author(s):  
Giampaolo Co’ ◽  
Stefano De Leo
Keyword(s):  
Random Phase Approximation ◽  
Random Phase ◽  
Solvable Model ◽  
Phase Approximation ◽  
Many Body ◽  
Hartree Fock ◽  
Ideal System ◽  
The Many ◽  
Effective Theories ◽  
Number Of Particles

We present an ideal system of interacting fermions where the solutions of the many-body Schrödinger equation can be obtained without making approximations. These exact solutions are used to test the validity of two many-body effective approaches, the Hartree–Fock and the random phase approximation theories. The description of the ground state done by the effective theories improves with increasing number of particles.

NUCLEAR EXCITATIONS AND WEAK INTERACTION RATES AT FINITE TEMPERATURE

2010 ◽  
Vol 25 (21n23) ◽  
pp. 1767-1770 ◽  
Author(s):  
N. PAAR ◽  
T. MARKETIN ◽  
D. VRETENAR ◽  
Y. F. NIU ◽  
G. COLÒ ◽  
...  
Keyword(s):  
Cross Sections ◽  
Finite Temperature ◽  
Random Phase Approximation ◽  
Random Phase ◽  
Mean Field ◽  
Transition Strength ◽  
Density Functionals ◽  
Hartree Fock ◽  
Relativistic Mean Field ◽  
Low Energies

Self-consistent theory frameworks have been introduced for description of excitations in nuclei at finite temperature, based on energy density functionals formulated using i) relativistic mean field Lagrangian with density dependent meson-nucleon vertex functions, and ii) Skyrme-type functionals. Finite temperature random phase approximation (FTRPA) has been employed in description of multipole excitations and charge-exchange modes. It is shown that in the temperature range T = 1–2 MeV additional transition strength appears at low energies due to thermal unblocking of single-particle orbitals close to the Fermi level. Within the finite temperature Hartree-Fock+RPA based on Skyrme functionals, the electron capture cross sections have been studied for target nuclei at temperatures relevant in modeling the supernova evolution.

scholarly journals THE METHOD OF INCREMENTS — A WAVEFUNCTION-BASED AB-INITIO CORRELATION METHOD FOR SOLIDS

2007 ◽  
Vol 21 (13n14) ◽  
pp. 2204-2214 ◽  
Author(s):  
BEATE PAULUS
Keyword(s):  
Experimental Data ◽  
Ab Initio ◽  
Ground State ◽  
Infinite System ◽  
Correlation Energy ◽  
Correlation Method ◽  
Many Body ◽  
Hartree Fock ◽  
The Many ◽  
Good Agreement

The method of increments is a wavefunction-based ab initio correlation method for solids, which explicitly calculates the many-body wavefunction of the system. After a Hartree-Fock treatment of the infinite system the correlation energy of the solid is expanded in terms of localised orbitals or of a group of localised orbitals. The method of increments has been applied to a great variety of materials with a band gap, but in this paper the extension to metals is described. The application to solid mercury is presented, where we achieve very good agreement of the calculated ground-state properties with the experimental data.

Potential barrier effect and discrete structure o between 40 and 120 Å in the Rb I absorption spectrum

1975 ◽  
Vol 344 (1637) ◽  
pp. 303-309 ◽  
Keyword(s):  
Absorption Spectrum ◽  
Absorption Maximum ◽  
Random Phase Approximation ◽  
Random Phase ◽  
Particle Model ◽  
Discrete Structure ◽  
Model Calculations ◽  
Hartree Fock ◽  
Independent Particle ◽  
Independent Particle Model

Investigation of the Rb I absorption spectrum between 40 and 120 Å has revealed a broad absorption maximum in the 3d photoionization continuum, as well as discrete features associated with the excitation of a 3d-subshell electron. The discrete structure is identified, Hartree-Fock calculations of the transition energies are given and the absorption maximum is discussed in relation to similar spectra and to recent random phase approximation with exchange (r.p.a.e.) and independent particle model calculations.

Analysis of Collective Resonances in Clusters: Metals and Carbon

1992 ◽  
Vol 272 ◽  
Author(s):  
Vitaly V. Kresin
Keyword(s):  
Random Phase Approximation ◽  
Sum Rules ◽  
Random Phase ◽  
Closed Shell ◽  
Dynamical Response ◽  
Many Body ◽  
Resonance Frequencies ◽  
Unified View ◽  
Small Clusters ◽  
Good Agreement

ABSTRACTDipole photoabsorption spectra of small clusters are analyzed. Two types of systems are considered: metal clusters and the carbon fullerenes. Both have been found to exhibit strong collective photoabsorption modes associated with the motion of delocalized electrons. We describe analytical results for the resonance frequencies in both spherical (closed-shell metallic, C60 ) and spheroidal (openshell metallic, C70) particles. The calculation is based on the techniques of many-body physics (random-phase approximation, sum rules), affords a unified view of the dynamical response of microscopic clusters, and leads to good agreement with experimental data.

Mesonic and isobar degrees of freedom in the ground state of the nuclear many-body system

1978 ◽  
Vol 18 (5) ◽  
pp. 2416-2429 ◽  
Author(s):  
M. R. Anastasio ◽  
Amand Faessler ◽  
H. Müther ◽  
K. Holinde ◽  
R. Machleidt
Keyword(s):  
Ground State ◽  
Degrees Of Freedom ◽  
Body System ◽  
Many Body
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