scholarly journals Many-Body Calculations for Medium-Mass Nuclei by the Unitary Transformation Method

2015 ◽  
Author(s):  
Takayuki Miyagi ◽  
Takashi Abe ◽  
Ryoji Okamoto ◽  
Takaharu Otsuka
Keyword(s):  
Unitary Transformation ◽  
Transformation Method ◽  
Many Body ◽  
Medium Mass

scholarly journals Nuclear response at zero and finite temperature

2019 ◽  
Vol 223 ◽  
pp. 01033
Author(s):  
Elena Litvinova ◽  
Peter Schuck ◽  
Herlik Wibowo
Keyword(s):  
Finite Temperature ◽  
Nucleon Nucleon ◽  
Many Body ◽  
Nucleon Interaction ◽  
Medium Mass ◽  
Recent Developments ◽  
Nucleon Nucleon Interaction ◽  
Energy Dependent ◽  
Finite Nuclei ◽  
Nuclear Response

We present some recent developments on the nuclear many-body problem, such as the treatment of high-order correlations and finite temperature in the description of in-medium two-nucleon propagators. In this work we discuss two-time propagators of the particle-hole type, which describe the response of finite nuclei to external probes without nucleon transfer. The general theory is formulated in terms of the equation of motion method for these propagators with the only input from the bare nucleon-nucleon interaction. The numerical implementation was performed on the basis of the effective mason-nucleon Lagrangian in order to study the energy-dependent kernels of different complexity. The finite-temperature extension of the theory with ph ⊗ phonon configurations is applied to a study of the multipole response of medium-mass nuclei.

UNITARY TRANSFORMATION APPROACH FOR THE PHASE OF THE DAMPED DRIVEN HARMONIC OSCILLATOR

2003 ◽  
Vol 17 (26) ◽  
pp. 1365-1376 ◽  
Author(s):  
JEONG-RYEOL CHOI
Keyword(s):  
Wave Function ◽  
Harmonic Oscillator ◽  
Unitary Transformation ◽  
Operator Method ◽  
Classical Equation ◽  
Transformation Method ◽  
Invariant Operator ◽  
Harmonic Oscillators ◽  
Parabolic Cylinder ◽  
Parabolic Cylinder Function

Using the invariant operator method and the unitary transformation method together, we obtained discrete and continuous solutions of the quantum damped driven harmonic oscillator. The wave function of the underdamped harmonic oscillator is expressed in terms of the Hermite polynomial while that of the overdamped harmonic oscillator is expressed in terms of the parabolic cylinder function. The eigenvalues of the underdamped harmonic oscillator are discrete while that of the critically damped and the overdamped harmonic oscillators are continuous. We derived the exact phases of the wave function for the underdamped, critically damped and overdamped driven harmonic oscillator. They are described in terms of the particular solutions of the classical equation of motion.

scholarly journals SIMULATION OF SYMMETRIC NUCLEI AND THE ROLE OF PAULI POTENTIAL IN BINDING ENERGIES AND RADII

2009 ◽  
Vol 18 (03) ◽  
pp. 705-719
Author(s):  
M. ÁNGELES PÉREZ-GARCÍA ◽  
K. TSUSHIMA ◽  
A. VALCARCE
Keyword(s):  
Finite Size ◽  
Mass Range ◽  
Nucleon Nucleon ◽  
Binding Energies ◽  
Many Body ◽  
Nucleon Interaction ◽  
Pauli Potential ◽  
Medium Mass ◽  
Nucleon Number ◽  
Nucleon Nucleon Interaction

It is shown that the use of a density-dependent effective Pauli potential together with a generic nucleon–nucleon interaction potential plays a crucial role to reproduce not only the binding energies but also the matter root mean square radii of medium mass range spin–isospin saturated nuclei. This study is performed with a semiclassical Monte Carlo many-body simulation within the context of a simplified nucleon–nucleon interaction to focus on the effect of the genuine correlations due to the fermionic nature of nucleons. The procedure obtained is rather robust and it does not depend on the detailed features of the nucleon–nucleon interaction. For nuclei below saturation the density dependence may be represented in terms either of the nucleon number, A, or the associated Fermi momenta. When testing the simulation procedure for idealized "infinite" symmetric nuclear matter within the corresponding range of densities, we find that, beyond the low particle number limit, finite size effects do not affect the Pauli potential strength parametrization.

Intensity-dependent and multi-photon Hamiltonian of two two-level atoms and two-mode field in a Kerr medium solved by virtue of supersymmetric unitary transformation

2021 ◽  
pp. 2150060
Author(s):  
N. H. Abd El-Wahab ◽  
R. A. Zait
Keyword(s):  
Unitary Transformation ◽  
Atomic System ◽  
Quantum Effects ◽  
Transformation Method ◽  
Kerr Medium ◽  
Atomic Systems ◽  
Mode Field ◽  
Q Function ◽  
Supersymmetric Structure ◽  
Intensity Dependent Coupling

We consider a generalized multi-photon interaction of two collectively two-level atoms with two-mode of electromagnetic field in the presence of Kerr medium and intensity-dependent coupling. We show that this atomic system possesses supersymmetric structure. We solved this system by virtue of supersymmetric unitary transformation. The supersymmetric generators of this atomic system are constructed. The diagonalization of the corresponding Hamiltonian is performed by introducing a supersymmetric unitary transformation. Accordingly, the eigenvalues and eigenfunctions of the Hamiltonian of the atomic system are obtained. The time evolution of the atom–field wave functions is derived in an exact form for two cases of the initial states of the atoms and the field modes. Some quantum effects such as the second-order correlation function, cross-correlation, purity and Husimi Q-function are investigated. The effects of the Kerr medium, detuning parameter, intensity-dependent coupling and multi-photon transition on the evolution of these quantum effects are examined. We conclude that the supersymmetric unitary transformation method is very simple and can be applied to a variety of atomic systems which possess a supersymmetric structure.

Sign in / Sign up

Export Citation Format

Share Document