scholarly journals GCM Solver (Ver. 3.0): A Mathematica Notebook for Diagonalization of the Geometric Collective Model (Bohr Hamiltonian) with Generalized Gneuss–Greiner Potential

Computation ◽  
2018 ◽  
Vol 6 (3) ◽  
pp. 48 ◽  
Author(s):  
Fabrizio Ferrari-Ruffino ◽  
Lorenzo Fortunato
Keyword(s):  
Nuclear Physics ◽  
Predictive Power ◽  
Energy Levels ◽  
Energy Operator ◽  
Collective Model ◽  
Linear Combinations ◽  
Oscillator Basis ◽  
Theoretical Predictions ◽  
Scalar Invariants ◽  
Hamiltonian Operators

The program diagonalizes the Geometric Collective Model (Bohr Hamiltonian) with generalized Gneuss–Greiner potential with terms up to the sixth power in β . In nuclear physics, the Bohr–Mottelson model with later extensions into the rotovibrational Collective model is an important theoretical tool with predictive power and it represents a fundamental step in the education of a nuclear physicist. Nuclear spectroscopists might find it useful for fitting experimental data, reproducing spectra, EM transitions and moments and trying theoretical predictions, while students might find it useful for learning about connections between the nuclear shape and its quantum origin. Matrix elements for the kinetic energy operator and for scalar invariants as β 2 and β 3 cos ( 3 γ ) have been calculated in a truncated five-dimensional harmonic oscillator basis with a different program, checked with three different methods and stored in a matrix library for the lowest values of angular momentum. These matrices are called by the program that uses them to write generalized Hamiltonians as linear combinations of certain simple operators. Energy levels and eigenfunctions are obtained as outputs of the diagonalization of these Hamiltonian operators.

scholarly journals A Ternary Map of Ni–Mn–Ga Heusler Alloys from Ab Initio Calculations

Metals ◽  
2021 ◽  
Vol 11 (6) ◽  
pp. 973
Author(s):  
Yulia Sokolovskaya ◽  
Olga Miroshkina ◽  
Danil Baigutlin ◽  
Vladimir Sokolovskiy ◽  
Mikhail Zagrebin ◽  
...  
Keyword(s):  
First Principles ◽  
Predictive Power ◽  
Computational Study ◽  
Heusler Alloys ◽  
Functional Materials ◽  
Ternary Diagram ◽  
Compositional Stability ◽  
Theoretical Predictions ◽  
Simultaneous Stability ◽  
Tetragonal Martensite

In the search for new magnetic functional materials, non-stoichiometric compounds remain a relatively unexplored territory. While experimentalists create new compositions looking for improved functional properties, their work is not guided by systematic theoretical predictions. Being designed for perfect periodic crystals, the majority of first-principles approaches struggle with the concept of a non-stoichiometric system. In this work, we attempt a systematic computational study of magnetic and structural properties of Ni–Mn–Ga, mapped onto ternary composition diagrams. Compositional stability was examined using the convex hull analysis. We show that the cubic austenite has its stability region close to the stoichiometric Ni2MnGa, in agreement with experimental data, while the tetragonal martensite spreads its stability over a wider range of Mn and Ni contents. The unstable compositions in both austenite and martensite states are located in the Ga-rich corner of the ternary diagram. We note that simultaneous stability of the austenite and martensite should be considered for potentially stable compounds suitable for synthesis. The majority of compounds are predicted to be ferrimagnetically ordered in both austenitic and martensitic states. The methodology used in this work is computationally tractable, yet it delivers some predictive power. For experimentalists who plan to synthesize stable Ni–Mn–Ga compounds with ferromagnetic order, we narrow the target compositional range substantially.

scholarly journals Observation of ultra-fine structures in energy levels of prolate nuclei

2018 ◽  
Vol 96 (9) ◽  
pp. 1059-1062 ◽  
Author(s):  
Hassan Hassanabadi ◽  
Hadi Sobhani
Keyword(s):  
Energy Spectrum ◽  
Commutation Relation ◽  
Atomic Physics ◽  
Nuclear Physics ◽  
Energy Levels ◽  
Zeeman Effect ◽  
Three Dimensions ◽  
Energy Splitting ◽  
Commutation Relations ◽  
Fine Structures

This work discusses the observation of splitting in the energy levels of prolate nuclei. Similar effects in atomic physics are known as the Zeeman effect, but in nuclear physics the feasibility of such phenomena has not been observed. After introducing a deformation in the commutation relation in three dimensions, we used these commutation relations in X(3) model. After enough derivation, we then evaluate the energy spectrum relation for the considered system, which has resulted in energy splitting. With these observations in the energy splitting we referred to such an effect as the ultra-fine structures in energy levels. At the end some plots have been depicted to illustrate the results.

Dynamic observation of X-ray Laue diffraction on single-crystal tungsten during pulsed heat load

2019 ◽  
Vol 26 (5) ◽  
pp. 1644-1649 ◽  
Author(s):  
Aleksey S. Arakcheev ◽  
Vladimir M. Aulchenko ◽  
Ilya I. Balash ◽  
Aleksandr V. Burdakov ◽  
Aleksandr D. Chernyakin ◽  
...  
Keyword(s):  
Single Crystal ◽  
Nuclear Physics ◽  
Heat Load ◽  
Diffraction Peak ◽  
Budker Institute ◽  
Peak Shape ◽  
Pulsed Heating ◽  
Dynamic Observation ◽  
Theoretical Predictions ◽  
Residual Plastic Deformation

The dynamics of the diffraction peak shape during pulsed heat load on mosaic single-crystal tungsten were measured at the `Plasma' scattering station on the eighth beamline of the VEPP-4 synchrotron radiation source at the Budker Institute of Nuclear Physics. The observed evolution of the diffraction peak shape agrees with theoretical predictions based on calculations of deformation caused by pulsed heating. Three clearly distinguishable stages of the diffraction-peak evolution were found, correlating with the evolution of temperature and deformation distributions. The residual plastic deformation increased with subsequent heating pulses.

Using a clinical linac to determine the energies of gamma-ray transitions and half-lives of barium nuclei

2020 ◽  
Vol 35 (10) ◽  
pp. 2050062
Author(s):  
Abdullah Engin Çalık ◽  
Kaan Manisa ◽  
Ahmet Biçer ◽  
Mehmet Erdoğan ◽  
Mürsel Şen ◽  
...  
Keyword(s):  
Gamma Rays ◽  
Linear Accelerator ◽  
Nuclear Physics ◽  
Hpge Detector ◽  
Gamma Ray ◽  
Energy Levels ◽  
Photonuclear Reactions ◽  
High Purity Germanium ◽  
Physics Experiment ◽  
First Time

Photonuclear reactions have great importance in understanding the structure of the nuclei. These reactions, performed using the gamma rays obtained by way of bremsstrahlung, are a standard nuclear physics experiment. In this study, a non-enriched barium sample was activated for the first time by using a clinical linear accelerator (cLINACs). The spectrum of barium radioisotopes was obtained by using a gamma spectrometry with a high purity germanium (HPGe) detector. The obtained spectroscopic data were analyzed and energy levels and half-life values together with their uncertainties were obtained. Some energy levels and half-lives of [Formula: see text]Ba were determined with more precision than those of literature values.

COLLECTIVE EXCITED STATES IN EVEN–EVEN NUCLEI WITH QUADRUPOLE AND OCTUPOLE DEFORMATIONS

2012 ◽  
Vol 21 (04) ◽  
pp. 1250044 ◽  
Author(s):  
M. S. NADIRBEKOV ◽  
G. A. YULDASHEVA ◽  
N. MINKOV ◽  
W. SCHEID
Keyword(s):  
Rare Earth ◽  
Excited States ◽  
Energy Levels ◽  
Collective Model ◽  
Rare Earth Nuclei ◽  
The Rare Earth

Deformed even–even nuclei with quadrupole and octupole deformations are investigated on the basis of a nonadiabatical collective model. It is shown that the model satisfactorily describes energy levels of the yrast and first nonyrast bands with alternating parity in the rare-earth nuclei 150 Nd , 152, 154 Sm , 154 Gd , 156 Dy , 162, 164 Er and the actinides 232, 234, 236, 238 U . In the nuclei 156, 158 Gd , 224 Ra , 228 Th and 240 Pu the energy levels of second nonyrast bands are also described. The structure of the considered alternating-parity bands is examined in terms of odd–even staggering diagrams.

scholarly journals ON THE STABILITY OF PERIODICALLY TIME-DEPENDENT QUANTUM SYSTEMS

2008 ◽  
Vol 20 (06) ◽  
pp. 725-764 ◽  
Author(s):  
P. DUCLOS ◽  
E. SOCCORSI ◽  
P. ŠŤOVÍČEK ◽  
M. VITTOT
Keyword(s):  
Transition Probabilities ◽  
Initial Conditions ◽  
Energy Levels ◽  
Sufficient Conditions ◽  
Energy Operator ◽  
Mean Value ◽  
Quantum Systems ◽  
Time Dependent ◽  
Dense Subspace ◽  
Periodically Driven

The main motivation of this article is to derive sufficient conditions for dynamical stability of periodically driven quantum systems described by a Hamiltonian H(t), i.e. conditions under which it holds true sup t ∈ ℝ|〈ψt, H(t)ψt〉| < ∞ where ψt denotes a trajectory at time t of the quantum system under consideration. We start from an analysis of the domain of the quasi-energy operator. Next, we show, under certain assumptions, that if the spectrum of the monodromy (Floquet) operator U(T, 0) is pure point then there exists a dense subspace of initial conditions for which the mean value of the energy is uniformly bounded in the course of time. Further, we show that if the propagator admits a differentiable Floquet decomposition then ‖H(t)ψt‖ is bounded in time for any initial condition ψ0, and one employs the quantum KAM algorithm to prove the existence of this type of decomposition for a fairly large class of H(t). In addition, we derive bounds uniform in time on transition probabilities between different energy levels, and we also propose an extension of this approach to the case of a higher order of differentiability of the Floquet decomposition. The procedure is demonstrated on a solvable example of the periodically time-dependent harmonic oscillator.

Dirac equation with CPRS potential and Cornell tensor interaction in the presence of spin and pseudospin symmetry

2020 ◽  
Vol 29 (08) ◽  
pp. 2050064
Author(s):  
Parisa Sedaghatnia ◽  
Hassan Hassanabadi ◽  
Marc de Montigny
Keyword(s):  
Dirac Equation ◽  
Nuclear Physics ◽  
Energy Levels ◽  
Pseudospin Symmetry ◽  
Tensor Interaction ◽  
Wave Functions ◽  
Nuclear Spectroscopy ◽  
Exactly Solvable

Motivated by the prominent role of tensor interactions in nuclear spectroscopy and many applications of spin and pseudospin symmetry in hadronic and nuclear physics, we solve the Dirac equation with a CPRS potential and a Cornell tensor interaction, in the spin and pseudospin symmetry limits, by using the quasi-exactly solvable method. We obtain explicitly the wave functions for the two lowest energy levels, both for spin and pseudospin symmetry. We also discuss the degeneracy of the system.

NUCLEAR PHYSICS HAMILTONIANS, INVERSE PROBLEM AND THE RELATED ISSUE OF PREDICTIVE POWER

2012 ◽  
Vol 21 (05) ◽  
pp. 1250053 ◽  
Author(s):  
J. DUDEK ◽  
B. SZPAK ◽  
A. DROMARD ◽  
M.-G. PORQUET ◽  
B. FORNAL ◽  
...  
Keyword(s):  
Field Theory ◽  
Inverse Problem ◽  
Nuclear Physics ◽  
Predictive Power ◽  
Mean Field Theory ◽  
Mean Field ◽  
Sensu Stricto ◽  
Hartree Fock ◽  
Numerical Predictions ◽  
Self Consistent

In this paper we formulate and discuss the strategy of constructing theories capable of providing not only the numerical predictions sensu stricto but also the distributions of probability that such predictions apply in the predefined physics context. Examples of applications of the presented ideas are illustrated using as a choice the nuclear mean-field theory with two realistic realizations of the underlying Hamiltonians: Phenomenological Woods–Saxon and self-consistent Skyrme–Hartree–Fock.

scholarly journals Strangeness at Intermediate Baryon Density

2018 ◽  
Vol 171 ◽  
pp. 02002
Author(s):  
David Tlusty
Keyword(s):  
Phase Diagram ◽  
Nuclear Physics ◽  
Chemical Potential ◽  
Gluon Plasma ◽  
Baryon Density ◽  
Density Region ◽  
Qcd Phase Diagram ◽  
Theoretical Predictions ◽  
Hadron Gas ◽  
Phase Equilibrium Curve

Exploration of the QCD phase diagram has been one of the main programs of contemporary nuclear physics. The intermediate baryon density region covers a broad range of the baryon chemical potential, between 100 and 700 MeV, and is expected to include a possible critial point at the end of a phase equilibrium curve between the hadron gas and quark gluon plasma phases. Experimental programs at the SPS and RHIC facilities have provided valuable insights in this range. These proceedings motivate the exploration of the QCD phase diagram through the use of strangeness. A selection of relevant experimental results from RHIC and SPS beam energy scan programs with associated theoretical predictions is presented along with a discussion of possible physical conclusions and future plans.

Variational calculations of rovibrational states: a precise high-energy potential surface for HCN

1990 ◽  
Vol 332 (1625) ◽  
pp. 309-327 ◽  
Keyword(s):  
Potential Surface ◽  
Energy Levels ◽  
Energy Operator ◽  
High Energy ◽  
Exact Expression ◽  
Hamiltonian Matrix ◽  
Energy Potential ◽  
Advantages And Disadvantages ◽  
Variational Calculations ◽  
Rovibrational States

We report the results of variational calculations of the rovibrational energy levels of HCN for J = 0, 1 and 2, where we reproduce all the ca . 100 observed vibrational states for all observed isotopic species, with energies up to 18000 cm -1 , to about + 1 cm -1 , and the corresponding rotational constants to about +0.001 cm -1 . We use a hamiltonian expressed in internal coordinates r 1 , r 2 and 0 , using the exact expression for the kinetic energy operator T obtained by direct transformation from the cartesian representation. The potential energy V is expressed as a polynomial expansion in the Morse coordinates y for the bond stretches and the interbond angle 0 . The basis functions are built as products of appropriately scaled Morse functions in the bond-stretches and Legendre or associated Legendre polynomials of cos 0 in the angle bend, and we evaluate matrix elements by Gauss quadrature. The hamiltonian matrix is factorized using the full rovibrational symmetry, and the basis is contracted to an optimized form ; the dimensions of the final hamiltonian matrix vary from 240 x 240 to 1000 x 1000. We believe that our calculation is converged to better than 1 cm -1 at 18000 cm -1 . Our potential surface is expressed in terms of 31 parameters, about half of which have been refined by least squares to optimize the fit to the experimental data. The advantages and disadvantages and the future potential of calculations of this type are discussed.

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