Energy Levels Of Nuclei Research Articles

Investigation of Alignment Effects of Neutron and Proton Pairs in High Spin States of Band Crossing for <sup>159,160</sup>Sm Isotopes Using Projected Shell Model (PSM)

Energy spectrum of nucleus is one the important information for better recognition of nuclear force and interaction of nucleon inside of the nucleus. Energy levels of nucleus are measured by detecting gamma- ray energy spectrum when a target nucleus bombarded with a special projectile to excite it in to levels higher than ground state. On the other hand, there are several models to calculate nuclear energy levels. Solution of the Schrödinger equation by considering a suitable potential is direct method to obtain energy levels of a quantum mechanical system like nucleus. Projected shell model is a model of this type that is developed by solving the Schrödinger equation for a set of potentials along with role of spin. Band structure and yrast bands for even-even and odd-even isotopes of Samarium (^159,160Sm) are calculated using a Fortran code founded based on the projected shell model (PSM). Energy levels of negative and positive parity bands of ¹⁵⁹Sm and ¹⁶⁰Sm isotopes of Samarium nucleus are obtained separately for each spin. Kinetic and dynamic moments of inertias are also calculated for these isotopes. The acquired results are compared with the experimental data. The electromagnetic reduced transition probabilities, B(M1)/B(E2) the behavior of dynamic moment of inertia J², rotational kinetic energy and moment of inertia J¹ as a function of spin have also been investigated and proper comparison is made between the calculated results and the experimental data. The alignment phenomena of neutron-proton pairs in view of the rotational movement in high spin states has also been studied with reference to band crossing.

Calculating Energy Levels in 25Mg/25Al Mirror Nuclei


 
 
 
 Coulomb Displacement Energies in mirror nuclei 25Mg, 25Al have been calculated using shell model code OXBASH [1] and compared with experimental results. The code calculations were done in the USD model space with the W Hamiltonian [2]. The OXBASH code which is based on famous nuclear model, the shell model, deals with evaluating energy levels in nuclei. A comparison had been made between our results and the available experimental data [3] to test theoretical shell model description of nuclear structure in mirror nuclei. The energy states of mirror nuclei are almost identical, except for the small effects due to Coulomb interaction where the symmetry in being broken. Energy spectrum calculated with this code was in good agreement with the published experimental data [3].
 
 
 
 

Energy Levels Calculations in <sup>23</sup>Mg/<sup>23</sup>Na and <sup>47</sup>Cr/<sup>47</sup>V Mirror Nuclei

Coulomb Displacement Energies in mirror nuclei ²³Mg, ²³Na and ⁴⁷Cr, ⁴⁷V have been calculated using shell model code OXBASH [1] and compared with experimental results. The calculations were carried out in the USD model space with the W Hamiltonian [2]. This code which is based on one of the most applicable nuclear models, the shell model, deals with evaluating energy levels in nuclei. A comparison had been made between computational results in this paper and the available experimental data to test theoretical shell model description of nuclear structure in mirror nuclei. The energy states of mirror nuclei are almost identical, except for the small effects due to Coulomb interaction where the symmetry in being broken. The calculated energy spectrum is in good agreement with the available experimental data.

Energy Levels Calculations of 24 Al and 25 Al Isotopes

In this article, the energy levels of Aluminum isotopes 24Al and 25Al are calculated using OXBASH shell model code. The calculations were carried out in the SD model space with the W and CW Hamiltonian [1, 2] using the code OXBASH for windows PC [3]. This code which is based on one of the most applicable nuclear models, the shell model, deals with evaluating energy levels in nuclei. Using this code to calculate the energy levels of an isotope, produces several files that contains a set of data. The ground state energy of a nucleus and also the probable energies of excitation levels can be calculated by OXBASH. Programs will be reliable only when results meet experimental procedures. A compilation of SD-shell energy levels calculated with the USD Hamiltonian was published around 1988. A comparison had been made between our results and the available experimental data to test theoretical shell model description of nuclear structure in Aluminum isotopes. The calculated energy spectrum is in good agreement with the available experimental data.

Calculating Energy Levels in <sup>49</sup>Mn/<sup>49</sup>Cr Mirror Nuclei with OXBASH Code

Coulomb Displacement Energies in mirror nuclei 49 Mn and 49 Cr have been calculated using shell model code OXBASH and compared with experimental results. The calculations were carried out in the F7PN model space with the F748BPN Hamiltonian. This code which is based on one of the most applicable nuclear models, the shell model, deals with evaluating energy levels in nuclei. A comparison had been made between calculated results and the available experimental data to test theoretical shell model description of nuclear structure in mirror nuclei. The energy states of mirror nuclei are almost identical, except for the small effects due to Coulomb interaction where the symmetry in being broken. The calculated energy spectrum is in good agreement with the available experimental data.

Quantum algorithms for computational nuclear physics

While quantum algorithms have been studied as an efficient tool for the stationary state energy determination in the case of molecular quantum systems, no similar study for analogical problems in computational nuclear physics (computation of energy levels of nuclei from empirical nucleon-nucleon or quark-quark potentials) have been realized yet. Although the difference between the above mentioned studies might seem negligible, it will be examined. First steps towards a particular simulation (on classical computer) of the Iterative Phase Estimation Algorithm for deuterium and tritium nuclei energy level computation will be carried out with the aim to prove algorithm feasibility (and extensibility to heavier nuclei) for its possible practical realization on a real quantum computer.

Power spectrum of nuclear spectra with missing levels and mixed symmetries

Sequences of energy levels in nuclei are often plagued with missing levels whose number and position are unknown. It is also quite usual that all the quantum numbers of certain levels cannot be experimentally determined, and thus levels of different symmetries are mixed in the same sequence. The analysis of these imperfect spectra (from the point of view of spectral statistics) is unavoidable if one wants to extract some statistical information. The power spectrum of the δq statistic has emerged in recent years as an important tool for the study of quantum chaos and spectral statistics. We derive analytical expressions for the observed power spectrum in terms of the fraction of observed levels and the number of mixed sequences. These expressions are tested with large shell model spectra simulating realistic experimental situations. A good estimation of the number of mixed symmetries and the fraction of missing levels is obtained by means of a least-squares fit in a wide set of different situations.

Mean single-particle potentials and single-particle energies in a microscopic model of the nucleus

A method for calculating mean single-particle potentials and the corresponding single-particle energy levels in nuclei is presented. Specific formulas for these quantities are written for Slater determinant wave functions in the case of polarized orbitals and a central exchange nucleon-nucleon potential featuring a Gaussian radial dependence. The resulting theoretical estimates of single-particle properties of the nuclei considered in the present study are in satisfactory agreement with relevant experimental data.

Effective interaction for N=50 isotones.

Standard shell-model techniques of constructing and diagonalizing Hamiltonians in finite Hilbert spaces have been used to treat the N=50 isotones with an expanded model space and a new empirical effective interaction. A vector space with active 0${f}_{5/2}$, 1${p}_{3/2}$, 1${p}_{1/2}$, and 0${g}_{9/2}$ proton orbits is used to model the low-lying excitations of these nuclei. The effective interaction is obtained by varying 35 parameters, distributed over the 65 two-body matrix elements and four single particle energies of the model space, to fit over 170 experimental energy levels in nuclei from $^{82}\mathrm{Ge}$ through $^{96}\mathrm{Pd}$. Nearly all of the experimental level energies of N=50 nuclei involved in the fit are well reproduced by the final interaction.

Analytic expression for the single-particle energy levels in nuclei

An analytic expression is given for single-particle energy levels in the nucleus. It is built through a phenomenological treatment of the main features of the shell model, as suggested by its foundations in the Hartree-Fock procedure. Such features are the nonlocality of the self-consistent potential and the correlation between its shape and the nucleon structure and nuclear reactions. The numerical results thus obtained agree fairly well with experimental data and Hartree-Fock calculations.

Proof of a Conjecture by Dyson in the Statistical Theory of Energy Levels

A conjectured identity relating the statistical properties of two types of ensembles occurring in a statistical theory of the distribution of energy levels in nuclei and other complex systems is proved.

Gamma rays emitted in inelastic scattering of neutrons at 3 Mev energy

The inelast ic scattering of fast neutrons on nuclei is of considerable interest both for the study of the structure of the nucleus and for the pra t ica l design of fast reactors, b io logica l shielding in nuclear faci l i t ies , etc. The present paper reports studies of the energy levels in nuclei ,based on measurements of the energy of ), rays emi t ted in the inelast ic scattering of neutrons of energy E 0 = 3 Mev. The energy spectra of g a m m a rays emi t ted from t i tanium, chromium, stront ium, iodine, barium, tungsten, iridum, and ir idium, and bisrnuth nuclei were measured by means of a sc in t i l la t ion ~/ spect rometer using Nai(Tt) crystal scinti l lators.

A note on rotational energy levels in nuclei

It is shown that the kinetic energy T of any system of interacting particles may be written in a “canonical form”, which displays the dependence of T on the total angular momentum. A formula is given for the zero order moments of inertia associated with collective rotation of the system. The formalism is applied to nuclei, and for purposes of comparison, to molecules. In addition, it is shown that an unsymmetric formulation of the many particle problem, in which only the nucleons of a “core” participate in the definition of the body fixed axes, leads to a Hamiltonian which is related by a simple averaging process with the “unified” model of Bohr and Mottelson. Finally, a connection is established between the “unified” model of Bohr-Mottelson and the “cranking model” of Inglis.