Magic Nucleon Numbers Research Articles

Study of spectroscopic factors at N = 29 using isobaric analogue resonances in inverse kinematics

Shell closures and their associated magic numbers of nucleons provide a unique means for studying the structure of exotic nuclei far from stability. An experiment was recently performed at the National Superconducting Cyclotron Laboratory to measure resonant elastic proton scattering on 46Ar in inverse kinematics in the region containing isobaric analogue states of 47Ar, an N=29 nucleus with one neutron above the N=28 shell closure. Four candidate resonances were observed: one corresponding to the 3/2− ground state of 47Ar, another corresponding to its 1/2− first excited state, and two that likely correspond to states in the 47K compound nucleus. The observed properties of the ground state resonance were compatible with values from the literature, but a significantly lower spectroscopic factor was found for the 1/2− state resonance.

Dispersive optical potential for nuclei with N and Z values changing toward the nucleon drip lines

A method for constructing dispersive optical potentials is proposed for calculating single-particle energies in isotopic chains of spherical and nearly spherical nuclei up to nucleon drip lines. The potential of this method is demonstrated by calculating the neutron and proton single-particle energies in calcium, nickel, and zirconium isotopes. The results agree well with experimental data available for stable isotopes. Predictive calculations of single-particle spectra are performed for isotopes lying far from the beta-stability valley. A comparison of the results with the energies of nucleon separation from nuclei of mass number A and A+1 revealed features of the single-particle spectrum that are characteristic of nuclei containing classical and nonclassical magic numbers of nucleons.

Evidences for magicity in superdeformed shapes

Many empirical evidences that point to the existence of preferred magic nucleon numbers for superdeformed (SD) shapes are presented in this paper. We use a simple premise based on the 4-parameter formula fitted using observed γ-rays of SD bands. In particular, plots of γ-ray energy ratios, nuclear softness parameter values and the number of SD bands for given N and Z are used to pinpoint the magicity (N, Z numbers) that are most favoured as the SD magic numbers. This analysis also leads to several new predictions on the occurrence of SD bands specially in neutron-rich nuclei.

Digital Nuclear Shell Model

The subject of this thesis is a digital approach to the investigation of the digital basis of digitalnuclear shell model. The shell model is partly analogous to the atomic shell model which describes thearrangement of electrons in an atom, in that a filled shell results in greater stability. Whenadding nucleons to a nucleus, there are certain points where the binding energy of the next nucleon issignificantly less than the last one. Magic numbers of nucleons: 2, 8, 20, 28, 50, 82, 126 which aremore tightly bound than the next higher number, is the origin of the shell model. “In a threedimensionalharmonic oscillator the total degeneracy at level n is (n+1)(n+2)/2. Due to the spin, thedegeneracy is doubled and is (n+1)(n+2). Thus the magic numbers would be ∑kn=0(n+1)(n+2)=(k+1)(k+2)(k+3)/3 for all integer k. This gives the following magic numbers:2,8,20,40,70,112..., which agree with experiment only in the first three entries. These numbers aretwice the tetrahedral numbers (1,4,10,20,35,56...) from the Pascal Triangle”.http://en.wikipedia.org/wiki/Nuclear_shell_model. The digital mechanism of shell model have beenanalyzed by the application of cybernetic methods, information theory and system theory,respectively. This paper is to report that we discovered new methods for development of the newtechnologies in nuclear physics and chemistry. It is about the most advanced digital technology whichis based on program, cybernetics and informational systems and laws. The results in practicalapplication of the new technology could be useful in physics, chemistry, bioinformatics, and othernatural sciences.

Digital Nuclear Shell Model

The subject of this thesis is a digital approach to the investigation of the digital basis of digitalnuclear shell model. The shell model is partly analogous to the atomic shell model which describes thearrangement of electrons in an atom, in that a filled shell results in greater stability. Whenadding nucleons to a nucleus, there are certain points where the binding energy of the next nucleon issignificantly less than the last one. Magic numbers of nucleons: 2, 8, 20, 28, 50, 82, 126 which aremore tightly bound than the next higher number, is the origin of the shell model. “In a threedimensionalharmonic oscillator the total degeneracy at level n is (n+1)(n+2)/2. Due to the spin, thedegeneracy is doubled and is (n+1)(n+2). Thus the magic numbers would be ∑kn=0(n+1)(n+2)=(k+1)(k+2)(k+3)/3 for all integer k. This gives the following magic numbers:2,8,20,40,70,112..., which agree with experiment only in the first three entries. These numbers aretwice the tetrahedral numbers (1,4,10,20,35,56...) from the Pascal Triangle”.http://en.wikipedia.org/wiki/Nuclear_shell_model. The digital mechanism of shell model have beenanalyzed by the application of cybernetic methods, information theory and system theory,respectively. This paper is to report that we discovered new methods for development of the newtechnologies in nuclear physics and chemistry. It is about the most advanced digital technology whichis based on program, cybernetics and informational systems and laws. The results in practicalapplication of the new technology could be useful in physics, chemistry, bioinformatics, and othernatural sciences.

The systematics of (n, α) reaction cross-sections at 14.5 MeV neutron energy

A comprehensive review of the experimental data for 14.5 MeV neutron induced reaction crosssections for (n, α) reaction has been made for the isotopes having Z up to 82. Two different parameter groups have been considered by the classification of nuclei into odd-mass and even-even nuclei. The empirical formulae with two parameters for the evaluation of (n, α) reaction cross-sections are discussed in the present study. The odd-even effects have been observed as the cross-sections of odd-mass nuclei are higher as compared to their neighboring even-even nuclei. The shell effects have also been established at magic nucleon numbers for these reaction cross-sections.

Empirical relation and establishment of shell effects in (n, 2n) reaction cross-sections at 14 MeV

The experimental data for (n, 2n) reaction cross-sections around 14 MeV neutron energy have been collected from the literature and analysed for the isotopes having 1 ≤ Z ≤ 82. The empirical relations for the reaction cross-sections have been obtained, which show fairly good fits with the experimental values. The shell effects have been established at magic nucleon numbers for (n, 2n) reaction cross-sections around 14 MeV neutron energy. The odd-even effects have also been observed as the cross-sections for odd-mass nuclei are higher than their neighbouring even-even nuclei.

Valleys due to Pb and Sn on the potential energy surface of superheavy and lighter α-emitting nuclei

The strong shell effects of the magic nuclei 208Pb, 132Sn and 102Sn are the origin of valleys on the potential energy surfaces (PES) of the superheavy nucleus 294118 and of the alpha emitters 212Po and 106Te. We use the most advanced asymmetric two-centre shell model allowing us to obtain shell and pairing corrections which are added to the Yukawa plus exponential model deformation energy. For the first time the alpha valley of a nucleus (106Te) calculated by using the macroscopic–microscopic method is clearly seen on a PES. The α-decay half-lives calculated within fission theories (analytical superasymmetric fission model, universal curve, semiempirical formula based on fission theory) are very close to the experimental ones. The increased deviations in the neighbourhood of magic numbers of nucleons, present in other frequently used relationships (e.g. Viola–Seaborg formula), are smoothed out by the semiempirical formula based on fission theory.

α-decay half-lives of superheavy nuclei

The half-lives against \ensuremath{\alpha} decay of transuranium nuclei including superheavies are calculated by three methods: a semiempirical formula taking into account the magic numbers of nucleons, the analytical superasymmetric fission model, and the universal curves. The calculations based on $Q$ values determined by using the recently published compilations of atomic masses are compared to the experimental results.

Facilities and Methods: High-Resolution Gamma-Ray Spectroscopy at TRIUMF-ISAC

It is no accident that the rapid technical evolution of radioactive beam facilities has coincided with challenges to the standard models of nuclear structure and fundamental interactions. In nuclear structure, the shell model is a de facto standard model. The properties and systematics of nuclei near stability are well understood in terms of the magic nucleon numbers at shell closures. However, when confronted with experimental data on increasingly exotic nuclei, the model fails. The near-stability magic nucleon numbers disappear, and new ones emerge [1]. This is evidenced for example by the energies and γ transition rates of excited states. These excitations may be probed by reactions induced with accelerated radioactive beams, or by a parent β decay. At the same time, high production yield for selected isotopes allows for very high precision measurements of specific decay processes. Because β decay is a nuclear manifestation of the weak interaction, high precision measurements of nuclear β decay provide a strict test of fundamental symmetries [2].

Further evidence for magic neutron number N=16 in neutron-rich nuclei

The properties of light exotic neutron-rich nuclei far from beta-stability have been found to differ substantially from the well known properties of nuclei near the valley of beta-stability. A very principal drastic changes can be seen in the locations of magic nucleon numbers that are of fundamental importance in nuclear physics as they form the basis of nuclear shell structure. We present an analysis of experiments performed at GANIL resulting in an appearance of a neutron magic number, N=16, in very neutron-rich nuclei. The behavior of the two neutron separation energies S 2 n gives a very clear evidence for the existence of the new shell closure N=16 for Z=9 and 10 appearing between 2 S 1 2 and 1 d 3 2 orbitals. Moreover, the analysis of its derivate, confirms the magic character of N=16 in the region 6⩽Z⩽10, while the shell closure at N=20 tends to disappear for Z⩽13.

Spectroscopy in the second and third minimum of actinide nuclei

Progress in our understanding of the nuclear structure in the second and third minimum of the potential energy surface is reported emphasizing recent achievements via complementary experimental approaches. Detailed spectroscopic results of collective properties are obtained in the second and third minimum as well as for spin dependent fission properties. A novel approach could be established to determine the depth of the potential wells. Empirical collective level systematics developed for normal deformed nuclei were tested upon their predictive power for extremely deformed configurations. A phenomenological approach based on a valence correlation scheme was applied to the second potential well in order to predict β vibrational phonon energies and magic nucleon numbers. Perspectives for future experimental efforts will be discussed.

The kinetic energy deficit in the symmetric fission of 259Md

Abstract

Study of many-nucleon correlations in32S as a model for fragment shell effects in fission

The formation and break-up of substructures is studied in32S as a calculable microscopic model for analogous long-range many-nucleon correlations in the fission of actinides. The calculations are performed for alpha-cluster wave functions with Volkov and Brink-Boeker interaction allowing forα,12C,16O and20Ne clustering. It turns out that the correlated motion of large magic numbers of nucleons in two groups (16O+16O) is energetically favorable already at relatively small deformations. In the second minimum the16O+16O substructure occurs with high probability (about 80%). In analogy to these results the “pre-formation” of fragments and “fragment shell” effects occuring in the fission of actinides are explained in terms of probability statements for the formation of the corresponding heavy clusters in the many-body wave function.

Systematics of electric-dipole transitions

The aim of the present paper is a systematical analysis of average radiative properties of nuclear levels lying near the nuclear binding energy. Theoretical estimates of electric-dipole radiative widths as well as of elastic-scattering cross-sections are presented. All the calculations have carried out by an extrapolation of theE1 giant resonance at lower energies, following a procedure suggested by Axel. A quantitative agreement with experiment has been obtained in most cases. We can thus confirm that, at least away from closed shells, Axel’s extrapolation procedure allows us to reproduce the systematical trend ofE1 radiative widths below the giant resonance; large shell effects are conversely evident near magic nucleon numbers.

SHELL EFFECTS ON THE SPACING OF NUCLEAR LEVELS

Recent measurements of resonances in slow neutron total cross sections yield good estimates of the average level spacing, D, in medium and heavy nuclei. These spacings show large variations, by factors of 103 to 105, in the region of magic numbers of nucleons. There are also variations by smaller factors between nuclei with even and odd numbers of protons or neutrons. The even–odd effect is a co-operative phenomenon; it can be approximately treated by redefining the ground state to be used for a Fermi gas model. After this correction the gas model should predict D with reasonable accuracy since it is required only to define the density of a complete set of states. The magic number variations are shown to be fitted by an improved approximation to the single-nucleon level density. This is obtained from the observed sequence of single-particle spins and the assumption that the energy interval between spin subshells is constant. Fifty-two observed spacings are fitted by a two-parameter formula with an average uncertainty factor 3. Many of the larger remaining differences between observation and the predictions of the model are qualitatively explicable as expected departures from this uniform spacing hypothesis.