24Mg Nuclei Research Articles

Gamow-Teller strength as a function of excitation energy

We study the dependence of the total Gamow-Teller strength in an N = Z nucleus (24Mg) as a function of excitation energy within a complete 0ħω shell-model space (the 0d1s shell). We find an essentially monotonic increase in strength with increasing excitation energy. We are able to relate this behavior to a decrease in spatial symmetry (increase in SU(4) symmetry) as a function of excitation energy.

A Combined EPR and Quantum Chemical Approach to the Structure of Surface Fs+(H) Centers on MgO

Fs+(H) color centers at the surface of MgO have been studied using a combined EPR and quantum chemical approach. Fs+(H) are paramagnetic excess electrons centers where the unpaired electron is trapped in a surface anion vacancy. They are formed at the surface of thoroughly dehydrated MgO (1073K) upon UV irradiation under hydrogen in parallel with the formation of minor fractions of different color centers. The whole EPR spectrum resulting from irradiation has been analyzed by simulation of the experimental profile. Fs+(H) centers are characterized by an axial g tensor and display a hyperfine interaction with a hydrogen nucleus (belonging to an hydroxyl group stabilized nearby the vacancy) and two distinct families of 25Mg nuclei characterized by a large (10.5 G) and a small (0.7 G) hyperfine coupling constant, respectively. Both EPR and ab initio calculations on clusters of ions converge in indicating that the features of the centers are due to the polarization of the electron density by the positive charge of the hydrogen in the OH group toward two (or possibly three) equivalent magnesium ions of the vacancy close to the OH group itself. The formation mechanism of the centers is strictly analogous to that occurring upon contact of low ionization energy metals with the surface of MgO leading to the formation of another type of color centers. Partially hydrated MgO samples also give rise to another family of paramagnetic center based on electrons trapped in anion vacancies. This finding indicates that the structure of the partially hydroxylated oxide and the mechanism of its dehydration are still open questions.

INTERACTIONS OF RELATIVISTIC 24Mg NUCLEI WITH EMULSION NUCLEI AT 4.5 GeV/c PER NUCLEON

Nuclear emulsions are used to investigate spallations produced by 108 GeV/c 24Mg nuclei. The main experimental characteristics (inelastic cross-sections and multiplicities of various types of secondary particles and their dependence on the masses of the colliding nuclei) in inelastic interactions of 24Mg nuclei with nuclei of nuclear emulsion at 4.5 GeV/c per nucleon have been studied. The integral multiplicity distribution of disintegrated particles from target nuclei is used to separate the inelastic interactions with the free hydrogen (H), the light (CNO), and the heavy (AgBr) nuclei. Multiplicity scaling in the shower particles obeys a scaling function of Koba-Neilsen-Olesen (KNO) type in this energy region.

Nuclear clusters and nuclear molecules

The idea that clusters of nucleons might exist in the nucleus has a long history and dates back to the earliest days of nuclear physics. Recently there have been significant advances in our theoretical treatment of clustering and in the experimental methods available to identify cluster structure in nuclei. These developments are reviewed with particular reference to the 24Mg nucleus where a rich variety of cluster configurations is observed.

Spectroscopic factors from one-proton stripping reactions on sd-shell nuclei: experimental measurements and shell-model calculations

The ( 3He,d) reaction has been investigated at 25 MeV on the target nuclei 16O, 18O, 19F, 23Na, 24Mg, 25Mg, 26Mg, 27Al, 28Si, 29Si, 30Si, 31P, 32S, 34S, 35Cl, 37Cl and 39K. Attention is restricted to the few even-parity levels in each final nucleus which are strongly populated. Values of the single-nucleon Spectroscopic factors C 2 S are obtained from the differential cross sections measured for these levels by analyzing them in the framework of the DWBA theory of nuclear reactions. The DWBA calculations use sets of 3He and deuteron optical-potential parameters which are experimentally validated and internally consistent. The absolute values of C 2 S thus extracted are rather insensitive to which sets of equivalent optical-model parameters are used in the DWBA analyses (variations of the order of ±15%) and the variations in the relative values for the different transitions are very insensitive to these choices. Most of the sensitivity which does exist can be traced to the specification of the absorptive part of the deuteron potential. The values of C 2S are not sensitive to the presence of spin-orbit terms in either the deuteron or the 3He potential. Contrary to the case for optical-model potentials, however, absolute values of C 2 S are very sensitive to the radius parameter r 0 chosen for the potential which binds the transferred proton, although relative values are almost completely insensitive to this choice. The effects of the spin-orbit part of this bound-state potential on j = l + 1 2 and j = l − 1 2 transitions have also been carefully investigated. Evidence is developed that the radius parameter r s.o. of the spin-orbit part of the bound-state potential should be smaller than that of the central part. The values of C 2 S extracted from the present data both with standard DWBA analyses ( r 0 = r s.o. and a 0 = a s.o.) and with analyses which incorporate a modified treatment of the spin-orbit term of the bound-state potential ( r 0 ≠ r s.o. and a 0 ≠ a s.o.) are compared with the predictions of the USD shell-model hamiltonian. The ratios between the experimentally based spectroscopic factors and the model predictions exhibit a marked difference between transitions into the 1 d 3 2 orbit and transitions into the 1 d 5 2 orbit when the standard DWBA analysis is used. However, this difference between 1d 3 2 and 1d 5 2 transitions is greatly reduced if, while the conventional values r 0 = 1.25 fm and a 0= 0.65 fm continue to be used for the central component of the bound-state potential, values of r s.o. = 1.00 fm and a s.o. = 0.52 fm are used for the spin-orbit part.

EVIDENCE OF INTRA- AND INTERGROUP AZIMUTHAL CORRELATIONS IN NUCLEAR INTERACTIONS AT A FEW GeV/c

The paper presents new data on azimuthal correlations in angles between different types of secondary charged particles emitted in inelastic interactions between 24Mg nuclei with the AgBr nuclei of nuclear emulsion. Azimuthal correlations are observed in some cases of intergroup correlations, and an asymmetry is found to exist in the emission of the same type of particles. The present data is compared in some cases, with those of p-emulsion, d-emulsion, α-emulsion and 12C-emulsion interactions at 4.5 A GeV/c and 84Kr-emulsion interaction at 1.4 A GeV.

Shapes of N = Z nuclei in the mass A = 20–48 region

The shapes of the even-even N = Z nuclei 20Ne, 24Mg, 28Si, 32S, 36Ar, 40Ca, 44Ti and 48Cr are studied using axially symmetric deformed relativistic mean-field theory. Large deformations (|β| ∼ 0.5) for ground states and hyperdeformations (β ∼ 1.5 and larger) for excited configurations are found for these nuclei. We obtain hyperdeformed states ( β = 5.2, β = 6.5 and β = 5.7) for 20Ne, 32S and 36Ar about 54, 50 and 73 MeV, respectively, above the ground configurations.

A Molecular Model for High-Spin Heavy-Ion Resonances

A new molecular model is presented in detail, in which collective motions of the di-nuclear system are described in the rotating molecular frame. The model is applied to high-spin resonances observed in 24Mg + 24Mg scattering. A stable configuration of the system is found to be a pole-pole one, due to the prolate shape of the 24Mg nuclei. Normal modes at the equilibrium are solved to give rise to various molecular levels, which appear to be in good correspondence with the experiment.

Coupled channel calculations for 24Mg+24Mg and implications for molecular configurations with pole-to-pole orientation

Coupled channels calculations for 24Mg+24Mg are performed. The employed coupling potential is expanded around a molecular pole-to-pole configuration of the two prolate 24Mg nuclei. The resulting Schrodinger equation is solved and the decay widths of the corresponding molecular eigenstates are calculated. A formalism for a coupled channel calculation which explicitly considers these molecular states is presented.

On resonances of the 24Mg+ 24Mg system

Resonances in heavy-ion scattering of 24 Mg+ 24 Mg are studied by the use of a new molecular model, in which collective motions of the system are described in the rotating molecular frame of the di-nuclear system. A stable configuration of the system is found to be a pole-pole one, due to the prolate shape of the 24Mg nuclei. Normal modes at the equilibrium are solved and various molecular levels are obtained, which appear to be in good correspondence with experiment.

Contracted symplectic model with ds-shell applications

A contracted version of the symplectic model, with the raising and lowering generators of Sp(6, R) replaced by boson creation and annihilation operators, is presented. The symmetry of this scheme is shown to be Ub(6) × Us(3) where Us(3) is the familiar 0/khω Elliott shell-model symmetry and Ub(6) is the group of the six-dimensional oscillator that is generated by bilinear products of the boson (l = 0 and 2) creation and annihilation operators. While this boson symmetry is realized in the same way as the U(6) group of the IBA model, they are different theories because in the present case the bosons are associated with intershell excitations and not intrashell ones. This scheme is also known as the U(3) boson model. Mathematical justification for the simplifying assumptions is provided through an application of the group deformation mechanism. A simple hamiltonian that takes into account the shell structure, couplings to major shells through a quadrupole-quadrupole interaction, and a residual rotor term is expressed in terms of generators of the Ub(6) × Us(3) model. Calculated excitation spectra and E2 transition strengths for the ds-shell nuclei 20Ne, 22Ne and 24Mg are compared with the available experimental numbers.

Systematic Construction Method of Multi-Cluster Pauli-Allowed States

We review the projection method to construct systematically the Pauli· allowed states of multi· cluster systems with the use of the concept of the 5U(3) fractional parentage coefficients. Applying the projection method, we obtain the Pauli· allowed states of 4a and 5a systems. In certain cases in which the system includes non·a clusters or core + na, we show that the projection method proposed by Horiuchi should be generalized to obtain the correct Pauli· allowed states. Using an advanced form of the projection method, we obtain the Pauli·allowed states of a+3N + N, 2a+3N + N, 12C+3a and 160+3a systems. In order to construct the Pauli· allowed states with higher harmonic oscillator quanta, we propose a useful method with the help of the raising operators in the 5p(6, R) group with respect to degrees of freedom of relative motion between clusters. l ) of the cluster structure have been carried out for low-lying states up to 10~ 15 MeVexcitation energy of 8Be~24Mg nuclei by using two-cluster and simple three-cluster models such as 3a and l60+2a. For highly-excited states we have to treat more complex multi-cluster models, because various kinds of multi-cluster configurations are expected to be activated with increase of the excitation energy as shown in the Ikeda diagram. However calculations of complex multi-cluster models are not easy due to the increase of degrees of freedom. Therefore, it is necessary to develop further the treatment of the multi-cluster model. The investigation of the model space of the multi-cluster systems is very impor­ tant to the microscopic study of the multi-cluster models. 4 ) Especially, construction of the Pauli-allowed states (PAS's) is indispensabie for the orthogonality condition model (OCM)5) which takes account of an important role of the Pauli principle on the relative motion of the multi-cluster system. The PAS's are obtained by solving an eigenvalue problem of the norm kernel for the cluster system. Recently, a great progress of the method how to calculate the norm kernel and how to solve the eigenvalue equation has been performed by Fujiwara and Hbriuchi 6 ) and Hecht et a1. 7 ) However, it is still not easy and it requires long computer time to obtain many PAS's of the complex multi-cluster system up to large values of the total harmonic oscillator quantum number. Another method, called the projection method, to construct PAS's of the multi­ cluster system has been proposed by HoriuchL 8 ),4) This method is based on the hypothesis that the functional space Hn spanned by all the PAS's of the multi-cluster

Has the nucleus 24Mg a triaxial shape? a relativistic investigation

We report on the first 3D calculations using the Walecka model: The ground state shape of the nucleus 24Mg is investigated within the framework of a constrained three-dimensional relativistic mean field Theory. The energy surface is calculated as a function of the quadrupole deformation parameters β and γ, using several parameter sets from the literature. We find a minimum at an axially symmetric prolate deformation, which is in full agreement with recent non-relativistic density dependent Hartree-Fock calculations using Skyrme forces.

The deformation of23Na from inelastic alpha scattering

Inelastic scattering of 42 MeV alpha particles on 23Na has been measured to the low-lying members of the ground-state rotational band. Angular distributions for these states have been analysed in a coupled-channels framework to determine quadrupole and hexadecapole deformation lengths. The results indicate a deformation for 23Na comparable to the neighbouring 24Mg nucleus.

Partial photonucleon cross sections and the 24Mg giant dipole resonance

The ( γ, n i ) cross sections in the region of the giant dipole resonance (GDR) of the self-conjugate 24Mg nucleus have been obtained on the basis of the experimental ( γ, p i ) cross sections ( i specifies states of the final nucleus) and the isospin symmetry of photonucleon decays. In the ( γ, n i ), ( γ, p i ) cross sections, the total photonucleon cross sections, and the photoabsorption cross sections, we have identified the components due to semidirect GDR decay using the ratios of the semidirect decay widths resulting from the R-matrix theory. In the integrated photoabsorption, photoproton, and photoneutron cross sections the probability of semidirect decays was found to be 57–67%, 45–60%, and 80–90%, respectively. The semidirect decays dominate in the low-energy (<22 MeV) group of the GDR containing the transitions 1 d2 s → 1 f2 p and 1 p 1 2 → 1 d2 s and the statistical decays dominate in the high-energy (> 22 MeV) group of the transitions 1 p 3 2 → 1 d2 s .

Nuclear shape-isomeric vibrations

It is argued that the correlated resonances observed in low-energy collisions of light heavy-ions may be vibrational-rotational states built on the shape-isomeric configurations of the composite nuclear system. These states are calculated for the shape-isomer of the 24Mg nucleus by studying the response of the system to an external perturbation.

Excitation of the even-even nuclei 24Mg, 28Si and 32S by neutron scattering at incident energies between 7 and 14 MeV

Neutron scattering on 24Mg, 28Si and 32S was studied in the incident energy range from 7 to 14 MeV. In the experiment natural samples and the time-of-flight technique were used. The theoretical analysis was extended including other experiments to bombarding energies around 14 MeV. The excitation of the first 2 + levels shows for these nuclei, despite their quite different nulcear structure, some similarities. For 24Mg also higher-lying states up to E x = 6.01 MeV have been investigated. The sum of compound-reaction and collective-model contributions reasonably reproduces all the experimental data.

Analysis of fragmented GQR in the nucleus24Mg

The fragments of the isoscalar giant quadrupole resonance (GQR) found in the ( alpha , alpha ') reaction on the nucleus 24Mg have been analysed by two different methods developed by MacDonald and by Monahan and Elwyn. These methods permit one to determine the position, the spreading width and the strength of the simple structure state mixed into the more complicated neighbouring states by the coupling interaction. In this way the parameters of the GQR were determined: the position Ex=18.1 MeV, the spreading width Gamma down arrow =3.0 MeV and the strength is 75% of the energy-weighted sum rule (EWSR), in good agreement with both methods. The analysis of different reactions exciting the same energy region of the nucleus 24Mg has helped to clarify the question of the correlation between the different channels.

Configuration Space, Cranked Hartree-Fock Calculations for the Nuclei 16O, 24Mg and 32S

Configuration Space, Cranked Hartree-Fock Calculations for the Nuclei 16O, 24Mg and 32S

Transferred hyperfine interactions between25Mg nuclei and neighbouring Cr3+impurities in magnesium oxide (ENDOR study)

Using the ENDOR technique, magnetic hyperfine and quadrupole interactions of 25Mg nuclei close to Cr3+ and Ni2+ substitutional impurities in MgO have been measured. The results are discussed in terms of the amount of unpaired spin in the Mg2+ orbitals. It is shown that the size of the isotropic part of the magnetic hyperfine interaction is explained better if the Mg2+ 1s orbitals are included in the calculation that if only the outer, 2s orbitals are used. The anisotropic part is described well by a combination of the effects of the magnetic dipole interaction and the overlap of Mg2+ 2p orbitals with O2+ orbitals containing unpaired spin. The quadrupole interactions can only be partly analysed because of insufficient information but it is shown that charge transfer only accounts for a small part of the observed interactions.