Neutron Quadrupole Research Articles

Handling the Functional Features of Accelerator Components Using ISO GPS Situation Features

The building blocks of a scientific facility based on particle beams comprise magnets and electro-magnetic devices. The optical design usually imposes a demanding accuracy with respect to their theoretically exact position and orientation. It happens that the functional features are either not clearly defined – what is the « axis » of a magnet –, or not explicitly used along their lifecycle. Improving how to handle these functional features would contribute to meeting demanding challenges. The European Spallation Source (ESS) is aiming at providing a powerful proton linear accelerator and a target system to produce pulsed neutrons. The challenging complex design and integration yielded to introducing a tool shared in common by all stakeholders along the lifecycle: the “situation features”, as defined in ISO GPS (Geometrical Product Specifications) standards. They are here developed, and extended to beyond-mechanics use cases. Two examples of fiducialization and installation phases are presented for neutron beam guides and quadrupole magnets. Perspectives of generic use are also highlighted.

Directional dependence of the event-by-event neutron- γ multiplicity correlations in Cf252(sf)

We differentiate the event-by-event n-$\gamma$ multiplicity data from \ce{^{252}Cf}(sf) with respect to the energies of the emitted particles as well as their relative angles of emission. We determine that neutron emission enhances $\gamma$-ray emission around $0.7$ and $1.2$ MeV, but the only directional alignment was observed for $E_\gamma \leq 0.7$ MeV and tended to be parallel and antiparallel to neutrons emitted in the same event. The emission of $\gamma$ rays at other energies was determined to be nearly isotropic. The presence of the emission and alignment enhancements is explained by positive correlations between neutron emission and quadrupole $\gamma$-ray emission along rotational bands in the de-exciting fragments. This observation corroborates the hypothesis of positive correlations between the angular momentum of a fragment and its intrinsic excitation energy. The results of this work are especially relevant in view of the recent theoretical and experimental interest in the generation of angular momentum in fission. Specifically, we have determined an alignment of the fragments angular momenta in a direction perpendicular to the direction of motion. We interpret the lack of $n$-$\gamma$ angular correlations for fission fragments near closed shells as a weakening of the alignment process for spherical nuclei. Lastly, we have observed that statistical $\gamma$ rays are emitted isotropically, indicating that the average angular momentum removed by this radiation is small. These results, and the analysis tools presented in this work, represent a stepping stone for future analysis of $n$-$\gamma$ emission correlations and their connection to angular momentum properties.

Quadrupole moments and proton-neutron structure in p -shell mirror nuclei

Electric quadrupole ($E2$) matrix elements provide a measure of nuclear deformation and related collective structure. Ground-state quadrupole moments in particular are known to high precision in many $p$-shell nuclei. While the experimental electric quadrupole moment only measures the proton distribution, both proton and neutron quadrupole moments are needed to probe proton-neutron asymmetry in the nuclear deformation. We seek insight into the relation between these moments through the ab initio no-core configuration interaction (NCCI), or no-core shell model (NCSM), approach. Converged ab initio calculations for quadrupole moments are particularly challenging due to sensitivity to long-range behavior of the wave functions. We therefore study more robustly converged ratios of quadrupole moments: across mirror nuclides, or of proton and neutron quadrupole moments within the same nuclide. In calculations for mirror pairs in the $p$ shell, we explore how well the predictions for mirror quadrupole moments agree with experiment and how well isospin (mirror) symmetry holds for quadrupole moments across a mirror pair. The comparison with experiment confirms the predictive power of the ab initio description, indicating that the predicted ratios are physically relevant for understanding proton-neutron structure as well.

Quadrupole phonon excitations and transition probabilities for low-lying states of neutron-rich Cd isotopes

In this paper we study the low-lying states of neutron-rich $^{122,124,126,128}\mathrm{Cd}$ and $^{130,132,134,136,138}\mathrm{Cd}$ within the nucleon-pair approximation of the shell model. We adopt the phenomenological Hamiltonian for $^{122,124,126,128}\mathrm{Cd}$, and the shell-model effective interaction $jj46$ for $^{130,132,134,136,138}\mathrm{Cd}$. The available experimental excitation energies and quadrupole transition probabilities are well reproduced by our calculation, and we also make predictions for very neutron-rich Cd nuclei. Based on our calculation, the $B(E2;{0}_{\mathrm{g}.\mathrm{s}.}^{+}\ensuremath{\rightarrow}{2}_{1}^{+})$ values exhibit an asymmetric feature with respect to the $N=82$ shell closure, which mainly comes from the contributions of the proton transition matrix elements. We also investigate for the eight open-shell Cd nuclei, whether two low-lying yrast states with spins differing by 2 can be connected by a quadrupole-phonon excitation, and here we take the proton and neutron quadrupole operators multiplied by $1/{r}_{0}^{2}$ as our quadrupole phonon operators. We calculate explicit overlaps between the low-lying yrast states and the constructed quadrupole-phonon states based on the low-lying yrast states with lower spins, and the results indicate that, for all eight open-shell Cd nuclei, $|{2}_{1}^{+}\ensuremath{\rangle}$ and $|{4}_{1}^{+}\ensuremath{\rangle}$ can be well described to be the states constructed by coupling the proton or neutron phonon to $|{0}_{\mathrm{g}.\mathrm{s}.}^{+}\ensuremath{\rangle}$ and $|{2}_{1}^{+}\ensuremath{\rangle}$, respectively. Very interestingly, for $^{126,124,122}\mathrm{Cd}$ and $^{136,138}\mathrm{Cd}$, the ${2}_{1}^{+}$ state can be well described to be both the proton phonon state and the neutron phonon state, which indicates a nonorthogonal feature of these two phonon states. We further present an analytic relation for the overlap between these two phonon states, which implies that the proton and neutron phonon states constructed using the quadrupole operators and the ${0}_{\mathrm{g}.\mathrm{s}.}^{+}$ state in an open-shell nucleus are almost impossibly orthogonal.

Investigation of some nuclear structure properties of213Bi,201Tl,188Re,186Re,133Xe,131I,125I,123I,111In,94Tc,90Y,67Ga,67Cu,62Cu,61Cu,55Co, and48Vnuclei used in SPECT in axial deformation

The present work mainly purposed to investigate significant nuclear structure properties nuclei used in single photon emission computed tomography (SPECT), in addition to ground state nuclear properties such as the binding energy per particle, the root mean square (rms) charge, and proton and neutron radii. Besides, we calculated the neutron skin thicknesses (NST), the proton, neutron quadrupole moments ($Q_{P}, Q_{N})$, quadrupole deformation parameter ($\beta_{2})$, and the proton and neutron pairing energies ($P_{P}, P_{N})$ to determine shapes and deformations of SPECT nuclei including odd-odd or odd-even/even-odd nuclei in axial symmetry for Skyrme and Gogny interactions. To analyze the accuracy of the calculated results, the calculated results were compared with available experimental and the theoretical finite-range liquid-drop model (FRDM), and discussed for 12 different force interactions. Notably, the results provide thorough nuclear data to the literature for deformed nuclei of SPECT.

Investigation of the existence of new nuclear magic number in even-even O isotopes using shell model and Hartree–Fock Bogoliubov method

In the present work, the features of some excited states in some even–even 14-26O isotopes have been investigated. The aim is to predict the evaluated existence of magic numbers in these isotopes using shell model and Hartree-Fock Bogoliubov method based on SLy4, SkC, SkD Skyrme parameterizations. In particular, root mean square radius, binding energies, one and two neutron separation energies, pairing gaps, transition probabilities, excitation energies, energy levels, transition densities and quadrupole deformation parameters have been investigated. The results are compared with the available experimental data.

Neutron quadrupole transition strength in C10 deduced from the C10(α,α′) measurement with the MAIKo active target

Elastic and inelastic alpha scatterings on $^{10}$C were measured using a 68-MeV/u radioactive $^{10}$C beam incident on the recently developed MAIKo active target system. The phenomenological effective $\alpha$-$N$ interaction and the point-nucleon density distribution in the ground state were determined from the elastic scattering data. The cross sections of the inelastic alpha scattering were calculated using this interaction and density distribution and were compared with the experiment to determine the neutron quadrupole transition matrix element $M_{n}$ between the ground state and the $2_{1}^{+}$ state at $E_{x} = 3.35$ MeV in $^{10}$C. The deduced neutron transition matrix element is $M_{n} = 6.9\, \pm0.7\, \mathrm{(fit)}\, \pm1.2\, \mathrm{(sys)}$ fm$^{2}$. The ratio of the neutron transition strength to proton transition strength was determined as $M_{n}/M_{p} = 1.05\, \pm0.11\, \mathrm{(fit)}\, \pm0.17\, \mathrm{(sys)}$, which indicates that the quadrupole transition between the ground state and the $2_{1}^{+}$ state in $^{10}$C is less neutron dominant compared to that in $^{16}$C.

Observation of excited states in Mg20 sheds light on nuclear forces and shell evolution

The exotic Borromean nucleus $^{20}$Mg with $N$ = 8, located at the proton drip-line provides a unique testing ground for nuclear forces and the evolution of shell structure in the neutron-deficient region. We report on the first observation of proton unbound resonances together with bound states in $^{20}$Mg from the $^{20}$Mg($d$,$d'$) reaction performed at TRIUMF. Phenomenological shell-model calculations offer a reasonable description. However, our experimental results present a challenge for current first-principles nuclear structure approaches and point to the need for improved chiral forces and {\it ab initio} calculations. Furthermore, the differential cross section of the first excited state is compared with distorted-wave Born approximation calculations to deduce a neutron quadrupole deformation parameter of $\beta_n$=0.46$\pm$0.21. This provides the first indication of a possible weakening of the $N$ = 8 shell closure at the proton drip-line.

A study of some nuclear structure properties of 11C, 13N, 15O, 18F, 52Mn, 52Fe, 60Cu, 62Zn, 63Zn, 66Ga, 68Ga, 76Br, 81Rb, 82Rb, 82Sr, 83Sr, 86Y, 89Zr and 92Rb nuclei used for PET in the axial deformation

In this paper, we mainly investigated important nuclear structure properties of nuclide used in positron-emission tomography for 13 different Skyrme force parameters in the axial deformation such as the binding energy, root mean square charge, proton and density radii, neutron skin thicknesses, quadrupole deformation parameter (β2), proton and neutron quadrupole moments (Qm). To analyze accuracy of the obtained results, the calculated data also were compared with available experimental and the theoretical results in the literature, such as relativistic mean-field theory and the finite-range liquid-drop model. According to Hartree–Fock–Bogolyibov approach with the axial deformation, we discussed Skyrme force parameters on the basis of the obtained result. Further, when taking into account the enormous number of the existing Skyrme-force parameterizations, it has been noticed the obtained results reveal appropriate Skyrme force parameters for each nucleus.

Matrix elements of the proton–neutron symplectic model

The tensor properties of the [Formula: see text] algebra generators are determined in respect to the reduction chain [Formula: see text], which defines a shell-model coupling scheme of the proton–neutron symplectic model (PNSM). They are further used to calculate the matrix elements of the basic [Formula: see text] operators of the PNSM in the space of fully symmetric representations in the [Formula: see text]-coupled basis using a generalized Wigner–Eckart theorem. The obtained results allow further the matrix elements of any physical operator of interest, such as the relevant transition operators or the collective potential, to be calculated. As an illustration, the matrix elements of the basic irreducible tensor terms which appear in the [Formula: see text] decomposition of the long-range full major-shell mixing proton–neutron quadrupole–quadrupole interaction are presented.

E2 decay strength of the M1 scissors mode of ^{156}Gd and its first excited rotational state.

The E2/M1 multipole mixing ratio δ_{1→2} of the 1_{sc}^{+}→2_{1}^{+} γ-ray decay in ^{156}Gd and hence the isovector E2 transition rate of the scissors mode of a well-deformed rotational nucleus has been measured for the first time. It has been obtained from the angular distribution of an artificial quasimonochromatic linearly polarized γ-ray beam of energy 3.07(6)MeV scattered inelastically off an isotopically highly enriched ^{156}Gd target. The data yield first direct support for the deformation dependence of effective proton and neutron quadrupole boson charges in the framework of algebraic nuclear models. First evidence for a low-lying J^{π}=2^{+} member of the rotational band of states on top of the 1^{+} band head is obtained, too, indicating a significant signature splitting in the K=1 scissors mode rotational band.

Semi-phenomenological description of the chiral bands in 188,190Os

A set of interacting particles are coupled to a phenomenological core described using the generalized coherent state model. Among the particle–core states, a finite set which have the property that the angular momenta carried by the proton and neutron quadrupole bosons and the particles, separately, are mutually orthogonal are identified. The magnetic properties of such states are studied. All terms of the model Hamiltonian exhibit chiral symmetry except the spin–spin interaction one. There are four bands of the type with two-quasiparticle–core dipole states, exhibiting properties which are specific to magnetic twin bands. An application is presented, for the isotopes Os.

A new picture for the chiral symmetry properties within a particle–core framework

The generalized coherent state model (GCSM), proposed previously for a unified description of magnetic and electric collective properties of nuclear systems, is extended to account for the chiral-like properties of nuclear systems. To a phenomenological core described by the GCSM, a set of interacting particles is coupled. Among the particle–core states, one identifies a finite set which has the property that the angular momenta carried by the proton and neutron quadrupole bosons and the particles, respectively, are mutually orthogonal. All terms of the model Hamiltonian satisfy the chiral symmetry except for the spin–spin interaction. The magnetic properties of the particle–core states, where the three mentioned angular momenta are orthogonal, are studied. A quantitative comparison of these features with the similar properties of states, where the three angular momenta belong to the same plane, is performed.

Performance Analysis of Techniques Used for Determining Land Mines

Today, remote sensing is used for different methods and different purposes. In all of the detection methods, some considerations such as low energy consumption, low cost, insensitivity to environmental changes, high accuracy, high reliability and robustness become important. Taking into account these facts, remote sensing methods are used in applications such as geological and archeological research, engineering areas, health services, preserving and controlling natural life, determination of underground sources, controlling air, sea and road traffic, military applications, etc. The method to be used is based on the object type to be detected, material to be made, and location to be found. The remote sensing methods from the past up to today can be listed as acoustic and seismic, ground penetration radar (GPR) detection, electromagnetic induction, infrared (IR) imaging, neutron quadrupole resonance (NQR), thermal neutron activation (TNA), neutron back scattering, X-ray back scattering, and magnetic anomaly detection. In these methods, detected raw images have to be processed, filtered and enhanced. In order to achieve these operations, some algorithms are needed to be developed. In this study, the methods used in detecting land mines remotely and their performance analysis have been given. In this way, the last situation on the advantages and disadvantages of methods used, application areas and detection accuracies are determined. Furthermore, the algorithms such as transmission line matrix (TLM), finite difference time-domain (FDTD), the method of moment (MoM), split step parabolic equation (SSPE) and image processing and intelligent algorithms are presented in detail.

RELATIVISTIC MEAN FIELD STUDY OF ISLANDS OF INVERSION IN NEUTRON-RICH Z = 17–23, 37–40 AND 60–64 NUCLEI

We study the extremely neutron-rich nuclei for Z = 17–23, 37–40 and 60–64 regions of the periodic table by using axially deformed relativistic mean field formalism with NL3* parametrization. Based on the analysis of binding energy, two neutron separation energy, quadrupole deformation and root mean square radii, we emphasized the speciality of these considered regions which are recently predicted islands of inversion.

Evolution of the one-phonon [formula omitted] mixed-symmetry state in [formula omitted] isotones as a local measure for the proton–neutron quadrupole interaction

An inverse kinematics Coulomb excitation experiment was performed to obtain absolute E2 and M1 transition strengths in 134Xe. The measured transition strengths indicate that the 23+ state of 134Xe is the dominant fragment of the one-phonon 21,ms+ mixed-symmetry state. Comparing the energy of the 21,ms+ mixed-symmetry state in 134Xe to that of the 21,ms+ levels in the N=80 isotonic chain indicates that the separation in energy between the fully-symmetric 21+ state and the 21,ms+ level increases as a function of the number of proton pairs outside the Z=50 shell closure. This behavior can be understood as resulting from the mixing of the basic components of a two-fluid quantum system. A phenomenological fit based on this concept was performed. It provides the first experimental estimate of the strength of the proton–neutron quadrupole interaction derived from nuclear collective states with symmetric and antisymmetric nature.

First lifetime measurement of [formula omitted] state in 12Be

The lifetime of the 21+ state at 2.1 MeV in 12Be has been measured using inelastic scattering of a 12Be beam at 43 MeV/nucleon with a gold target. Through the Doppler shift attenuation method, the mean-life of the 21+ state has been determined as 2.5±0.7 (stat) ±0.3 (syst) ps, which gives a B(E2;21+→0g.s.+) value of 4.9±1.3±0.5 in Weisskopf units. The result shows a large quadrupole strength in the ground state transition, providing further evidence on the disappearance of the N=8 magic number. The B(E2;21+→0g.s.+) value together with the deformation length measured by proton inelastic scattering yields a neutron quadrupole matrix element two times larger than those for 14C and 16O.

Shape Evolution of C Isotopes in (β, γ) Deformation Plane

We study the shape evolution of C isotopes in the full (beta, gamma) deformation plane using a constrained Skyrme Hartree-Fock + BCS method in coordinate space. It is shown that; the reformation of the energy minimum varies markedly in the (beta, gamma) plane as a. function of mass number; which can be viewed as a clear manifestation of the spontaneous symmetry breaking effect in finite many-body systems. We also study the difference in deformations between protons and neutrons in the total (beta, gamma) plane. It is found that the proton and neutron quadrupole moments are almost the same in light C isotopes; while the neutron quadrupole moment is about 3 times larger than the proton one in C isotopes heavier than (16)C. The isospin symmetry of the mirror nuclei (10)C and (10)Be is also examined in connection with the deformation in the (beta, gamma) plane.

Fission barriers in the neutron-proton isospin plane for heavy neutron-rich nuclei

We discuss the sensitivity of fission barrier for heavy neutron-rich nuclei to fission paths in the two-dimensional neutron-proton quadrupole plane. To this end, we use the constrained Skyrme-Hartree-Fock + BCS method, and examine the difference of fission barriers obtained with three constraining operators, that is, the neutron, proton, and mass quadrupole operators. We investigate $^{220}\mathrm{U}$, $^{236}\mathrm{U}$, and $^{266}\mathrm{U}$, that is relevant to r-process nucleosynthesis. We find that the fission barrier heights are almost the same among the three constraining operators even for neutron-rich nuclei, indicating that the usual way to calculate fission barriers with the mass quadrupole operator is well justified. We also discuss the difference between proton and neutron deformation parameters along the fission paths.

Enhancement of neutron quadrupole motion beyondN=8

For Be and C isotopes with $N>8$, the shell-model study with $2\ensuremath{\hbar}\ensuremath{\omega}$ basis states shows the enhancement of neutron quadrupole matrix elements. The neutron-rich nuclei such as $^{14}\mathrm{Be}$ and $^{16}\mathrm{C}$ have a few neutrons in the $1{s}_{1/2}$ and $0{d}_{5/2}$ orbits, and the neutrons in these orbits give the large neutron quadrupole motion because these orbits have almost the same single-particle energies. A large ratio of proton and neutron quadrupole matrix elements in these nuclei indicates decoupled motions of proton and neutron, which are suggested in the measurements of the $B(E2)$ values.