Quadrupole Pairing Research Articles

Quantum-number-projected generator-coordinate-method analysis of low-lying states in nuclei around mass 80

The quantum-number-projected generator coordinate method (QNPGCM) is applied to the neutron-rich Ge and Se isotopes where the monopole and quadrupole pairing plus quadrupole-quadrupole interaction is employed as an effective interaction. The energy spectra calculated with both axial and triaxial deformations are compared to the shell-model results and the experimental data. In both cases, the QNPGCM reproduces well the energy levels of the even-spin yrast states. However, the QNPGCM results by only assuming axial deformations are not satisfactory enough to reproduce the energy levels of the quasi-$\ensuremath{\gamma}$ bands. Taking account of triaxial deformations is essentially important to describe the yrast and quasi-$\ensuremath{\gamma}$ bands simultaneously.

Magnetic anisotropy in uranium monosulfide probed by magnetic torque measurements

We have studied the magnetic torque in uranium monosulfide (US) single crystals to explore the magnetic anisotropy in this material. Uranium monosulfide crystallizes in cubic, NaCl-type of crystal structure and exhibits the largest magneto-crystalline anisotropy observed in cubic systems. By performing detailed torque measurements we observe a strongly anisotropic behavior in the paramagnetic phase due to crystal defects and quadrupolar pair interactions. Our studies also confirm the presence of a large anisotropy in the ferromagnetic state of the US system with the <100>, <111>, and <110> directions being hard, easy, and intermediate axis, respectively. Furthermore, the anisotropy in the paramagnetic phase shows similar characteristics to the anisotropy observed in the ferromagnetic phase, as characterized by second and fourth rank susceptibility terms. The similarity of the anisotropic behaviors in paramagnetic and ferromagnetic phases is the consequence of strong magneto-elastic properties in this system, which possibly lead to the rhombohedral structural distortion, not only in the ferromagnetic phase but also in the paramagnetic phase (induced by applied magnetic fiield).

Computational evaluation of a new digital tandem quadrupole mass filter.

A tandem mass filter consists of two low-resolution mass filters arranged in series that operate with a small offset between their mass windows. In principle, the overlap of the two individual mass windows defines the tandem window. Tandem operation provides improved resolution and transmission compared to a single mass filter operated with the same mass window. The improvement in transmission is owed to the larger acceptance of the low-resolution quadrupoles. The tandem filter resolution and transmission are adjusted by changing the amount of offset separating the mass windows of the individual filters. Sine wave systems create this offset through voltage changes. Digital tandem mass filters depart from convention because they do not change voltage. The tandem mass window is created when the individual filters are operated with two slightly different duty cycles. Both quadrupoles operate at the same frequency, phase, and voltage. When the frequency, phase, and voltage of each quadrupole are identical, there theoretically are no changes to the Mathieu parameters to cause ion excitation and loss during transition between the quadrupole pair. The work presented here shows that a fixed AC voltage digital tandem mass filter can only operate in higher stability zones. However, unlike sine mass filters, the mass range of a digital system is not limited. This makes the digital tandem mass filter feasible as a commercial product. For the tandem digital mode to be successful, the duty cycles of each quadrupole must be precisely controlled because the duty cycle differences required to shift the mass windows are small. The creation of these mass window offsets requires waveform generation that can obtain high duty cycle resolution. Our method of generating waveforms can meet this demand; however, modifications to our current printed circuit board must be made. These modifications are minor and will be discussed.

Electromagnetic properties of neutron-rich Ge isotopes * * Supported by National Natural Science Foundation of China (11875188), Open Project Fund of Shanghai Key Laboratory of Particle Physics and Cosmology (18DZ2271500-2), Sichuan Science and Technology Program (2019JDRC0017), and the Doctoral Program of Southwest University of Science and Technology (18zx7147)

The electric quadrupole moment and the magnetic moment (or the factor) of low-lying states in even-even nuclei 72-80Ge and odd-mass nuclei 75-79Ge are studied in the framework of the nucleon pair approximation (NPA) of the shell model, assuming the monopole and quadrupole pairing plus quadrupole-quadrupole interaction. Our calculations reproduce well the experimental values of and for 72,74,76Ge, as well as the yrast energy levels of these isotopes. The structure of the states and the contributions of the proton and neutron components in and are discussed in the -pair truncated shell-model subspace. The overall trend of and as a function of the mass number , as well as their signs, are found to originate essentially from the proton contribution. The negative value of in 72,74Ge is suggested to be due to the enhanced quadrupole-quadrupole correlation and configuration mixing.

Particle- $\gamma$ γ coincidence spectroscopy of the N = 90 nucleus 154Gd by ( $p,t\gamma$ p , t γ )

A segmented Si-telescope and HPGe array, STARS-LIBERACE, was used to study the 156Gd( $p,t\gamma$ )154Gd direct reaction by particle- $ \gamma$ coincidence spectroscopy. New cross sections with a 25MeV proton beam are reported and compared to previous (p,t) and (t,p) studies. Furthermore, additional evidence for coexisting $ K^{\pi}=0_{1}^{+},2_{1}^{+}$ and $0_{2}^{+}$ , $2_{2}^{+}$ configurations at N = 90 is presented. Direct and indirect population patterns of the low-lying states are also explored. Review of the new and existing evidence favors an interpretation based on a configuration-dependent pairing interaction. The weakening of monopole pairing strength and an increase in quadrupole pairing strength could bring 2p-2h $0^{+}$ states below $2\Delta$ . This may account for a large number of the low-lying $0^{+}$ states observed in two-nucleon transfer reactions. A hypothesis for the origin of the $0_{2}^{+}$ and $ 0_{3}^{+}$ states is provided.

Odd-even staggering of binding energy for nuclei in thesdshell

In this paper we study odd-even staggering phenomena of binding energy in the framework of the nuclear shell model for nuclei in the $sd$ shell. We decompose the USDB effective interaction into the monopole interaction and multipole (residual) interactions. We extract the empirical proton-neutron interaction, the Wigner energy, and the one-neutron separation energy using calculated binding energies. The monopole interaction, which represents the spherical mean field, provides contributions to the empirical proton-neutron interaction, the symmetry energy, and the Wigner energy. It does not induce odd-even staggering of the empirical proton-neutron interaction or the one-neutron separation energy. Isovector monopole and quadrupole pairing interactions and isoscalar spin-1 pairing interactions play a key role in reproducing an additional binding energy in both even-even and odd-odd nuclei. The Wigner energy coefficients are sensitive to residual two-body interactions. The nuclear shell structure has a strong influence on the evolution of the one-neutron separation energy, but not on empirical proton-neutron interactions. The so-called three-point formula is a good probe of the shell structure.

A new renormalization procedure of the quasiparticle random phase approximation

The ground state of a many body Hamiltonian considered in the quasiparticle representation is redefined by accounting for the quasiparticle quadrupole pairing interaction. The residual interaction of the newly defined quasiparticles is treated by the quasiparticle random phase approximation (QRPA). Solutions of the resulting equations exhibit specific features. In particular, there is no interaction strength where the first root is vanishing. A comparison with other renormalization methods is presented. Application to a single [Formula: see text]-shell allows for the results interpretation by comparing them with those obtained by exact calculations.

Quasi-particle structure of proton–hole cobalt isotopes

Projected Shell Model calculations have been employed for the description of the ground band in odd mass 57–67Co isotopes. In the present work, quadrupole and monopole pairing interactions as well as quadrupole–quadrupole interactions are effectively included in the Hamiltonian for obtaining various nuclear structure properties using the angular momentum projection technique. The yrast spectra of these isotopes are described as interplay between the angular momentum projected states around the Fermi level. The quasi-particle structure of these nuclei is found to be comprised of different intrinsic K-quantum numbers. Rotational alignments in terms of kinetic moment of inertia (ℑ(1)) have also been discussed. The electromagnetic transition probabilities [B(E2) and B(M1)] are also obtained in the present work and are found to be in good agreement with the available experimental as well as the other theoretical data, which tests the consistency of the applied projected shell model. The present PSM calculations also report the existence of low lying deformed structure along with the spherical structure at N=40.

Application of the generator coordinate method to neutron-rich Se and Ge isotopes

The quantum-number projected generator coordinate method (GCM) is ap- plied to the neutron-rich Se and Ge isotopes, where the monopole and quadrupole pairing plus quadrupole-quadrupole interaction is employed as an effective interaction. The en- ergy spectra obtained by the GCM are compared to both the shell model results and the experimental data. The GCM reproduces well the energy levels of high-spin states as well as the low-lying states. The structure of the low-lying collective states is analyzed through the GCM wave functions.

Fan‐beam intensity modulated proton therapy

This paper presents a concept for a proton therapy system capable of delivering intensity modulated proton therapy using a fan beam of protons. This system would allow present and future gantry-based facilities to deliver state-of-the-art proton therapy with the greater normal tissue sparing made possible by intensity modulation techniques. A method for producing a divergent fan beam of protons using a pair of electromagnetic quadrupoles is described and particle transport through the quadrupole doublet is simulated using a commercially available software package. To manipulate the fan beam of protons, a modulation device is developed. This modulator inserts or retracts acrylic leaves of varying thickness from subsections of the fan beam. Each subsection, or beam channel, creates what effectively becomes a beam spot within the fan area. Each channel is able to provide 0-255 mm of range shift for its associated beam spot, or stop the beam and act as an intensity modulator. Results of particle transport simulations through the quadrupole system are incorporated into the MCNPX Monte Carlo transport code along with a model of the range and intensity modulation device. Several design parameters were investigated and optimized, culminating in the ability to create topotherapy treatment plans using distal-edge tracking on both phantom and patient datasets. Beam transport calculations show that a pair of electromagnetic quadrupoles can be used to create a divergent fan beam of 200 MeV protons over a distance of 2.1 m. The quadrupole lengths were 30 and 48 cm, respectively, with transverse field gradients less than 20 T/m, which is within the range of water-cooled magnets for the quadrupole radii used. MCNPX simulations of topotherapy treatment plans suggest that, when using the distal edge tracking delivery method, many delivery angles are more important than insisting on narrow beam channel widths in order to obtain conformal target coverage. Overall, the sharp distal falloff of a proton depth-dose distribution was found to provide sufficient control over the dose distribution to meet objectives, even with coarse lateral resolution and channel widths as large as 2 cm. Treatment plans on both phantom and patient data show that dose conformity suffers when treatments are delivered from less than approximately ten angles. Treatment time for a sample prostate delivery is estimated to be on the order of 10 min, and neutron production is estimated to be comparable to that found for existing collimated systems. Fan beam proton therapy is a method of delivering intensity modulated proton therapy which may be employed as an alternative to magnetic scanning systems. A fan beam of protons can be created by a set of quadrupole magnets and modified by a dual-purpose range and intensity modulator. This can be used to deliver inversely planned treatments, with spot intensities optimized to meet user defined dose objectives. Additionally, the ability of a fan beam delivery system to effectively treat multiple beam spots simultaneously may provide advantages as compared to spot scanning deliveries.

Band structure of neutron rich Se and Ge isotopes

The band structure of the neutron-rich Se and Ge isotopes has been studied in terms of the full-fledged shell model. The monopole and quadrupole pairing plus quadrupole-quadrupole interaction is employed as an effective interaction. The model reproduces well the energy levels of high-spin states as well as the low-lying states. In order to investigate the structure of the high-spin states and low-lying collective states, the energy spectra in the shell model are compared with those in the quantum-number-projected generator coordinate method. It is shown that the triaxial components play essential roles in describing the γ bands.

Feedback of slow extraction in CSRm

The transverse tune of the beam in a synchrotron will fluctuate due to the main quadrupole power supply ripple, which leads the spill ripple through the variation of the separatrices area. To reduce the spill ripple, an additional pair of fast-response quadrupoles (FQ) is adopted to compensate for the tune ripple caused by the main quadrupoles. After using the FQ feedback, the amplitude of the spill ripple with a frequency of less than 800Hz has been reduced to a tenth of that in the normal mode.

B(E2;01+→21+)values of even-even Sn isotopes

The ${2}_{1}^{+}$ energies and $B(E2;{0}_{1}^{+}\ensuremath{\rightarrow}{2}_{1}^{+})$ values of even-even Sn nuclei with mass numbers between 102 and 130 have been calculated within the framework of the $SD$-pair approximation of the nuclear shell model. We employ monopole and quadrupole pairing plus quadrupole-quadrupole interaction with optimized parameters. Good agreement is obtained between the calculated results and experimental data. The robustness of our calculated ${2}_{1}^{+}$ level and $E2$ transition rates with respect to different sets of effective charge and different forms of the Hamiltonian is studied.

Seniority isomers in nuclei

Seniority isomers are nuclear states with an electromagnetic decay that is hindered by selection rules related to the seniority quantum number. A simple analysis is presented of their possible formation with reference to the nickel isotopes 70–76Ni and the N = 50 isotones from molybdenum to cadmium. It is shown that the existence of seniority isomers in a j = 9/2 shell is predominantly governed by the quadrupole pairing matrix element of the nucleon-nucleon interaction. The analysis is generalized to shells with larger j.

E2transitions in Sn isotopes within the quasiparticle-phonon model

The evolution of the structure of the first ${{2}_{1}}^{+}$ state along the chain of Sn isotopes is investigated within the quasiparticle-phonon model through the analysis of the energies and the $B(E2;{{0}_{1}}^{+}\ensuremath{\rightarrow}{{2}_{1}}^{+})$ strengths. The calculation reproduces the trend of the energies and, partly, the observed deviations of the $E2$ strengths from the parabolic behavior obtained in some large-scale shell-model calculations. Such an asymmetric trend is shown to be the outcome of several factors: single-particle energies, polarization of the $N=Z=50$ core, interplay between pairing plus quadrupole, and quadrupole pairing interactions.

Validity of pair approximations for nuclei in open shells

We study the validity of pair approximations of the nuclear shell model (SM) for a few realistic nuclei (${}^{130\ensuremath{-}131}$Te and ${}^{132}$I here) in open shells (i.e., nuclei with both valence protons and valence neutrons). We take a phenomenological shell model Hamiltonian, which includes the single-particle energy term, monopole and quadrupole pairing interactions for like particles, and quadrupole-quadrupole interactions between all valence nucleons. We make comparisons of energy levels and $B(E2)$ values calculated by pair approximations with those in the SM calculations. The overlaps between wave functions of the nucleon pair approximation (NPA) and those of the SM are presented explicitly for the low-lying states. Our calculated results demonstrate that the NPA is a remarkable approximation of the SM for these nuclei. The important role played by pairs with negative parity in some low-lying states is discussed.

Low-lying structure of neutron-rich Zn and Ga isotopes

Low-lying states of even-even Zn and odd-mass Ga nuclei with neutron numbers between 42 and 50 have been calculated within the framework of the $SDG$-pair approximation of the nuclear shell model. We employ a monopole and quadrupole pairing plus quadrupole-quadrupole interaction with optimized parameters, which are assumed to be constants for nuclei with the same proton number or neutron number. We calculate low-lying level schemes, electric quadrupole and magnetic dipole moments, and $E2$ and $M1$ transition rates. Reasonable agreement is achieved between the calculated results and experimental data. Dominant configurations in the ground states of odd-mass Ga nuclei are discussed in terms of pair correlations. The weak-coupling picture for some states of odd-mass Ga nuclei is studied.

Pair-truncated shell-model analysis of nuclei around mass 130

Low-lying states for even-even, odd-mass, and doubly odd nuclei in the mass $A~130$ region are systematically investigated using a pair-truncated shell model. In this model the collective nucleon pairs with angular momenta zero and two are the basic ingredients for even-even nuclei. Additional unpaired nucleons are added to the even-even core for a description of odd-mass and doubly odd nuclei. The effective interactions consist of single-particle energies and monopole and quadrupole pairing plus quadrupole-quadrupole interactions, whose strengths are assumed to be linearly changed as functions of the number of nucleons so as to describe the level schemes of the even-even and odd-mass nuclei. Energy levels of the low-lying collective states for even-even Xe, Ba, Ce, and Nd isotopes are reproduced very well along with intraband and interband $B(E2)$ values, which simulate the typical features of the O(6) limit of the interacting boson model. For odd-mass and doubly odd nuclei, complicated level schemes and electromagnetic moments are in excellent agreement with the experimental data.

Low-lying states of valence-hole nuclei in the 208Pb region

Systematic calculations of low-lying states for Ir, Pt, Au, Hg and Tl isotopes with neutron numbers between 120 and 125 have been performed within the framework of the SDG-pair approximation of the shell model. We employ a monopole and quadrupole pairing plus quadrupole–quadrupole-type interaction with optimized parameters, which are assumed to be constants for nuclei with the same proton number or neutron number. We calculate binding energies of the ground states, low energy level schemes, electric quadrupole and magnetic dipole moments, and E2 transition rates. Our results are reasonably consistent with the available experimental data as well as previous theoretical studies, in particular, for low-lying yrast states. We also demonstrate that low-lying states of nuclei studied here are usually well represented by very simple configurations in collective nucleon-pair basis.

Does the isotropic–biaxial nematic transition always exist? A new topology for the biaxial nematic phase diagram

The biaxial nematic phase diagram for the second rank Straley quadrupolar pair potential, as explored until now, implies that a direct transition from a biaxial nematic to an isotropic phase can occur, either at a single Landau point or even, as recently shown using mean field theory, along a line. We show by an extensive Monte Carlo investigation that a different topology can be found in a wide region of parameter space, with the passage from biaxial to isotropic always going through a uniaxial phase. We argue that this may hint in part at the difficulty in realising a biaxial nematic phase.