The g-factors and magnetic rotation in 82Rb

The g-factors of the intra-band states 12,13,14,15 in a magnetic-rotational band built on the 11 state in 82 Rb are measured for the first time by using a transient magnetic field-ion implantation perturbed angular distribution (TMF-IMPAD) method.The magnetic-rotational band in 82 Rb is populated by the 60 Ni(27 Al,4pn) 82 Rb reaction,and the time-integral Larmor precessions are measured after recoil implantation into a polarized Fe foil.The calculation of g-factors is also carried out in terms of a semi-classical model of independent particle angular momentum coupling on the basis of the four-quasiparticle configuration π(g 9/2) 2  π(p 3/2,f 5/2)  ν (g 9/2).The measured and calculated g-factors are in good agreement with each other.The g-factors and deduced shear angles decrease with the increase of spin along the band.This clearly illustrates the shear effect of a step-by-step alignment of the valence protons and neutrons in magnetic rotation.The semi-classical calculation also shows that the alignment of the valence neutron angular momentum is faster than that of the valence protons,which results in a decrease of g-factors with increasing spin.The present results provide solid evidence of the shear mechanism of magnetic rotation.     

Study of magnetic-rotation in ~(82)Rb by g-factor measurements

Magnetic rotation in ⁸²Rb has been investigated for the first time by g-factor measurement of intra-band states of the magnetic-rotational band built on the 11- state. The g-factors were measured by a TMF-IMPAD method and calculated by a semi-classical model of independent particle angular momentum coupling assumption. The g-factors and deduced shears angles decrease with the increasing of spin along the band, illustrating a step-by-step alignment of the valence protons and neutrons. The rapid alignment of the valence neutrons leads to a decrease of g-factors. The present results vividly reveal the shears mechanism of magnetic rotation.     

Rotational symmetry of classical orbits, arbitrary quantization of angular momentum and the role of the gauge field in two-dimensional space

We study quantum–classical correspondence in terms of the coherent wave functions of a charged particle in two- dimensional central-scalar potentials as well as the gauge field of a magnetic flux in the sense that the probability clouds of wave functions are well localized on classical orbits. For both closed and open classical orbits, the non-integer angular-momentum quantization with the level space of angular momentum being greater or less than is determined uniquely by the same rotational symmetry of classical orbits and probability clouds of coherent wave functions, which is not necessarily 2π-periodic. The gauge potential of a magnetic flux impenetrable to the particle cannot change the quantization rule but is able to shift the spectrum of canonical angular momentum by a flux-dependent value, which results in a common topological phase for all wave functions in the given model. The well-known quantum mechanical anyon model becomes a special case of the arbitrary quantization, where the classical orbits are 2π-periodic.     

Blocking Effect and Moments of Inertia of K = 1/2 Rotational Band in 171Yb

The K = 1/2 rotational band in 171yb is investigated using the particle number conserving (PNC) method for treating the cranked shell model with monopole and quadrupole pairing interactions. The experimental moments of inertia of 171 Yb [521]1/2 (signature α = 1/2) are reproduced well by the PNC calculation, in which no free parameter is involved. The difference in the contribution to the moment of inertia between protons and neutrons is mainly due to the blocking effect of neutron normal orbitals. The ω variation of the occupation probability of each cranked orbital and the contribution to the moment of inertia from each major shell and from each cranked orbital are investigated.     

Nucleon internal structure: a new set of quark, gluon momentum, angular momentum operators and parton distribution functions

It is unavoidable to deal with the quark and gluon momentum and angular momentum contributions to the nucleon momentum and spin in the study of nucleon internal structure. However we never have the quark and gluon momentum, orbital angular momentum and gluon spin operators which satisfy both the gauge invariance and the canonical momentum and angular momentum commutation relation. The conflicts between the gauge invariance and canonical quantization requirement of these operators are discussed. A new set of quark and gluon momentum, orbital angular momentum and spin operators, which satisfy both the gauge invariance and canonical momentum and angular momentum commutation relation, are proposed. The key point to achieve such a proper decomposition is to separate the gauge field into the pure gauge and the gauge covariant parts. The same conflicts also exist in QED and quantum mechanics and have been solved in the same manner. The impacts of this new decomposition to the nucleon internal structure are discussed.     

The first principles investigation of ferrite magnetic response with mismatch stress

The quasi-ferrite model is proposed and an appropriate PBE exchange functional with the spin density functional theory(SDFT) is selected for the calculation of the relation between magnetic moment and residual stress in ferrite using a quantum mechanics code. The relationship between ferrite magnetism and the carbon content is determined,and then a ferrite interstitial solid solution(ISS) model in a low carbon concentration state is replaced with an α- Fe model in the case of majority magnetic calculation. The band structure of the loaded-Fe is compared with that of the unloaded α-Fe. The comparison shows that the energy of Fe atomic 3d orbital changes a little,while the energy of electron orbital of iron core below 3d almost keeps unchanged. The relationship between the magnetic moment and the stress appears intermittent due to the Bragg total reflection. The change in the magnetic moment due to lattice mismatch is much larger than that caused by mechanical loading.     

一九八三年CUSPEA试题(二)(英文)

Solve 5 of the following 6 problems.B1. Consider a neutral particle with intrinsic angular momentum where S=h/2 i. e. a spin1/2 article. Assume the particle bas a magnetic moment M =rS where r is a constant. Thequantum mechanical state of the particle can be described in a spin space spanned by the eigenvectors | + > and | - > representing alignment parallel and antiparallel to the Z axis. (i.e.Szl + ) ). At time t = 0 the state of the system is >. The particlemoves along the Y axis throug…     

Gauge invariance and quantization applied to atom and nucleon internal structure

The prevailing theoretical quark and gluon momentum,orbital angular momentum and spin operators,satisfy either gauge invariance or the corresponding canonical commutation relation,but one never has these operators which satisfy both except the quark spin.The conflicts between gauge invariance and the canonical quantization requirement of these operators are discussed.A new set of quark and gluon momentum,orbital angular momentum and spin operators,which satisfy both gauge invariance and canonical momentum and angular momentum commutation relation,are proposed.To achieve such a proper decomposition the key point is to separate the gauge field into the pure gauge and the gauge covariant parts.The same conflicts also exist in QED and quantum mechanics,and have been solved in the same manner.The impacts of this new decomposition to the nucleon internal structure are discussed.     

Structure of high spin state in proton-rich ~(74,76,78)Kr isotopes:A projected shell model description

The N≈Z nuclei in the mass A~80 region has been researched because of an abundance of nuclear structure phenomena.The projected shell model(PSM)was adopted to investigate the structure of high spin state in proton-rich 74,76,78Kr isotopes including yrast spectra,moment of inertia,electric quadrupole transitions and the behavior of single particle.The calculated results are in good agreement with available data and the shape coexistence in low-spin is also discussed.     

Electronic and Magnetic Properties of the p-NPNN

In this paper, we study the electronic band structure and the ferromagnetic properties of the organic radical p-NPNN by employing density-functional theory with generalized gradient approximation (GGA ) and local-spin density approximation (LSDA). The density of states, the total energy, and the spin magnetic moment are calculated. The calculations reveal that the δ-phase of p-NPNN has a stable ferromagnetic ground state. It is found that an unpaired electron in this compound is localized in a single occupied molecular orbital (SOMO) constituted primarily of π^* (NO) orbitals, and the main contribution of the spin magnetic moment comes from the π^* (NO) orbitals. By comparison, we find that the GGA is more suitable to describe free radical systems than LSDA.     

Electronic and Magnetic Properties of the p-NPNN

In this paper, we study the electronic band structure and the ferromagnetic properties of the organic radicalp-NPNN by employing density-functional theory with generalized gradient approximation (GGA) and local-spin densityapproximation (LSDA). The density of states, the total energy, and the spin magnetic moment are calculated. Thecalculations reveal that the δ-phase of p-NPNN has a stable ferromagnetic ground state. It is found that an unpairedelectron in this compound is localized in a single occupied molecular orbital (SOMO) constituted primarily of π* (NO)orbitals, and the main contribution of the spin magnetic moment comes from the π* (NO) orbitals. By comparison, wefind that the GGA is more suitable to describe free radical systems than LSDA.     

Levitation and lateral forces between a point magnetic dipole and a superconducting sphere

The dipole–dipole interaction model is employed to investigate the angular dependence of the levitation and lateral forces acting on a small magnet in an anti-symmetric magnet/superconducting sphere system. Breaking the symmetry of the system enables us to study the lateral force which is important in the stability of the magnet above a superconducting sphere in the Meissner state. Under the assumption that the lateral displacement of the magnet is small compared to the physical dimensions of our proposed system, analytical expressions are obtained for the levitation and lateral forces as a function of the geometrical parameters of the superconductor as well as the height, the lateral displacement, and the orientation of the magnetic moment of the magnet. The dependence of the levitation force on the height of the levitating magnet is similar to that in the symmetric magnet/superconducting sphere system within the range of proposed lateral displacements. It is found that the levitation force is linearly dependent on the lateral displacement whereas the lateral force is independent of this displacement. A sinusoidal variation of both forces as a function of the polar and azimuthal angles specifying the orientation of the magnetic moment is observed. The relationship between the stability and the orientation of the magnetic moment is discussed for different orientations.     

Challenges in uncovering the origin of the proton's spin

One of the most fascinating challenges facing modern strong interaction physics is to understand the origin of the spin of the nucleon in terms of the spin and orbital angular momentum of the quarks and gluons.We review recent progress on this problem as well as some of the uncertainties associated with state of the art lattice QCD simulations.In particular,we explain the importance of the corrections associated with chiral extrapolation and finite volume corrections,especially for the term B（0） extracted from the appropriate low moment of the deeply virtual Compton scattering amplitude.     

Transition magnetic moments of J~P=3/2~+ decuplet to J~P=1/2~+ octet baryons in the chiral constituent quark model

In light of the developments of the chiral constituent quark model(χ~(CQM)) in studying low energy hadronic matrix elements of the ground-state baryons, we extend this model to investigate their transition properties.The magnetic moments of transitions from the J~P=3/2~+ decuplet to J~P=1/2~+ octet baryons are calculated with explicit valence quark spin, sea quark spin and sea quark orbital angular momentum contributions. Since the experimental data is available for only a few transitions, we compare our results with the results of other available models. The implications of other complicated effects such as chiral symmetry breaking and SU(3) symmetry breaking arising due to confinement of quarks are also discussed.     

The low-lying rotational bands of the neutron-rich nucleus <Superscript>172</Superscript>Tm

The microscopic mechanism of four experimentally observed bands in 172Tm is investigated using the particle-number conserving method of the cranked shell model with monopole and quadrupole paring interactions.The experimental results,including the moments of inertia and angular momentum alignments of four bands in 172Tm are reproduced well by the particle-number conserving calculations.The ω variation of the occupation probability of each cranked orbital and the contribution to moment of inertia from each c...     

Calculation of the fine structure of the level in Rydberg state of lithium

The level shift and level formula of lithium atom in Rydberg states are achieved by means of the calculation of polarization of the atomic core （including the contribution of dipole moment, quadrupole moment and octupole moment） ; meanwhile, the effect of relativity theory, the orbital angular momentum L and the spin angular momentum S coupling （IS coupling）, and high order correction of the effective potential are considered. Thesome fine structures （N = 5- 12, L = 4-9, J = L ± 1/2） and the corresponding level intervals in Rydberg statescan be calculated by the above-mentioned level formula and compared with correlated experimental data.     

Geodesics of Spherical Dilaton Spacetimes

The properties of spherical dilaton black hole spacetimes are investigated through a study of their geodesics. The closed and non-closed orbits of test particles are analysed using the effective potential and phase-plane method. The stability and types of orbits are determined in terms of the energy and angular momentum of the test particles. The conditions of the existence of circular orbits for a spherical dilaton spacetime with an arbitrary dilaton coupling constant α are obtained. The properties of the orbits and in particular the position of the innermost stable circular orbit are compared to those of the Reissner-Nordstrom spacetime. The circumferential radius of innermost stable circular orbit and the corresponding angular momentum of the test particles increase for α≠ 0.     

Rayleigh-like distribution of particle transverse momenta in collisions at high energies

The transverse momentum distributions of final-state particles produced in collisions at high en-ergies are studied by using a two-component Rayleigh-like distribution.This representation is based on Liu＇s multisource ideal gas model which describes protons and fragments in high energy nucleus-nucleus collisions.The calculated results are in good agreement with the experimental data of Au-Au,Cu-Cu,d-Au,and pp collisions at the relativistic heavy ion collider energies.The experimental particle momentum distributions of p-Be collisions at 6.4,12.3,and 17.5 GeV/c,as well as Au-Au collisions at 1.5 AGeV are well described by a model based on a single Rayleigh-like distribution of particle transverse momenta.     

Electronic and Magnetic Properties of Double Perovskite Ca2CrSbO6

First-principles calculations have been performed for the study of the electronic band structure and ferromagnetic properties of double perovskite Ca2CrSbO6. The density of states, total energy, spin magnetic moment, and charge density were calculated and analyzed in details. It is found that Ca2CrSbO6 has a stable ferromagnetic ground state and the spin magnetic moment per molecule is about 2.99#B. The chromium contributes the most in the total magnetic moments. The results indicate that Ca2CrSbO6 is half-metallic.     

Nuclear structure of proton-rich unstable nucleus 28P studied by g-factor measurement*

Nuclear structure of proton-rich unstable nucleus 28P has been studied by measuring its g-factor for the first time. The g-factor of 28P (Iπ =3+, T1/2=270.3 ms) was measured by means of β-NMR technique combined with the new polarization technique for charge exchange reaction product in the intermediate energy heavy ion collisions. The obtained g-factor of g=0.1028(27) is very much quenched from the Schmidt value,but is well reproduced by the shell model (+0.102). In connection with the magnetic moment of the mirror partner and the β-ray transition probability, the orbital angular momenta and intrinsic spins of protons and neutrons have been determined as 〈lp〉 = 0.43(29), 〈ln〉 = 1.85(29), 〈Sp〉 = 0.28(4), and 〈Sn〉 = 0.44(4).