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Spherical to deformed shape transition in the nucleon-pair shell model  [PDF]
Y. Lei,S. Pittel,G. J. Fu,Y. M. Zhao
Physics , 2012, DOI: 10.1063/1.4759411
Abstract: A study of the shape transition from spherical to axially deformed nuclei in the even Ce isotopes using the nucleon-pair approximation of the shell model is reported. As long as the structure of the dominant collective pairs is determined using a microscopic framework appropriate to deformed nuclei, the model is able to produce a shape transition. However, the resulting transition is too rapid, with nuclei that should be transitional being fairly well deformed, perhaps reflecting the need to maintain several pairs with each angular momentum.
Densities, Parton Distributions, and Measuring the Non-Spherical Shape of the Nucleon
Miller, Gerald A.
High Energy Physics - Phenomenology , 2007, DOI: 10.1103/PhysRevC.76.065209
Abstract: Spin-dependent quark densities, matrix elements of specific density operators in proton states of definite spin-polarization, indicate that the nucleon may harbor an infinite variety of non-spherical shapes. We show that these matrix elements are closely related to specific transverse momentum dependent parton distributions accessible in the angular dependence of the semi-inclusive processes electron plus proton goes to electron plus pion plus anything, and the Drell-Yan reaction proton plus proton goes to a lepton anti-lepton pair plus anything. New measurements or analyses would allow the direct exhibition of the non-spherical nature of the proton.
Densities, Parton Distributions, and Measuring the Non-Spherical Shape of the Nucleon  [PDF]
Gerald A. Miller
Physics , 2007, DOI: 10.1103/PhysRevC.76.065209
Abstract: Spin-dependent quark densities, matrix elements of specific density operators in proton states of definite spin-polarization, indicate that the nucleon may harbor an infinite variety of non-spherical shapes. We show that these matrix elements are closely related to specific transverse momentum dependent parton distributions accessible in the angular dependence of the semi-inclusive processes electron plus proton goes to electron plus pion plus anything, and the Drell-Yan reaction proton plus proton goes to a lepton anti-lepton pair plus anything. New measurements or analyses would allow the direct exhibition of the non-spherical nature of the proton.
Hadron deformation from Lattice QCD  [PDF]
C. Alexandrou
Physics , 2003, DOI: 10.1016/S0920-5632(03)02451-4
Abstract: We address the issue of hadron deformation within the framework of lattice QCD. For hadrons with spin greater than 1/2 the deformation can be determined by evaluating the charge and matter distributions. Deviation of the nucleon shape from spherical symmetry is determined by evaluating the quadrupole strength in the transition $\gamma N \to \Delta(1232)$ both in the quenched and in the unquenched theory.
The shape of the nucleon  [PDF]
Franz Gross,Peter Agbakpe
Physics , 2004, DOI: 10.1103/PhysRevC.73.015203
Abstract: We show that all four of the nucleon form factors can be very well explained using the manifestly covariant spectator theory. The nucleon is modeled as a spherical state of three constituent quarks with electromagnetic form factors, all determined by the fit to the data.
Ovrview: The Shape of Hadrons
Bernstein, A. M.;Papanicolas, C. N.
High Energy Physics - Phenomenology , 2007, DOI: 10.1063/1.2734399
Abstract: In this article we address the physical basis of the deviation of hadron shapes from spherical symmetry (non-spherical amplitudes) with focus on the nucleon and $\Delta$. An overview of both the experimental methods and results and the current theoretical understanding of the issue is presented. At the present time the most quantitative method is the $\gamma^{*} p \to \Delta$ reaction for which significant non-spherical electric (E2) and Coulomb quadrupole (C2) amplitudes have been observed with good precision as a function of Q^{2} from the photon point through 6 GeV^{2}. Quark model calculations for these quadrupole amplitudes are at least an order of magnitude too small and even have the wrong sign. Lattice QCD, chiral effective field theory, and dynamic model calculations which include the effects of the pion-cloud are in approximate agreement with experiment. This is expected due to the spontaneous breaking of chiral symmetry in QCD and the resulting, long range (low Q^{2}) effects of the pion-cloud. Other observables such as nucleon form factors and virtual Compton scattering experiments indicate that the pion-cloud is playing a significant role in nucleon structure. Semi-inclusive deep inelastic scattering experiments with transverse polarized beam and target also show the effect of non-zero quark angular momentum.
Spherical symmetry breaking in cold gravitational collapse of isolated systems  [PDF]
Tirawut Worrakitpoonpon
Physics , 2014, DOI: 10.1093/mnras/stu2159
Abstract: We study, using $N$-body simulation, the shape evolution in gravitational collapse of cold uniform spherical system. The central interest is on how the deviation from spherical symmetry depends on particle number $N$. By revisit of the spherical collapse model, we hypothesize that the departure from spherical symmetry is regulated by the finite-$N$ density fluctuation. Following this assumption, the estimate of the flattening of relaxed structures is derived to be $N^{-1/3}$. In numerical part, we find that the virialized states can be characterized by the core-halo structures and the flattenings of the cores fit reasonably well with the prediction. Moreover the results from large $N$ systems suggest the divergence of relaxation time to the final shapes with $N$.We also find that the intrinsic shapes of the cores are considerably diverse as they vary from nearly spherical, prolate, oblate or completely triaxial in each realization. When $N$ increases, this variation is suppressed as the final shapes do not differ much from initial symmetry. In addition, we observe the stable rotation of the virialized states. Further investigation reveals that the origin of this rotation is related in some way to the initial density fluctuation.
Octupole response and stability of spherical shape in heavy nuclei  [PDF]
V. I. Abrosimov,O. I. Davidovskaya,A. Dellafiore,F. Matera
Physics , 2003, DOI: 10.1016/j.nuclphysa.2003.08.014
Abstract: The isoscalar octupole response of a heavy spherical nucleus is analyzed in a semiclassical model based on the linearized Vlasov equation. The octupole strength function is evaluated with different degrees of approximation. The zero-order fixed-surface response displays a remarkable concentration of strength in the $1\hbar\omega$ and $3\hbar\omega$ regions, in excellent agreement with the quantum single-particle response. The collective fixed-surface response reproduces both the high- and low-energy octupole rsonances, but not the low-lying $3^{-}$ collective states, while the moving-surface response function gives a good qualitative description of all the main features of the octupole response in heavy nuclei. The role of triangular nucleon orbits, that have been related to a possible instability of the spherical shape with respect to octupole-type deformations, is discussed within this model. It is found that, rather than creating instability, the triangular trajectories are the only classical orbits contributing to the damping of low-energy octupole excitations.
Charge form factors and nucleon shape
Buchmann, A. J.
High Energy Physics - Phenomenology , 2013, DOI: 10.1063/1.2734297
Abstract: To obtain further information on the geometric shape of the nucleon, the proton charge form factor is decomposed into two terms, which are connected respectively with a spherically symmetric and an intrinsic quadrupole part of the proton's charge density. Quark model relations are employed to derive expressions for both terms. In particular, the proton's intrinsic quadrupole form factor is obtained from a relation between the N -> Delta and neutron charge form factors. The proposed decomposition shows that the neutron charge form factor is an observable manifestation of an intrinsic quadrupole form factor of the nucleon. Furthermore, it affords an interpretation of recent electron-nucleon scattering data in terms of a nonspherical distribution of quark-antiquark pairs in the nucleon.
Shape Deformations in Atomic Nuclei  [PDF]
Ikuko Hamamoto,Ben R. Mottelson
Physics , 2011, DOI: 10.4249/scholarpedia.10693
Abstract: The ground states of some nuclei are described by densities and mean fields that are spherical, while others are deformed. The existence of non-spherical shape in nuclei represents a spontaneous symmetry breaking.
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