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Journal articles on the topic 'BETHE-GOLDSTONE EQUATION'

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Published: 4 June 2021

Last updated: 10 February 2022

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1

TOGASHI, TOMOAKI, TAKAOMI MURAKAMI, and KIYOSHI KATŌ. "THE DESCRIPTION OF NUCLEAR STRUCTURES WITH THE BRUECKNER-AMD." International Journal of Modern Physics E 17, no. 10 (November 2008): 2081–86. http://dx.doi.org/10.1142/s0218301308011136.

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We propose a new approach of the Brueckner-AMD that makes the antisymmetrized molecular dynamics (AMD) calculations possible with realistic nuclear forces. In this method, we solve the Bethe-Goldstone equation and calculate the G-matrix for every nucleon pair described by wave packets of AMD. In addition, we calculate the G-matrix in the spin and parity projection correctly using the two-body correlation functions derived from the solutions of the Bethe-Goldstone equation. We report the results of applications to light nuclei with the Brueckner-AMD plus the spin and parity projection.

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2

Koinov, Zlatko, and Israel Chávez Villalpando. "Speed of the Goldstone Sound Mode of an Atomic Fermi Gas Loaded on a Square Optical Lattice with a Non-Abelian Gauge Field in the Presence of a Zeeman Field." Advances in Condensed Matter Physics 2018 (July 2, 2018): 1–11. http://dx.doi.org/10.1155/2018/6809265.

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The speed of the Goldstone sound mode of a spin-orbit-coupled atomic Fermi gas loaded in a square optical lattice with a non-Abelian gauge field in the presence of a Zeeman field is calculated within the Gaussian approximation and from the Bethe-Salpeter equation in the generalized random phase approximation. It is found that (i) there is no sharp change of the slope of the Goldstone sound mode across the topological quantum phase transition point and (ii) the Gaussian approximation significantly overestimates the speed of sound of the Goldstone mode compared to the value provided by the BS formalism.

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3

Sartor, R. "Solution of the Bethe-Goldstone equation with an exact propagator." Physical Review C 54, no. 2 (August 1, 1996): 809–14. http://dx.doi.org/10.1103/physrevc.54.809.

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4

Koinov, Z. G. "Collective Modes of an Ultracold6Li-40K Mixture in an Optical Lattice." Advances in Condensed Matter Physics 2015 (2015): 1–12. http://dx.doi.org/10.1155/2015/952852.

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A low-energy theory of the Nambu-Goldstone excitation spectrum and the corresponding speed of sound of an interacting Fermi mixture of Lithium-6 and Potassium-40 atoms in a two-dimensional optical lattice at finite temperatures with the Fulde-Ferrell order parameter has been formulated. It is assumed that the two-species interacting Fermi gas is described by the one-band Hubbard Hamiltonian with an attractive on-site interaction. The discussion is restricted to the BCS side of the Feshbach resonance where the Fermi atoms exhibit superfluidity. The quartic on-site interaction is decoupled via a Hubbard-Stratonovich transformation by introducing a four-component boson field which mediates the Hubbard interaction. A functional integral technique and a Legendre transform are used to give a systematic derivation of the Schwinger-Dyson equations for the generalized single-particle Green’s function and the Bethe-Salpeter equation for the two-particle Green’s function and the associated collective modes. The numerical solution of the Bethe-Salpeter equation in the generalized random phase approximation shows that there exist two distinct sound velocities in the long-wavelength limit. In addition to low-energy (Goldstone) mode, the two-species Fermi gas has a superfluid phase revealed by two roton-like minima in the asymmetric collective-mode energy.

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5

Lucha, Wolfgang, and Franz F. Schöberl. "Instantaneous Bethe–Salpeter view of Goldstone-type pseudoscalar mesons." International Journal of Modern Physics A 31, no. 36 (December 28, 2016): 1650202. http://dx.doi.org/10.1142/s0217751x1650202x.

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Describing the lightest pseudoscalar mesons as bound states of quark and antiquark within the framework of an instantaneous Bethe–Salpeter formalism constructed such as to retain (in contrast to Salpeter’s equation) as much information on the relativistic effects provided by the full quark propagator as conceivable allows for a surprisingly simple implementation of their near masslessness mandatory for their interpretability as pseudo-Goldstone bosons related to the spontaneous breaking of the chiral symmetries of quantum chromodynamics.

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6

CAHILL, REGINALD T., and SUSAN M. GUNNER. "A NEW MASS FORMULA FOR NG BOSONS IN QCD." Modern Physics Letters A 10, no. 39 (December 21, 1995): 3051–58. http://dx.doi.org/10.1142/s0217732395003185.

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An oftenly used mass formula for Nambu-Goldstone (NG) bosons in QCD, such as the pions, involves the condensate [Formula: see text], fπ and the quark current masses. We argue, within the context of the global color model to QCD, that this expression is wrong. Analysis of the interplay between the Dyson-Schwinger equation for the constituent quark effect and the Bethe-Salpeter equation for the NG boson results in a new mass formula.

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7

TOGASHI, TOMOAKI, KIYOSHI KATŌ, and TAKAOMI MURAKAMI. "CLUSTER STRUCTURE STUDY BASED ON REALISTIC NUCLEAR FORCE: BRUECKNER-AMD." International Journal of Modern Physics A 24, no. 11 (April 30, 2009): 2142–49. http://dx.doi.org/10.1142/s0217751x09045728.

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We propose a new approach of the Brueckner-AMD that makes the antisymmetrized molecular dynamics (AMD) calculations possible with realistic nuclear forces. In this method, we solve the Bethe-Goldstone equation and calculate the G-matrix for every nucleon pair described by wave packets of AMD correctly. We report the results of applications to light nuclei with the Brueckner-AMD.

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8

RASHDAN, M. "ELASTIC SCATTERING OF 28Si–27Al IN A REALISTIC OPTICAL POTENTIAL." International Journal of Modern Physics E 05, no. 03 (September 1996): 533–41. http://dx.doi.org/10.1142/s021830139600027x.

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Within a realistic model for the optical potential between nuclei based on the solution of the Bethe-Goldstone equation with the Reid soft-core potential, the differential cross-sections of the 28 Si –27 Al system, recently measured at energies around the Coulomb barrier, are calculated. The experimental data are well-reproduced over the entire energy range without any adjustable parameters to fit the cross-section.

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9

BALDO, M., and G. F. BURGIO. "THE BETHE–BRUECKNER–GOLDTONE THEORY OF THE NUCLEAR EQUATION OF STATE AND NEUTRON STARS." International Journal of Modern Physics B 17, no. 28 (November 10, 2003): 5127–37. http://dx.doi.org/10.1142/s0217979203020259.

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The microscopic many-body theory of the Nuclear Equation of State is discussed in the framework of the Bethe–Brueckner–Goldstone method. The expansion is extended up to the three hole-line diagrams contribution. The Brueckner equation for the two-body G-matrix and the Bethe–Fadeev equation for the three-body scattering matrix are solved both for the gap and continuous choices of the single particle potential. For symmetric and pure neutron matter strong evidence of convergence in the expansion is found. Once three-body forces are introduced, the phenomenological saturation point is reproduced. In order to study neutron stars static properties, the theory is extended to include strangeness, and the possible quark-gluon plasma component is described in the simplified MIT bag model. The results for the mass and radius of neutron stars are briefly discussed.

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10

Nuppenau, C., A. D. Mackellar, and Y. J. Lee. "Study of nucleon-nucleus scattering based on the relativistic Brueckner-Bethe-Goldstone equation." Nuclear Physics A 511, no. 3-4 (May 1990): 525–40. http://dx.doi.org/10.1016/0375-9474(90)90108-x.

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11

Cheon, Taksu, and Edward F. Redish. "Exact treatment of the Pauli exclusion operator in the nuclear matter Bethe-Goldstone equation." Physical Review C 39, no. 2 (February 1, 1989): 331–35. http://dx.doi.org/10.1103/physrevc.39.331.

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12

Ong, Michael K. "The solution of the s‐wave Bethe–Goldstone equation with a standard hard core potential." Journal of Mathematical Physics 29, no. 6 (June 1988): 1477–85. http://dx.doi.org/10.1063/1.527943.

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13

RASHDAN, M. "A SKYRME PARAMETRIZATION BASED ON NUCLEAR MATTER BHF CALCULATIONS." Modern Physics Letters A 15, no. 20 (June 28, 2000): 1287–99. http://dx.doi.org/10.1142/s0217732300001663.

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Using a modified energy density functional of nuclear matter derived by solving the Bethe–Goldstone equation with a realistic nucleon–nucleon interaction and by including corrections due to relativistic and three-body effects, an effective Skyrme parameter set is derived. These corrections are found to be important in order to well describe the saturation properties of nuclear matter. The obtained Skyrme parameter set, which we denoted by SKRA, is found to better account for nuclear correlations and satisfactory describes finite nuclei, when used in the Skyrme–Hartree–Fock theory. The SKRA interaction can also be considered as an important step toward removing the ambiguities in the determination of Skyrme parameters.

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14

Ong, Michael K. "A closed form solution of the s‐wave Bethe–Goldstone equation with an infinite repulsive core." Journal of Mathematical Physics 27, no. 4 (April 1986): 1154–58. http://dx.doi.org/10.1063/1.527398.

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15

ZUO, WEI. "EQUATION OF STATE AND SINGLE-PARTICLE PROPERTIES OF NEUTRON-RICH NUCLEAR MATTER." International Journal of Modern Physics E 17, supp01 (December 2008): 256–71. http://dx.doi.org/10.1142/s0218301308011902.

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We report our research work on the equation of state (EOS) and single-particle (s.p.) properties of neutron-rich nuclear matter within the framework of the Brueckner–Bethe–Goldstone approach extended to include a microscopic three-body force (TBF). We show that inclusion of the TBF provide a largely improvement of the predicted nuclear matter saturation properties and leads to a strongly stiffening of the density dependence of symmetry energy at high densities. The neutron effective mass turns out to be greater than the proton one in neutron-rich nuclear matter in both cases of including and not including the TBF. The TBF induces a strongly repulsive rearrangement contribution to nucleon s.p. potential at high densities and large momenta. The TBF rearrangement contribution reduces considerably the attraction of the neutron and proton s.p. potentials and enhances strongly their momentum-dependence at high densities and high momenta. The TBF effect on nucleon superfluidity in neutron star matter has also been discussed.

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16

HAIDER, W., and MANJARI SHARMA. "MICROSCOPIC LOCAL OPTICAL POTENTIALS AND THE NUCLEON–NUCLEUS SCATTERING AT 65 MeV." International Journal of Modern Physics E 19, no. 03 (March 2010): 465–82. http://dx.doi.org/10.1142/s021830131001487x.

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Microscopic local optical potentials from two sources were calculated by folding the numerical g-matrices over point proton and neutron RMF densities of target nuclei. The hard-core Hamada–Johnston and the soft-core Urbana v-14 local inter-nucleon potentials have been used to generate numerical g-matrices by solving Bethe–Goldstone integral equation. The calculated potentials have been used to analyze successfully both the proton and neutron differential elastic scattering and polarization data at 65 MeV over a wide mass region of targets: 12 C –208 Pb . Comparison of the present results with a phenomenological optical model analyzes is also presented. Mass number dependence of the mean square radii of the two microscopic potentials are in close agreement with each other as well as with empirical results.

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17

Boroński, Edward. "Influence of Electron-Electron Correlations and Lattice Effects on Positron-Electron Enhancement Factors." Materials Science Forum 666 (December 2010): 5–9. http://dx.doi.org/10.4028/www.scientific.net/msf.666.5.

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We present an approach taking into account the effect of electron-electron (e-e) correlations on electron-positron (e-p) momentum density distributions. The approach bases on the modification of the Bethe-Goldstone (B-G) equation for the positron in the electron gas due to self-energy effects. The example calculations have been performed for selected parameters corresponding to simple metals. The calculated dependencies exhibit the increase of the e-p enhancement factors below Fermi momentum, like Kahana enhancements, and a decrease above the Fermi sphere, leading to a many-body “tail” in the e-p momentum density distributions. Moreover, the influence of lattice effects on enhancement factors (EF) is taken into account. This decreases by a few percent the absolute values of the e-p momentum distributions and the corresponding annihilation rates and for real metals such as Mg or Cu evidently improve the agreement with experiment.

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18

Bonatsos, Dennis, and H. Muether. "Microscopic Calculation of the Optical Model Potential from One Boson Exchange Potentials." HNPS Proceedings 1 (February 18, 2020): 86. http://dx.doi.org/10.12681/hnps.2827.

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A new method for calculating the optical model potential from One Boson Exchange Potentials (OBEPs) is developed. The G-matrix is calculated by solving the Bethe-Goldstone equation in momentum space. Using vector brackets these G-matrix elements can be transformed from the center of mass representation into the laboratory system. This allows the evaluation of the (r-matrix interaction between nucleons in bound states and those in a plane-wave state. The lowest order contribution to the real part of the potential comes from the Hartree-Fock term, while the lowest order contribution to the imaginary part comes from the two-particle-one-hole (2p1h) diagram. Calculations for 16O and 40Ca have been carried out. Local approximations are obtained by describing the results for the central part in terms of a Woods-Saxon potential and those for the spin-orbit part in terms of the corresponding derivatives. The dependence of these potentials on energy and angular momentum is discussed. The parameters for these local approximations are in good agreement with empirical fits.

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19

Bombaci, Ignazio, and Domenico Logoteta. "Equation of state of dense nuclear matter and neutron star structure from nuclear chiral interactions." Astronomy & Astrophysics 609 (January 2018): A128. http://dx.doi.org/10.1051/0004-6361/201731604.

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Aims. We report a new microscopic equation of state (EOS) of dense symmetric nuclear matter, pure neutron matter, and asymmetric and β-stable nuclear matter at zero temperature using recent realistic two-body and three-body nuclear interactions derived in the framework of chiral perturbation theory (ChPT) and including the Δ(1232) isobar intermediate state. This EOS is provided in tabular form and in parametrized form ready for use in numerical general relativity simulations of binary neutron star merging. Here we use our new EOS for β-stable nuclear matter to compute various structural properties of non-rotating neutron stars. Methods. The EOS is derived using the Brueckner–Bethe–Goldstone quantum many-body theory in the Brueckner–Hartree–Fock approximation. Neutron star properties are next computed solving numerically the Tolman–Oppenheimer–Volkov structure equations. Results. Our EOS models are able to reproduce the empirical saturation point of symmetric nuclear matter, the symmetry energy Esym, and its slope parameter L at the empirical saturation density n0. In addition, our EOS models are compatible with experimental data from collisions between heavy nuclei at energies ranging from a few tens of MeV up to several hundreds of MeV per nucleon. These experiments provide a selective test for constraining the nuclear EOS up to ~4n0. Our EOS models are consistent with present measured neutron star masses and particularly with the mass M = 2.01 ± 0.04 M⊙ of the neutron stars in PSR J0348+0432.

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20

Malik, F. B. "A Bethe-Goldstone type of equation with explicit antisymmetrisation for a three-body-fermion cluster in a finite system with three-body interaction." Journal of Physics G: Nuclear Physics 13, no. 7 (July 1987): 933–43. http://dx.doi.org/10.1088/0305-4616/13/7/007.

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21

YAMAWAKI, KOICHI. "CONFORMAL HIGGS, OR TECHNI-DILATON — COMPOSITE HIGGS NEAR CONFORMALITY." International Journal of Modern Physics A 25, no. 27n28 (November 10, 2010): 5128–44. http://dx.doi.org/10.1142/s0217751x10050913.

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In contrast to the folklore that Technicolor (TC) is a "Higgsless theory", we shall discuss existence of a composite Higgs boson, Techni-Dilaton (TD), a pseudo-Nambu-Goldstone boson of the scale invariance in the Scale-invariant/Walking/Conformal TC (SWC TC) which generates a large anomalous dimension γm ≃ 1 in a wide region from the dynamical mass [Formula: see text] of the techni-fermion all the way up to the intrinsic scale ΛTC of the SWC TC (analogue of ΛQCD), where ΛTC is taken typically as the scale of the Extended TC scale Λ ETC : Λ TC ≃ Λ ETC ~ 103 TeV (≫ m). All the techni-hadrons have mass on the same order [Formula: see text], which in SWC TC is extremely smaller than the intrinsic scale Λ TC ≃ Λ ETC , in sharp contrast to QCD where both are of the same order. The mass of TD arises from the non-perturbative scale anomaly associated with the techni-fermion mass generation and is typically 500-600 GeV, even smaller than other techni-hadrons of the same order of [Formula: see text], in another contrast to QCD which is believed to have no scalar [Formula: see text] bound state lighter than other hadrons. We discuss the TD mass in various methods, Gauged NJL model via ladder Schwinger-Dyson (SD) equation, straightforward calculations in the ladder SD/ Bethe-Salpeter equation, and the holographic approach including techni-gluon condensate. The TD may be discovered in LHC.

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22

FAESSLER, AMAND, A. BUCHMANN, and Y. YAMAUCHI. "THE QUARK MODEL, DEUTERON FORM FACTORS AND NUCLEAR MAGNETIC MOMENTS." International Journal of Modern Physics E 02, no. 01 (March 1993): 39–185. http://dx.doi.org/10.1142/s0218301393000030.

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The study of the deuteron electromagnetic form factors based on the quark cluster model is reviewed. The deuteron wave function is derived from a microscopic quark Hamiltonian with the help of the Resonating Group Method. One-pion and one-gluon exchange potentials are included in addition to a quadratic confinement potential. The photon is coupled directly to the quarks. Aside from the one-body impulse current, pion and gluon exchange currents are included on the quark level. Due to the Pauli principle on the quark level, new electromagnetic currents arise which are not present on the nucleon level. These currents, called quark exchange currents, describe processes in which a photon couples to a quark or a pair of quarks interacting via gluon or pion exchange and which are accompanied by a simultaneous quark interchange between the two threequark clusters (nucleons). They are small for low momentum transfers but appreciably influence the electromagnetic structure of the deuteron beyond a momentum transfer of q=5 fm−1. The discussion is extended to the magnetic moments of 15N, 17O and 39K by introducing the quark exchange currents as effective operators on the nucleon level. The quark exchange currents written in terms of nonlocal and spin-isospin dependent nuclear operators are effective only at short distances. They are evaluated with shell-model (harmonic oscillator) wave functions including the (short-range) Brueckner correlations. The Bethe-Goldstone equation is solved with our effective NN potential, which is derived from a microscopic quark Hamiltonian. The quark exchange currents shift the isovector magnetic moment of 39K by −20% from its Schmidt value.

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23

SHOVKOVY, IGOR. "THE SPECTRUM OF DIQUARK COMPOSITES IN COLD DENSE QCD." International Journal of Modern Physics A 16, supp01c (September 2001): 1271–73. http://dx.doi.org/10.1142/s0217751x01009508.

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The Bethe-Salpeter equations for spin zero diquark composites in the color superconducting phase of Nf = 2 and Nf = 3 cold dense QCD are studied. The explicit form of the spectrum of the diquarks with the quantum numbers of the (pseudo-) Nambu-Goldstone bosons is derived.

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24

Ruckenstein, Andrei E., and Stefan Schmitt-Rink. "SINGLE SPIN FLIP IN THE INFINITE U HUBBARD MODEL: HUBBARD OPERATORS, THREE-BODY FADEEV EQUATIONS AND GUTZWILLER WAVE FUNCTIONS." International Journal of Modern Physics B 03, no. 12 (December 1989): 1809–32. http://dx.doi.org/10.1142/s0217979289001160.

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We investigate a recently proposed many-body theory for composite (Hubbard) operators (A.E. Ruckenstein and S. Schmitt-Rink, Phys. Rev. B38, 7188 (1988)) in the context of the problem of a single spin flip in the saturated ferromagnetic state of the infinite U Hubbard model. We prove that the suitably defined strong coupling Hartree-Fock mean field theory leads to results identical to those obtained from the Gutzwiller wave function through exact evaluation of the kinetic energy. Most interestingly, we also show how exactly the same results can be obtained starting from the weak coupling limit by solving analytically the three-body t-matrix (Fadeev) equations in the infinite U limit. This work also sheds light on the physical content of slave boson approximations to which our approach was previously shown to be equivalent in the limit of large spin or orbital degeneracy. For the single spin flip problem we compare our results with those obtained by Bethe-Goldstone perturbation theory, Bethe Ansatz in one dimension, and exact diagonalization studies.

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25

Amos, K., P. J. Dortmans, and S. Karataglidis. "Signatures of Medium Effects on NN Interactions in Proton Scattering from Nuclei." Australian Journal of Physics 50, no. 1 (1997): 245. http://dx.doi.org/10.1071/p96027.

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Effective two nucleon (NN) interactions in the nuclear medium have been defined from an accurate mapping of NN g matrices obtained by solving the Brueckner–Bethe–Goldstone (BBG) equations for infinite nuclear matter. Those effective interactions have been used in fully microscopic calculations of proton-light nuclei (nonlocal) effective interactions from which predictions of the elastic scattering differential cross sections and analysing powers have been obtained. Results for incident proton energies of 65 and 200 MeV are considered in particular herein. The associated relative motion wave functions have been used as the distorted waves in distorted wave approximation (DWA) studies of select inelastic scattering events. The same effective interactions were used as the transition operators in those calculations. The relevant nuclear spectroscopy for the elastic and DWA (p, p′) calculations has been found from full (0 + 2)hϖ shell model evaluations of the nuclear structure; wave functions of which give good descriptions of form factors obtained from electron scattering.

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26

White, L., and F. Sammarruca. "Solution of the Bethe-Goldstone equation without partial-wave decomposition." Physical Review C 88, no. 5 (November 27, 2013). http://dx.doi.org/10.1103/physrevc.88.054619.

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27

Simo, I. Ruiz, R. Navarro Pérez, J. E. Amaro, and E. Ruiz Arriola. "Coarse graining the Bethe–Goldstone equation: Nucleon–nucleon high-momentum components." Physical Review C 96, no. 5 (November 27, 2017). http://dx.doi.org/10.1103/physrevc.96.054006.

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28

Shang, X. L., J. M. Dong, W. Zuo, P. Yin, and U. Lombardo. "Exact solution of the Brueckner-Bethe-Goldstone equation with three-body forces in nuclear matter." Physical Review C 103, no. 3 (March 22, 2021). http://dx.doi.org/10.1103/physrevc.103.034316.

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