Showing papers on "Mass formula published in 1972"
TL;DR: In this paper, a relativistic particle is represented by a pair (xμ,ξμ) of 4-vectors, and the authors lead to a group H5 of canonical transformations which includes the Poincare group and dilatations.
Abstract: Characterizing the state of a relativistic particle by a pair (xμ,ξμ) of 4‐vectors, we are led, in a natural way, to a group H5 of canonical transformations which includes the Poincare group and dilatations. The structure of the group and its induced irreducible unitary representations are explored. It is shown that H5 has a semisimple noncompact subgroup which permits a systematic treatment of exact and of broken dilatation symmetry. The relevance of these ideas to scale dimension and to a new symmetry, scale conjugation, is discussed. As an application, a mass formula is derived from broken dilatation symmetry.
17 citations
TL;DR: In this paper, a nonlinear realization of SU3×SU3 for the pseudoscalar mesons is constructed, which is achieved through a one-parameter unitary transformation which has a structure similar to a generalized Cabibbo rotation.
Abstract: A nonlinear realization ofSU3×SU3 for the pseudoscalar mesons is constructed. First, theSU3×SU3 symmetry is broken, while keepingSU2×SU2 exact, by letting the K and η mesons acquire a mass. This model provides a generalization of K-π effective Lagrangians consistent with the Callan-Treiman relations. The symmetry is further broken toSU2×U1 by allowing the pion to have a mass. This is achieved through a one-parameter unitary transformation which has a structure similar to a generalized Cabibbo rotation. This « mass rotation » introduces a part which transforms as the « 27 » representation into the symmetry-breaking term. This term breaks the Gell-Mann-Okubo mode ofSU3 violation and leads to an alternative, accurate mass formula. Divergences of the currents are calculated in both broken-symmetry schemes.
9 citations
TL;DR: In this paper, a second-order correction to the isobaric mass equation is calculated taking into account the Coulomb mixing of the analog state with the configuration state, and the coefficient of the T z 3 term is found to be of the order of 1-3 keV.
8 citations
TL;DR: In this paper, the nuclear forces were taken into account using the Kodama-Yamada mass formula for compressible nuclei, and the energy density was calculated for a superdense star composed of neutrons.
Abstract: We have several theories of gravitation other than Einstein's theory of general reiativity. Distinction among these theories might be possible from the study of superdense objects. The best-studied superdense object is the so-called neutron star. Its mass, radius and other properties can be determined from the equation of state for the stellar matter and the theory of gravitation. Although the general relativity has been mainly used as the theory of gravitation, Salmona1> applied· the scalar-tensor theory of Brans and Dicke.2> In his calculation he assumed the equation of state for a noninteracting Fermi gas neglecting the effects of nuclear forces. In this letter we take into account the nuclear forces using the Kodama-Yamada mass formula for compressible nuclei. 8> As for the model of neutron star we assume, for simplicity, that the star is static and spherically symmetric. We also assume that the star is composed of neutrons only. Then, the energy density e is written as
8 citations
TL;DR: In this article, it was shown that for the free particles and antiparticles with the mass m > 0 and the arbitrary spin s ≥ 12, there also exist three types of nonequivalent equations.
Abstract: In previous papers [1, 2] we have shown that there exist three types of the relativistic equations for the massless particles. Here we show that for the free particles and antiparticles with the mass m > 0 and the arbitrary spin s ≥ 12 there also exist three types of nonequivalent equations. For the sake of brevity we shall only dwell upon the equations of motion for the particles with spin s = 12 . From the text it would be clear that all results of the paper can be formulated for arbitrary spin. Let us consider the eight-component equation of the Dirac type [3]
7 citations
7 citations
TL;DR: In this article, the form factor in eikonal approximation for the whole region of momentum transfer t in electrodynamics and in φ 3 theory is investigated, and the poles in the time-like region below the threshold are determined.
5 citations
TL;DR: In this paper, the properties of higher isospin states in doubly even s-d shell nuclei are studied in the projected Hartree-Fock-Bogoliubov (HB) model by treating the ground states of neighbouring nuclei as their analogues.
3 citations
3 citations
01 Jan 1972
TL;DR: In this paper, the authors used a combination of improved shell model and deformation corrections to the liquid-drop mass law to calculate fission barrier heights and fission Q-values.
Abstract: Development within the past decade of improved shell model and deformation corrections to the liquid-drop mass law has not only improved its accuracy but also allowed use in more aspects of nuclear physics, such as calculation of fission barriers. Additional experimental data are thus available as input for determination of mass-formula parameters. Preliminary results including fission barrier heights and fission Q-values as input data will be presented. Statistical tests have been performed on fits to the 1971 mass table and to the input reactions and doublets, indicating a possible discrepancy between the two forms of data.
3 citations
01 Jan 1972
TL;DR: In this paper, the results of the nonrelativistic quark model can be reproduced by a fully relativistic model of deeply bound spin - 1 2 quarks.
Abstract: A study is made to determine if the results of the nonrelativistic quark model can be reproduced by a fully relativistic model of deeply bound spin - 1 2 quarks. It is found that the relativistic model does not reproduce the nonrelativistic results, even when the quarks have nonrelativistic momenta. However, the model is rather successful in accounting for the known properties of mesons. Numerical solutions to the Bethe-Salpeter equation are obtained for pseudoscalar and vector bound states of equal mass quark-antiquark pairs, with either a scalar, pseudoscalar, or neutral vector exchange interaction. The interaction function corresponds to single particle exchange, with the addition of either one or two regulating terms. It is found that the second regulator allows the internal quark momentum to be nonrelativistic, but that the spinor structure of the wave function remains highly relativistic. Only the scalar interaction can account for the observed spectrum of states. The pseudoscalar interaction yields a vector state of lower mass than the pseudoscalar state, and the vector interaction leads to a vector state which lies approximately one quark mass above the pseudoscalar state. The λ quark is taken as slightly heavier than the p and n, and the perturbation treatment of the mass difference leads to a quadratic mass formula. The decay amplitudes for π, K → μν are calculated, and it is found, independent of parameters, that ƒ π ≈ ƒ K for either a scalar or vector interaction, in agreement with experiment and in contrast with the nonrelativistic model. The amplitudes for ϱo, ω, φ → e+e−, μ+μ− are also calculated, but in this case the ratios (again parameter independent) are in minor discrepancy with experiment. The question of the additivity of quark amplitudes is examined by calculating (with significant restrictions) the magnetic moments of the vector mesons and the amplitudes for magnetic transitions such as ω → πoγ. The magnetic moments of the vector mesons have the same (trivial) ratios to each other as in the nonrelativistic model, but they are strongly enhanced over the sum of the quark magnetic moments. The amplitude for magnetic transitions, however, is related to the quark magnetic moments in approximately the same ratio as in the nonrelativistic model. The model is also used to obtain parameter dependent predictions for the masses and decay amplitudes. These predictions are not experimentally correct, but are generally well within an order of magnitude for a wide range of the parameters. The most significant defect discovered of the model is the presence of ghost states (the daughters of the vector mesons, with JPC = 0+−) with masses of about 2 BeV.
TL;DR: In this article, the eikonal approximation has the non-trivial features of providing falling form factors and correct relativistic mass formula for the bound-states, it can be taken as a theoretical laboratory to derive S -matrix elements of n composite particles from an underlying S-matrix element of 2 n elementary particles.
TL;DR: In this article, the authors consider the case where the Gell-Mann-Okubo (G~O) mass formula is well satisfied for tile ground states of the octet and the decuplet trajectories.
Abstract: The hypothesis that the dominant par t of the hadron Regge-trajectory function is linear in (mass) 2 has recently been used very popularly in many theoretical works. On lhe other hand, the Gell-Mann-Okubo (G~O) mass formula (~) is well satisfied for tile ground states of the octet and the decuplet trajectories. I t will be a natural expectation that the same symmetry breaking scheme, thus GMO mass formula, is valid for all higher excited states. But by the incompleteness of the experimental mass data, this hypothesis is not yet confirmed. For the mesons the above two hypotheses are trivially compatible and one of the solutions is a universali ty of the slopes. The compatibility, however, offers new problem for baryons, because the mass formlfla is now linear in mass but the t rajectory is quadratic. Experimental ly, the slopes of the baryon trajectories are different from each other. In this note we discuss the consequence of the compatibili ty of the two hypotheses for the baryon case together with the experimental situation. First of all we consider the very extreme case where the GMO formula is regorously satisfied for all physical points on the linear baryon trajectories; for the octet baryons (i)
TL;DR: In this article, the core renormalization in light nuclei is introduced through a dependence of the core radius on the occupation number of the last shell, in a linear approximation.
Abstract: Core renormalization in light nuclei is introduced through a dependence of the core radius on the occupation number of the last shell, in a linear approximation. The corresponding coefficient for the shells 1p3/2, 1p1/2, 1d5/2, 2s1/2, 1d3/2, 1f7/2 is obtained by fitting experimental Coulomb energy differences with a modified Hecht's mass formula, containing four adjustable parameters. Evidence is found for a renormalization effect corresponding to a dilatation of the core.