Mass formula

About: Mass formula is a research topic. Over the lifetime, 1248 publications have been published within this topic receiving 22043 citations.

Soliton Solutions of Relativistic Hartree's Equations

Abstract: We study a model based on $N$ scalar complex fields coupled to a scalar real field, where all fields are treated classically as c-numbers. The model describes a composite particle made up of $N$ constituents with bare mass $m_0$ interacting both with each other and with themselves via the exchange of a particle of mass $\mu_0$. The stationary states of the composite particle are described by relativistic Hartree's equations. Since the self-interaction is included, the case of an elementary particle is a nontrivial special case of this model. Using an integral transform method we derive the exact ground state solution and prove its local stability. The mass of the composite particle is calculated as the total energy in the rest frame. For the case of a massless exchange particle the mass formula is given in closed form. The mass, as a function of the coupling constant, possesses a well pronounced minimum for each value of $\mu_0/m_0$, while the absolute minimum occurs at $\mu_0=0$.

Pions as collective modes in the glueball condensate vacuum

Abstract: The glueball condensate vacuum model is extended to incorporate the effects of light quarks. The resulting model exhibits spontaneous breaking of chiral SU(2)/sub f/ symmetry, and has a new kind of collective excitations, pions, which are distinct from the usual bag-model-type states. The dynamics of the pions are described by a sigma model, and the parameters and f/sub ..pi../ are calculated in terms of the radius R of the vacuum cells. The pion mass is related to and m/sub q/ via the usual partial conservation of axial-vector current relation. The model is extended to broken SU(3)/sub f/ using lowest-order chiral perturbation theory, and a mass formula for the eta' meson is obtained by including effects of the axial anomaly.

The Relativistic Oscillator and Mass Formulas

Abstract: The mass spectrum of hadrons is as important a problem in relativistic physics as the energy spectrum of molecules and nuclei was in non-relativistic quantum mechanics. In molecular physics the spectrum is explained in terms of single particle excitations and collective rotations and vibrations [1]. In nuclear physics the “parts” of the collective model are also rotations and vibrations [2], with the main difference between molecular and nuclear collective motions being that in molecular physics the rotational and vibrational mode are well separated from each other and from the particle excitations and in nuclear physics these “parts” are not well separated from each other and rotation-vibration particle interactions play an important role. Hadrons are relativistic extended objects and if the analogy between molecular and nuclear physics persists also for the relativistic domain we would expect the collective mode of hadrons to be relativistic rotators and relativistic oscillators.

Gravitational vacuum hypothesis and cosmology with variable particle number

Abstract: We discuss a heurisitic model of gravitational vacuum as a set of virtual, radiating planckeons, particles with Planck size (L) and mass (ħ/cL). Combined with Dirac's large number hypothesis, this gives the minimum universe scale factor valuea min∼10−13 cm, the strong interaction length (a = L just whena=a min ). Taking this state as an initial one using standard quantum techniques, we consider particle creation by planckeons. Under some reasonable assumptions we obtain the present number of particles with nucleon mass close to observations,N ∼ 1080. A criterion for gravitational stability of particles is formulated and some applications of the corresponding mass formula are considered. In particular, Fermi's weak interaction constant is expressed in terms ofa andL and a finite value for the neutrino mass is obtained.