Mass formula

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

Atomic Mass: Origin, Units and Constants

Abstract: Absolute and relative atomic mass values are obtained in kg/atom, MeV, C, and u for the chemical elements. The results show that: (i) Absolute atomic mass value is, of course, given by the classical mass formula m = hϑ/c2; however, rotational speed per radius ω/r correlates with strain τ on the element’s intrinsic electromagnetic (e-m) transverse radiation to give the coefficient k whose value turns out to be atomic mass unit energy equivalent amu/eV = k = τ/(ω/r)½. (ii) Each component of the wave-particle doublet plays unique roles in atomic mass phenomenology; these roles readily account for H atom’s seeming fundamentality and preponderance of internal structures in virtually all particulate matter down to the electron. (iii) The mass constants amu/eV and amu/C are linear correlation coefficients of different dimensions of atomic units; the values are thus not specific to particular elements but obtainable from any element including the electron. (iv) The empirical expression e- = F/NA is incorrect; theoretically, charge q = mrF = mabsNAF. The error translates to values of NA, me, and e/me that are twenty orders of magnitude lower than theoretical values, e.g., e-theor. = 47.062 C c.f. e-lit. = 1.6022 x 10-19 C. It is posited that the charge determinants ω and τ, might be suppressed or virtually nullified in an external e-m environment above some threshold voltage. (v) The error reflects also in all empirical E/c2 values. A comparison of empirical and theoretical quantitative expressions for evaluating gravitational (gm) from electrostatic (E/c2) atomic mass shows that the former redeems the inherent error to retrieve proximate gm from E/c2 value. (vi) Given the current literature E/c2 values, the electron waveform mass does converge with the photon’s value, i.e., mw(e) ≅ mphoton. It is submitted, therefore, that particle physics has already struck matter’s fundamental unit in the photon mass, maybe unknowingly for lack of litmus test.

A new method for obtaining the spectrum of baryon resonances in the Killingbeck potential

Abstract: In this paper, we investigate the spin- and flavor-dependent SU(6) violations in the baryon resonances spectrum using a simple approach based on the G?rsey?Radicati (GR) mass formula. The relativistic energy spectrum has some very important features that makes it vastly superior to the nonrelativistic one; so, in order to obtain the average energy value of each SU(6) multiplet, we have exactly solved the Dirac equation for the Killingbeck potential analytically by using the wave function ansatz method. The results of our model (the combination of our proposed hypercentral potential and the generalized GR mass formula for the description of the spectrum) show that the strange and nonstrange baryon spectra are, in general, fairly well reproduced. The overall good description of the spectrum which we obtain shows that our model can also be used to give a fair description of the energies of the excited multiplets with more than 2?GeV mass and negative-parity resonance. Moreover, we have shown that our model reproduces the position of the Roper resonance of the nucleon. Finally, we compare the results obtained by the Dirac equation for the Killingbeck potential with the corresponding results of the Schr?dinger equation for the Cornell potential and we find that our model has improved the results of the nonrelativistic model.

On static Poincaré-Einstein metrics

Abstract: The classification of solutions of the static vacuum Einstein equations, on a given closed manifold or an asymptotically flat one, is a long-standing and much-studied problem. Solutions are characterized by a complete Riemannian n-manifold (M, g) and a positive function N, called the lapse. We study this problem on Asymptotically Poincare-Einstein n-manifolds, n ≥ 3, when the conformal boundary-at-infinity is either a round sphere, a flat torus or smooth quotient thereof, or a compact hyperbolic manifold. Such manifolds have well-defined Wang mass, and are time-symmetric slices of static, vacuum, asymptotically anti-de Sitter spacetimes. By integrating a mildly generalized form of an identity used by Lindblom, Shen, Wang, and others, we give a mass formula for such manifolds. There are no solutions with positive mass. In consequence, we observe that either the lapse is trivial and (M, g) is Poincare-Einstein or the Wang mass is negative, as in the case of time symmetric slices of the AdS soliton. As an application, we use the mass formula to compute the renormalized volume of the warped product (X, γ) ≃ (M 3 , g) × N 2 (S 1 , dt 2). We also give a mass formula for the case of a metric that is static in the region exterior to a horizon on which the lapse function is zero. Then the manifold (X, γ) is said to have a “bolt” where the S 1 factor shrinks to zero length. The renormalized volume of (X, γ) is expected on physical grounds to have the form of the free energy per unit temperature for a black hole in equilibrium with a radiation bath at fixed temperature. When M is 3-dimensional and admits a horizon, we apply this mass formula to compute the renormalized volume of (X, γ) and show that it indeed has the expected thermodynamically motivated form. We also discuss several open questions concerning static vacuum asymptotically Poincare-Einstein manifolds.