Showing papers on "Mass formula published in 2016"

Smarr formula for Lovelock black holes: A Lagrangian approach

Abstract: The mass formula for black holes can be formally expressed in terms of a Noether charge surface integral plus a suitable volume integral, for any gravitational theory. The integrals can be constructed as an application of Wald's formalism. We apply this formalism to compute the mass and the Smarr formula for static Lovelock black holes. Finally, we propose a new prescription for Wald's entropy in the case of Lovelock black holes, which takes into account topological contributions to the entropy functional.

Mass Formulae for Broken Supersymmetry in Curved Space-Time

Abstract: We derive the mass formulae for N=1, D=4 matter-coupled Supergravity for broken (and unbroken) Supersymmetry in curved space-time. These formulae are applicable to De Sitter configurations as is the case for inflation. For unbroken Supersymmetry in anti-de Sitter (AdS) one gets the mass relations modified by the AdS curvature. We compute the mass relations both for the potential and its derivative non-vanishing.

Hall viscosity and electromagnetic response of electrons in graphene

Abstract: We derive an analytic expression for the geometric Hall viscosity of noninteracting electrons in a single graphene layer in the presence of a perpendicular magnetic field. We show that a recently derived formula in C. Hoyos and D. T. Son [Phys. Rev. Lett. 108, 066805 (2012)], which connects the coefficient of ${q}^{2}$ in the wave-vector expansion of the Hall conductivity ${\ensuremath{\sigma}}_{xy}(q)$ of the two-dimensional electron gas (2DEG) to the Hall viscosity and the orbital diamagnetic susceptibility of that system, continues to hold for graphene, in spite of the lack of Galilean invariance, with a suitable definition of the effective mass. We also show that, for a sufficiently large number of occupied Landau levels in the positive-energy sector, the Hall conductivity of electrons in graphene reduces to that of a Galilean-invariant 2DEG with an effective mass given by $\ensuremath{\hbar}{k}_{F}/{v}_{F}$ (cyclotron mass). Even in the most demanding case, i.e., when the chemical potential falls between the zeroth and the first Landau levels, the cyclotron mass formula gives results accurate to better than 1%. The connection between the Hall conductivity and the viscosity provides a possible avenue to measure the Hall viscosity in graphene.

Formula for growth rate of mixing width applied to Richtmyer-Meshkov instability

Abstract: The mixing zone width and its growth rate are of great significance in the study of the Richtmyer-Meshkov instability (RMI). In this paper, a formula for the growth rate of the mixing width is proposed for analysis of the RMI-induced mixing process. A new definition of the mixing width h , based on the mass fraction ϕ, is used to derive the formula of the growth rate of the mixing width, h . In the derivation, the velocity field and the diffusion term are concisely introduced into the formula by using the mass equation and mass fraction equation. This formula is used together with two-dimensional (2D) and three-dimensional (3D) numerical data to quantitatively study the effects of compressibility and the diffusion process on the development of the RMI. The results based on our simulations show the following. After a shock, the magnitudes of the contributions of compressibility and diffusion to h increase initially, and in the middle stage of the RMI, they appear to attain a maximum value, around 10%...

A note on black-hole physics, cosmic censorship, and the charge–mass relation of atomic nuclei

Abstract: Arguing from the cosmic censorship principle, one of the fundamental cornerstones of black-hole physics, we have recently suggested the existence of a universal upper bound relating the maximal electric charge of a weakly self-gravitating system to its total mass: , where Z is the number of protons in the system, A is the total baryon (mass) number, and is the dimensionless fine-structure constant. In order to test the validity of this suggested bound, we here explore the functional relation of atomic nuclei as deduced from the Weizsacker semi-empirical mass formula. It is shown that all atomic nuclei, including the meta-stable maximally charged ones, conform to the suggested charge–mass upper bound. Our results support the validity of the cosmic censorship conjecture in black-hole physics.

Exact power series solutions of the structure equations of the general relativistic isotropic fluid stars with linear barotropic and polytropic equations of state

Abstract: Obtaining exact solutions of the spherically symmetric general relativistic gravitational field equations describing the interior structure of an isotropic fluid sphere is a long standing problem in theoretical and mathematical physics. The usual approach to this problem consists mainly in the numerical investigation of the Tolman-Oppenheimer-Volkoff and of the mass continuity equations, which describes the hydrostatic stability of the dense stars. In the present paper we introduce an alternative approach for the study of the relativistic fluid sphere, based on the relativistic mass equation, obtained by eliminating the energy density in the Tolman-Oppenheimer-Volkoff equation. Despite its apparent complexity, the relativistic mass equation can be solved exactly by using a power series representation for the mass, and the Cauchy convolution for infinite power series. We obtain exact series solutions for general relativistic dense astrophysical objects described by the linear barotropic and the polytropic equations of state, respectively. For the polytropic case we obtain the exact power series solution corresponding to arbitrary values of the polytropic index $n$ . The explicit form of the solution is presented for the polytropic index $n=1$ , and for the indexes $n=1/2$ and $n=1/5$ , respectively. The case of $n=3$ is also considered. In each case the exact power series solution is compared with the exact numerical solutions, which are reproduced by the power series solutions truncated to seven terms only. The power series representations of the geometric and physical properties of the linear barotropic and polytropic stars are also obtained.

Exact power series solutions of the structure equations of the general relativistic isotropic fluid stars with linear barotropic and polytropic equations of state

Abstract: Obtaining exact solutions of the spherically symmetric general relativistic gravitational field equations describing the interior structure of an isotropic fluid sphere is a long standing problem in theoretical and mathematical physics. The usual approach to this problem consists mainly in the numerical investigation of the Tolman-Oppenheimer-Volkoff and of the mass continuity equations, which describes the hydrostatic stability of the dense stars. In the present paper we introduce an alternative approach for the study of the relativistic fluid sphere, based on the relativistic mass equation, obtained by eliminating the energy density in the Tolman-Oppenheimer-Volkoff equation. Despite its apparent complexity, the relativistic mass equation can be solved exactly by using a power series representation for the mass, and the Cauchy convolution for infinite power series. We obtain exact series solutions for general relativistic dense astrophysical objects described by the linear barotropic and the polytropic equations of state, respectively. For the polytropic case we obtain the exact power series solution corresponding to arbitrary values of the polytropic index $n$. The explicit form of the solution is presented for the polytropic index $n=1$, and for the indexes $n=1/2$ and $n=1/5$, respectively. The case of $n=3$ is also considered. In each case the exact power series solution is compared with the exact numerical solutions, which are reproduced by the power series solutions truncated to seven terms only. The power series representations of the geometric and physical properties of the linear barotropic and polytropic stars are also obtained.

Surface area products for Kerr-Taub-NUT space-time

Abstract: We examine properties of the inner and outer horizon thermodynamics of Taub-NUT (Newman-Unti-Tamburino) and Kerr-Taub-NUT (KTN) black hole (BH) in four-dimensional Lorentzian geometry . We compare and contrasted these properties with the properties of Reissner Nordstrom (RN) BH and Kerr BH. We focus on “area product”, “entropy product”, “irreducible mass product” of the event horizon and Cauchy horizons. Due to mass dependence, we speculate that these products have no nice quantization feature. Nor do they have any universal property. We further observe that the first law of BH thermodynamics and Smarr-Gibbs-Duhem relations do not hold for Taub-NUT (TN) and KTN BH in Lorentzian regime. The failure of these aforementioned features are due to the presence of the non-trivial NUT charge which makes the space-time be asymptotically non-flat, in contrast with RN BH and Kerr BH. Another reason for the failure is that Lorentzian TN and Lorentzian KTN geometries contain Dirac-Misner–type singularity , which is a manifestation of a non-trivial topological twist of the manifold. The black-hole mass formula and Christodoulou-Ruffini mass formula for TN and KTN BHs are also computed. These thermodynamic product formulae give us further understanding of the nature of inner as well as outer BH entropy at the microscopic level.

Thermodynamics and phase transition in rotational Kiselev black hole

Abstract: In this work, we investigate the thermodynamic properties of rotational Kiselev black holes (KBH). Specifically, we use the first-order approximation of the event horizon (EH) to calculate thermodynamic properties for general equations of state $\omega$. These thermodynamic properties include areas, entropies, horizon radii, surface gravities, surface temperatures, Komar energies and irreducible masses at the Cauchy horizon (CH) and EH. We study the products of these thermodynamic quantities, we find that these products are determined by the equation of state $\omega$ and strength parameter $\alpha$. In the case of the quintessence matter ($\omega=-2/3$), radiation ($\omega=1/3$) and dust ($\omega=0$), we discuss their properties in detail. We also generalize the Smarr mass formula and Christodoulou-Ruffini mass formula to rotational KBH. Finally we study the phase transition and thermodynamic geometry for rotational KBH with radiation ($\omega=1/3$). Through analysis, we find that this phase transition is a second order phase transition. Furthermore, we also obtain the scalar curvature in the thermodynamic geometry framework, indicating that the radiation matter may change the phase transition condition and properties for Kerr black hole.

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.

The Lorentz Transformation at the Maximum Velocity for a Mass

Abstract: Haug [1, 2] has recently shown there is a speed limit for fundamental particles just below the speed of light. This speed limit means that the mass of a fundamental particle not will go towards infinity as v approaches c in the Einstein relativistic mass equation. The relativistic mass limit for a fundamental particle is the Planck mass. In this paper we use the same velocity limit in the Lorentz transformation. This leads to what we think could be significant results with some interesting interpretations. In addition we look at rapidity as well as relativity of simultaneity for subatomic particles at this maximum velocity for masses.

Group schemes and local densities of ramified hermitian lattices in residue characteristic 2 Part I

Abstract: The obstruction to the local-global principle for a hermitian lattice (L, H) can be quantified by computing the mass of (L, H). The mass formula expresses the mass of (L, H) as a product of local factors, called the local densities of (L, H). The local density formula is known except in the case of a ramified hermitian lattice of residue characteristic 2. Let F be a finite unramified field extension of Q_2. Ramified quadratic extensions E/F fall into two cases that we call Case 1 and Case 2. In this paper, we obtain the local density formula for a ramified hermitian lattice in Case 1, by constructing a smooth integral group scheme model for an appropriate unitary group. Consequently, this paper, combined with the paper of W. T. Gan and J.-K. Yu, allows the computation of the mass formula for a hermitian lattice (L, H) in Case 1.

Analytical mass formula and nuclear surface properties in the ETF approximation. Part II: asymmetric nuclei

Abstract: Properties of the nuclear medium M Baldo and G F Burgio-Estimating the relevance of predictions from the Skyrme-Hartree-Fock model P-G Reinhard-Recent citations Nuclear skin and the curvature of the symmetry energy Ad. R. Raduta and F. Gulminelli-Constraints on the nuclear equation of state from nuclear masses and radii in a Thomas-Fermi meta-modeling approach D. Chatterjee et al-This content was downloaded from IP address 192.93.53.6 on 17/03 Abstract We have recently addressed the problem of the determination of the nuclear surface energy for symmetric nuclei in the framework of the extended Thomas-Fermi (ETF) approximation using Skyrme functionals. We presently extend this formalism to the case of asymmetric nuclei and the question of the surface symmetry energy. We propose an approximate expression for the diffuseness and the surface energy. These quantities are analytically related to the parameters of the energy functional. In particular, the influence of the different equation of state parameters can be explicitly quantified. Detailed analyses of the different energy components (local/non-local, isoscalar/iso-vector, surface/curvature and higher order) are also performed. Our analytical solution of the ETF integral improves previous models and leads to a precision of better than 200keV per nucleon in the determination of the nuclear binding energy for dripline nuclei.

A New Method for Obtaining the Baryons Mass under the Killingbeck Plus Isotonic Oscillator Potentials

Abstract: The spectrum of ground state and excited baryons (N, Δ, Λ, Σ, , and Ω particles) has been investigated by using nonrelativistic quantum mechanics under the Killingbeck plus isotonic oscillator potentials. Using the Jacobi coordinates, anzast method, and generalized Gursey Radicati (GR) mass formula the three-body-wave equation is solved to calculate the different states of the considered baryons. A comparison between our calculations and the available experimental data shows that the position of the Roper resonances of the nucleon, the ground states, and the excited multiplets up to three GeV are in general well reproduced. Also one can conclude that the interaction between the quark constituents of baryon resonances could be described adequately by using the combination of Killingbeck and isotonic oscillator potentials form.

Mass chains of light hypernuclei and separation energies of mirror hypernuclei from BWMH mass formula

Abstract: In this work, by using generalized semi-empirical mass formula, decay chains of light hypernuclei for odd-A and even-A are calculated and the unstable hypernuclei of mass chains are presented. The ...

Baryon spectroscopy in a three-quark model

Abstract: In this paper, we present a three-body quark model for investigating the internal structure of baryons as well as baryon spectroscopy. In order to describe the SU(6) -invariant part of the spectrum, we assumed the spin-independent part of the interaction hypercentral, and treated using the hyperspherical formalism. For SU(6) -invariant potential, we used a generalized version of the popular “Coulomb-plus-linear” potential which contains “linear-plus-logarithmic” terms as confinement part and some inverse power terms. To obtain an analytical solution, we applied some approximations for dealing with problematic linear and logarithmic terms, leading to a qualitative reproducing of the spectrum. Then, to describe the hyperfine structure of the baryon and the splittings within the SU(6) -multiplets, we used the generalized Gursey-Radicati Mass Formula as a SU(6) breaking interaction. Our calculations lead to a generally fair description of the baryon spectrum.

Updated $1/N_c$ expansion analysis of $[56,2^+]$ and $[70,\ell^+]$ baryon multiplets

Abstract: The mass spectra of the $[{\bf 56, 2^+}]$ and $[{\bf 70, \ell+}]$ multiplets, both belonging to the $N$ = 2 band, is reviewed in the $1/N_c$ expansion method. Previous studies, separately made for each multiplet, are presently updated to the 2014 Particle Data Group. The mass formula including corrections up to $\mathcal{O}(1/N_c)$ and first order in SU(3) flavor symmetry breaking, has the same independent operator basis in both cases. A special emphasis is made on the role of the SU(3) symmetry breaking operators $B_i$ $(i = 1,2,3)$. This can allow for multiplet assignment of $\Lambda$ and $\Sigma$ hyperons, which generally is quite difficult to make. Tentative assignments of hyperons with two- and one-star resonances are made to the $[{\bf 70, \ell+}]$ multiplet. Another important aim is to find out whether or not a common value of the coefficient $c_1$ of the dominant operator in the mass formula, can well fit the present data in both multiplets. A negative answer, which is here the case, implies distinct Regge trajectories for symmetric and mixed symmetric states.

Nuclear physics from QCD on lattice

Abstract: We have presented a strategy to study nuclei and nuclear matters from first principles, namely, from QCD. We first compute nucleon-nucleon potentials numerically in lattice QCD, and then use them to investigate properties of nuclei and nuclear matter by various methods developed in nuclear physics. As a demonstration that this strategy works, mass and structure of 4 He, 16 O and 40 Ca, and equation of state of nuclear matters are determined with the lattice QCD induced twonucleon potentials in a heavy quark region as an input. We have found that these nuclei and the symmetric nuclear matter are bound at one quark mass corresponding to the pseudo-scalar meson (pion) mass of 469 MeV (the octet baryon (nucleon) mass of 1161 MeV). The obtained binding energy per nucleon has a uniform mass-number A dependence which is consistent with the BetheWeizsacker mass formula qualitatively. The present study demonstrates that our strategy works well to investigate various properties of atomic nuclei and nuclear matter starting from QCD, without depending on models or experimental information about the nuclear force.

The restoration of Wigner’s SU(4)-symmetry in the superheavy nucleus and its correlation with the problem “island of stability”, or does the “island of stability” exist?

Abstract: This paper reviews the history and stages of experimental verification of the hypothesis of Wigner’s spin–isospin SU(4)-symmetry restoration in the field of heavy atomic nuclei and its implications on hypothesis of the “island of stability”. Energies of α-decay of a number of α-chains of new superheavy nuclei were calculated based on Wigner’s mass formula without contribution of spin–orbit interaction that correspond to the restoration of Wigner’s spin–isospin symmetry. Calculated energies of the α-decay fit the experimental data better than other theoretical approaches. It is concluded that there is a need to continue theoretical research of the “island of stability” taking into account mechanisms of restoration of Wigner’s spin–isospin SU(4)-symmetry.

Mass Shift Due to the Nonlinear Lorentz Group.

Abstract: We determine nonlinear Lorentz transformations between coordinate systems which are mutually in a constant symmetrical accelerated motion. The maximal acceleration as an analogue of the maximal velocity in special relativity follows from the nonlinear Lorentz group of transformtion. The mass formula was derived by the same method as the Thomas precession formula by author. It can play crucial role in particle physics and cosmology

Modelling Hadronic Matter

Abstract: Hadron physics stands somewhere in the diffuse intersection between nuclear and particle physics and relies largely on the use of models. Historically, around 1930, the first nuclear physics models known as the liquid drop model and the semi-empirical mass formula established the grounds for the study of nuclei properties and nuclear structure. These two models are parameter dependent. Nowadays, around 500 hundred non-relativistic (Skyrme-type) and relativistic models are available in the literature and largely used and the vast majority are parameter dependent models. In this review I discuss some of the shortcomings of using non-relativistic models and the advantages of using relativistic ones when applying them to describe hadronic matter. I also show possible applications of relativistic models to physical situations that cover part of the QCD phase diagram: I mention how the description of compact objects can be done, how heavy-ion collisions can be investigated and particle fractions obtained and show the relation between liquid-gas phase transitions and the pasta phase.

Improved Numerical Generalization of Bethe- Weizsacker Mass Formula

Abstract: In this paper is presented explicit improved numerical generalization of Bethe-Weizsacker mass formulae which describes the values of measured 2654 nuclear mass in AME2012 nuclear database with accuracy less than 2.2 MeV, starting from the number of protons Z=1 and number of neutrons N=1. In the obtained generazation of the Bethe-Weizsacker formula the influence of magic numbers and boundaries of their influence between them is defined for nine proton (2, 8, 14, 20, 28, 50, 82, 108, 124) and ten neutron (2, 8, 14, 20, 28, 50, 82, 124, 152, 202) magic numbers.

Generalised Einstein mass-variation formulae: II Superluminal relative frame velocities

Abstract: In part I of this paper we have deduced generalised Einstein mass variation formulae assuming relative frame velocities v c . Here we present corresponding new expressions for superluminal relative frame velocities v > c . We again use the notion of the residual mass m 0 ( v ) which for v > c is defined by the equation m ( v ) = m 0 ( v ) [ ( v / c ) 2 - 1 ] - 1 / 2 for the actual mass m ( v ) . The residual mass is essentially the actual mass with the Einstein factor removed, and we emphasise that we make no restrictions on m 0 ( v ) . Using this formal device we deduce corresponding new mass variation formulae applicable to superluminal relative frame velocities, assuming only the extended Lorentz transformations and their consequences, and two invariants that are known to apply in special relativity. The present authors have previously speculated a dual framework such that both the rest mass m 0 ∗ and the residual mass at infinite velocity m ∞ ∗ (by which we mean p ∞ ∗ / c , assuming finite momentum at infinity) are equally important parameters in the specification of mass as a function of its velocity, and the two arbitrary constants can be so determined. The new formulae involving two arbitrary constants may also be exploited so that the mass remains finite at the speed of light, and two distinct mass profiles are determined as functions of their velocity with the rest mass assumed to be alternatively prescribed at the origin of either frame. The two profiles so obtained ( M ( U ) , m ( u ) ) and ( M ∗ ( U ) , m ∗ ( u ) ) although distinct have a common ratio M ( U ) / M ∗ ( U ) = m ( u ) / m ∗ ( u ) that is a function of v > c , indicating that observable mass depends upon the frame in which the rest mass is prescribed.

Surface energy coefficient determination in global mass formula from fission barrier energy

Abstract: Semi-empirical mass formula of the atomic nucleus describe binding energies of the nuclei. In the simple form of this formula, there are five terms related to the properties of the nuclear structure. The coefficients in each terms can be determined by various approach such as fitting on experimental binding energy values. In this study, the surface energy coefficient in the formula which is a correction on total binding energy has been obtained by a method that is not previously described in the literature. The experimental fission barrier energies of nuclei have been used for this task. According to the results, surface energy coefficient in one of the most conventional formula has been improved by a factor 3.4.

Light Baryons Mass in a Non-Relativistic Quark Model within an Hypercentral Power Low Potential

Abstract: In this work, we calculated the baryon mass within a non-relativistically quark model using an approach based on the G\"ursey Radicati mass formula (GR). The average energy value of each SU(6) multiplet is described using the SU(6) invariant interaction given by a hypercentral potential. In our series studies we investigate different interactions and situations to gain the best possible model. This goal can be obtained by checking and studying various potentials in different situations. In this paper we present the solution of the Schr\"odinger equation with an hypercentral power low potential. The results of our model (the combination of our proposed hypercentral Potential and generalized GR mass formula to description of the spectrum) show that the strange and non-strange baryons spectra are in general fairly well reproduced. The overall good description of the mass which we obtain shows that our model can also be used to give a fair description of the energies of the excited multiplets up to three GeV and the position of the Roper resonances of the nucleon.

Baryon masses in a nonrelativistic model with the quantum isotonic oscillator potential

Abstract: The nonrelativistic quark model and a new baryon mass formula have been applied to study the baryon octet and decuplet masses. To describe the quark-quark interacting forces inside baryons, a suitable phenomenological form of the potential and quantum isotonic oscillator potential have been proposed. A comparison between calculations reported in this study and the available experimental data is investigated. The description of the spectrum shows that the position of the Roper resonances of the nucleon, the ground states and the excited multiplets up to three GeV are in general well reproduced.