Showing papers on "Mass formula published in 2011"

Further improvements on a global nuclear mass model

Abstract: The semi-empirical macroscopic-microscopic mass formula is further improved by considering some residual corrections. The rms deviation from 2149 known nuclear masses is significantly reduced to 336 keV, even lower than that achieved with the best of the Duflo-Zuker models. The $\ensuremath{\alpha}$-decay energies of super-heavy nuclei, the Garvey-Kelson relations, and the isobaric multiplet mass equation (IMME) can be reproduced remarkably well with the model, and the predictive power of the mass model is good. With a systematic study of 17 global nuclear mass models, we find that the quadratic form of the IMME is closely related to the accuracy of nuclear mass calculations when the Garvey-Kelson relations are reproduced reasonably well. Fulfilling both the IMME and the Garvey-Kelson relations seem to be two necessary conditions for improving the quality of the model prediction. Furthermore, the $\ensuremath{\alpha}$-decay energies of super-heavy nuclei should be used as an additional constraint on global nuclear mass models.

A new baryonic equation of state at sub-nuclear densities for core-collapse simulations

Abstract: We calculate a new equation of state for baryons at sub-nuclear densities meant for the use in core-collapse simulations of massive stars. The abundances of various nuclei are obtained together with the thermodynamic quantities. The formulation is the nuclear statistical equilibrium description and the liquid drop approximation of nuclei. The model free energy to minimize is calculated by relativistic mean field theory for nucleons and the mass formula for nuclei with atomic number up to ~1000. We have also taken into account the pasta phase, thanks to which the transition to uniform nuclear matter in our equation of state (EOS) occurs in the conventional manner: nuclei are not dissociated into nucleons but survive right up to the transition to uniform nuclear matter. We find that the free energy and other thermodynamical quantities are not very different from those given in the H. Shen's EOS, one of the standard EOSs that adopt the single nucleus approximation. On the other hand, the average mass is systematically different, which may have an important ramification to the rates of electron captures and coherent neutrino scatterings on nuclei in supernova cores. It is also interesting that the root mean square of the mass number is not very different from the average mass number, since the former is important for the evaluation of coherent scattering rates on nuclei but has been unavailable so far. The EOS table is currently under construction, which will include the weak interaction rates.

A new baryonic equation of state at sub-nuclear densities for core-collapse simulations

Abstract: We calculate a new equation of state for baryons at sub-nuclear densities meant for the use in core-collapse simulations of massive stars. The abundance of various nuclei is obtained together with the thermodynamic quantities. The formulation is the NSE description and the liquid drop approximation of nuclei. The model free energy to minimize is calculated by relativistic mean field theory for nucleons and the mass formula for nuclei with the atomic number up to ~ 1000. We have also taken into account the pasta phase, thanks to which the transition to uniform nuclear matter in our EOS occurs in the conventional manner: nuclei are not dissociated to nucleons but survive right up to the transition to uniform nuclear matter. We find that the free energy and other thermodynamical quantities are not very different from those given in the Shen's EOS, one of the standard EOS's that adopt the single nucleus approximation. The average mass is systematically different, on the other hand, which may have an important ramification to the rates of electron captures and coherent neutrino scatterings on nuclei in supernova cores. It is also interesting that the root mean square of the mass number is not very different from the average mass number, since the former is important for the evaluation of coherent scattering rates on nuclei but has been unavailable so far. The EOS table is currently under construction, which will include the weak interaction rates.

Dynamical equation of the effective gluon mass

Abstract: In this article, we derive the integral equation that controls the momentum dependence of the effective gluon mass in the Landau gauge. This is accomplished by means of a well-defined separation of the corresponding ''one-loop dressed'' Schwinger-Dyson equation into two distinct contributions, one associated with the mass and one with the standard kinetic part of the gluon. The entire construction relies on the existence of a longitudinally coupled vertex of nonperturbative origin, which enforces gauge invariance in the presence of a dynamical mass. The specific structure of the resulting mass equation, supplemented by the additional requirement of a positive-definite gluon mass, imposes a rather stringent constraint on the derivative of the gluonic dressing function, which is comfortably satisfied by the large-volume lattice data for the gluon propagator, both for SU(2) and SU(3). The numerical treatment of the mass equation, under some simplifying assumptions, is presented for the aforementioned gauge groups, giving rise to a gluon mass that is a nonmonotonic function of the momentum. Various theoretical improvements and possible future directions are briefly discussed.

Brief note on Ashtekar-Magnon-Das conserved quantities in quadratic curvature theories

Abstract: In this note, we correct a mistake in the mass formula in [N. Okuyama and J. i. Koga, Phys. Rev. D 71, 084009 (2005).] which generalizes the Ashtekar-Magnon-Das method to incorporate extended gravities with quadratic curvature terms. The corrected mass formula confirms that the black hole masses for recently discovered critical gravities vanish.

Mass varying neutrinos, quintessence, and the accelerating expansion of the Universe

Abstract: We analyze the mass varying neutrino scenario. We consider a minimal model of massless Dirac fermions coupled to a scalar field, mainly in the framework of finite-temperature quantum field theory. We demonstrate that the mass equation we find has nontrivial solutions only for special classes of potentials, and only within certain temperature intervals. We give most of our results for the Ratra-Peebles dark energy (DE) potential. The thermal (temporal) evolution of the model is analyzed. Following the time arrow, the stable, metastable, and unstable phases are predicted. The model predicts that the present Universe is below its critical temperature and accelerates. At the critical point, the Universe undergoes a first-order phase transition from the (meta)stable oscillatory regime to the unstable rolling regime of the DE field. This conclusion agrees with the original idea of quintessence as a force making the Universe roll towards its true vacuum with a zero $\ensuremath{\Lambda}$ term. The present mass varying neutrino scenario is free from the coincidence problem, since both the DE density and the neutrino mass are determined by the scale $M$ of the potential. Choosing $M\ensuremath{\sim}{10}^{\ensuremath{-}3}\text{ }\text{ }\mathrm{eV}$ to match the present DE density, we can obtain the present neutrino mass in the range $m\ensuremath{\sim}{10}^{\ensuremath{-}2}--1\text{ }\text{ }\mathrm{eV}$ and consistent estimates for other parameters of the Universe.

Spectrum of strange and nonstrange baryons by using generalized guersey radicati mass formula and hypercentral potential

Abstract: In this work, we study the spin and flavor dependent SU(6) violations in the strange and nonstrange baryons spectrum using a simple approach based on the Gürsey 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 this paper the hypercentral potential is regarded as a combination of the Coulombic-like term plus a linear confining term and we have added the harmonic oscillator potential. In fact, we have built up a potential scheme for the internal baryon structure which has three-body forces among three quarks. 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 nonstrange baryons spectrum 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 at least up to 2 GeV and negative-parity resonance. Moreover, we have shown that our model reproduces the position of the Roper resonances of the nucleon.

Isobaric multiplet mass equation for A = 7 and 8

Abstract: Deviations from the isobaric multiplet mass equation are presented and discussed for the $A=7$, $T=3/2$ quartet and the $A=8$, $T=2$ quintet.

Where is the pseudoscalar glueball

Abstract: The pseudoscalar mesons ?(1300), K(1460), ?(1295), ?(1405) and ?(1475) are assumed to form the meson decuplet which includes the glueball as the basis state supplementing the standard SU(3)F nonet of light states (q = u, d, s). The decuplet is investigated by using the algebraic approach based on the hypothesis of vanishing exotic commutators of SU(3)F 'charges' and their time derivatives. This leads to a system of master equations determining: (a) octet contents of the physical isoscalar mesons, (b) the mass formula relating all masses of the decuplet and (c) the mass ordering rule. The states of the physical isoscalar mesons ?(1295), ?(1405), ?(1475) are expressed as superpositions of the 'ideal' (N and S) states and the glueball G one. The 'mixing matrix' realizing transformation from the unphysical states to the physical ones follows from the octet contents and is totally expressed by the decuplet meson masses. Among four one-parameter families of the resulting mixing matrices (multitude of the solutions arising from bad quality of data on the ?(1300) and K(1460) meson masses) there is a family attributing the glueball-dominated composition to the ?(1405) meson. The pseudoscalar decuplet is similar in some respects to the scalar one: both are composed of the excited states and G; the mass ordering of their N, S, G?dominated isoscalars is the same. Contrary to the lattice QCD and other predictions, the mass of the pseudoscalar pure glueball state is smaller than the scalar one.

Proton dripline in a new formula for nuclear binding energy

Abstract: The location of the proton dripline in a new phenomenological mass formula is calculated. Predictions of different mass formulas for the dripline are compared. The implications of the new mass formula for rapid proton nucleosynthesis beyond 56 Ni are discussed. It is seen that the new formula indicates that masses up to A = 80 are easily synthesized in a typical X-ray burst.

Self-gravitating discs and the Sobolev inequality

Abstract: We estimate the minimal mass of self-gravitating polytropic discs using the famous Sobolev inequality. This resembles the well-known mass formula for Lane–Emden stars. For ideal gas with the polytropic index n= 3, the minimal mass is not smaller than the Jeans mass. The accuracy of the estimate is verified in a number of numerical examples. The bound works well for heavy self-gravitating discs and is less useful for light discs.

Mass formula of division algebras over global function fields

Abstract: In this paper we give two proofs of the mass formula for definite central division algebras over global function fields, due to Denert and Van Geel. The first proof is based on a calculation of Tamagawa measures. The second proof is based on analytic methods, in which we establish the relationship directly between the mass and the value of the associated zeta function at zero.

SU(6) $[{\bf 70},1^-]$ baryon multiplet in the $1/N_c$ expansion

Abstract: The masses of excited states of mixed orbital symmetry of nonstrange and strange baryons belonging to the lowest [70,1{sup -}] multiplet are calculated in the 1/N{sub c} expansion to order 1/N{sub c} with a new method which allows one to considerably reduce the number of linearly independent operators entering the mass formula. This study represents an extension to SU(6) of our work on nonstrange baryons, the framework of which was SU(4). The conclusion regarding the role of the flavor operator, neglected in previous SU(6) studies, is reinforced. Namely, both the flavor and spin operators contribute dominantly to the flavor-spin breaking.

A quark-diquark baryon model

Abstract: A simple quark-diquark model for the baryons is constructed as a partial solution to the well known missing resonances problem. A complete classification of the baryonic states in the quark-diquark framework is given and the spectrum is calculated through a mass formula built to reproduce the rotational and vibrational Regge trajectories.

Glueballs and the Pomeron

Abstract: Glueballs are considered to be bound states of constituent gluons. Relativistic wave equation for two massive gluons interacting by the funnel-type potential is analyzed. Using two exact asymptotic solutions of the equation, we derive an interpolating mass formula and calculate glueball masses in agreement with the lattice data. We obtain the complex non-linear Pomeron trajectory, $\alpha_P(t)$, in the whole region of $t$. The real part of the trajectory corresponds to the soft Pomeron, parameters of which are found from the fit of recent HERA data.

Mass gain and loss of non-relativistic electrons in photon-electron interactions

Abstract: It is shown that the electrons gain mass as their non-relativistic velocities increase. This process is realized by the absorption of photons in the colliding process. In an inverse manner, they loss their mass when they radiate photons. The related equations are derived by using the relativistic mass equation and independently by considering the non-relativistic energy relation. The Compton scattering and photon emission phenomena are revisited with the new theory.

Proton dripline in a new formula for nuclear binding energy

Abstract: The location of the proton dripline in a new phenomenological mass formula is calculated. Predictions of different mass formulas for the dripline are compared. The implications of the new mass formula for rapid proton nucleosynthesis beyond $^{56}$Ni are discussed. It is seen that the new formula indicates that masses up to A=80 are easily synthesized in a typical X-ray burst.

Infrared properties of the gluon mass equation

Abstract: The gauge-invariant generation of a dynamical, momentum-dependent gluon mass is intimately connected with the presence of non-perturbative massless poles in the vertices of the theory, which trigger the well-known Schwinger mechanism In the deep infrared the integral equation that governs this effective gluon mass assumes a particularly simple form, which may be derived following two seemingly different, but ultimately equivalent procedures In particular, it may be obtained either as a deviation from a special identity that enforces the masslessness of the gluon in the absence of massless poles, or as a direct consequence of the appearance of a non-vanishing bound-state wave function, associated with the details of the actual formation of these massless poles In this presentation we demonstrate that, due to profound relations between the various ingredients, the two versions of the gluon mass equation are in fact absolutely identical

Siegel's mass formula and averages of Dirichlet $L$-functions over function fields

Abstract: Let D be a square-free polynomial in F_q[t], where q is odd, and let G be a genus of definite ternary lattices over F_q[t] of determinant D. In this paper we give self-contained and relatively elementary proofs of Siegel's formulas for the weighted sum of primitive representations numbers over the classes of G and for the mass of G. Our proof of the mass formula shows an interesting relation with certain averages of Dirichlet L-functions.

A new equation of state Based on Nuclear Statistical Equilibrium for Core-Collapse Simulations

Abstract: We calculate a new equation of state for baryons at sub-nuclear densities for the use in core-collapse simulations of massive stars. The formulation is the nuclear statistical equilibrium description and the liquid drop approximation of nuclei. The model free energy to minimize is calculated by relativistic mean field theory for nucleons and the mass formula for nuclei with atomic number up to ~ 1000. We have also taken into account the pasta phase. We find that the free energy and other thermodynamical quantities are not very different from those given in the standard EOSs that adopt the single nucleus approximation. On the other hand, the average mass is systematically different, which may have an important effect on the rates of electron captures and coherent neutrino scatterings on nuclei in supernova cores.

Mixed symmetric baryon multiplets in large $N_c$ QCD: two and three flavours

Abstract: We propose a new method to study mixed symmetric multiplets of baryons in the context of the $1/N_c$ expansion approach. The simplicity of the method allows to better understand the role of various operators acting on spin and flavour degrees of freedom. The method is tested on two and three flavours. It is shown that the spin and flavour operators proportional to the quadratic invariants of SU$_S$(2) and SU$_F$(3) respectively are dominant in the mass formula.

Mixed symmetric baryon multiplets in large $N_c$ QCD: Two and three flavours

Abstract: We propose a new method to study mixed symmetric multiplets of baryons in the context of the $1/N_c$ expansion approach. The simplicity of the method allows to better understand the role of various operators acting on spin and flavour degrees of freedom. The method is tested on two and three flavours. It is shown that the spin and flavour operators proportional to the quadratic invariants of SU$_S$(2) and SU$_F$(3) respectively are dominant in the mass formula.

Emergence String and Mass Formulas of Hadrons

Abstract: Assume that hadrons are formed from the emergence string Usual string should possess two moving states: oscillation and rotation, so we propose corresponding potential and the equation of the emergence string, whose energy spectrum is namely the GMO mass formula and its modified accurate mass formula These are some relations between the string and observable experimental data

Infrared Properties of the Gluon Mass Equation

Abstract: The gauge-invariant generation of a dynamical, momentum-dependent gluon mass is intimately connected with the presence of non-perturbative massless poles in the vertices of the theory, which trigger the well-known Schwinger mechanism. In the deep infrared the integral equation that governs this effective gluon mass assumes a particularly simple form, which may be derived following two seemingly different, but ultimately equivalent procedures. In particular, it may be obtained either as a deviation from a special identity that enforces the masslessness of the gluon in the absence of massless poles, or as a direct consequence of the appearance of a non-vanishing bound-state wave function, associated with the details of the actual formation of these massless poles. In this presentation we demonstrate that, due to profound relations between the various ingredients, the two versions of the gluon mass equation are in fact absolutely identical.

Temeprature-dependent Seeger's liquid drop energy for nuclei up to Z=118

Abstract: Seeger's semi-empirical mass formula is revisited for two of its constants (bulk constant �(0) and neutron-proton asymmetry constant aa) readjusted to obtain the ground-state (gs) binding energies of nuclei within a precision of <15 MeV and for nuclei up to Z=118 The aim is to include the temperature T-dependence on experimental binding energies, and not to obtain the new parameter set of Seeger's liquid drop energy VLDM Our proceedure is to define the gs binding energy B = VLDM +�U, as per Strutinsky renormalization procedure, and using the empirical shell correctionsU of Myers and Swiatecki, fit the constants of VLDM to obtain the experimental binding energy Bexpt or theoretically calculated Btheo if data were not available The T-dependence of the constants of VLDM, is introduced as per the work of Davidson et al, where the pairing energy �(T) is modified as per new calculations on compound nucleus decays The newly fitted constants of VLDM at T=0 are made available here for use of other workers interested in nuclear dynamics of hot and rotating nuclei PACS numbers: 2110Dr, 2160Cs, 2570-z Seeger's mass formula (1) was given in 1961, with its constants fitted to ground-state (gs) binding energies of some 488 nuclei available at that time The temperature T-dependence of these constants was later introduced by Davidson et al (2) on the basis of thermodynamical considerations of the nucleus These constants, however, need be fitted again since a large amount of data on experimental gs binding energies (3), and their theoretically calculated values (4) for, not-yet observed, neutron- and proton-rich nuclei have now become available Furthermore, the T-dependence of the constants, in particular the pairing constant �(T), need be looked in to because of their recent un-successful use in calculating the decay properties of some excited compound nuclear systems (5)-(7) Note that our aim here is not to obtain a new set of constants for Seeger's mass formula, but simply to include the T-dependence on experimental binding energies Bexpt For this purpose, a readjustment of only two of the four constants, the bulk constant �(0) and the neutron-proton asymmetry constant aa, are enough to obtain the Bexpt within <15 MeV A similar job was first done in (8) for nuclei up to Z=56, and then in (9) up to Z=97, but is redone here with an improved accuracy and up to Z=118 Thus, the domain of the work is extended to neutron-deficient and neutron-excess nuclides where Bexpt are not available, but theoretical binding energies Btheo are available (4) These re-fitted constants have been successfully used in the number of recent calculations (5)-(24) for studying the decay of hot and rotating compound nucleus (CN) formed in heavy ion reactions over a wide range of incident centre-of-mass (cm) energies A brief outline of the Seeger's mass formula, and the methodology used to workout the temperature-dependent binding energies, are presented in section II Possible applications of the liquid drop energy in heavy ion reaction studies are also included in this section The calculations and results are given in section III, together with the table of fitted constants, which could be of huge importance for people working in the relevant area of nuclear physics Finally, the results are summarized in section IV