Showing papers on "Mass formula published in 2000"
TL;DR: In this paper, a ten-parameter Skyrme force along with a fourparameter ε-function pairing force were fitted to the masses of 1719 nuclei, both spherical and deformed, with an rms error of 0.754 MeV.
Abstract: A ten-parameter Skyrme force, along with a four-parameter $\ensuremath{\delta}$-function pairing force, have been fitted, using the Hartree-Fock-BCS method, to the masses of 1719 nuclei, both spherical and deformed, with an rms error of 0.754 MeV. The corresponding value of the symmetry coefficient J is 28.0 MeV, and that of the effective nucleon mass ${M}^{*}$ is $1.05M.$
120 citations
TL;DR: In this article, a nuclear mass formula is constructed which is composed of two parts, one describing the general trend of the masses as a function of Z and N and the other representing deviations of individual masses from this general trend.
76 citations
TL;DR: In this paper, a semi-empirical shell model mass equation applicable to superheavy elements up to $Z=126$ is presented and shown to have a high predictive power.
Abstract: A semiempirical shell model mass equation applicable to superheavy elements up to $Z=126$ is presented and shown to have a high predictive power. The equation is applied to the recently discovered superheavy nuclei ${}^{293}118$ and ${}^{289}114$ and their decay products.
65 citations
TL;DR: In this paper, the authors give a simple and conceptual proof of the local density formula for p 6 = 2, and show that there exists a smooth affine group scheme G over Zp with generic fiber AutQp(L,Q), which satisfies G(Zp) = AutZp(l,Q).
Abstract: The subject matter of this paper is an old one with a rich history, beginning with the work of Gauss and Eisenstein, maturing at the hands of Smith and Minkowski, and culminating in the fundamental results of Siegel. More precisely, if L is a lattice over Z (for simplicity), equipped with an integral quadratic form Q, the celebrated Smith-Minkowski-Siegel mass formula expresses the total mass of (L,Q), which is a weighted class number of the genus of (L,Q), as a product of local factors. These local factors are known as the local densities of (L,Q). Subsequent work of Kneser, Tamagawa and Weil resulted in an elegant formulation of the subject in terms of Tamagawa measures. In particular, the local density at a non-archimedean place p can be expressed as the integral of a certain volume form ωld over AutZp(L,Q), which is an open compact subgroup of AutQp(L,Q). The question that remains is whether one can find an explicit formula for the local density. Through the work of Pall (for p 6= 2) and Watson (for p = 2), such an explicit formula for the local density is in fact known for an arbitrary lattice over Zp (see [P] and [Wa]). The formula is obviously structured, though [CS] seems to be the first to comment on this. Unfortunately, the known proof (as given in [P] and [K]) does not explain this structure and involves complicated recursions. On the other hand, Conway and Sloane [CS, §13] have given a heuristic explanation of the formula. In this paper, we will give a simple and conceptual proof of the local density formula, for p 6= 2. The view point taken here is similar to that of our earlier work [GHY], and the proof is based on the observation that there exists a smooth affine group scheme G over Zp with generic fiber AutQp(L,Q), which satisfies G(Zp) = AutZp(L,Q). This follows from general results of smoothening [BLR], as we explain in Section 3. For the purpose of obtaining an explicit formula, it is necessary to have an explicit construction of G. The main contribution of this paper is to give such an explicit construction of G (in Section 5), and to determine its special fiber (in Section 6). Finally, by comparing ωld and the canonical volume form ωcan of G, we obtain the explicit formula for the local density in Section 7. The smooth group schemes constructed in this paper should also be of independent interest.
62 citations
TL;DR: In this paper, the authors derived a list of three dimensional symmetric space σ-models obtained by dimensional reduction of a class of four dimensional gravity theories with abelian gauge fields and scalars.
Abstract: In a previous paper with Gibbons [1] we derived a list of three dimensional symmetric space σ-models obtained by dimensional reduction of a class of four dimensional gravity theories with abelian gauge fields and scalars. Here we give a detailed analysis of their group theoretical structure leading to an abstract parametrization in terms of “triangular” group elements. This allows for a uniform treatment of all these models. As an interesting application we give a simple derivation of a “Quadratic Mass Formula” for strictly stationary black holes.
47 citations
TL;DR: In this article, it was shown that the Hidden Local Symmetry Model, supplemented with well-known procedures for breaking avor SU(3) and nonet symmetry, provides all the information contained in the standard Chiral Perturbation Theory (ChPT) LagrangianL (0) + L (1).
Abstract: We show that the Hidden Local Symmetry Model, supplemented with well-known procedures for breaking avor SU(3) and nonet symmetry, provides all the information contained in the standard Chiral Perturbation Theory (ChPT) LagrangianL (0) +L (1) . This allows to rely on radiative decays of light mesons (VP and P) in order to extract some numerical information of relevance to ChPT: a value for 1 =0 :20 0:04, a quark mass ratio of’ 21:2 2:4, and a negligible departure from the Gell-Mann{Okubo mass formula. The mixing angles are8 = 20:400:96 and0 = 0:050:99. We also give the values of all decay constants. It is shown that the common mixing pattern with one mixing angle P is actually quite appropriate and algebraically related to the = 0 mixing pattern presently preferred by the ChPT community. For instance the traditional P is functionally related to the ChPT 8 and fullls P ’ 8=2. The vanishing of 0, supported by all data on radiative decays, gives a novel relation between mixing angles and the violation of nonet symmetry in the pseudoscalar sector. Finally, it is shown that the interplay of nonet symmetry breaking through U(3)! SU(3) U(1) satises all requirements of the physics of radiative decays without any need for additional glueballs.
36 citations
TL;DR: Within the framework of the ETFSI (extended Thomas-Fermi plus Strutinsky integral) mass formula, a precision fit of nuclear masses with Skyrme forces, subject to the constraint that neutron matter does not collapse at nuclear or subnuclear densities, is possible if, but only if, the nuclear-matter symmetry coefficient J lies close to 28 MeV.
29 citations
TL;DR: In this article, the one-loop correction to the spectrum of Kaluza-Klein system for the 3 model on 1,d × (θ2)L is evaluated in the high temperature limit, where the 1+d dimensions are the ordinary flat Minkowski spacetimes and the L extra two-dimensional tori are chosen to be the non-commutative torus with noncommutativity θ.
Abstract: The one-loop correction to the spectrum of Kaluza-Klein system for the 3 model on 1,d × (θ2)L is evaluated in the high temperature limit, where the 1+d dimensions are the ordinary flat Minkowski spacetimes and the L extra two-dimensional tori are chosen to be the non-commutative torus with noncommutativity θ. The corrections to the Kaluza-Klein mass formula are evaluated and used to compute the Casimir energy with the help of the Schwinger perturbative formula in the zeta-function regularization method. The results show that the one-loop Casimir energy is independent of the radius of torus if L = 1. However, when L > 1 the Casimir energy could give repulsive force to stabilize the extra non-commutative torus if d−L is a non-negative even integral. This therefore suggests a possible stabilization mechanism of extra radius in high temperature, when the extra spaces are non commutative.
19 citations
21 Feb 2000
TL;DR: In this article, it was shown that non-supersymmetric black holes carrying both electric and magnetic charge with respect to a single Kaluza-Klein gauge field have much in common with supersymmetric Black Holes and other general physics principles underlies some of their basic features.
Abstract: Non-supersymmetric black holes carrying both electric and magnetic charge with respect to a single Kaluza-Klein gauge field have much in common with supersymmetric black holes. Angular momentum conservation and other general physics principles underlies some of their basic features. Kaluza-Klein black holes are interpreted in string theory as bound states of D6-branes and D0-branes. The microscopic theory reproduces the full nonlinear mass formula of the extremal black holes.
19 citations
TL;DR: In this paper, the formulae describing the radiative decays η′(η)→γγ in QCD beyond the chiral limit were derived, and the modifications of the conventional PCAC formula due to the gluonic contribution to the axial anomaly in the flavour singlet channel were precisely described.
15 citations
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TL;DR: In this article, the Dyson-Schwinger equation is applied to the problem of estimating pseudoscalar meson masses, an associated model-independent mass formula and the approach to the heavy-quark limit.
Abstract: We illustrate the contemporary application of Dyson-Schwinger equations using two examples: the calculation of pseudoscalar meson masses, an associated model-independent mass formula and the approach to the heavy-quark limit; and the study of nucleon observables, including a calculation of its mass, $M$, via a covariant Fadde'ev equation and an estimate of pion-loop contributions to $M$.
TL;DR: In this paper, the Coleman-Glashow formula for the baryon octet e.m. masses (derived using unbroken flavor SU3) is satisfied to an extraordinary level of precision.
TL;DR: In this article, the q-exciting number n describing generations and the scaling indexes Mi describing families of the quark-lepton mass spectra in q-deformed quantum mechanics were investigated.
Abstract: The quark-lepton mass spectra in q-deformed quantum mechanics are investigated. The theoretical formula of the spectrum includes two new quantum numbers: the q-exciting number n describing generations and the scaling indexes Mi describing families. This formula shows two exponential increases in the mass distribution as generation n increases, the intervals of masses in a given family exponentially increase, and the mass splittings among different members in a generation also exponentially increase. The theoretical values of masses of quarks and leptons reasonably agree with the experimental data except for the electron mass which is one order larger.
TL;DR: In this paper, the problem of the derivation of a proper formula for the mechanical (or electrical) mobility of large, heavy (l.h.) particles in a simple neutral gas in any regime is carefully examined and solved under the usual hypotheses that the l.h. particles are subject to the action of a constant external force and undergo only elastic collisions with the gas particles.
TL;DR: In this paper, a string-network representation of 1/8 supersymmetric BPS states is given by considering (periodic) non-planar (p, q, r)-string networks of eight dimensional type II string theory on T3.
Abstract: Type-II strings in D = 5 contain particle-like 1/8 supersymmetric BPS states. In this note we give a string-network representation of such states by considering (periodic) non-planar (p,q,r)-string networks of eight dimensional type II string theory on T3. We obtain the BPS mass formula of such states, in terms of charges and generating-vectors of the torus, and show its invariance under an SL(3,) ? SL(3,) group of transformations. Results are then generalized to string-networks associated with the SL(5,) U-duality in seven dimensions. We also discuss reinterpretation of the above (D = 5) mass formula in terms of BPS states in world-volume theories of U2-branes in D = 8.
TL;DR: In this article, the mass spectrum of the L = 1 orbitally excited heavy baryons with light quarks in the spin-flavor symmetric representation is studied by the 1/Nc expansion method in the framework of heavy quark effective theory.
Abstract: The mass spectrum of the L = 1 orbitally excited heavy baryons with light quarks in the spin-flavor symmetric representation is studied by the 1/N-c expansion method in the framework of heavy quark effective theory The mixing effect from the baryons in the mixed representation is considered The general pattern of the spectrum is predicted which will be verified by experiments in the near future The 1/m(Q) and SU(3) corrections are also considered Mass relations for the baryons Lambda (()(cl)*()), Sigma (()(cl)*()), Xi (()(cl)'()()*()), and delta (()(cl)*()) are derived
10 Oct 2000
TL;DR: In this article, the Dyson-Schwinger equation is applied to the problem of estimating pseudoscalar meson masses, an associated model-independent mass formula and the approach to the heavy-quark limit.
Abstract: We illustrate the contemporary application of Dyson-Schwinger equations using two examples: the calculation of pseudoscalar meson masses, an associated model-independent mass formula and the approach to the heavy-quark limit; and the study of nucleon observables, including a calculation of its mass, $M$, via a covariant Fadde'ev equation and an estimate of pion-loop contributions to $M$.
01 Jan 2000
TL;DR: In this article, the Hidden Local Symmetry Model, supplemented with well-known procedures for breaking flavor SU(3) and nonet symmetry, provides all the information contained in the standard Chiral Perturbation Theory (ChPT) Lagrangian L (0) + L (1).
Abstract: We show that the Hidden Local Symmetry Model, supplemented with well-known procedures for breaking flavor SU(3) and nonet symmetry, provides all the information contained in the standard Chiral Perturbation Theory (ChPT) Lagrangian L (0) + L (1) . This allows to rely on radiative decays of light mesons (V P and P) in order to extract some numerical information of relevance to ChPT: a value for �1 = 0.20 ± 0.04, a quark mass ratio of ≃ 21.2 ± 2.4, and a negligible departure from the Gell-Mann–Okubo mass formula. The mixing angles are �8 = −20.40 ◦ ±0.96 ◦ and �0 = −0.05 ◦ ±0.99 ◦ . We also give the values of all decay constants. It is shown that the common
TL;DR: In this paper, the authors studied field theories on spaces with additional compact noncommutative dimensions and showed that the spectrum of Kaluza-Klein excitations can be very different from the analogous commuting theory.
Abstract: We study field theories on spaces with additional compact noncommutative dimensions. As an example, we study \phi^3 on R^{1,3}\times T^{2}_\theta using perturbation theory. The infrared divergences in the noncompact theory give rise to unusual dynamics for the mode of \phi which is constant along the torus. Correlation functions involving this mode vanish. Moreover, we show that the spectrum of Kaluza-Klein excitations can be very different from the analogous commuting theory. There is an additional contribution to the Kaluza-Klein mass formula that resembles the contribution of winding states in string theory. We also consider the effect of noncommutativity on the four dimensional Kaluza-Klein excitations of a six dimensional gauge field.
TL;DR: In this article, it was shown that non-supersymmetric black holes carrying both electric and magnetic charge with respect to a single Kaluza-Klein gauge field have much in common with supersymmetric Black Holes and other general physics principles underlies some of their basic features.
Abstract: Non-supersymmetric black holes carrying both electric and magnetic charge with respect to a single Kaluza-Klein gauge field have much in common with supersymmetric black holes. Angular momentum conservation and other general physics principles underlies some of their basic features. Kaluza-Klein black holes are interpreted in string theory as bound states of D6-branes and D0-branes. The microscopic theory reproduces the full nonlinear mass formula of the extremal black holes.
29 Nov 2000
TL;DR: In this article, the authors consider the quantum corrections to the mass and the central charge of the susy kink and find that the mass corrections give an incorrect result, but deduce through smoothing of the cut-off an extra term in the mass formula, which produces the correct result.
Abstract: We review our work on computations of the quantum corrections to the mass and the central charge of the susy kink. For the mass corrections, we find that the widely used momentum cut-off scheme gives an incorrect result, but we deduce through smoothing of the cut-off an extra term in the mass formula, which produces the correct result. We discover the importance of boundary effects for the mode number cut-off regularization scheme. We introduce the notion of delocalized boundary energy. We discuss two discrete $Z_2$ symmetries and their importance to the mode number approach. For the central charge corrections, we use momentum cut-off regularization with two cut-offs, one for propagators and another for Dirac delta functions. We then compute the quantum anomaly in the central charge, and find that it restores the BPS bound at the one-loop level if the two cut-offs are equal.
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TL;DR: In this paper, the authors consider the quantum corrections to the mass and the central charge of the susy kink and find that the mass corrections give an incorrect result, but deduce through smoothing of the cut-off an extra term in the mass formula, which produces the correct result.
Abstract: We review our work on computations of the quantum corrections to the mass and the central charge of the susy kink. For the mass corrections, we find that the widely used momentum cut-off scheme gives an incorrect result, but we deduce through smoothing of the cut-off an extra term in the mass formula, which produces the correct result. We discover the importance of boundary effects for the mode number cut-off regularization scheme. We introduce the notion of delocalized boundary energy. We discuss two discrete $Z_2$ symmetries and their importance to the mode number approach. For the central charge corrections, we use momentum cut-off regularization with two cut-offs, one for propagators and another for Dirac delta functions. We then compute the quantum anomaly in the central charge, and find that it restores the BPS bound at the one-loop level if the two cut-offs are equal.
TL;DR: In this article, an effective supergravity description of all instabilities of N_4=4 superstrings is derived, based on the N 4=4 BPS mass formula at finite temperature and using the properties of N 4 = 4 gauged supergravity.
Abstract: An effective supergravity description of all instabilities of N_4=4 superstrings is derived. The construction is based on the N_4=4 BPS mass formula at finite temperature and uses the properties of N_4=4 gauged supergravity. It provides the boundaries of the various thermal phases in the non-perturbative moduli space. It also draws a precise picture of the dynamics in the high-temperature heterotic phase. This brief contribution summarizes results obtained in collaboration with I. Antoniadis and C. Kounnas.
TL;DR: In this paper, the mass of a fundamental string described as a BPS solution of a D-brane's world volume is obtained by using the Hamiltonian density on the world volume, based on transformation properties required for it.
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TL;DR: In this article, the authors derived a mass formula for n-dimensional unimodular lattices having any prescribed root system using Katsurada's formula for the Fourier coefficients of Siegel Eisenstein series.
Abstract: We derive a mass formula for n-dimensional unimodular lattices having any prescribed root system. We use Katsurada's formula for the Fourier coefficients of Siegel Eisenstein series to compute these masses for all root systems of even unimodular 32-dimensional lattices and odd unimodular lattices of dimension n < 31. In particular, we find the mass of even unimodular 32-dimensional lattices with no roots, and the mass of odd unimodular lattices with no roots in dimension n < 31, verifying Bacher and Venkov's enumerations in dimensions 27 and 28. We also compute better lower bounds on the number of inequivalent unimodular lattices in dimensions 26 to 30 than those afforded by the Minkowski-Siegel mass constants.
The ASCII text file table.txt (1.3 MB) at arXiv:math.NT/0012231 includes the complete table of masses of 32-dimensional even unimodular lattices with any given root system, and may be dowloaded using the source link.
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TL;DR: A new mass formula capable of explaining the binding energies of almost all the known isotopes from Li to Bi is prescribed in this article, which can predict the existence of 26O,31F, 32Ne, 35Na, 38Mg, 41Al as bound nuclei and 28O as unbound.
Abstract: A new mass formula capable of explaining the binding energies of almost all the known isotopes from Li to Bi is prescribed. In addition to identifying the new magic number at neutron number N=16 (Z=7-9), pseudo-magic numbers at N=14 (Z=7-10), Z=14 (N=13-19), and at N=6 (Z=3-8), the formula accounts for the loss of magicity for nuclei with N=8 (Z=4) and N=20 (Z=12-17). The redefinition of the neutron drip line resulting from this formula further allows us to predict the existence of 26O,31F, 32Ne, 35Na, 38Mg, 41Al as bound nuclei and 28O as unbound.
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TL;DR: In terms of the energy band theory, from the symmetries of the body center cubic periodic field, Wang et al. as discussed by the authors deduced the baryon spectrum with a united mass formula using only 2 flavored quarks u and d.
Abstract: From the quark confinement idea, we conjecture that the quarks compose colorless particles (uud and udd - the Lee Particles) and then the Lee Particles construct a body center cubic lattice in the vacuum. In terms of the energy band theory, from the symmetries of the body center cubic periodic field, we deduce the baryon spectrum (with a united mass formula) using only 2 flavored quarks u and d. We also predict some new baryons: $\Lambda^{0}$(2559), $\Lambda_{C}^{+}$(6659), $\Lambda_{b}^{0}$(10159).... The experiments to find the long lifetime baryon $\Lambda^{0}$(2559) should be done first.