Showing papers on "Mass formula published in 2003"

Further explorations of Skyrme-Hartree-Fock-Bogoliubov mass formulas. II: Role of the effective mass

Abstract: We have constructed four new complete mass tables, referred to as (Hartree-Fock-Bogoliubov) HFB-4 to HFB-7, each one including all the 9200 nuclei lying between the two drip lines over the range of $Z$ and $N\ensuremath{\geqslant}8$ and $Z\ensuremath{\leqslant}120$. HFB-4 and HFB-5 have the isoscalar effective mass ${M}_{s}^{*}$ constrained to the value $0.92M$, with the former having a density-independent pairing, and the latter a density-dependent pairing. HFB-6 and HFB-7 are similar, except that ${M}_{s}^{*}$ is constrained to $0.8M$. The rms errors of the mass-data fits are 0.680, 0.675, 0.686, and $0.676\phantom{\rule{0.3em}{0ex}}\text{MeV}$, respectively, almost as good as for the HFB-2 mass formula, for which ${M}_{s}^{*}$ was unconstrained. However, as usual, the single-particle spectra depend significantly on ${M}_{s}^{*}$. This decoupling of the mass fits from the fits to the single-particle spectra has been achieved only by making the cutoff parameter of the $\ensuremath{\delta}$-function pairing force a free parameter. An improved treatment of the center-of-mass correction was adopted, but although this makes a difference to individual nuclei it does not reduce the overall rms error of the fit. The extrapolations of all four new mass formulas out to the drip lines are essentially the same as for the original HFB-2 mass formula.

A mass formula for unimodular lattices with no roots

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 ≤ 30 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 ≤ 30, 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

Masses of 32Ar and 33Ar for fundamental tests.

Abstract: Masses of the short-lived radionuclides 3 2 Ar (T 1 / 2 = 98 ms) and 3 3 Ar (T 1 / 2 = 173 ms) have been determined with the Penning trap mass spectrometer ISOLTRAP Relative uncertainties of 60 X 10 - 8 (δm = 18 keV) and 14 × 10 - 8 (δm = 044 keV), respectively, have been achieved At present, these new mass data serve as the most stringent test of the quadratic form of the isobaric-multiplet mass equation Furthermore, the improved accuracy for the mass of 3 2 Ar will allow for a better constraint on scalar contributions to the weak interaction New mass values have also been measured for 4 4 Ar and 4 5 Ar, and a 20σ deviation for 4 4 Ar from the literature value was found and interpreted

Mass parametrizations and predictions of isotopic observables

Abstract: We discuss the accuracy of mass models for extrapolating to very asymmetric nuclei and the impact of such extrapolations on the predictions of isotopic observables in multifragmentation. We obtain improved mass predictions by incorporating measured masses and extrapolating to unmeasured masses with a mass formula that includes surface symmetry and Coulomb terms. We find that using accurate masses has a significant impact on the predicted isotopic observables.

Scalar Solitons in Non(anti)commutative Superspace

Abstract: We study solitonic solutions of a deformed Wess-Zumino model in 2 dimensions, corresponding to a deformation of the usual ${\cal N}=1,D=2$ superspace to the one with non-anticommuting odd supercoordinates. The deformation turns out to add a kinetic term for the auxiliary field besides the known $F^{3}$ term coming from the deformation of the cubic superpotential. Both these modifications are proportional to the effective deformation parameter $\lambda \equiv \det C$, where $C$ denotes the non-anticommutativity matrix. We find a modified ``orbit'' equation which on the EOM relates the auxiliary and the scalar components of the scalar superfield as a first order correction to the usual relation in terms of the small parameter $\lambda $. Subsequently, we obtain the modified form of the first order BPS equation for the scalar field and find its solution to first order in $\lambda $. Issues such as modification of the BPS mass formula and a non-linear realization of the ${\cal N}=1$ supersymmetry are discussed.

Inverting the seesaw formula

Abstract: By inverting the seesaw formula we determine the heavy neutrino mass matrix. The impact on baryogenesis via leptogenesis and the radiative lepton decays in supersymmetric models is described. Links to neutrinoless double beta decay are also briefly discussed. The analysis leads to two distinct matrix models. One has small mixing while the other one has maximal mixing. Both cannot give a sufficient amount of baryon asymmetry. Then we also comment on a different form of the Dirac neutrino mass matrix, which does provide sufficient baryon asymmetry. In a supersymmetric scenario the branching ratios of radiative lepton decays are enhanced for this model.

A semiempirical mass formula for spherical Coulomb crystals

Abstract: In analogy to the Bethe–Weizs¨ acker formula for nuclei we establish a semiempirical mass formula for the energies of Coulomb crystals including Madelung, surface, compression and curvature energy terms. The surface tension and the incompressibility are extracted as well. The coefficients are fitte da td ata obtained from molecular dynamics calculations for spherically confined systems of charged particles with particle numbers up to about 100 000 under their mutual Coulomb repulsion and under constant radial focusing. The systems are cooled down until the excess energy stays constant up to 10 −8 . Fo rp article numbers below about 10 000, they settle in icosahedral structures whose faces are rounded off. At about 10 000 particles there is a transition to body centred cubic (bcc) crystals where particles are arranged in parallel layers. The icosahedra have lower surface energy but slightly higher Madelung energy of −0.8949, in contrast to the bcc crystals which have the lower Madelung energy of −0.8959 but essentially larger surface energy. The icosahedra are more compressible than the bcc crystals. (Some figures in this article are in colour only in the electronic version)

Chiral QCD, general QCD parameterization and constituent quark models

Abstract: Several recent papers -using effective QCD chiral Lagrangians- reproduced results obtained with the general QCD parameterization (GP). These include the baryon 8+10 mass formula, the octet magnetic moments and the coincidental nature of the "perfect" -3/2 ratio between the magnetic moments of p and n. Although we anticipated that the GP covers the case of chiral treatments, the above results explicitly exemplify this fact. Also we show by the GP that -in any model or theory (chiral or non chiral) reproducing the results of exact QCD- the Franklin (Coleman Glashow) sum rule for the octet magnetic moments must be violated.

Inertial Mass and Vacuum Fluctuations in Quantum Field Theory

Abstract: Motivated by recent works on the origin of inertial mass, we revisit the relationship between the mass of charged particles and zero-point electromagnetic fields. To this end we first introduce a simple model comprising a scalar field coupled to stochastic or thermal electromagnetic fields. Then we check if it is possible to start from a zero bare mass in the renormalization process and express the finite physical mass in terms of a cut-off. In scalar QED this is indeed possible, except for the problem that all conceivable cut-offs correspond to very large masses. For spin-1/2 particles (QED with fermions) the relation between bare mass and renormalized mass is compatible with the observed electron mass and with a finite cut-off, but only if the bare mass is not zero; for any value of the cut-off the radiative correction is very small.

Sum rules for total hadronic widths of light mesonsand rectilinear stitch of the masses on the complex plane

Abstract: Mass formulae for light meson multiplets derived by means of the exotic commutator technique are written for complex masses and considered as complex mass sum rules (CMSR). The real parts of the CMSR give the well known mass formulae for real masses (Gell-Mann-Okubo, Schwinger and ideal mixing ones) and the imaginary parts of CMSR give appropriate sum rules for the total hadronic widths - width sum rules (WSR). Most of the observed meson nonets satisfy the Schwinger mass formula (S nonets). The CMSR predict for the S nonet that the points $(m,\Gamma{})$ form a rectilinear stitch (RS) on the complex mass plane. For low-mass nonets the WSR are strongly violated due to "kinematical" suppression of the particle decays, but the violation decreases as the mass increases and disappears above $\sim 1.5$ GeV. The slope k s of the RS is not predicted, but the data show that it is negative for all S nonets and its numerical values are concentrated in the vicinity of the value -0.5. If k s is known for a nonet, we can evaluate "kinematical" suppressions of its individual particles. The masses and the widths of the S nonet mesons submit to some rules of ordering which matter in understanding the properties of the nonet. We give the table of the S nonets indicating masses, widths, mass and width orderings. We show also mass-width diagrams for them. We suggest to recognise a few multiplets as degenerate octets. In the appendix we analyze the nonets of the 1+ mesons.

Spectroscopy of pentaquark states

Abstract: We construct a complete classification of pentaquark states in terms of the spin-flavour SU(6) representations. We find that only some definite SU(3) representations are allowed, singlets, octets, decuplets, anti-decuplets, 27-plets and 35-plets. The latter three contain exotic states, which cannot be constructed from three quarks only. This complete classification scheme is general and model independent and is useful both for model builders and experimentalists. The mass spectrum is obtained from a Gursey-Radicati type mass formula, whose coefficients have been determined previously by a study of qqq baryons. The ground state pentaquark which is identified with the recently observed Theta(1540) state, is predicted to be an isosinglet anti-decuplet state. Its parity depends on the interplay between the spin-flavour and orbital contributions to the mass operator.

Two-dimensional clusters of liquid 4 He

Abstract: The binding energies of two-dimensional clusters (puddles) of 4 He are calculated in the framework of the diffusion Monte Carlo method. The results are well fitted by a mass formula in powers of x=N - 1 / 2 , where N is the number of particles. The analysis of the mass formula allows for the extraction of the line tension, which turns out to be 0.121 K/A. Sizes and density profiles of the puddles are also reported.

A Formula for the Mass Spectrum of Baryons and Mesons

Abstract: A mass formula for all the Baryons and Mesons is proposed. A comparison with the actual masses shows that about 63 % of the errors are less than 1 % while in about 93 % of the cases errors are less than 2 %. In all cases the error is less than 3 % with the lone exception of omega (782) Meson in which case the error is 3.6 %.A rationale for the proposed mass formula is also touched upon.

A QCD Generated Mass Spectrum

Abstract: Using the interquark potential we obtain a formula for the mass spectrum of elementary particles. The simple formula gives the masses of all known elementary particles with an error of about three percent or less. This includes the recently discovered Ds (2317) and 1.5GeV Pentaquark particles.

Neutron and proton drip lines using the modified Bethe-Weizsacker mass formula

Abstract: Proton and neutron separation energies have been calculated using the extended Bethe-Weizsacker mass formula. This modified Bethe-Weizsacker mass formula describes minutely the positions of all the old and the new magic numbers. It accounts for the disappearance of some traditional magic numbers for neutrons and provides extra stability for some new neutron numbers. The neutron and proton drip lines have been predicted using this extended Bethe-Weizsacker mass formula. The implications of the proton drip line on the astrophysical rp-process and of the neutron drip line on the astrophysical r-process have been discussed.

Baryon resonances and strong QCD

Abstract: Light-baryon resonances (with u,d, and s quarks in the SU(3) classification) fall on Regge trajectories. When their squared masses are plotted against the intrinsic orbital angular momenta {\rm L}, $\Delta^*$'s with even and odd parity can be described by the same Regge trajectory. For a given {\rm L}, nucleon resonances with spin {\rm S}=3/2 are approximately degenerate in mass with $\Delta$ resonances. To which total angular momentum {\rm L} and {\rm S} couple has no significant impact on the baryon mass. Nucleons with spin 1/2 are shifted in mass; the shift is - in units of squared masses - proportional to the component in the wave function which is antisymmetric in spin and flavor. Based on these observations, a new baryon mass formula is proposed which reproduces nearly all known baryon masses. It is shown that the masses are compatible with a quark-diquark picture while the richness of the experimentally known states require three particles to participate in the dynamics. This conflict is resolved by proposing that quarks polarize the QCD condensates and are surrounded by a polarization cloud shielding the color. A new interpretation of constituent quarks as colored quark clusters emerges; their interaction is responsible for the mass spectrum. Fast flavor exchange between the colored quark clusters exhausts the dynamical richness of the three-particle dynamics. The colored-quark-cluster model provides a mechanism in which the linear confinement potential can be traced to the increase of the volume in which the condensates are polarized. The quark-spin magnetic moment induces currents in the polarized condensates which absorb the quark-spin angular momentum: the proton spin is not carried by quark spins. The model provides a new picture of hybrids and glueballs.

The mass of unimodular lattices

Abstract: The purpose of this paper is to show how to obtain the mass of a unimodular lattice from the point of view of the Bruhat-Tits theory. This is achieved by relating the local stabilizer of the lattice to a maximal parahoric subgroup of the special orthogonal group, and appealing to an explicit mass formula for parahoric subgroups developed by Gan, Hanke and Yu. Of course, the exact mass formula for positive defined unimodular lattices is well-known. Moreover, the exact formula for lattices of signature (1,n) (which give rise to hyperbolic orbifolds) was obtained by Ratcliffe and Tschantz, starting from the fundamental work of Siegel. Our approach works uniformly for the lattices of arbitrary signature (r,s) and hopefully gives a more conceptual way of deriving the above known results.

Motion of a charged particle in the magnetic dipole field

Abstract: This note discusses the motion of a charged particle in the magnetic dipole field and a modified Barut's lepton mass formula It is shown that a charged particle in the magnetic dipole filed has no bound states, which means that Barut's lepton mass formula may have no physical basis

Mass Formulae for Supernarrow Dibaryons and Exotic Baryons

Abstract: The mass formulae for the supernarrow dibaryons and the exotic baryons with small masses are consructed With this aim their self energies are calculated in one loop approximation using the dispersion relations with two subtractions The values of the masses obtained in this approach are in a good agreement with the experimental data The mass formula for the baryons is also used to calculate the mass of the $\Delta(1232)$ resonance

Constituent-Quark Model and New Particles

Abstract: An elementary constituent-quark (CQ) model by Mac Gregor is reviewed with currently published data from light meson spectroscopy. It was previously shown in the CQ model that there existed several mass quanta m = 70 MeV, B = 140 MeV and X = 420 MeV, which were responsible for the quantization of meson yrast levels. The existence of a 70-MeV quantum was postulated by Mac Gregor and was shown to fit the Nambu empirical mass formula mn = (n/2)137me, n a positive integer. The 70-MeV quantum can be derived in three different ways: 1) pure electric coupling, 2) pure magnetic coupling, and 3) mixed electric and magnetic charges (dyons). Schwinger first introduced dyons in a magnetic model of matter. It is shown in this paper that recent data of new light mesons fit into the CQ model (a pure electric model) without the introduction of magnetic charges. However, by introducing electric and magnetic quarks (dyons) into the CQ model, new dynamical forces can be generated by the presence of magnetic fields internal to the quarks (dyons). The laws of angular momentum and of energy conservation are valid in the presence of magnetic charge. With the introduction of the Russell-Saunders coupling scheme into the CQ model, several new meson particles are predicted to exist. The existence of the f0(560) meson is predicted and is shown to fit current experimental data from the Particle Data Group listing. The existence of meson partners or groupings is shown.

Evidence for Magnetic Fields in Light Meson Spectra

Abstract: Mac Gregor's constituent-quark model is reviewed with currently published data from light meson spectroscopy It was previously shown that magnetic sources were responsible for the quantization of several mass-splittings in Mac Gregor's model The existence of a 70-MeV quantum was postulated by Mac Gregor and was shown to fit the Nambu empirical mass formula mn = (n/2)137me, n a positive integer It is shown in this paper that the light meson spectra also fit into the constituent-quark model and are in agreement with the Russell-Saunders coupling scheme The existence of magnetic fields is suggested by the successful accounting of these meson spectra

The semiempirical mass formula for spheroidal and rotating Coulomb crystals

Abstract: The recently proposed semiempirical mass formula for spherical Coulomb crystals is generalized to include spheroidal deformations and Maclaurin-type rotations. The external focusing frequencies are adjusted in such a way that in the interior the forces due to focusing and Coulomb repulsion are cancelled out exactly. With the help of molecular dynamics calculations isometric configurations of non-spherical Coulomb crystals formed due to a non-spherical trapping potential or due to rotation are found to have less energy than the spherical ground state with the same number of particles. Possible collective multipole excitations of the neutral background are discussed.

Mass formula for two-dimensional flavor non-singlet mesons

Abstract: We analytically and numerically investigate the 't Hooft equations, the lowest order mesonic light-front Tamm-Dancoff equations for SU(NC) and U(NC) gauge theories, generalized to flavor non-singlet mesons. We find that the wave function can be well approximated by new basis functions and obtain an analytic and an empirical formula for the mass of the lightest bound state. Its value is consistent with the precedent results.