Mass formula

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

Phenomenological Nuclear Level Densities using the KTUY05 Nuclear Mass Formula for Applications Off-Stability

Abstract: A new parametrization for the phenomenological nuclear level density taking account of the shell and pairing energies of the recent nuclear mass formula of Koura, Tachibana, Uno, and Yamada (KTUY05) a is proposed. Such a level density formula is often required to calculate nuclear reaction cross sections for nuclei off-stability, especially for fission systems and astrophysical applications. With the phenomenological level density formula of Gilbert-Cameron with the energy dependent level density parameter of Ignatyuk, a smooth dependence of the asymptotic level density parameter a* on the mass number is obtained. At low energies, systematics for the constant temperature model are also derived by connecting the Fermi gas level density and the discrete level information available for more than 1,000 nuclei. Some comparisons with the discrete level data and the microscopic model are made to validate our approach, and it is concluded that the parametrization obtained can be used for nuclear reaction calculat...

Mass formula for strange and nonstrange quark matter.

Abstract: A mass formula for spherical lumps of two- and three-flavor quark matter is derived self-consistently from an asymptotic expansion within the MIT bag model, taking into account bulk, surface, curvature, and Coulomb contributions For massless quarks the asymptotic expansion fits exceedingly well with exact mode-filling calculations A bulk approximation to the mass formula is also discussed The curvature energy is extremely important, adding up to 400[ital A][sup [minus]2/3] MeV to the energy per baryon for baryon number [ital A]

Quark-Diquark Model of Baryons and SU (6)

Abstract: A model in which a baryon can be regarded as a bound state of two particles has been generalized to be approximately invariant under $\mathrm{SU}(6)$. In the model, one of the constituent particles of a baryon can be regarded as a quark and the other particle can be considered as a tightly bound state of two quarks, or diquark. The quark is taken to belong to a six-dimensional representation of $\mathrm{SU}(6)$, while the diquark is taken to belong to a twenty-one-dimensional representation. With this model, which can be considered as a specific dynamical approximation to the three-quark model, the baryon medium-strong mass splittings are calculated beyond lowest-order perturbation theory. The model provides a mechanism for breaking the Gell-Mann\char22{}Okubo baryon-octet mass formula while breaking the baryon-decuplet equal-spacing rule by a smaller amount.

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.

Renormalization group analysis of the gluon mass equation

Abstract: We carry out a systematic study of the renormalization properties of the integral equation that determines the momentum evolution of the effective gluon mass in pure Yang--Mills theory, without quark effects taken into account. A detailed, all-order analysis of the complete kernel appearing in this particular equation, derived in the Landau gauge, reveals that the renormalization procedure may be accomplished through the sole use of ingredients known from the standard perturbative treatment of the theory, with no additional assumptions. However, the subtle interplay of terms operating at the level of the exact equation gets distorted by the approximations usually employed when evaluating the aforementioned kernel. This fact is reflected in the form of the obtained solutions, for which the deviations from the correct behavior are best quantified by resorting to appropriately defined renormalization-group invariant quantities. This analysis, in turn, provides a solid guiding principle for improving the form of the kernel, and furnishes a well-defined criterion for discriminating between various possibilities. Certain renormalization-group inspired Ans\"atze for the kernel are then proposed, and their numerical implications are explored in detail. One of the solutions obtained fulfills the theoretical expectations to a high degree of accuracy, yielding a gluon mass that is positive definite throughout the entire range of physical momenta, and displays in the ultraviolet the so-called ``power-law'' running, in agreement with standard arguments based on the operator product expansion. Some of the technical difficulties thwarting a more rigorous determination of the kernel are discussed, and possible future directions are briefly mentioned.