Mass formula

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

The $[{\bf 70},1^-]$ baryon multiplet in the $1/N_c$ expansion revisited

Abstract: The mass splittings of the baryons belonging to the $[{\bf 70},1^-]$-plet are derived by using a simple group theoretical approach to the matrix elements of the mass formula. The basic conclusion is that the first order correction to the baryon masses is of order $1/N_c$ instead of order $N^0_c$, as previously found. The conceptual difference between the ground state and the excited states is therefore removed.

Generalized Algebraic Mass Formulas. I

Abstract: It is shown that the SL(2, C)‐Poincare associative algebraic model of Bohm can be extended without essential difficulty to an SL(2, C)‐de Sitter model which gives rise to a meson mass formula with both spin and isospin dependence.

On the applications of Shimura's mass formula (Proceedings of the Symposium on Algebraic Number theory and Related Topics)

Abstract: We explain how to compute the mass of the genus of maximal lattices for quadratic form of the sum of squares by applying Shimura’s mass formula when the basic field is a real quadratic field (Section 1), and consider its applications in special cases (Section 2). This paper is also a survey on [Mu] to which several examples are added. §1. Shimura’s mass formula for computation To apply Shimura’s mass formula in [ \mathrm{S}99\mathrm{a} , Theorem 5.8] to the case treated below, we first recall some basic facts following [S]. Let V be the row vector space F^{n} over a real quadratic field F of dimension n and $\varphi$ the identity matrix 1_{n} of size n(n>1) . For x, y\in V , we set $\varphi$(x, y)=x $\varphi$\cdot yt=x\cdot yt and $\varphi$[x]= $\varphi$(x, x)=x\cdot xt . We define G=\{ $\gamma$\in GL_{n}(F)| $\gamma \varphi$\cdot{}^{t}$\gamma$= $\varphi$\}, G_{+}=\{ $\gamma$\in G|\det( $\varphi$)=1\}, which are written as G^{ $\varphi$}, G_{+}^{ $\varphi$} in [\mathrm{S}99\mathrm{a}] and [Mu], and also as O^{ $\varphi$}(V) , SO^{ $\varphi$}(V) in [S], Let G_{\mathrm{A}} be the adelization of G . For a \mathrm{g}‐lattice L in V , which is a finitely generated \mathrm{g}‐submodule in V containing a basis of V , and $\alpha$\in G_{\mathrm{A}} , we denote by L $\alpha$ the \mathfrak{g}‐lattice in V such that (L $\alpha$)_{v}=L_{v}$\alpha$_{v} for any finite prime v of F . Here \mathrm{g} is the ring of integers of F and L_{v} is the localization of L at v . We call \{L $\alpha$| $\alpha$\in G_{\mathrm{A}}\} (resp. \{L $\alpha$| $\alpha$\in G\} ) the genus (resp. class) of L with respect to G ; we also call it the G‐genus (resp. G‐class) of L . It is known that the genus of L consists of finitely many classes (cf. [\mathrm{S} , Lemma 9.21(iv) and (\mathrm{v}) ]) Let \{L_{i}\}_{i=1}^{h} be a complete set of representatives for G‐classes in the G‐genus of L. Then we set \displaystyle \mathfrak{m}(L)=\sum_{i=1}^{h}[$\Gamma$_{i}:1]^{-1} This is an expanded version of an address for Algebraic Number Theory and Related Topics”’ at RIMS, 2006, held in Kyoto, Japan. I express my thanks to Professor Ki‐ichiro Hashimoto for giving the opportunity. * Department of Mathematical Sciences, Ritsumeikan University © 2007 Research Institute for Mathematical Sciences, Kyoto University. All rights reserved,

The Study of Modified Semi-Empirical Mass Formula (SEMF) by Considering Isospin Effects in Liquid Drop Model

Abstract: We do theoretically study of Modified Semi-Empirical Mass Formula (SEMF) based on macroscopic approach in liquid drop model by considering isospin effects. Isospin is one of internal symmetry properties in hadron group, particularly the nucleon multiplet, it represented by isospin group. Hadron is a group of elementary particles take place in the strong interaction. The role of strong interactions represents homogeneous nuclear force, interactions between proton-proton, proton-neutron, and neutron-neutron are same. In other words, protons and neutrons are indistinguishable because mass (energy) between protons and neutrons is almost the same, by removing charge between them (charge independent). The dependence of isospin effects on nuclear symmetry term and oddeven (pairing) term made the formulation of SEMF should be modificated, in order to obtain nuclear mass and binding energy of a nucleus close to the experimental results. We do two accuracy testing. First, by comparing for nuclei using SEMF before and after being modified, the result shows that using SEMF before modification the value of and for modified SEMF we obtained at . The value of for modified SEMF is smaller than before modification, it indicates that Modified SEMF is a good formula to calculate the mass of nuclei. Second, by comparing Modified SEMF with other models such as FRDM, HFB-14, and HFB-17 using accuracy parameter in the form of rms deviation and number of model parameters. The results show that rms deviation decrease 21% to 0,516 and number of model parameters decrease to 15, consists of 13 macroscopic model parameters and two microscopic model parameters and . The value of model parameters was obtained by fitting to experimental results, as a reason it is called semi-empiric.