Quark model relation for kaon charge radii

We derive the equation r²_E(K⁰)/r²_E(K⁺) = -(m²_s ? m²_n)/(2m²_s + m²_n) relating the kaon electric charge radii and the strange (m_s) and non-strange (m_n) quark masses in the nonrelativistic quark model, and suggest an inequality which we expect to hold in the presence of relativistic corrections. New data for these charge radii are presently being analysed by two experimental groups.     

Quark model relation for kaon charge radii

We derive the equation r_E²(K⁰)/r_E²(K⁺) = m_s² − m_n²))/(2m_s² + m_n²) relating the kaon electric charge radii and the strange (m_s) and non-strange (m_n) quark masses in the nonrelativistic quark model, and suggest an inequality which we expect to hold in the presence of relativistic corrections. New data for these charge radii are presently being analysed by two experimental groups.     

Fine structure in the mass number dependence of rms charge radii

A comprehensive study of experimental rms charge radii shows that the deviation from the rough $\text{A}{}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}$ dependence follows simple trends. For the isotopic sequence of an element, the values of rms radii, normalized by an approximate $\text{A}{}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}$ law and plotted as a function of neutron number, lie on or close to straight lines. The slopes of these lines vary systematically as a function of atomic number. There are discontinuities in the values of the slopes for elements that contain N = 20, 28, 50, 82, 88, 90 and 126 neutrons as well as between Z = 8 and 10; a significant change can be found also for the region Z = 76 (N ≈ 114). These changes can be explained qualitatively by the shell model and by the effect of deformation. An “odd-even staggering” of the order of 6 × 10^?4 has also been observed.     

On the decrease in charge radii of multi-quasi particle isomers

We report changes in mean-square charge radii, δ〈r²〉$\delta 〈r^2〉$, magnetic moments and quadrupole moments for three multi-quasi particle isomers; ^97m2Y, ^176mYb and ^178m1Hf. All the isomers are observed to display a decrease in 〈r²〉$〈r^2〉$ compared to the lower-lying nuclear state on which the isomer is built. The decreases in 〈r²〉$〈r^2〉$ occur despite the isomers showing increases in quadrupole moment. Possible mechanisms for the effect, which is now seen for six multi-quasi particle isomers, are discussed.     

Anisotropic surface tension and the liquid drop model

The liquid drop model assumes that the surface tension of all nuclei is isotropic. The consequences of relaxing this assumption are studied. First a macroscopic theory of anisotropic surface tension is presented. Then with a particular choice for the functional form of the surface tension tensor, this theory is applied to a charged liquid drop. A small anisotropy in the surface tension can significantly distort a highly charged drop and lower its fission barrier.     

关于原子核电荷半径的研究

结合原子核电荷半径实验数据, 对885个中子数N≥8和质子数Z≥8的核电荷半径做了系统的研究. 对于单参数核电荷半径公式, Z^1/3律公式计算的结果优于A^1/3律的结果, 而对于两参数和三参数公式, Z^1/3律和A^1/3律的结果基本相当. 考虑到壳效应及奇偶摆动现象, 在原有的三参数公式基础上提出了加入Casten因子项和δ项的核电荷半径新公式. 利用该公式计算得到的核电荷半径理论值和实验值符合得非常好, 均方根偏差仅为σ=0.0266 fm, 此值比常用的三参数公式的结果下降了近50%, 理论计算值能更好地反映出壳效应及核电荷半径奇偶摆动的变化趋势.     

Ternary fission in the liquid drop model

The fissioning of a nucleus into three equal fragments is considered in the liquid drop model. Saddlepoint energies for prolate and oblate ternary fission are given as a function of the fissiity parameter.     

Barrett moments and rms charge radii

An empirical relation is established between Barrett equivalent radii R _k,α and rms charge radii < r ² >^1/2 based on the results of model-independent and Fermi model analyses of 2p → 1s transitions in muonic atoms. This relation follows simple Z dependence, and can be usefully applied to derive rms radii < r ² >^1/2 or differences δ ^AA ′ < r ² >^1/2 in cases where only R _k,α data or isotope shifts δ ^AA ′ R _k,α are published. The atomic number dependence of the Barrett parameters k(Z) and α(Z) is also given by empirical formulae. It is shown that the Barrett moment can be expanded in a sum of integer moments < r ^m > (m ≥ 2) using an effective exponential parameter α _eff(Z). The moments < r ^m > and isotopic differences δ < r ^m > of the two-parameter Fermi distribution expressed in terms of the parameters c and a are given in the Appendix for m = 1 – 10.     

On the light meson mass formulae from quantum chromodynamics

We reconsider the Gell-Mann-Okubo light meson mass formulae using the moment sum rules ratios and taking into account non-leading quark masses and vacuum condensate effects. We also extract the strange quark mass value from the ?-ρ mass difference. The poorly known masses of the (I=0,J ^PC =0⁺⁺) scalar mesons are discussed.     

Semi-empirical mass formula and nuclear radii

The semi-empirical mass formula is extended to include different radii for the proton and neutron distributions. By minimising the energy, the radii are determined. Our model predicts that the proton radius equals the neutron radius for all stable nuclei and that this radius has an accurate A^1/2 dependence.     

Investigation of proton radioactivity with the effective liquid drop model

Proton radioactivity has been investigated using the effective liquid drop model with varying mass asymmetry shapes and effective inertial coefficients. An effective nuclear radius constant formula replaces the old empirical one in the calculations. The theoretical half-lives are in good agreement with the available experimental data. All the deviations between the calculated logarithmic half-lives and the experimental values are less than 0.8.The root-mean-square(rms) deviation is 0.523. Predictions for the half-lives of proton radioactivity are made for elements across the periodic table. From the theoretical results, there are 11 candidate nuclei for proton radioactivity in the region Z <51. In the region Z >83, no nuclei are suggested as probable candidate nuclei for proton radioactivity within the selected range of half-lives studied.     

Correlation effects on the charge radii of exotic nuclei

The structures and distributions of light nuclei are investigated within a microscopic correlation model. Two particle correlations are responsible for the scattering of model particles either to low momentum- or to high momentum-states. The low momentum states form the model space while the high momentum states are used to calculate the G-matrix. The three and higher order particle correlations do not play a role in the latter calculation especially if the correlations induced by the scattering operator are of sufficient short range. They modify however, via the long tail of the nuclear potential, the Slater determinant of the (A) particles by generating excited Slater’s determinants.      

Charge and mass radii of the tin isotopes

Data on the isotope shift of the nuclear charge densities of the tin isotopes and of their mean square charge radii are considered from the viewpoint of the Hartree-Fock and Droplet Models. Attention is paid to the electromagnetic corrections of order 1/m². Through a leptodermous analysis of charge and matter densities we find: (i) differences of m.s. charge radii are mainly sensitive to the external region, (ii) the electromagnetic corrections are important in that region, (iii) despite different leptodermous properties, forces Ska and GO-P lead to the same neutron skin thickness. The average rate of variation of the proton m.s. radius is interpreted as favouring either a low valueQ≈30 MeV for the droplet model asymmetry parameter, or a zero value for the saturation asymmetry parameterL.     

Neutrino dipole moments and charge radii in non-commutative space-time

In this paper we obtain a bound TeV on the scale of space-time non-commutativity considering photon-neutrino interactions. We compute *-dipole moments and *-charge radii originating from space-time non-commutativity and compare them with the dipole moments calculated in the neutrino-mass extended standard model (SM). The computation depends on the nature of the neutrinos, Dirac versus Majorana, their mass and the energy scale. We focus on Majorana neutrinos. The *-charge radius is found to be at TeV.Received: 17 June 2004, Published online: 18 August 2004