abstract

Exact solutions of the equations of motion for the non-relativistic arbitrary spin particle in the Coulomb field are obtained. Galilei-invariant two-particle equations for spin-\(\frac {1}{2} \) particles are proposed.

abstract

The relativistic field equations for interacting massless attractive scalar and source-free electromagnetic fields in a cylindrically symmetric spacetime of one degree of freedom with reflection symmetry have been reduced to a first order implicit differential equation depending upon time which enables one to generate a class of solution to the field equations. The nature of the scalar and electromagnetic fields is discussed. It is shown that the geometry of the spacetime admits of an irrotational stiff fluid distribution without prejudice to the interacting electromagnetic fields.

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It is argued that an external gravitational field may substantially influence atomic spectra. As an example, a hydrogen atom falling freely in Schwarzschild’s space-time is investigated.

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We study quark-lepton mass pattern in a phenomenological manner. We consider the self interaction to be responsible for generation of the mass. We find that the ratio of average current quark mass and charged lepton mass bears a constant ratio for each family. We predict top quark mass to be 25 GeV.

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Using the considerations connected with the scaling hypothesis and the Regge pole model the phenomenological expressions for differential single-particle inclusive cross- -sections of \(\Delta \)-, \(\varrho \)- and \(\omega \)-resonances produced in \(N\)–\(N\) and \(\pi \)–\(N\) inelastic collisions at high energies are obtained. These expressions describe the known experimental data in a wide energy region from 10 to several thousands GeV.

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The consequences of isospin invariance for \(\bar p p \to \bar N\Delta \), \(\bar \Delta N\), \(\bar \Sigma \Sigma \) and \(\bar \Delta \Delta \) are derived. We obtain the isospin bounds on \(\sigma _{\rm tot}(\bar \Sigma ^0\Sigma ^0)\) from \(\sigma _{\rm tot} (\bar \Sigma ^+\Sigma ^+)\) and compare them to experiment. The present experimental upper bound on \(\sigma _{\rm tot}(\bar \Sigma ^0\Sigma ^0)\) are roughly as strong as the upper isospin bounds we obtain. The lower isospin bounds imply \(\sigma _{\rm tot}(\bar \Sigma ^0\Sigma ^0)\) \(\geq \) 2 \(\mu \)b at a \(\bar p\)-momentum around 3 GeV/\(c\). No violation of isospin symmetry is observed. We also obtain the isospin bounds on differential, polarized and unpolarized cross sections. The consequences of saturation of these bounds are derived.

abstract

On the base of a minimal preon mnemonic operating with spin-\(\frac {1}{2} \) and spin-0 subconstituents of lepton and quarks as well as of \(W^{\pm }\) and \(Z^0\), we predict some nonstandard bosons. One of them, being a colour octet (though no quark–antiquack pair), can decay into two or three gluons and so might be relevant for recent CERN collider experiments in progress.

abstract

The \(^6\)Li nucleus is taken in the present work as composed of an alpha particle, a proton and a neutron. With this structure, the \(^6\)Li nucleus, it can be studied as a three-body problem. Three-body integral equations for the three body system are obtained by taking separable potentials for the nuclear interactions between the alpha, the proton and the neutron particles in pairs. The \(^6\)Li nucleus is studied in the ground and the first excited states. In the ground state of \(^6\)Li nucleus \((J^{\pi } = 1^+)\), the nucleon–nucleon interaction is taken as the triplet \(^3S_1\) potential, while for the excited state of the \(^6\)Li\(^{\star }\) nucleus \((J^{\pi } = 0^+)\), these nucleon–nucleon interactions are taken to act in the singlet \(^1S_0\) state. The Pauli principle restricts the central part of the nucleon-alpha interaction in the \(^6\)Li nucleus to being taken only as a \(^1P_1\)- interaction. In the present work we have used Gaussian potential forms for the two-body interactions. The various parameters of the two-body interactions are obtained by fitting the corresponding two-body phase shifts. Numerical calculations of the resulting three-body integral equations, give the different form factors for both the ground and excited states of the \(^6\)Li nucleus. The effective ranges for both states are also calculated. Solving the obtained coupled integral equations numerically, we calculate the binding energies for the ground and excited states of the \(^6\)Li nucleus. Good agreements are found between the theoretically calculated values of the binding energies and the experimental values.

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Owing to the inhibition due to the \({\mit \Delta } K\) selection rule in \(\beta \)-decay, the calculated value of the Fermi matrix element of the isospin-forbidden \(\beta ^+\) decay of \(^{57}\)Ni is in reasonably good agreement with the experimental value.

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The \(B(E2)\) values of the 217.3, 261.4, 306.4, 397.2, 522.8, 606.2 and 761.7 keV states of \(^{79}\)Br and the 275.9, 538.2, 566.2, 650.0, 767.1, 828.5 and 836.5 keV states of \(^{81}\)Br have been measured from Coulomb excitation with 2.5 MeV protons by observing the de-excited gamma-rays with a high resolution Ge(Li) detector. The low-energy protons have been used for the first time to Coulomb — excite the levels of bromine isotopes. The properties of the excited states of these nuclei have been discussed and compared with the results reported so far in the literature.

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Neutron capture cross sections on \(^{191,193}\)Ir were measured by the activation technique. The results are discussed in terms of the compound nucleus formation mechanism.