First-order relativistic corrections to the theory of Coulomb excitation

It is suggested that relativistic effects may be significant in high-precision Coulomb-excitation experiments. First-order corrections to the non-relativistic theory of Coulomb excitation are determined with the restriction that all of the states involved in the excitation have the same parity and that the scattering angle is 180°. The results of some numerical calculations are presented to give an indication of the magnitude of the correction. A recent experiment to determine the B(E2;0⁺ → 2⁺) and excited-state quadrupole moment of ¹⁹⁸Hg is reanalyzed and the relativistic correction to the B(E2) is found to be several times the experimental uncertainty. Sizeable effects are also found in multiple Coulomb excitation.     

A QED description of relativistic Coulomb excitation in heavy ion collisions

A quantum electrodynamical treatment of Coulomb excitation in relativistic heavy ion collisions is presented. It is shown that a subtle interplay between quantum and relativistic kinematical effects induced by the nuclear recoil due to excitation generates a qualitatively different prediction (under certain kinematical conditions) from the corresponding prediction of conventional theories. The present formalism is applied to the clear fission problem and the results seem to solve the puzzle associated with this process for some time.     

Corrections to the Alder-Winther theory of Coulomb excitation

An expansion scheme is developed for studying corrections to the Alder-Winther theory of Coulomb excitation. The zeroth-order term in the expansion of the excitation cross section is identical to the expression provided by the Alder-Winther theory and there are several kinds of first-order corrections. All of these can be calculated by making simple changes in existing computer programs for the Alder-Winther theory. These corrections can be interpreted as a change in the deflection function for the relative motion and a change in the excitation probabilities due to the deviations of the relative motion from a Rutherford orbit. Some of the terms that describe the change in the excitation probabilities correspond to an energy symmetrisation and others can be interpreted as an angular momentum symmetrisation. Numerical comparisons with results of full quantal coupled-channels calculations are presented.     

The classical-limit S-matrix for Coulomb excitation

An expression for the classical-limit S-matrix for Coulomb excitation is derived and directly evaluated without resorting to stationary phase integration methods. The results obtained are in quantitative agreement with quantum mechanical calculations. This agreement and the simplicity of the method suggest tha feasibility of extending it to cases where other methods are not easily applied.     

Interacting quantum wires: A possible explanation for the 0.7 anomalous conductance

We investigate an effective one-dimensional conducting channel considering both the contact umklapp and the Coulomb electron-electron interaction. We show that, at low electronic density, the proximity to the Wigner crystal reproduces the anomaly in conductance at 0.7G₀. The crucial ingredient of our theory is the fact that the gate voltage acts as a bias controlling the intensity of the umklapp term. At large gate voltages, the umklapp vanishes and we obtain a conducting quantum wire with a perfect conductance. At low gate voltages, the Wigner crystal is pinned by the umklapp term, giving rise to an insulating behavior with vanishing conductance. This crossover pattern has a transition point which can be identified with the anomalous conductance around 0.7G₀. This picture is obtained within the framework of a renormalization group calculation. The conductance static regime is achieved by taking first the limit of finite length and then the limit of zero frequency.     

A possible explanation of the colinearity effect

There have been indications that in deuteron break-up at low energy, an unexpected enhancement in the cross section is present in kinematic situations for which the residual nucleus is close to being at rest in the overall c.m. system, the three final particles thus being located on the same straight line (the so-called colinearity effect). The extent to which such an enhancement can be explained in terms of off-shell effects within the quasi-free scattering mechanism and in terms of rescattering effects is examined. A formalism is developed for an arbitrary nucleon knock-out reaction A(a, aN)B on a light target, and the reaction d(d, dp)n is then studied as a numerical example.     

A contribution to the explanation of the electronic spectrum of amorphous materials

In this article the electronic spectrum is explained on the basis of a polycrystalline model of amorphous material. It is shown that from the given model the origin of the “tail profile” function can be derived which expresses the dependence of the density of states on energy. Taking into consideration the small density of states in the region of the tail, “the increase” of activation energy of amorphous materials in comparison with monocrystalline materials can easily be explained.     

The generalized Coulomb interactions for relativistic scalar bosons

Approximate analytical solutions of Duffin–Kemmer–Petiau (DKP) equation are obtained for the truncated Coulomb, generalized Cornell, Richardson and Song–Lin potentials via the quasi-exact analytical ansatz approach.     

Method for calculating the relativistic Coulomb scattering amplitudes of electrons

The scattering amplitudes for the scattering of electrons by a point charge nucleus can be represented by power series in the variables (sin Θ/2)² or (cos Θ/2)², whereΘ is the scattering angle. A method for calculating the coefficients of these series including all terms up to an arbitrarily high order in (Z/137)², whereZ is the nuclear charge, is described. The method makes extensively use of recurrence relations and does not contain any approximation. Since all power series occurring in the course of the computation converge rapidly, very accurate results can be obtained with the help of a computer. The method is particularly advantageous for small and large scattering angles, where other methods fail to give accurate results.     

Coulomb excitation of the even-mass selenium nuclei

The properties of the low-lying states of the doubly even selenium nuclei have been investigated via multiple Coulomb excitation effected with 39.2 MeV oxygen projectiles. The excitation probabilities of the first 2⁺ states of ⁷⁶Se, ⁷⁸Se and ⁸⁰Se have been determined directly by resolving inelastically and elastically scattered ⁴He projectiles on thin targets. These measurements yielded values of B(E2; 0⁺ → 2⁺) equal to $\text{0.421 ± 0.009 (}{}^{76}\text{Se}\text{), 0.321 ± 0.009 (}{}^{78}\text{Se}\text{)}\text{and}\text{0.248 ± 0.005 (}{}^{80}\text{Se}\text{) e}{}^2\text{· b}{}^2$. The multiple Coulomb excitation experiments enabled us to detect 2⁺ and 4⁺ levels in all isotopes studied up to 2.1 MeV. Moreover the double Coulomb excitation of 0⁺' states at 854.1 keV (⁷⁴Se), 1498.5 keV (⁷⁸Se), and 1478.3 keV (⁸⁰Se) was also observed. The enhancement of the E2 transition between these 0⁺' levels and the first 2⁺ states decreases rapidly with the increase of the neutron number, i.e., $\text{B(}\text{E}\text{2; 0}{}^{\mathrm{+}}\text{′ → 2}{}^{\mathrm{+}}\text{)/B(}\text{E}\text{2; 2}{}^{\mathrm{+}}\text{→ 0}{}^{\mathrm{+}}\text{) = 2.04 ± 0.08 (}{}^{74}\text{Se}\text{), 0.91 ± 0.08 (}{}^{78}\text{Se),}\text{and}\text{0.28 ± 0.04 (}{}^{80}\text{Se}\text{)}$. States interpreted as the result of direct E3 Coulomb excitation have been observed at 2350.2, 2429.2, 2507.6, and 2717.6 keV in ⁷⁴Se, ⁷⁶Se, ⁷⁸Se and ⁸⁰Se, respectively. Their B(E3; 0⁺ → 3^?) values are $\text{2.1 ± 0.5 (}{}^{74}\text{Se}\text{), 4.0 ± 0.5 (}{}^{76}\text{Se}\text{), 2.7±0.3 (}{}^{78}\text{Se}\text{)}\text{and}\text{0.9 ± 0.2 ( × 10}{}^{\mathrm{?2}}\text{e}{}^2\text{·}\text{b}{}^3$ which represent enhancements of 9.2 ± 2.2, 16.6 ± 2.1, 10.8 ± 1.2 and 3.2 ± 0.7 respectively. Furthermore, angular distribution measurements of γ-rays following Coulomb excitation with 42 MeV ¹⁶O ions in ⁷⁸Se and ⁸⁰Se have been performed. The E2 content of the 2⁺' → 2⁺ transition in these two nuclei is 87.9 % (⁷⁸Se), and 96.2 % or 33.5 % (⁸⁰Se).