Calculation of the Coulomb potential between spherical-deformed and deformed-deformed nuclei using the Monte Carlo method

The Coulomb potential between spherical-deformed and deformed-deformed nuclei has been calculated using the Monte Carlo simulation. The results obtained for the Coulomb potential in the ¹⁶O$ + $²³⁸U and ²⁷Al$ + $⁷⁰Ge reactions are in good agreement with those obtained using the double-folding method. The simulation technique employed here has the ability of calculating the Coulomb potential taking into account the finite diffuseness parameter, all the possible deformation degrees of freedom, and different orientations of the symmetry axes of the target and the projectile nuclei with respect to each other. The accuracy of this simulation technique is high and the computer time taken to do these calculations is much less than those of the double-folding method.     

Coulomb energy of nuclei

The density functional determining the Coulomb energy of nuclei is calculated to the first order in e ². It is shown that the Coulomb energy includes three terms: the Hartree energy; the Fock energy; and the correlation Coulomb energy (CCE), which contributes considerably to the surface energy, the mass difference between mirror nuclei, and the single-particle spectrum. A CCE-based mechanism of a systematic shift of the single-particle spectrum is proposed. A dominant contribution to the CCE is shown to come from the surface region of nuclei. The CCE effect on the calculated proton drip line is examined, and the maximum charge Z of nuclei near this line is found to decrease by 2 or 3 units. The effect of Coulomb interaction on the effective proton mass is analyzed.     

Stationary entanglement between two nanomechanical oscillators induced by Coulomb interaction

We propose a scheme for entangling two nanomechanical oscillators by Coulomb interaction in an optomechanical system. We find that the steady-state entanglement of two charged nanomechanical oscillators can be obtained when the coupling between them is stronger than a critical value which relies on the detuning. Remarkably, the degree of entanglement can be controlled by the Coulomb interaction and the frequencies of the two charged oscillators.     

Two-particle density matrix for Coulomb interaction

An integral representation is derived for the density matrix of two particles interacting via a Coulomb potential. In particular this representation yields a simple expression for the exchange term of the Slater sum of two identical particles which is suitable for numerical calculations. Results are given for several values of the parameter ξ=e ²/kT      

Microscopic systems with and without Coulomb interaction, fragmentation and phase transitions in finite nuclei

We test the influence of the Coulomb interaction on the thermodynamic and cluster generation properties of a system of classical particles described by different lattice models. Numerical simulations show that the Coulomb interaction produces essentially a shift in temperature of quantities like the specific heat but not qualitative changes. We also consider a cellular model. The thermodynamic properties of the system are qualitatively unaltered. Received: 7 November 2000 / Accepted: 17 May 2001     

Gaussian approximations for the nuclear Coulomb interaction

The kernel 1/¦r-r′¦=1/y in the direct term of the average Coulomb potential of the nuclear Hartree-Fock model is approximated by a sum of gaussians iny. For 0.5≦y≦30 Fm, a sixteen term expression is found such the direct Coulomb energy is obtained to one part in 10³. The exchange Coulomb potential is estimated in the statistical model. Applications of these accurate and practical approximations to fission calculations are discussed.     

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).     

Coulomb breakup of neutron-rich isotopes of light nuclei

The effects of higher order multipole transitions, in particular, E2 and E1–E2 interference, in the Coulomb dissociation of neutron-rich nuclei ¹¹Be, ¹⁴B, ¹⁵C, and ¹⁹C on Pb targets at energies of 72, 86, 550, and 77 A MeV, respectively, within the framework of the eikonal-approximation approach are studied. The main steps involved in the derivation of the explicit expressions corresponding to dipole, quadrupole, and dipole-quadrupole-interference terms are outlined. The calculations reveal that the contribution of E2 transitions to the total cross section is finite but small, while that ofE1–E2 interference is nil.Nevertheless, the E1–E2 interference term introduces small distortions in the peak of the relative-energy spectrum. The calculated results are compared with the corresponding data and the comparison favors a value of 0.530 MeV as the ground-state binding energy of ¹⁹C. The text was submitted by the authors in English.     

Calculation of proton-deuteron breakup reactions including the Coulomb interaction between the two protons

The Coulomb interaction between the two protons is fully included in the calculation of proton-deuteron breakup with realistic interactions for the first time. The hadron dynamics is based on the purely nucleonic charge-dependent (CD) Bonn potential and its realistic extension CD Bonn +Delta to a coupled-channel two-baryon potential, allowing for single virtual Delta-isobar excitation. Calculations are done using integral equations in momentum space. The screening and renormalization approach is employed for including the Coulomb interaction. The Coulomb effect on breakup observables is seen at all energies in particular kinematic regimes.     

Study of exotic nuclei with the skyrme interaction

The stability (with respect to nucleon emission) of highly neutron-rich nuclei of He, C, O and Si is investigated in the framework of the Hartree-Fock approximation with several sets of Skyrme interactions. The existence (in the sense of stability against decay with the emission of a neutron) of as yet undetected ²⁰C, ²²C, ²⁸O and ⁴²Si nuclei is predicted. The relevance of the triplet-triplet component of the nuclear interaction to the stability of the neutron-rich nuclei is demonstrated.     

Enhancing stationary entanglement between two optomechanical oscillators by Coulomb interaction with Kerr medium

We theoretically study the stationary entanglement of two charged nanomechanical oscillators coupling via Coulomb interaction in an optomechanical system with an additional Kerr medium. We show that the degree of entanglement between two nanomechanical oscillators is suppressed by Kerr interaction due to photon blockade and enhanced by Coulomb coupling strength. We also show other parameters for adjusting and obtaining entanglement, such as the driving power and the frequencies of the two oscillators, and the entanglement is robust against temperature. Our study proves a way for adjusting stationary entanglement between two optomechanical oscillators by Coulomb interaction and Kerr medium.     

Many-times formalism and Coulomb interaction

We extend here the many-times formalism, formerly used mainly for particles moving in given classical fields, to interacting particles. In order to minimize the difficulties associated with an equal-time interaction, we limit ourselves to nonrelativistic quantum mechanics and a two-particle interaction, such as that corresponding to the Coulomb force between charged particles. We obtain a set of differential equations which are really not consistent, but they serve as a guide to a formulation in terms of integral equations that has the same perturbation expansion as the usual theory for the scattering of particles. The integral equation for two-particle amplitudes can be modified to give the correct theory for bound states, but this is not the case for more than two particles. We expect that this theory can be generalized to a formulation of relativistic quantum mechanics of interacting particles.     

The effect of surface and Coulomb interaction on the liquid–gas phase transition of finite nuclei

By means of the Furnstahl, Serot and Tang's model, the effects of surface tension and Coulomb interaction on the liquid–gas phase transition for finite nuclei are investigated. A limit pressure p_lim above which the liquid–gas phase transition cannot take place has been found. It is found that comparing to the Coulomb interaction, the contribution of surface tension is dominate in low temperature regions. The binodal surface is also addressed.     

The effect of nuclear and Coulomb interactions on the nuclear shapes of two colliding208Pb nuclei

Using a complex energy density functional derived from the Reid soft-core potential, the changes in nuclear shapes of two colliding²⁰⁸Pb are investigated. At each separation distanceR, the total binding energy of the Pb + Pb system is minimized w.r.t. the quadrupole deformation and diffuseness parameters of nuclear densities. It is found that the nuclear shapes are strongly affected by the nuclear and Coulomb interactions. A sudden transition occurs from oblate to prolate shapes around R16.8fm and a smooth one from prolate to oblate shapes aroundR?11.76 fm.