The role of the Coulomb interaction in isospin-violating direct nuclear reactions

We investigate possible sources of isospin mixing in direct nuclear reactions. We find that there are mainly two effects which enter coherently into the direct reaction amplitude : “induced isospin mixing” caused by the Coulomb interaction between the target and the projectile, and “wavefunction effects” of the target nuclear states. These arise mainly through the difference of corresponding neutron and proton single-particle wave functions. These differences are especially noticeable just in the surface region where direct reactions take place. As illustrative examples we perform model calculations for the pick-up reactions ¹³C(d, ³H)¹²C¹(1⁺, 15.11 MeV) and ¹³C(d, ³He)¹²B_g.s.(1⁺) and the inelastic scattering ¹²C(d, d′)¹²C¹ leading to the 1⁺ states at 12.71 MeV and 15.11 MeV. These model calculations are compared with the corresponding experimental data.     

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      

Bound s-state energies for the exponential cosine screened Coulomb potential in Ecker-Weizel approximations

Bound s-state energies of an electron in the exponential cosine screened Coulomb potential, V(r) = ?e²e^?δrcos(δr)/r, are obtained analytically using the Ecker-Weizel approximation. For reasonable values of the screening parameter δ, the predicted results are in excellent agreement with the variational calculation of Lam and Varshni. The effect of screening on the shift of the quantum numbers from their normal values is also studied for various s-states.     

Screened Coulomb potentials for astrophysical nuclear fusion reactions

The electron-screening acceleration of laboratory fusion reactions at astrophysical energies is an unsolved problem of great importance to astrophysics. That effect is modeled here by considering the fusion of hydrogen-like atoms whose electron probability density is used in Poisson's equation in order to derive the corresponding screened Coulomb potential energy. That way atomic excitations and deformations of the fusing atoms can be taken into account. Those potentials are then treated semiclassically in order to obtain the screening (accelerating) factor of the reaction. By means of the proposed model the effect of a superstrong magnetic field on laboratory hydrogen fusion reactions is investigated here for the first time showing that, despite the considerable increase in the cross-section of the dd reaction, the pp reaction is still too slow to justify experimentation. The proposed model is finally applied on the H² d, pH³ fusion reaction describing satisfactorily the experimental data although some ambiguity remains regarding the molecular nature of the deuteron target. Notably, the present method gives a sufficiently high screening energy for hydrogen fusion reactions so that the take-away energy of the spectator nucleus can also be taken into account. Received: 19 May 2000 / Accepted: 4 September 2000     

Models and approximations for the momentum distribution in nuclear matter

As a step toward development of a framework for phenomenological analysis of nuclear momentum distributions in terms of dynamical interparticle correlations, the momentum distribution n(k) of symmetrical nuclear matter described by a Jastrow wave function is studied within a variety of approximation schemes. In particular, two simple low-cluster-order approximations are proposed, one of which may be readily adapted to finite nuclei. For two choices of pair correlations tailored respectively to soft and moderately stiff repulsive cores, the results based on these approximations compare favorably with the standards set by Fermi-hypernetted-chain evaluation and (for the kinetic energy) by Monte Carlo integration — even at densities somewhat beyond the empirical equilibrium density of nuclear matter. The crucial role played by the Jastrow wound parameter, as a determinant of the overall behavior of n(k), emerges clearly from these calculations.     

On the Coulomb interaction in granular systems

The previous theories on the behaviour of the conductivity of high-resistivity granular metals are analysed in terms of the Coulomb interaction between the charge carriers. In these theories a non-interacting system of carriers is considered, but it turns out that the Coulomb interaction is involved elsewhere in the calculations. Leaving out this interaction is shown to be a rather wrong assumption. The application of the Efros-Shklovskii theory leads to a real Coulomb gap. A second method is used to confirm the existence of this gap, which width is determined. The results we obtain seem to be consistent with those obtained on the systems with impurities.     

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.     

Coulomb corrections to nuclear beta decay

A calculation of the Coulomb correction to the nuclear beta decay is presented, in the context of the elementary-particle treatment of Kim and Primakoff, making use of the low-energy approximants to nuclear form factors.     

Prospects for coherently driven nuclear radiation by Coulomb excitation

Possible experiments are discussed in which Coulomb excitation of nuclear isomers would be followed by sequential energy release. The possibility of coherent Coulomb excitation of nuclei ensconced in a crystal by channeled relativistic heavy projectiles is considered. The phase shift between neighbor-nuclei excitations may be identical to the photon phase shift for emission in the forward direction. Thus, the elementary string of atoms may radiate coherently with emission of characteristics nuclear γ rays, and the intensity of the radiation would be increased due to the summation of amplitudes. Mössbauer conditions should be important for this new type of collective radiation, which could be promising in the context of the γ-lasing problem.     

Coulomb effects in relativistic nuclear collisions

We derive simple analytical formulas for Coulomb final-state interactions and apply them to the analysis of recent data on nuclear collisions. The π^?/π⁺ ratio, the π⁺ inclusive cross section, and the n/p ratio are studied. A relativistic field theoretic model is used to derive the formulas to first order in Zα. Using well-known non-perturbative results, we recast those formulas into an approximate non-perturbative form valid when finite-size effects are negligible. This allows us to calculate the important k → 0 limit. The final formulas are covariant and take into account multiple independently moving charged fragments of finite size and finite thermal expansion velocities. Our studies demonstrate analytically the complexity and importance of Coulomb distortions in nuclear collisions.     

Semiclassical approximations for nuclear Hamiltonians II. Spin-dependent potentials

A systematic semiclassical expansion procedure for physical quantities in nuclei, based on the Thomas-Fermi approximation to the Hartree-Fock equations and constructed in a previous work, is extended here to the realistic case where the effective one-body Hamiltonian for nucleons contains spin-dependent terms. Spin-induced corrections to the kinetic energy density and surface energy of the nucleus, and expressions for various spindependent densities inside the nucleus are computed up to fourth order in for several nuclear Hamiltonians.     

Study of approximations in the nuclear pairing-force problem

The accuracy of the Lipkin-Nogami version of the BCS method is examined and compared with other methods, for the ground and 0⁺ excited states of a symmetric two-level model. Unlike many other methods which fail for either very weak or very strong couplings, the Lipkin-Nogami method works well for any value of the force strength.     

Study of Coulomb interaction for two diffuse spherical-deformed nuclei

The Coulomb interaction for a spherical—deformed interacting pair is derived assuming realistic nuclear charge distributions. The effect of a finite diffuseness parameter is described either by the folding product of spherical or deformed sharp-surface distribution and a spherical short-range function or by using a Fermi two-parameter distribution function. The approximate solutions obtained using these categories of charge distributions are then compared to the numerical solution obtained within the framework of the double-folding model. We found that the finite surface diffuseness parameter affects slightly the inner region of the total Coulomb potential, while it produces large errors in calculating the Coulomb form factors used frequently in nuclear reactions and fusion numerical codes. The text was submitted by the authors in English     

Two-center Coulomb problem with Calogero interaction

Physics of Atomic Nuclei - We show that the Calogero-type perturbation preserves the integrability and partial separation of variables for the Stark–Coulomb and two-center Coulomb problems,...     

Coulomb interaction and first-order superconductor-insulator transition

The superconductor-insulator transition (SIT) in regular arrays of Josephson junctions is studied at low temperatures. We derived an imaginary time Ginzburg-Landau-type action properly describing the Coulomb interaction. The renormalization group analysis at zero temperature T=0 in the space dimensionality d=3 shows that the SIT is always of the first order. At finite T, a tricritical point separates the lines of the first- and second-order phase transitions. The same conclusion holds for d=2 if the mutual capacitance is larger than the distance between junctions.     

Statistical field theory for simple fluids: mean field and Gaussian approximations

We present an exact field theoretical representation of the statistical mechanics of simple classical liquids with short-range pairwise additive interactions. The action of the field theory is obtained by performing a Hubbard-Stratonovich transformation of the configurational Boltzmann factor. The mean field and Gaussian approximations of the theory are derived and applications to the liquid-vapour transition considered.     

One-electron relativistic molecules with Coulomb interaction

As an approximation to a relativistic one-electron molecule, we study the operator \(H = ( - \Delta + m^2 )^{1/2} - e^2 \sum\limits_{j = 1}^K {Z_j } |x - R_j |^{ - 1}\) withZ _j ≧0,e ^?2=137.04.H is bounded below if and only ife ² Z _j ≦2/π allj. Assuming this condition, the system is unstable whene ²∑Z _j >2/π in the sense thatE ₀=inf spec(H)→?∞ as the R _j →0, allj. We prove that the nuclear Coulomb repulsion more than restores stability; namely \(E_0 + 0.069e^2 \sum\limits_{i< j} {Z_i Z_j } |R_i - R_j |^{ - 1} \geqq 0\) . We also show thatE ₀ is an increasing function of the internuclear distances |R _i ?R _j |.