International Journal of Modern Physics E

We present an elementary and fairly detailed review of several Green’s function methods for treating nuclear and other many-body systems. We first treat the single-particle Green’s function, by way of which some details concerning linked diagram expansion, rules for evaluating Green’s function diagrams and solution of the Dyson’s integral equation for Green’s function are exhibited. The particle-particle hole-hole (pphh) Green’s function is then considered, and a specific time-blocking technique is discussed. This technique enables us to have a one-frequency Dyson’s equation for the pphh and similarly for other Green’s functions, thus considerably facilitating their calculation. A third type of Green’s function considered is the particle-hole Green’s function. RPA and high order RPA are treated, along with examples for setting up particle-hole RPA equations. A general method for deriving a model-space Dyson’s equation for Green’s functions is discussed. We also discuss a method for determining the normalization of Green’s function transition amplitudes based on its vertex function. Some applications of Green’s function methods to nuclear structure and recent deep inelastic lepton-nucleus scattering are addressed.

We review the topic of high-order correlations in heavy-ion collisions, concentrating on two classes of correlation that are of interest at intermediate bombarding energy: Bose-Einstein correlations among the produced pions, and collective flow correlations among the nuclear fragments.

The damping of the harmonic oscillator is studied in the framework of the Lindblad theory for open quantum systems. A generalization of the fundamental constraints on quantum mechanical diffusion coefficients which appear in the master equation for the damped quantum oscillator is presented; the Schrödinger, Heisenberg and Weyl-Wigner-Moyal representations of the Lindblad equation are given explicitly. On the basis of these representations it is shown that various master equations for the damped quantum oscillator used in the literature are particular cases of the Lindblad equation and that not all of these equations are satisfying the constraints on quantum mechanical diffusion coefficients. Analytical expressions for the first two moments of coordinate and momentum are obtained by using the characteristic function of the Lindblad master equation. The master equation is transformed into Fokker-Planck equations for quasiprobability distributions and a comparative study is made for the Glauber P representation, the antinormal ordering Q representation, and the Wigner W representation. The density matrix is represented via a generating function, which is obtained by solving a timedependent linear partial differential equation derived from the master equation. Illustrative examples for specific initial conditions of the density matrix are provided. The solution of the master equation in the Weyl-Wigner-Moyal representation is of Gaussian type if the initial form of the Wigner function is taken to be a Gaussian corresponding (for example) to a coherent wavefunction. The damped harmonic oscillator is applied for the description of the charge equilibration mode observed in deep inelastic reactions. For a system consisting of two harmonic oscillators the time dependence of expectation values, Wigner function and Weyl operator, are obtained and discussed. In addition models for the damping of the angular momentum are studied. Using this theory to the quantum tunneling through the nuclear barrier, besides Gamow’s transitions with energy conservation, additional transitions with energy loss are found. The tunneling spectrum is obtained as a function of the barrier characteristics. When this theory is used to the resonant atom-field interaction, new optical equations describing the coupling through the environment of the atomic observables are obtained. With these equations, some characteristics of the laser radiation absorption spectrum and optical bistability are described.

By invoking the existence of the zero-sound mode we have succeeded in generalizing the Bohm-Pines method, for the collective description of the interparticle interactions in a dense electron gas, to calculate the binding energy per nucleon in the ground state of a nuclear matter. The present calculation gives rise to a saturation Fermi wave vector k_FO=1.74 fm⁻¹, which is larger than the mostly accepted value of 1.43 fm⁻¹. Our calculated result for the velocity of the zero-sound mode is found to be well-agreeable with those of other theories. It is further seen that there is an instability in the nuclear matter, with respect to long wavelength density fluctuations, in the low density region n≤0.78n₀, n₀ being the saturation nuclear density. From the present theory, we obtain a compression modulus K=116.7 MeV at the saturation density, which is smaller than the well-known result (210±30) MeV. However, by adjusting the value of the effective mass, M*, of the nucleon, we are able to reproduce the correct result for the compression modulus. Such a value of M* is found to be greater than the bare nucleon mass M. From the present theory, we obtain the energy of the monopole resonance E_ph=32.38 MeV, which agrees reasonably well with the experimental data for heavy nuclei. By lowering the value of the saturation Fermi wave vector, we observe a decrease in the value of the compression modulus, which is just the opposite to the results of other theoretical calculations.

The effects of the finite size of the nucleus in the electromagnetic excitation of the quasi-elastic peak have been studied by comparing the responses calculated for ¹²C and ⁴⁰Ca with the Fermi gas and the shell model. The contribution of the Meson Exchange Currents has also been considered. We have investigated the possibility of improving the Fermi gas model with approximate estimations of the finite size effects. We found that the use of an effective Fermi momentum provides a better description of the shell model results than the Local Density Approximation.

A new picosecond lifetime measurement system developed at UNISOR was used to determine the half-life of the well-deformed levels in ¹⁸⁸Hg and ¹⁸⁶Hg. The half-life values were measured to be 204±45 ps in ¹⁸⁸Hg and ≤52 ps in ¹⁸⁶Hg. The corresponding values of ρ²(E0)×10³, obtained from the partial half-lives, were and ≥32, respectively. Additionally, the half-lives of the levels were determined to be 141±31 ps in ¹⁸⁸Hg and 48±27 ps in ¹⁸⁶Hg.

We consider multibaryon configurations in a SU(2) quark soliton model based on chiral invariant quark-meson couplings. We compute the energy of interaction between two nucleons by considering configurations which correspond to two B=1 solitons separated by a fixed distance. The gross features of the inter-nucleon potential are reproduced. We also find cylindrically symmetric, classically stable soliton solutions with B=2, 3 and 4. The energy distributions corresponding to these solutions are toroidal in nature. The results closely parallel the Skyrme-model calculations.

We calculate a mass parameter for nuclear collective motion within the framework of the Generator Coordinate Method. Two alternative phase space normalization schemes are presented, and a simple expression for the collective mass is obtained within the Gaussian Overlap Approximation. As an application, we calculate the mass parameter associated with β vibrations. A systematic study carried out in the mass range 12≤A≤100 shows pronounced shell effects. Our results in the spherical limit are shown to exceed the well known inertia for quadrapole oscillations in an irrotational fluid by a factor 2–3. It is argued that the application of this method to other problems in nuclear structure and reactions should be straightforward.

The double neutron capture reaction ¹⁶⁹Tm(n,γ)¹⁷⁰Tm(n,γ)¹⁷¹Tm and the proton transfer reaction ¹⁷⁰Er(³He,d)¹⁷¹Tm were used to study nuclear levels in ¹⁷¹Tm. The level scheme up to 1 MeV was confirmed and very precise level energies were determined. The results are compared with the quasiparticle-phonon model. Evidence was found, that the 1/2⁻[541] orbit has larger deformation than the other states.

The non-scaling version of the Color Dielectric Model is used to calculate the SU(3) baryon octet and decuplet masses with the mean-field approximation and momentum projection method of Peierls and Yoccoz. Quantum mechanical treatment of the dielectric field is done by taking the coherent state approximation. For suitable set of parameters it is observed that the masses in the momentum projection method are in better agreement with the observed values than those of the mean-field ones.

The backward multiplicity and angular distributions of the shower particles produced in the interactions of ²²Ne and ²⁸Si nuclei at 3.6 GeV in emulsions are presented, analysed and compared with the data from the interactions of ¹²C nuclei at the same incident energy. The results yield quite interesting information regarding the mechanism of production of backward shower particles. The pseudorapidity distributions of the produced shower particles in the backward hemisphere are independent of the projectile mass. The multiplicity distributions of the shower particles emitted in the backward direction, using the KNO representation, are described by an exponential form.