G-matrix effective interaction with the paris potential

An effective interaction is derived by fitting the oscillator matrix elements of the sum of the OBEP functions to the G-matrix elements derived from the Paris nucleon-nucleon interaction. The functional form, the mass dependence and the ambiguities of the effective interaction are discussed. For the application of the present effective interaction, we study the mass dependence of the G-matrices and estimate the Landau-Migdal parameter g′. We have obtained reasonable results for these cases.     

High momentum component in the deuteron

The high momentum component in the deuteron, which stems from the short range part of the nucleon-nucleon interaction, is studied in they-scaling function and the structure functionF ₂ of the deuteron. We use not only some non-relativistic wave functions but also relativistic ones. It is shown that the relativistic mechanism or a six-quark state in the nucleon-nucleon interaction yields a large high momentum component.     

Simulation of the Pauli-principle effects in the description of light ion scattering and bound states

A simple model which takes care phenomenologically of the effects of the Pauli principle is proposed to calculate, in the framework of the resonating group method, bound and scattering states of nuclear systems comprised of two light nuclei (n, t and α-particles) without performing a complete antisymmetrization of the wave functions. Retaining only the antisymmetrization between the nucleons belonging to a given cluster, the contributions of the terms corresponding to the exchange of two nucleons belonging to two different clusters are simulated by the matrix elements of an effective central, local, l-dependent, energy-independent nucleon-nucleon potential. The lowenergy levels of ⁸Be and ⁷Li as well as the phase shifts for l = 0 to 4 for energies below 10 MeV (c.m.) have been calculated with this effective potential (added to the regular nucleon-nucleon potential). Good agreement between exact and model calculations is achieved.     

Parity non-conservation in low energy scattering of nucleons by light nuclei: (I). Theoretical framework

The low energy scattering of nucleons by ²H, ³He and ⁴He are analyzed for parity non-conserving effects. The asymmetry in the total cross section of longitudinally polarized projectiles is formulated in terms of the optical theorem and a distorted wave Born approximation. For two nucleons at low energies it is only necessary to consider l = 0 to l = 1 matrix elements of the weak nucleon-nucleon potential. The asymmetries in the scattering from nuclear targets are related to the parameters of an effective weak nucleon-nucleon potential, so that they may be used to help differentiate between various proposed theoretical potentials.     

The role of nucleon-nucleon short-range correlations in the nuclear structure function in thex > 1 region

By using the Jastrow correlation wave function, the role of nucleon-nucleon short-range correlations in the nuclear structure function in thex > 1 region is reanalyzed. The result shows that, with the proper energy-momentum distribution of nucleons in the nucleus including the effect of nucleon-nucleon short-range correlations, the experimental data of the nuclear structure function in thex > 1 region can not be well explained. It seems that additional components which go beyond the conventional nuclear physics are necessary to describe the effect.     

The 1/Nc Expansion in Hadron Effective Field Theory

We study the N_c scalings of pion-nucleon and nucleon-nucleon scatterings in hadron effective field theory. By assuming Witten's counting rules are applied to matrix elements or scattering amplitudes, which use the relativistic normalization for the nucleons, we find that the nucleon axial coupling g_A is of order N_c0, and a consistent large N_c counting can be established for the pion-nucleon and nucleon-nucleon scatterings. We also justify the nonperturbative treatment of the low energy nucleon-nucleon interaction with the large N_c analysis and find that the deuteron binding energy is of order 1=N_c.     

Approximation of the microscopic effective pairing interaction by the off-shell T matrix for free nucleon-nucleon scattering

The effective pairing interaction in the ¹ S ₀ channel as calculated microscopically within the Brueckner method for a planar slab of nuclear matter by using the separable version of the Paris nucleon-nucleon potential is investigated. The effective interaction is determined for the model space including all negative-energy single-particle states. An analysis is performed for two values of the chemical potential, μ=?8 and ?4 MeV. It is shown that, to a high precision, the effective interaction can be approximated by the off-shell T matrix for free nucleon-nucleon interaction, the T matrix in question being taken at a negative value of the total energy of two nucleons E=2μ.     

Role of antisymmetrization in describing the excitation of the 1+, T = 1 level in the 12C nucleus by polarized protons

Inelastic polarized-proton scattering involving the excitation of the 1⁺, T = 1 level at 15.11 MeV in the ¹²C nucleus is described within the distorted-wave method. The effect of completely or approximately taking into account the antisymmetrization of the wave function for the projectile proton-intranuclear nucleons system on various observables, including the differential reaction cross section, the analyzing power, the difference of the polarization and analyzing power, and the depolarization parameter, is analyzed. The difference of the polarization and the analyzing power in the case of the excitation of anomalous-parity levels is shown to be especially sensitive to taking into account the above antisymmetrization. The reason for a large value of this difference for the level being studied and the sensitivity of this value to the parameters of the effective nucleon-nucleon interaction used are analyzed.     

Spectrum of <Superscript>10</Superscript>Be in the approximation of the leading irreducible representation of the <Emphasis Type="Italic">SU</Emphasis>(3) group

An algorithm for implementing the approximation of the leading irreducible representation of the SU(3) group is expounded for a microscopic Hamiltonian involving the potential energy of nucleon-nucleon interaction. An effective Hamiltonian is constructed that reproduces the results of calculations with nucleon-nucleon potentials used in the theory of light nuclei. It is shown that, in many respects, the structure of the effective Hamiltonian is similar to the structure of the Hamiltonian of a triaxial rotor and that, for the wave functions in the Elliott scheme, one can go over to a space where linear combinations of Wigner D functions appear to be the transforms of these functions, but where their normalization requires dedicated calculations.     

An extended time-dependent mean-field theory for strongly correlated nuclear systems

We perform an extension of the time-dependent mean-field theory by an explicit inclusion of strong two-body correlations of short range on a level of microscopic reversibility relating them to realistic nucleon-nucleon forces. Invoking a least action principle for correlated basis functions, equations of motion for the correlation functions and the single-particle model wave function are derived to the lowest order of the FAHT cluster expansion. Higher order effects as well as longrange correlations we consider only to the extent to which they contribute to the mean field via a readjusted phenomenological effective two-body interaction. The corresponding correlated stationary problem is investigated and appropriate initial conditions to describe a heavy ion reaction are proposed. The single-particle density matrix is evaluated. Norm, energy and particle number conservation are proved. Possible simplifications are discussed. Standard TDHF appears as a limiting case if the range of the explicitly considered part of the bare nucleon-nucleon interaction goes to zero.     

Tensor optimized antisymmetrized molecular dynamics for relativistic nuclear matter

We apply a newly developed many-body theory, tensor optimized antisymmetrized molecular dynamics (TOAMD), to nuclear matter using a relativistic bare nucleon-nucleon interaction in the relativistic framework. It becomes evident that the tensor interaction plays an important role in nuclear many-body system due to the role of the pion in a strongly interacting system. We take the relativistic nuclear matter (RNM) wave function as a basic state and add tensor and short-range correlation operators in the form of pion and omega-meson correlation functions acting on the RNM wave function using the concept of TOAMD. We use the Monte Carlo (Metropolis) method based on the Gaussian integration and the second quantization method for antisymmetrization to calculate all the matrix elements of the many-body Hamiltonian. We write the whole formula of the TOAMD method for numerical calculations of the nuclear binding and saturation properties of nuclear matter using one-boson exchange potential.     

Pionic decay of a possible dibaryon d’ and quark models of πB and πd’ couplings

The pionic decay of a possible dibaryon, d’ → πNN, is studied in the model assuming the production of ³ P ₀ quark-antiquark pairs and in other models of effective quark-pion coupling. The vertex constants and the form factors for pion-baryon and pion-dibaryon couplings are calculated. The effect of the internal pion structure on decay widths is investigated. It is shown that the quark structure of the nucleon-nucleon wave function in the overlap region plays an important role in dibaryon decays, and known models of nucleon-nucleon interaction are analyzed with allowance for this circumstance. The decay width of a dibaryon is estimated as a function of its effective mass in nuclear matter.     

Bound-pion absorption followed by emission of two nucleons

The bound-pion absorption reaction, viz. ¹²C(π^?, NN), is studied using Hartree-Fock (HF) wave functions obtained with the unitary-model-operator approach starting with the hard-core nucleon-nucleon (NN) interaction. The inequality of the energies of the two outgoing nucléons is treated exactly and calculations are done using the “1N model” for π-absorption. Other effects taken into account are: NN scattering in the final state, contributions of all excited states of ¹⁰B and ¹⁰Be with E < 5 MeV, and effects of the strong π-nucleus interaction and the finite nuclear size on the bound-π wave function. Branching ratios and angular distributions of absorption rates are in better agreement with experimental data. The correct order of magnitude of the total absorption rate is reproduced. Whatever the effects of short-range correlations present in the HF wave functions, they are not masked by the NN final-state interaction. The contribution of excited states in ¹⁰B and ¹⁰Be is found to be quite large. Absorption rates obtained with the HF and oscillator wave functions differ significantly both in size and shape.     

Short-range correlations with pseudopotentials. IV

Using a unitary model operator, the short-range correlations between nucleons in nuclei have been considered. To achieve healing in the wave functions, short-range pseudopotentials are required to be added to the nucleon-nucleon potential. With the introduction of the pseudopotentials, the matrix element for the effective interaction in nuclei is developed with correlated basis wave functions. The tensor forces and the short-range pseudopotentials are renormalized in second-order perturbation theory. Hartree-Fock calculations are carried out for the two finite closed-shell spherical nuclei¹⁶O and⁴⁰Ca. The calculations of the resulting effective Hamiltonian are carried out with an effective interaction derived from the Tabakin potential. The present calculations of the binding energies per particle for the¹⁶O and⁴⁰Ca nuclei are in agreement with the experimental measurements.     

On induced double-nucleon emission. III. 12C, (π−, NN) and short-range correlations

The reaction channel (π^?, NN) for the absorption of bound negative pions by nuclei is used as a means to study nuclear short range correlations. A three-body partial-wave analysis has been carried out for the final-state scattering which includes a Reid soft-core nucleon-nucleon interaction and an optical potential. This coupled-channel formalism rapidly converges as we eliminate the asymptotic single-nucleon and deuteron interactions. It is found that for ¹²C reasonable agreement with experiment cannot be obtained in this model without modification of the high relative-momentum components of bound shell model pair wave functions.     

Parametrization of the 1S0 two nucleon transition matrix

The ¹S₀ two-nucleon transition matrix T is constructed from the symmetric part σ of its half-shell elements. The on-shell component of σ is given by the phase shift, while a wide class of parametrizations is suggested for the off-shell part. Restrictions on the off-shell part of σ arising from the short range and the proper one-pion-exchange tail of the nucleon-nucleon interaction are investigated. Using σ in the ¹S₀ and the Reid soft-core potential in the other partial waves, the binding energy per particle in nuclear matter and ¹⁶O and the ¹⁸O shell-model spectrum are computed. The sensitivity of these nuclear-structure results is tested with respect to (i) smooth off-shell changes in σ, (ii) various assumptions on the high-energy phase shift, (iii) the charge dependence of the phase shift, and (iv) experimental uncertainties in the phase shift.     

The residual interaction of bound nucleons-two-nucleon matrix elements deduced from transfer experiments

Matrix elements for the effective two-nucleon interaction have been deduced from the population of multiplets near closed shells as observed in direct transfer reactions. In the evaluation, the limited purity of such multiples was taken into consideration, typically by weighting the observed fractions of the two-nucleon configurations by their spectroscopic strenghts and by using the resulting energy centroids. In a few cases, off-diagonal matrix elements are available from empirical wave funcitons. The systematic errors for particle-particle matrix elements extracted directly and those obtained from Pandya transformations were found to go in opposite directions. In some cases, this feautre of the empirical mehtod could be used to suggest upper and lower “bounds” for the extracted matrix elements. Diagonal matrix elements for the empirical residual interaction show a number of features suggestive of an underlying simplicity in the interaction of bound nucleons. Within experimental uncertainties (of about 10% for T=0 matrix elements) the monopole parts of the matrix elements are fit well with a simple A?0.75 dependence, and the data available to date do not reveal any significant monopole dependence on the quantum numbers of the interacting nucleons. The usefulness of scaling is suggested. Generally, diagonal matrix elements E_J(j₁, j₂) normalized by the extracted A-dependent monopole strength agree within expected experimental uncertainties whether derived from particle-particle or particle-hole multiples and whether extracted from the beginning or the end of a major shell. For values J≠0, the diagonal E_J(j²) matrix elements seem to follow two universal functions which depend on the semi-classical coupling angles θ₁₂, but are otherwise independent on j. For j₁≠j₂ several “typical” functions ?(θ₁₂) can be constructed which fit subsets of the data and differ in a predictable way. The general features of the bound-nucleon interaction appear consistent with those of theoretical matrix elements based on a number of short-range model forces or on calculations using the G matrix approach to deal with realistic free nucleon forces. For the latter, the available theoretical numbers for j₁=j₂ agree well with the T=1 set, but they differ quantitatively from the observed matrix elements for T=0, sometimes by many (experimental) standard deviations.     

A test of the DWIA at 135 MeV using the 207Pb(p,p′) reaction

Data for the excitation of the strongly collective octupole doublet in ²⁰⁷Pb at E_X = 2.64 MeV is used to test the distorted wave impulse approximation (DWIA) at a proton bombarding energy of 135 MeV. A complex, effective local interaction derived from the nucleon-nucleon phase shifts is used together with the wave functions of Ring and Speth for the low-lying octupole state in ²⁰⁸Pb. The DWIA (including central and spin-orbit terms) is found to be in reasonable agreement with both the magnitude and shape of the observed cross section.