Tabakin Potential Research Articles

Arguments against one-boson-exchange models of nuclear forces and new mechanism for intermediate-and short-range nucleon-nucleon interaction

Arguments against the traditional Yukawa-type approach to NN intermediate-and shortrange interaction due to scalar-isoscalar and heavy-meson exchanges are presented. Instead of the Yukawa mechanism for intermediate-range attraction, some new approach based on the formation of a symmetric six-quark bag in the state |(0s)6[6]X, L=0〉 dressed owing to strong coupling to π, σ, and ρ fields is suggested. This new mechanism offers a strong intermediate-range attraction, which replaces effective σ exchange (or excitation of two isobars in the intermediate state) in traditional force models. A similar mechanism with the production of a vector ρ meson in the intermediate six-quark state is expected to lead to a strong short-range spin-orbit nonlocal interaction in the NN system, which may resolve the long-standing puzzle of the spin-orbit force in baryons and in two-baryon systems. The effective interaction in the NN channel provided by the new mechanism will be enhanced significantly if the partial restoration of chiral symmetry is assumed to occur inside the six-quark symmetric bag. A simple illustrative model is developed that demonstrates clearly how well the suggested new mechanism can reproduce NN data. Strong interrelations have been shown to exist between the proposed microscopic model and one-component Moscow NN potential developed by the authors previously and also with some hybrid models and the one-term separable Tabakin potential. The new implications of the proposed model for nuclear physics are discussed.

Three-body collapse for Tabakin potentials and the Thomas effect.

A system constituted of three bosons interacting via two-body separable potentials with fixed two-boson binding is known to lead to bound-state collapse in the case where the potential parameters allow two-boson S-matrix poles close to (resonance) and on (continuum bound state) the real momentum axis. The collapse is shown to be accompanied by an increase in the average kinetic energy of the two-body bound state, which signals a decrease in the range of the two-body interaction for fixed two-body binding. The collapse is claimed to be a manifestation of the well-known Thomas effect which leads to a collapse of the three-body system when the range of the two-body interaction goes to zero for a fixed two-body binding.

Structure of 9Be Nucleus Using the Generator Coordinate Method and the Three-Body Model

The structure of the 9Be nucleus is considered as being composed of three clusters (two alpha particles and a neutron). The bound state of the 9Be nucleus is studied using the approaches of the generator coordinate method as well the three-body model formalism. The numerical calculations are carried out using different types of two-body interactions. Yamaguchi, Gaussian, Tabakin and Volkov type potentials are used. The three-body model is also used in treating the three clusters forming the 9Be nucleus by following the Faddeev formalism. In both approaches, the low-lying energy levels of the 9Be nucleus as well as its binding energy are numerically calculated. Good agreements are obtained between the present theoretically calculated values and the experimental data.

Pole term decomposition of the resolvent kernel in Fredholm’s form

The resolvent kernel represented by a ratio of two Fredholm’s series can be reformed into a sum of two ratios, only one of which contains Fredholm’s determinant in its denominator. The general results presented are then used to apply Faddeev’s residue prescription in the case of the rank N separable potential for determining those three-body scattering amplitudes in which a two-particle bound state is in the initial and/or final configuration. As a numerical example, the triton binding energy and the doublet scattering length for the Tabakin potential are calculated.

Three-nucleon bound-state collapse with Tabakin potentials.

The collapse of the three-nucleon ground state with separable two-body interactions of a Tabakin type is investigated. A simple scaling property of this phenomenon is derived. Moreover, an interpretation of the collapse is given in terms of the local equivalent of the Tabakin potential.

Laplace transform method for scattering on Coulomb plus nonlocal separable potentials

A Laplace transform method is derived to solve the Schrodinger equation for the Coulomb plus Tabakin potentials with the regular boundary condition. The results are used to construct expressions for on- and off-shell Jost functions in terms of Gaussian hypergeometric functions.

Photoneutron cross sections forN15

Photoneutron cross sections involving the emission of one and two neutrons from $^{15}\mathrm{N}$ have been measured over the excitation energy interval from threshold (10.8 MeV) to 38 MeV using monoenergetic photons from the annihilation in flight of fast positrons. A very broad giant dipole resonance extending from about 16 to 30 MeV was observed, with a maximum ($\ensuremath{\gamma}, {n}_{\mathrm{tot}}$) cross section of about 11 mb at 23.5 MeV. The magnitude of the measured average photoneutron energies shows that most of the strength below 15 MeV decays to the ground state of $^{14}\mathrm{N}$, whereas most of the strength in the giant resonance decays to excited states. Comparison with particle-capture cross-section data indicates that multiparticle-multihole interference effects probably account for some of the pronounced intermediate structure observed above 16 MeV in the ($\ensuremath{\gamma}, n$) cross section. Comparison with a recent shell-model calculation favors the use of a Tabakin potential over a $\ensuremath{\delta}$-function force with a Soper exchange mixture, in marked contrast with recent corresponding results for $^{13}\mathrm{C}$ and $^{17}\mathrm{O}$. Features of recently measured photoreaction cross sections for the $^{12}\mathrm{C}$, $^{13}\mathrm{C}$, $^{14}\mathrm{N}$, $^{15}\mathrm{N}$, $^{16}\mathrm{O}$, $^{17}\mathrm{O}$, and $^{18}\mathrm{O}$ nuclei are compared as well.NUCLEAR REACTIONS $^{15}\mathrm{N}(\ensuremath{\gamma}, n)$, ${E}_{\ensuremath{\gamma}}=10.8\ensuremath{-}38.0$ MeV; measured $4\ensuremath{\pi}$ neutron yield for monoenergetic photons; (${E}_{\ensuremath{\gamma}}, 1n$), (${E}_{\ensuremath{\gamma}}, 2n$), integrated cross sections; comparisons of results with other reaction channels and with cross sections for neighboring nuclei; comparison with shellmodel theory.

Nuclear matter test for a separable non-localN-N interaction

A nuclear matter test has been conducted on a separable non-localN-N interaction proposed by Sirohi and Srivastava. The potential had been constructed by fitting the phase-shifts. The results obtained compare with those obtained by Tabakin in each partial wave. The binding energy per particle and the symmetry energy coefficient obtained are 19.4 MeV and 66.5 MeV respectively atk F=1.65 fm−1, while the best estimated values for these quantities are 16 MeV and 30–35 MeV atk F=1.5 fm−1. Single particle potential generated out of this NLSI has in general the same shape as the one obtained through Tabakin potential. Finally as a test of non-locality the integrated photoabsorption cross-section parameterh has been calculated and the value of 1.03 agrees with other reported values.

Angular momentum projected quasiboson states in transitional nuclei

A microscopic method for determining the coefficients of a fourth-order boson expansion of the Hamiltonian is used to obtain angular momentum projected states, their energies, and electric quadrupole properties. A Tabakin potential is used in applying the method to the even-even Ba isotopes, $A=130\ensuremath{-}138$.[NUCLEAR STRUCTURE Angular momentum projected quasiboson formalism, $^{130,\phantom{\rule{0ex}{0ex}}132,\phantom{\rule{0ex}{0ex}}134,\phantom{\rule{0ex}{0ex}}136,\phantom{\rule{0ex}{0ex}}138}\mathrm{Ba}$, calculated levels, $J$, $\ensuremath{\pi}$, $B (E2)$, quadrupole moments. Tabakin interaction.]

Three-body model ofBe9andC12nuclei

The structure of light nuclei is considered using the $\ensuremath{\alpha}$ cluster model. On the basis of $\ensuremath{\alpha}$ clusters, the model structures of the nuclei $^{9}\mathrm{Be}$ and $^{12}\mathrm{C}$ are proposed as composed of three particles. The bound state problems for these nuclei are solved using separable potentials, where the Faddeev equations are given. Three different types of the nonlocal separable potentials are used, i.e., potentials of the Yamaguchi, Gaussian, and Tabakin forms. The Gaussian and Tabakin potentials contain both attraction and repulsion. Solving the Faddeev equations, numerical calculations are performed for the resulting integral equations. The present theoretically calculated values of binding energies for these nuclei are in good agreement with the experimental data. The very close agreement between theoretical and experimental values of the binding energies indicates that the repulsive forces of the nuclear potential are very important and should be taken into account.

Two-nucleon stripping reactions with tabakin potential

The theory of two-nucleon stripping reactions has been considered. Due to the short-range correlations in nuclei and to the strong repulsive nature of nuclear forces at very short distances, the short-range correlations in nuclei are investigated. To take into account the short-range correlations, the nucleon-nucleon interaction is taken as a short-range repulsive core surrounded by a long-range attractive potential. A more realistic potential is suggested by Tabakin as a separable but nonlocal interaction. The differential cross-sections for the two-nucleon stripping reaction (t, p) have been calculated in two different cases by taking Yamaguchi or Breitet al. type parameters for the Tabakin potential used. DWBA calculations have been used to calculate the angular distributions for different (t, p) stripping reactions on the different target nuclei31P,96Zr,116Sn,118Sn and206Pb. Good agreement is obtained between the present theoretical calculations and the experimental data. By fitting the calculated angular distributions to the experimental data, more reliable spectroscopic factors are extracted.

Short-range correlations in one- and two-nucleon transfer reactions with Tabakin potential

Short-range correlations in one- and two-nucleon transfer reactions with Tabakin potential

Deuteron stripping reactions with the Tabakin potential

Deuteron stripping reactions are considered. Due to the strong repulsion between nucleons at very short distances, we have investigated the nuclear short-range correlations. The neutron-proton nuclear potential in the deuteron is taken as a short-range repulsive core surrounded by a long-range attractive potential. The neutron-proton potential is taken as the Tabakin separable potential to take into account the short-range correlations. The differential cross-sections for deuteron stripping reactions have been calculated in two different cases by taking Yamaguchi or Breitet al. type parameters for the Tabakin potential used. The angular distributions for different (d, p) stripping reactions on the different target nuclei28Si,32,34S,36Ar,40,48Ca,50,52,54Cr have been calculated by means of the DWBA calculations. Our present theoretical calculations for the angular distributions of the different reactions considered have been fitted to the experimental data, with which good agreement is obtained. The extracted spectroscopic factors from the present work are found to be more reliable.

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.

Isospin splitting of giant resonances inC13andO17

The two-particle, one-hole shell model with a harmonic oscillator basis is employed for a calculation of isospin-split giant resonance states in $^{13}\mathrm{C}$ and $^{17}\mathrm{O}$ that can be reached from the ground state by $\ensuremath{\Delta}T=0,1$ transitions of type $E1$ or $M2$. Residual forces used were a zero-range Soper mixture as well as the separable Tabakin potential. We calculate photoabsorption strengths which for $^{13}\mathrm{C}$ agree with the available data and with a previous calculation of Easlea using the Soper force; for the Tabakin force, this agreement is achieved without Easlea's ad hoc modification of the interaction. We also evaluate the inelastic form factors for electroexcitation of the $^{13}\mathrm{C}$ resonance levels, thereby identifying isospin and spin-isospin collective states.NUCLEAR REACTIONS $^{13}\mathrm{C}$ calculated photonuclear cross sections, electron scattering form factors of giant and pygmy resonances (${T}_{>},{T}_{<}$); $^{17}\mathrm{O}$ calculated photonuclear cross sections. Used two-particle, one-hole shell model.

Repulsive-core effects in (t, p) stripping reactions by using a Tabakin potential

Repulsive-core effects in two-nucleon transfer reactions are in vestigated by referring to the (t, p) stripping reactions. The form factor for the (t, p) stripping reactions is calculated by using a Tabakin potential for the neutron-proton interaction. We considered two different cases by taking for the repulsive and attractive parts of the Tabakin potential a Yamaguchi-type or a Breitet al. type parameter, It is found that the repulsive-core effects are important and should be taken into account to extract reasonable spectroscopic factors.

Structure calculations for the odd-mass Pd isotopes

The structure of some light, odd-mass Pd isotopes is calculated and compared with experiment. The method uses a renormalized Tabakin potential in a deformed Hartree-Fock calculation, followed by a BCS calculation, to generate deformed quasiparticles. These are then used as input to the band-mixing calculation which yields the spectra of 101,103,105Pd. The interaction parameters and the single particle energies are fixed without reference to data on the Pd isotopes, but the moments of inertia and the core quadrupole moments are taken from experiments on the even Pd nuclei. The occurrence of highly decoupled bands is well-reproduced, including the relative energies of the band heads. The positions and properties of low-lying levels are also correctly predicted, especially in 105Pd for which the experimental data are the most complete.

Calculations in the50<N,Z<82region with an interaction derived from the Tabakin potential

The region of the Periodic Table with $50\ensuremath{\le}Z$, $N\ensuremath{\le}82$ is studied using fixed single particle energies and a semirealistic effective interaction derived from the Tabakin potential. All the free parameters are determined by fitting the data on the odd-mass Sn isotopes and $N=82$ isotones. A conventional quasiparticle formalism is then used to study the structure of a range of spherical nuclei near the $N=82$ and the $Z=50$ magic numbers. A deformed Hartree-Fock plus BCS method is used to obtain the structure and electromagnetic properties of deformed nuclei, particularly the neutron-deficient even Ba isotopes. Prolate deformation is found to be favored. In the Ba isotopes, although neutrons have BCS correlation, the protons develop an energy gap between occupied and unoccupied orbitals due to the Hartree-Fock field itself. The proton orbitals are then tested through spectroscopic calculations in La isotopes. Both for spherical and deformed nuclei, agreement between theory and experiment is very satisfactory.NUCLEAR STRUCTURE Mass region $100<A<150$; calculated levels, $J$, $\ensuremath{\pi}$, and other properties. Semirealistic forces; combination of deformed Hartree-Fock and BCS methods.

Author index

The Faddeev equations for three nucleons are iterated up to third order using separable interactions: the Tabakin potential for the first order and the Yamaguchi potential for the other orders. This method is applied to the quasi-free scattering 2H(p, 2p)n and 2H(s, np)p. Apparent convergence of the rescattering series is obtained for incident lab energies Elab ⪆ 40 MeV and the shape and magnitude of the experimental results are thus reproduced.

Unitary pole approximation andt-matrix perturbation theory in triton calculations

We find that the quality of the fits of the UPAt-matrix to the exactt-matrix for a given potential do not depend strongly on specific features, such as locality or inclusion of spin orbit forces in the potential. The accuracy of the UPA fits suggests the employment oft-matrix perturbation theory in triton ground state calculations. The accuracy of first ordert-matrix perturbation theory is satisfactory for the rank two separable tensor Tabakin potential.