Malfliet-Tjon Potential Research Articles

Variational calculations with correlated basis functions: Three-nucleon and three-alpha-particle systems.

A new variational method is applied to the solution of the Schroedinger equation for interacting few-body systems. The results for three nucleons interacting via the spin-dependent Malfliet-Tjon potential and three alpha particles interacting via the Ali-Bodmer potential are presented and compared with Faddeev and ATMS results, respectively.

Separable Ernst-Shakin-Thaler expansions of local potentials.

The boundary condition Ernst-Shakin-Thaler method, introduced previously to generate separable expansions of local potentials of finite range, is applied to the study of the triplet s-wave Malfliet-Tjon potential. The effect of varying the radius where the boundary condition is applied on the T matrix is analyzed. Further, we compare the convergence of the n-d scattering cross sections in the quartet state below the breakup threshold for expansions corresponding to two different boundaries.

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The ground state and the first excited state of $^{4}\mathrm{He}$ are investigated in harmonic oscillator shell-model bases including all the configurations up to 10\ensuremath{\Elzxh}\ensuremath{\omega} excitation energy. The Gogny et al. potential and versions I/III and V of the Malfliet-Tjon potential are used in the calculation. The difficulties in describing these states in a consistent manner are not overcome by substantially enlarging the shell-model bases. The lowest eigenvalue with a 1\ensuremath{\Elzxh}\ensuremath{\omega} center-of-mass wave function is also extracted from the energy matrices, providing the absolute energy of the first ${J}^{\ensuremath{\Pi}}$${=1}^{\mathrm{\ensuremath{-}}}$, T=0 level. It is found that the agreement with experiment for this level is significantly improved when the model space is enlarged.

Variational calculation of the ground state properties of the trinucleon system

A practical and flexible variational method is employed to calculate the trinucleon ground state energy, wave function, and charge form factor, using the $s$-wave Malfliet-Tjon potentials V and VI. The results are compared with existing accurate solutions of the same potentials. The charge form factor is found to be rather insensitive to the addition of different three-body forces.

The πNN bound-state problem

Bound-state solutions for the system composed of a pion and two nucleons are studied, and it is shown that their existence is essentially determined by the range of the πN interaction in momentum space. The relativistic Faddeev equations are solved to search for bound-state solutions of a negative pion and two neutrons, using the newly constructed πN separable potentials that reproduce the phase shift of the P 33 channel from 0 to 350 MeV, and realistic NN interactions such as the Reid soft-core, Paris, and Malfliet-Tjon potentials. It is found that bound-state solutions are possible for some of the πN interactions that have very long range in momentum space.

Iterative solution of bound-state equations

A method is proposed for solving bound-state equations in the momentum space, which are homogeneous Fredholm integral equations of the second kind. We rewrite such equations in the form of equivalent inhomogeneous Fredhold integral equations of the second kind with ''weaker'' kernels. Then the usual techniques for solving inhomogeneous integral equations can be used in the present case. A recently proposed method for an iterative Neumann series solution of inhomogeneous equations appears to be natural and very suitable for our purpose. The method is illustrated numerically in the case of the two nucleon bound state with the Yukawa and the Malfliet-Tjon potential and in the case of the s-wave three nucleon bound state in the Mitra-Amado model.

The reaction d(p, pp)n measured with bol at Ep = 50 MeV

We measured proton-deuteron breakup with the multi-detector system BOL for protons with an energy of 50 MeV hitting a deuterated polyethylene target. Proton-proton coincidences were registered with 40 position-sensitive detector telescopes. We present data covering ~ 85 % of the four-dimensional kinematical phase space. The data are compared with Faddeev calculations using two local S-wave Malfliet-Tjon potentials. Regions of discrepancy between data and theory in two-dimensional (2D) subspaces (cuts) are shown to be connected in 4D. The cross section structure (experimental and theoretical) is studied in a 4D representation consisting of a 2D matrix of 2D matrices. Prominent patterns are observed in the 4D differential cross section which can be traced back to quasi-two-body reaction mechanisms. Observed symmetries can be understood in terms of the simple impulse approximation.

Solution of the four-nucleon Schrödinger equation

We present a solution of the Schrödinger equation for the case of four nucleons interacting via the Malfliet-Tjon potential. The Schrodinger equation is integrated by means of the Green function Monte Carlo method. The adaption of this method to treat finite systems is given. For the four-nucleon case, the ground-state eigenvalue is found to be −31.3 ± 0.2 MeV and the rms point mass radius 1.36 ± 0.01 fm. The point mass distribution is given and does not exhibit a central depression. The method is also applied to the problem of four helium atoms interacting via the Lennard-Jones potential.

Separable expansions for local potentials with Coulomb interactions

If two particles are interacting via a short range potential and a repulsive Coulomb potential the t matrix can be written as a sum of the Coulomb and the ''nuclear'' t matrices. In order to solve the three-nucleon problem with Coulomb interactions usually we need a separable representation of this ''nuclear'' t matrix. A recently proposed method for finding a separable expansion for local potentials is here extended to find a rapidly convergent separable expansion, with analytic form factors, for the ''nuclear'' part of the t matrix of a local potential, in the presence of Coulomb interactions. The method is illustrated for a two-term Malfliet-Tjon potential. In each rank the ''nuclear'' phase shift is close to the corresponding phase shift when the Coulomb interaction is switched off. (AIP)

Test of the Unitary Pole Approximation to the Malfliet-Tjon Potential for Elastic Neutron-Deuteron Scattering

Abstract The quality of the unitary pole approximation to the soft-core Malfliet-Tjon potential is demon-strated for elastic neutron-deuteron scattering above breakup threshold.

Test of a separable approximation to a local soft-core potential in the three-body system

Three-nucleon observables below the break-up threshold are calculated employing the pole approximation to the soft-core Malfliet-Tjon potentials. The results are compared in detail to those obtained with the local potentials and to those calculated with the usual Yamaguchi interactions.