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Latest Results for Few-Body Systems

21 May 2024

• Approximate Solutions of the Dunkl–Schrödinger Equation for the Hyperbolic Pöschl–Teller Potential

  Abstract

  We construct an approximate solution to the Schrödinger equation for the hyperbolic Pöschl–Teller potential within the Dunkl formalism. Our approximation is based on a series expansion of the inverse quadratic term generated by the Dunkl operator. Two methods of establishing correct parity in the approximate solutions are discussed, and an example is presented.

• Momentum Dependent Nucleon–Nucleon Contact Interactions and Their Effect on $$p-d$$ Scattering Observables

  Abstract

  Starting from a complete set of relativistic nucleon–nucleon contact operators up to order \(O(p^4)\) of the expansion in the soft (relative or nucleon) momentum p, we show that non-relativistic expansions of relativistic operators involve twenty-six independent combinations, two starting at \(O(p^0)\) , seven at order \(O(p^2)\) and seventeen at order \(O(p^4)\) . This demonstrates the existence of two low-energy free constants that parameterize interactions dependent on the total momentum of the pair of nucleons P. The latter, through the use of a unitary transformation, can be removed in the two-nucleon fourth-order contact interaction of the Chiral Effective Field Theory, generating a three-nucleon interaction at the same order. Within a hybrid approach in which this interaction is considered together with the phenomenological potential AV18, we show that the LECs involved can be used to fit very accurate data on the polarization observables of the low-energy \(p-d\) scattering, in particular the \(A_y\) asymmetry.

• Meson Exchange Currents in the Clothed-Particle Representation: Calculation of the Deuteron Magnetic Form Factor

  Abstract

  We show an original way to build up a new family of electromagnetic meson exchange current operators via the method of unitary clothing transformations. Being introduced in such a way they do not depend on the choice of states with which we calculate the matrix elements. The new expressions for meson exchange currents has been compared with ones derived within the previous explorations. Special attention is paid to the deuteron eigenvalue problem and finding the proper deuteron states in a moving frame. An effective technique of ensuring the gauge independence based upon generalization of Siegert’s theorem is proposed. Magnetic form factor of the deuteron is calculated with both one-body and two-body mechanisms. The influence of relativistic effects in the one-body calculation has been considered. Besides, separate contributions from the different meson exchange mechanisms are discussed.