arXiv subjects

Sadhan K. Adhikari

Publications and source records attributed to Sadhan K. Adhikari.

112 records · Page 7Linked to original sources

arXiv1993

Relativistic three-particle dynamical equations: II. Application to the trinucleon system

We calculate the contribution of relativistic dynamics on the neutron-deuteron scattering length and triton binding energy employing five sets trinucleon potential models and four types of three-dimensional relativistic three-body equations suggested in the preceding paper. The relativistic correction to binding energy may vary a lot and even change sign depending on the relativistic formulation employed. The deviations of these observables from those obtained in nonrelativistic models follow the general universal trend of deviations introduced by off- and on-shell variations of two- and three-nucleon potentials in a nonrelativistic model calculation. Consequently, it will be difficult to separate unambiguously the effect of off- and on-shell variations of two- and three- nucleon potentials on low-energy three-nucleon observables from the effect of relativistic dynamics.

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arXiv1993

Relativistic three-particle dynamical equations: I. Theoretical development

Starting from the two-particle Bethe-Salpeter equation in the ladder approximation and integrating over the time component of momentum, we rederive three dimensional scattering integral equations satisfying constraints of relativistic unitarity and covariance, first derived by Weinberg and by Blankenbecler and Sugar. These two-particle equations are shown to be related by a transformation of variables. Hence we show how to perform and relate identical dynamical calculation using these two equations. Similarly, starting from the Bethe-Salpeter-Faddeev equation for the three-particle system and integrating over the time component of momentum, we derive several three dimensional three-particle scattering equations satisfying constraints of relativistic unitarity and covariance. We relate two of these three-particle equations by a transformation of variables as in the two-particle case. The three-particle equations we derive are very practical and suitable for performing relativistic scattering calculations.

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arXiv1993

Shape-Independent Expansion for the $^3S_1-^3D_1$ Mixing Parameter

A low-energy shape-independent expansion is suggested for the function $[tan(2ε_{BB})/(2k^2)]$, where $ε_{BB}$ is the Blatt-Biedenharn mixing parameter for the $^3S_1 -$ $^3D_1$ channel. This expansion allows an evaluation of the mixing parameter $ε_{BB}$ from a knowledge of the deuteron asymptotic $D$ to $S$ ratio, pion mass and other low-energy observables, such as the scattering lengths, deuteron binding etc., of the nucleon-nucleon system. We demonstrate that the correct long range behavior of the tensor potential is essential for a realistic reproduction of $ε_{BB}$.

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arXiv1993

Relativistic three-particle scattering equations

We derive a set of relativistic three-particle scattering equations in the three-particle c.m. frame employing a relativistic three-particle propagator suggested long ago by Ahmadzadeh and Tjon in the c.m. frame of a two-particle subsystem. We make the coordinate transformation of this propagator from the c.m. frame of the two-particle subsystem to the three-particle c.m. frame. We also point out that some numerical applications of the Ahmadzadeh and Tjon propagator to the three-nucleon problem use unnecessary nonrelativistic approximations which do not simplify the computational task, but violate constraints of relativistic unitarity and/or covariance.

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