THEORETICAL INVESTIGATIONS OF THE BOUND THREE NUCLEON SYSTEM

MUSLIM, Purdue University

Abstract

In this thesis, we investigate the asymptotic normalization C(, )(' ) for the ('3)H amd ('3)He bound states consisting of nucleon-dueteron (d) and nucleon-virtual deuteron (d*) clusters in the relative angular momentum state of the cluster constituents and discuss methods of extracting C(, ) from theoretical models and experimental data. The(' ) D(,2)(('3)H) parameter which is related to the ratio C(,2)(('3)H,dn)/C(,0)(('3)H,dn)(' ) and the triton-deuteron binding energy difference, is calculated from a solution of the Faddeev equations with the Reid soft-core potential. We find D(,2)(('3)H) = -0.24 Fm('2) in agreement both in phase and magnitude with the experimental value determined from the recent measurements of tensor analyzing powers for (d,('3)H) reactions. An(' ) estimate of D(,2) for ('3)He with a Coulomb correction gives D(,2)(('3)He) = -0.22 Fm('2) in agreement with the experimental value extracted from the (d,('3)He) reaction. The calculated value of C(,0)(('3)H,d*n) is found to(' ) be sensitive to the location of the virtual state pole, which is not known accurately. We investigate various different methods of generating the momentum-space wave functions for the scattering, bound and virtual states of a two-nucleon system interacting via a local-potential. We present a procedure of extracting a correctly normalized virtual state either from analytical continuation of a series of bound states generated by stronger potentials or from the scattering states with different energies. In an attempt to explain the discrepancy between theoretical predictions ((TURN) 7.0 MeV) based upon two-nucleon potentials (2NP) and the experimental value (8.5 MeV) of triton binding energy, we investigate the effect of three different types of two boson exchange three nucleon potentials involving 2(pi)-exchange (V(,(pi)(pi)F)), 2(sigma)-exchange (V(,SSF)) and 2((pi)+(rho))-exchange via (DELTA) between a nucleon pair through the third nucleon. The contributions of V(,(pi)(pi)F) and V(,SSF) to triton binding energy is calculated in the first order perturbation theory. To facilitate the numerical calculation which involves six dimensional integrals, we introduce a new method of parametrizing the antisymmetrized three-nucleon bound-state momentum-space wave function as sums of separable functions. The binding energy contribution is found to be 1.4 MeV which can account for most of the discrepancy between the 2NP prediction and the experimental triton binding energy.

Degree

Ph.D.

Subject Area

Nuclear physics

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