Trinucleon photoeffect to isospin 3/2, using coupled hyperspherical harmonics

We extend the Fabre-Levinger calculation of the ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ photoeffect ($E1\mathrm{}$ transition to final isospin 3/2) by including an additional grand orbital ($L=3\mathrm{}$) in the final state wave function. The coupled differential equations between $L=1\mathrm{}$ and $L=3\mathrm{}$ for the final state are given. We solve for two model potentials, and find the Blatt-Biedenharn eigenphase shifts and the mixing parameter, and also the total cross section for photodisintegration. We find reasonable agreement (generally within 10%) with the cross section found for one hyperspherical harmonic. The convergence speed of the hyperspherical harmonic expansion for the outgoing channel is also examined by comparison with sum rules for the integrated cross section: We find rapid convergence for both models.