Calculation of trinucleon photoeffect using hyperspherical harmonics

The spatial wavefunction of the trinucleon is expanded for both ground and continuum states in a series of hyperspherical harmonics. The calculation of photoeffect done by Fabre-Levinger (1975) is extended to the isospin 3/2 state, approximated as a single hyperspherical harmonics (h.h.) with grand orbital one, by putting in an additional grand orbital L = 3. The coupled differential equations (c.d.e.) are derived for the continuum state valid for any kind of two-body exchange force. Differential and cross sections for both two-body spin independent and spin dependent potentials are found. The c.d.e. are solved numerically for three model potentials, namely, Volkov spin independent potential, the first Volkov spin dependent potential, and the second Volkov spin dependent potential. The total cross section for electric dipole transition of ten incoming gamma ray energies are found for these three model potentials. For Volkov spin independent potential, the uncoupled channel (L = 1) calculation gives an integrated cross section of 21.1 MeV-mb, the coupled channels calculation gives 20.5 MeV-mb, while the Thomas-Reiche-Kuhn sum-rule gives an integrated cross section of 19.9 MeV-mb. By comparing them the rapid convergence speed of the h.h. expansion for the outgoing channel is indicated. The energy spectrum of the outgoing odd nucleon for the coupled case at Eγ = 12.33 MeV is also obtained. The same procedure is repeated for the other two spin dependent model potentials. The total cross section is obtained for ten gamma ray energies. The bremsstrahlung and integrated cross section of these three model potentials are compared with Fetisov's experiment (1965), three-body break-up for 3He. Finally, the effect of using coupled h.h. for three model potentials is discussed. Future proposals for the applications of hyperspherical harmonics are suggested. The computer program and its flow chart are given