Calculation of trinucleon photoeffect using hyperspherical harmonics

Fang, Kaung-King
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Levinger, Joseph S., 1921-
Brown, E.
McKinley, W. A.
Yergin, P. F.
Flaherty, J. E., 1943-
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We expand the spatial wave function of trinucleon for both ground and continuum states in a series of hyperspherical harmonics. We extend the calculation of photoeffect done by Fabre-Levinger ( 1975 ) 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. We derive the coupled differential equations (c.d.e) for the continuum s~ate valid for any ldnd 0 f two-body exchange force (Wigner, Bartlett , Heisenberg, Majorana ). The formulas of differential cross section and total cross section for both two-body spin independent and spin dependent potentials are found. We then proceed to solve the c.d.e. numerically for three model potentials namely, Volkov spin independent potential ( V1 +:: V1-:: V3+:: V3- ), the first Volkov spin dependent potential ( V1+:: V1-, V3+:: V3- ), the second Volkov spin dependent potential ( V1-:: V3-:: 0 ). The totalcross section for electric dipole transition of ten incoming gamma ray energies are found for these three model potentials. For Volkov spin independent potential, our uncoupled channel ( L=l ) calculation gives an integrated cross section of 21.1 Nev-mb, the coupled channels calculation gives 20.5 Mev-mb, while the Thomas-Reich-Kuhn sum-rule gives an integrated cross section of 19.9 Mev-mb. By comparing them, we note the discrepancy of 6% for the uncoupled case is reduced to 3% by including one higher grand orbital L=3. This clearly indicates the rapid convergence speed of the h.h expansion for the outgoing channel. The energy spectrum of the outgoing odd nucleon for the coupled case at E::12.33 Mev is also obtained. We repeat the same procedure namely, solving the c.d.e. for the other two spin dependent model potentials. We obtain the total cross section for ten gamma ray energies. The bremsstrahlung and integrated cross section of these three model potentials will be compared with Fetisov's experiment ( 1965 ), three body break-up for 3He.
May 1976
School of Science
Dept. of Physics
Rensselaer Polytechnic Institute, Troy, NY
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