Takashi Ohmura

Effect of Hard Cores on the Binding Energies of H3 and He3: Corrected Values

There was an error in the kinetlc energy formula of a previous paper by Ohmura (formerly Kikuta), Morita, and Yamada. The binding energy of H/sup 3/ as well as the Coulomb energy of He/sup 3/ are recalculated by using the correct value of the kinetic energy. The results obtained are almost the same. (auth)

Minimum Property in the Hulthén‐Type Variational Methods

The nature of the extremum of the phase shift in the variation principles, which are all based on the Schrodinger differential equation directly, is investigated in detail. If the system has no bound state, the scattering length determined by the original Hulthen method (5, 29) is proved to have the minimum character. The minimum nature is maintained even for the system which has several bound states, if the trial function is taken to be orthogonal to the bound state wave functions. The Kohn method and the second Hulthen method (15) give neither an upper bound nor a lower bound for the phase shift in general. The sufficient condition is, however, obtained for each case, under which the stationary expression for the scattering length has the minimum character. The condition does not hold true for the electron‐hydrogen atom scattering for the Kohn method and for the second Hulthen method. It is pointed out that a comparison of approximate values obtained by different methods using the same trial function do...

Note on the Low Energy Electron-Hydrogen Scattering

In a previous paper the low-energy electron-hydrogen scattering was discussed on the effective range approximation. An exa1aination of the energy range of the incident electron to which this method can be applied is presented. An error is corrected in the normalization of the ground state wave function of the negative hydrogen ion. A comparison is made of the results obtained by the variational method with those predicted by the effective rarge theory, (B.O.G.)

Variational Calculation of the Scattering Lengths in Electron-Hydrogen Scattering

The non-relativistic Schrodinger equation of electron plus hydrogen-atom system is solved by the Hulthen type variational method at the limit of zero incident electron energy. 8 and 5 parameter trial functions are used for the singlet and triplet states respectively, and the following upper bounds on the scattering length a are obtained,** a8~6.217a0 (singlet), at:S:2.272a0 (triplet). Some discussions are given on the accuracy of the result. It is shown that the relation a(m>a~m>ar.::>a(true) holds for trial functions of the same form if a(true) is positive.***

Stationary Expression for Effective Range

A variation principle is presented for the effective range of s wave scattering. This principle applies both to the bound state and to the scattering state. It is proved that some of the stationary expressions for the effective range has the minimum value for the exact solution, thus the calculated value by using an approximate wave function gives an upper bound for the effective range.A modified method is also proposed which may simplify the calculation in an actual application. The stationary expression gives, however, neither an upper bound nor a lower bound.

Effect of the Finite Size of the Proton on the Coulomb Energy of He3

Electron scatterirg experiments established the finite sue of the pioton, The effect of an assumed finlte charge distribution is estimated for the Coulomb energy arising from the small inter-proton distance In the He/sup 3/ ,nucleus, These calculated values for He/sup 3/ are compare;, with values obtalned for the H/sup 3/ nucleus. The precise values of the Coulomb energy are expected to be several per cent smaller than those calculated because of the simplification of this trial function. This seems to indicate that one extended proton is consistent with the experimental data without hard core. It is speculated that a slight violation of charge symmetry which guarantees the equality of nuclear forces for proton-proton and neutron-neutron systems may occur. The actual nuclear force is apparently not chargedependent. This is possibly the cause for the differences In the observed values for H/sup 3/ and He/ sup 3/, (B.O.G.)