Repulsive Core Potential Research Articles

Binding-energy calculations for finite nuclei

A method for computing nuclear binding energies without making recourse to the full Brueckner reaction matrix is discussed. The view presented is that with the aid of the Moszkowski-Scott technique ordinary Rayleigh-Schrödinger theory may suffice in handling repulsive core potentials provided approximate self-consistency is maintained. Our arguments are supported by results obtained in applying the method to 16O using two simple hard-core potentials.

Form factors of 3H and 4He with repulsive-core potentials

Form factors of 3H and 4He with repulsive-core potentials

The binding energy of the triton with a velocity-dependent potential

We have made a variational calculation of the binding energy of the triton using a two-body velocity-dependent central potential adjusted to fit two-body low and high energy scattering data and the binding energy of the deuteron. We have used a set of one, two and three parameter trial functions. The values of the binding energy of the triton obtained with these trial functions suggest that convergence has been nearly obtained. Obviously, the highest value for the binding energy is obtained with the three-parameter trial function and is equal to 7.17 MeV. We have also calculated the Coulomb energy of He 3 by the usual perturbation method and obtain a value equal to 0.663 MeV. These values of the binding energy of the triton and the Coulomb energy of He 3 agree reasonably well with similar calculations using repulsive hard core potentials but are lower than the experimental values.

Three-Nucleon Systems

We have made a preliminary calculation of the bare form factor ${F}_{B}({q}^{2})$ for the three-nucleon systems ${\mathrm{H}}^{3}$ and ${\mathrm{He}}^{3}$ with the wave function $\ensuremath{\psi}=N\mathrm{exp}[\ensuremath{-}(\frac{\ensuremath{\kappa}}{2})({r}_{12}+{r}_{23}+{r}_{13})]$. It is found that if we adjust $\ensuremath{\kappa}$ so as to fit the experimental value of the Coulomb energy for ${\mathrm{He}}^{3}$, or to fit the bremsstrahlung-weighted integral cross section for the photoeffect of ${\mathrm{He}}^{3}$, the agreement with experimental results for ${F}_{B}({q}^{2})$ is quite good. Also, we have made a variational calculation of the binding energy of the triton using two-body velocity-dependent central potentials and $\ensuremath{\psi}$ as a trial function with $\ensuremath{\kappa}$ as the adjustable parameter. Our preliminary results show that the binding energy is much lower than the experimental value and that given by a static well-behaved potential, though it is in fairly good agreement with similar calculations using repulsive hard core potentials.

Determination of the Deuteron Form Factor from Coherentπ0Photoproduction

Coherent photoproduction of ${\ensuremath{\pi}}^{0}$ mesons from deuterium has been used to measure the deuteron form factor. Measurements of the production cross section were carried out for photon energies from 470 to 514 MeV by detecting momentum-analyzed recoil deuterons. These measurements were analyzed in terms of the impulse approximation calculation of Hadjioannou. The deuteron form factor has been determined in the range of momentum transfers from 1.74 to 2.74 ${\mathrm{F}}^{\ensuremath{-}1}$. The results are consistent with the predictions of a repulsive core potential; however, there is some ambiguity in the interpretation due to the uncertainty in the magnitude of the multiple scattering corrections to the impulse approximation. Measurements of the cross section were also made as a function of photon energy for two constant momentum transfers, 1.76 and 1.96 ${\mathrm{F}}^{\ensuremath{-}1}$. The range of energies covered was 300 to 500 MeV. The results indicate that there is a large reduction of the cross section with respect to the impulse approximation prediction near the (3,3) resonance. This is in qualitative agreement with calculated corrections arising from multiple scattering of the meson in the deuteron. The measurements show that this deviation decreases as the photon energy increases in the region above resonance.

The proton-proton spin-orbit interaction and the repulsive core

It has been suggested that the phenomenological proton-proton spin-orbit force arises as a ‘Thomas term’ in the Schroedinger equation, associated with the repulsive core. Since the potentials involved are very strong, the usual derivations are inadequate. Here the problem is formulated as the scattering of two Dirac particles interacting via a truncated potential which couples only positive energy states. For mathematical simplicity a one-body problem is introduced. An iterative method of solution is proposed and carried out to second order in the case of a square repulsive core potential. The method is found to converge satisfactorily. The phase shifts show splitting of the type expected from the Thomas term argument.

Variational calculations with repulsive core potentials

A variational method is described which is suitable for fairly detailed calculations with repulsive core potentials. The method employs a wave function which goes over to an exact solution of the two-body Schrödinger equation whenever two nucleons are closer together than a certain distance b. The ideas of effective range theory suggest that the results should not be sensitive to the energy parameter which characterizes the exact solution, a suggestion which is seen to be valid to great accuracy in a numerical calculation with a simple but characteristic potential. The new method is compared with straightforward variational approaches to the same problem, as well as with variational procedures based on a cutoff potential, and is found superior to them both. A practical application of the new method in calculating the Li 6 structure is also cited.

Electron Scattering from the Deuteron and the Neutron-Proton Potential

Electron scattering by the deuteron was studied experimentally at 400 and 500 Mev. The results of the scattering are compared with the scattering expected by three different static deuteron models. All three models satisfy the usual deuteron requirements such as binding energy, effective range, quadrupole moment, and percent D slate. Two of the models have Yukawa neutron-proton potentials; the third has a repulsivecore potential. The experimental results agree with the repulsive-core model and disagree with the Yukawa models. This result applies only to the triplet-S neutron-proton potential. (auth)

Non-local structure of field theories with non-renormalizable interaction

Quantized field theories of the second kind, the so-called non-renormalizable theories, are investigated. It has recently been shown that a number of those theories actually can be renormalized. We show that field theories of the second kind, pertaining to derivative couplings, possess non-local structure. The full recoil neutral PS-PV theory in its non-linear form is discussed. The non-localizability of both the unrenormalized and the renormalized theories is due to the fact that the infinite set of topologically independent direct interactions, which characterizes PS-PV theory, is equivalent to a new type of indirect interaction. The non-localizability manifests itself in an indeterminacy in space-time of the light-cone. This indeterminacy can be interpreted in terms of a statistical spread in space-time of the positions of two interacting point-nucleons over a space-time volume the size of which is determined by the coupling constant |g| of the linear version of PS-PV theory. The length |g| loses its meaning as a coupling in the non-linear formalism in favour of the nucleon mass and plays now the role of a fundamental structure constant. In particular, |g| determines the region in which the equivalence theorem and the 1/r3-potential become invalid and repulsive-core potentials begin to act. In virtue of the oscillatory behaviour of the non-tempered momentum space operators in the high energy region, positive-definiteness conditions can be established only for regions |kv2|≳|1/g2| and |xv2|≳|1/g2|. The non-localizability is concentrated in these domains and |g| seems to play the role of the meson Compton wave length. A new interpretation of the non-linear PS-PV theory is suggested. It is conjectured that also β interactions give rise to non-local structures. Multiple propagators are introduced to render the formal coupling constant expansions in theories of the second kind mathematically meaningful without producing non-renormalizable infinities. Arguments are advanced against the mathematical consistency of the concept of creation (annihilation) and localizability of more than one point-particle at a single space-time point.

Effect of a repulsive core in the theory of complex nuclei

Using Brueckner’s method for the treatment of complex nuclei, the effect of an infinite repulsive core in the interaction between nucleons is studied. The Pauli principle is taken into account from the beginning. A spatial wave function for two nucleons is defined, and an integro-differential equation for this function is derived. Owing to the Pauli principle, the wave function contains no outgoing spherical waves. A solution is given for the case when only a repulsive core potential acts. The effective-mass approximation is investigated for virtual states of very large momentum.

Calculations on Charge Independence with Repulsive Core Potentials

Calculations on Charge Independence with Repulsive Core Potentials