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Manuscript Title: Calculation of the virtual photon spectrum for a finite nucleus in distorted wave method.
Authors: F. Zamani-Noor, D.S. Onley
Program title: VPS
Catalogue identifier: ABBR_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 48(1988)241
Programming language: Fortran.
Computer: IBM-4081.
Operating system: VS1, CTSS.
RAM: 80K words
Word size: 32
Keywords: Nuclear physics, Scattering, Virtual photon spectrum, Distorted wave, Dirac-coulomb, Electron, Coulomb excitation.
Classification: 17.13.

Nature of problem:
The virtual photon spectrum accompanying electrons or positrons scattering from an extended nucleus with atomic number A and charge Z is calculated in distorted-wave methods for E1, E2, E3 and M1 multipoles.

Solution method:
The radial integral over a Hankel function and incoming and outgoing electron wavefunctions is divided into two parts; the internal and ex- ternal radial integrals. The integration inside the nucleus is done numerically due to presence of nuclear charge and current densities. The external radial integrals have been calculated analytically by rewriting them in terms of a series of incomplete gamma functions. The summation over partial waves is carried out by using the fact that the matrix elements involving higher partial waves have very little Coulomb distortion effects and can be replaced by plane wave matrix elements which can be summed analytically.

The present code uses model distributions for charge and current densities but results are model independent up to about E1^- 200 MeV. For incoming electrons with energies > 200 MeV different charge and current distributions do not produce the same spectra. The hydrodynamical model treating the nucleus as an incompressible irrotational liquid, produces spikes in the virtual spectra for energies greater than 200 MeV while the modified Gaussian of the Yukawa distributions produce smooth spectra as expected. Below this limit the distributions agree with each other to within 5%. The present code calculates the virtual spectrum for E1, E2, E3, and M1 transitions only. This could be extended by including additional analytic expressions in the PWAVE subroutine. Due to high degree can- cellations (unless extended precision is available), the ZZero subroutine does not calculate the radial integral for large angular momentum partial waves (Kappa ^> 15). However for calculating the virtual photon spectra the technique that we use does not require a large number of partial waves in the plane wave limit.