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Manuscript Title: Computer program for the relativistic mean field description of the ground state properties of even-even axially deformed nuclei.
Authors: P. Ring, Y.K. Gambhir, G.A. Lalazissis
Program title: RMFAXIAL.f
Catalogue identifier: ADFR_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 105(1997)77
Programming language: Fortran.
Computer: DEC.
Operating system: UNIX, VMS, MS-DOS.
Keywords: Nuclear physics, Theoretical methods, Relativistic mean field, Theory, Binding energy, Nuclear radii, Deformations and, Densities.
Classification: 17.16.

Nature of problem:
Relativistic Mean Field (RMF) theory [1,2] has been very successful [3,4,5,6,7,8,9] in accurately describing nuclear matter properties and ground state properties of finite nuclei spread over the entire periodic table including those away from the stability line. Nucleonic and mesonic degrees of freedom are explicitly included from the very beginning in the relativistic framework. As a result nuclear saturation and the correct spin-orbit splitting emerges automatically. Initially RMF theory has been applied successfully to the description of the properties of spherical nuclei. As most of the nuclei are deformed, the generalization of the solution of the RMF equations for this case is required, which is a non trivial task. Therefore a computer program was developed [10,11] to solve the RMF equations, suitable for the calculation of the ground state properties of the axially deformed nuclei. The present program is an improved version and also is compatible for PC's.

Solution method:
In RMF theory one needs to solve self-consistently a set of coupled equations namely the Dirac equation with potential terms for the nucleons and the Klein-Gordon type equations with sources for the mesons and the photon. For this purpose we employ the well tested basis expansion method [16]. The bases used here, are generated by an anisotropic (axially symmetric) harmonic oscillator potential. The upper and lower components of the nucleon spinors, the fields as well as the baryon currents and densities are expanded separately in these bases. The expansion is truncated so as to include all the configurations up to a certain finite value of the major oscillator shell quantum number. In this expansion method the solution of the Dirac equation gets reduced to a symmetric matrix diagonalization problem, while that of the Klein Gordon equation reduces to a set of inhomogeneous equations. The solution provides the spinor fields, and the nucleon currents and densities (sources of the fields), from which all the relevant ground state nuclear properties are calculated.

Restrictions:
The present version is applicable to even-even nuclei due to the imposition of time reversal invariance and charge conservation. The program can be modified for the general case including that of odd mass nuclei by incorporating the additional currents arising due to time reversal breaking.

Running time:
from one minute to several hours depending upon the number of shells in the expansion and upon the computer for the general case. The computer time will increase considerably if one wishes to include a large number of oscillator shells, as for instance 20.

References:
[1] B.D. Serot and J.D. Walecka, Adv. Nucl. Phys. 16 (1986) 1.
[2] B.D. Serot, Rep. Prog. Phys. 55 (1992) 1855.
[3] Y.K. Gambhir, P. Ring and A. Thimet, Ann. Phys. (USA) 198 (1990) 132.
[4] M.M. Sharma, G.A. Lalazissis and P.Ring, Phys. Lett. B 317 (1993) 9.
[5] M.M. Sharma, M.A. Nagarajan and P.Ring, Phys. Lett. B 312 (1993) 377.
[6] M.M. Sharma, G.A. Lalazissis, W. Hillebrandt and P. Ring, Phys. Rev. Lett. 72 (1994) 1431.
[7] G.A. Lalazissis and M.M. Sharma, Nucl. Phys. A 586 (1995) 201.
[8] G.A. Lalazissis, M.M. Sharma and P. Ring, Nucl. Phys. A 597 (1996) 35.
[9] P. Ring, Prog. Part. Nucl. Phys. 37 (1996) 193.
[10] W. Pannert, P. Ring and J. Boguta, Phys. Rev. Lett. 59 (1987) 2420.
[11] Y.K. Gambhir and P. Ring, Phys. Lett. B 202 (1988) 5.
[12] D. Vautherin, Phys. Rev. C 7 (1973) 296.