Solving the eigenvalue problem of the nuclear Yukawa-folded mean-field Hamiltonian

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• 作者：A. Dobrowolski^a ; ^{arturd@kft.umcs.lublin.pl" class="auth_mail" title="E-mail the corresponding author} ; K. Pomorski^a ; J. Bartel^b
• 关键词：Mean-field ; Harmonic oscillator basis ; Matrix elements ; Folded potential ; Shape parametrization
• 刊名：Computer Physics Communications
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：199
• 期：Complete
• 页码：118-132
• 全文大小：910 K

文摘

The nuclear Hamiltonian with a Yukawa-folded mean-field potential is diagonalized within the basis of a deformed harmonic-oscillator in Cartesian coordinates. The nuclear shape is characterized by the equivalent sharp surface described either by the well known Funny–Hills or the Trentalange–Koonin–Sierk parametrizations. They are both able to describe a very vast variety of nuclear deformations, including necked-in shapes, left–right asymmetry and non-axiality. The only imposed limitation on the nuclear shape is the class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0010465515003720&_mathId=si41.gif&_user=111111111&_pii=S0010465515003720&_rdoc=1&_issn=00104655&md5=46a7894beb30172bbc550751398f859d" title="Click to view the MathML source">zclass="mathContainer hidden">class="mathCode">$z$-signature symmetry, which corresponds to a symmetry of the shape with respect to a rotation by an angle class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0010465515003720&_mathId=si42.gif&_user=111111111&_pii=S0010465515003720&_rdoc=1&_issn=00104655&md5=d77f69e3ae69a4ed03c66fefa79c4c90" title="Click to view the MathML source">πclass="mathContainer hidden">class="mathCode">$\pi$ around the class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0010465515003720&_mathId=si41.gif&_user=111111111&_pii=S0010465515003720&_rdoc=1&_issn=00104655&md5=46a7894beb30172bbc550751398f859d" title="Click to view the MathML source">zclass="mathContainer hidden">class="mathCode">$z$-axis. On output, the computer code produces for a given nucleus with mass number class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0010465515003720&_mathId=si44.gif&_user=111111111&_pii=S0010465515003720&_rdoc=1&_issn=00104655&md5=47a83f9c51ad8e8660f8cc23166ff153" title="Click to view the MathML source">Aclass="mathContainer hidden">class="mathCode">$A$ and charge number class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0010465515003720&_mathId=si13.gif&_user=111111111&_pii=S0010465515003720&_rdoc=1&_issn=00104655&md5=fa44b65af10d33fcdaf84f4bebfb548b" title="Click to view the MathML source">Zclass="mathContainer hidden">class="mathCode">$Z$ the energy eigenvalues and eigenfunctions of the mean-field Hamiltonian at chosen deformation.

Program summary

Program title: yukawa

Catalogue identifier: AEYI_v1_0

Program summary URL:class="interref" data-locatorType="url" data-locatorKey="http://cpc.cs.qub.ac.uk/summaries/AEYI_v1_0.html">http://cpc.cs.qub.ac.uk/summaries/AEYI_v1_0.html

Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland

Licensing provisions: Standard CPC licence, class="interref" data-locatorType="url" data-locatorKey="http://cpc.cs.qub.ac.uk/licence/licence.html">http://cpc.cs.qub.ac.uk/licence/licence.html

No. of lines in distributed program, including test data, etc.: 78599

No. of bytes in distributed program, including test data, etc.: 1551468

Distribution format: tar.gz

Programming language: Fortran 77.

Computer: Any PC machine.

Operating system: Windows or a system based on Linux.

RAM: bytes: 0.5 GB or more

Classification: 17.19.

Nature of problem:   The full single-particle nuclear Hamiltonian composed of the Yukawa-folded central, spin–orbit and Coulomb potentials is generated and diagonalized. The only symmetry of the problem is the so called class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0010465515003720&_mathId=si41.gif&_user=111111111&_pii=S0010465515003720&_rdoc=1&_issn=00104655&md5=46a7894beb30172bbc550751398f859d" title="Click to view the MathML source">zclass="mathContainer hidden">class="mathCode">$z$-signature symmetry which limits the nuclear shapes to those, being invariant with respect to a rotation by an angle class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0010465515003720&_mathId=si42.gif&_user=111111111&_pii=S0010465515003720&_rdoc=1&_issn=00104655&md5=d77f69e3ae69a4ed03c66fefa79c4c90" title="Click to view the MathML source">πclass="mathContainer hidden">class="mathCode">$\pi$ around the class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0010465515003720&_mathId=si41.gif&_user=111111111&_pii=S0010465515003720&_rdoc=1&_issn=00104655&md5=46a7894beb30172bbc550751398f859d" title="Click to view the MathML source">zclass="mathContainer hidden">class="mathCode">$z$-axis.

Solution method: The mean-field Hamiltonian is expressed in matrix form in the basis of an anisotropic harmonic-oscillator potential written in Cartesian coordinates, where the basis parameters are adjusted to the actual deformed nuclear shape. The eigensolutions of the Hamiltonian are determined by diagonalization of the corresponding matrix.

Running time: For a nucleus of spherical shape, with the inclusion of NMAX=14 major oscillator shells and including the option of printing out all the eigenfunctions, one program run takes around 7 s on an average dual-core 2 GHz notebook of 1 GB RAM memory. The same type of calculation for a complicated non-axial left–right asymmetric shape requires around 11 s.