Full Text Available
Note: Clicking the button above will open the full text document at the original institutional repository in a new window.
Relativistic eikonal formalism applied to inclusive quasielastic proton-induced nuclear reactions
Thesis (PhD (Physics))--University of Stellenbosch, 2011.
Saved in:
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Thesis |
| Language: | English |
| Published: |
Stellenbosch : University of Stellenbosch
2010
|
| Subjects: | |
| Tags: |
No Tags, Be the first to tag this record!
|
| _version_ | 1867614023636221953 |
|---|---|
| access_status_str | Open Access |
| author | Titus, Nortin, P-D |
| author2 | Van der Ventel, B. I. S. |
| author_browse | Titus, Nortin, P-D Van der Ventel, B. I. S. |
| author_facet | Van der Ventel, B. I. S. Titus, Nortin, P-D |
| author_sort | Titus, Nortin, P-D |
| collection | Thesis |
| dc_rights_str_mv | University of Stellenbosch |
| description | Thesis (PhD (Physics))--University of Stellenbosch, 2011. |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/5427 |
| institution | Stellenbosch University (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:45:26.037Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from SUNScholar — Stellenbosch University Repository |
| publishDate | 2010 |
| publishDateRange | 2010 |
| publishDateSort | 2010 |
| publisher | Stellenbosch : University of Stellenbosch |
| publisherStr | Stellenbosch : University of Stellenbosch |
| record_format | dspace |
| source_str | SUNScholar — Stellenbosch University Repository |
| spelling | oai:scholar.sun.ac.za:10019.1/5427 Relativistic eikonal formalism applied to inclusive quasielastic proton-induced nuclear reactions Titus, Nortin, P-D Van der Ventel, B. I. S. Hillhouse, G. C. University of Stellenbosch. Faculty of Science. Dept. of Physics. Relativistic eikonal formalism Quasielastic proton-induced nuclear reactions Dissertations -- Physics Theses -- Physics Theoretical formalism Numerical analysis Thesis (PhD (Physics))--University of Stellenbosch, 2011. ENGLISH ABSTRACT: In this dissertation we present, for the first time, a relativistic distorted wave impulse approximation formalism to describe quasielastic proton-nucleus scattering. We start from a full many-body description of the transition matrix element and show systematically how to derive the equivalent two-body form. This procedure allows for a clear and unambiguous method to introduce relativistic distorted waves. It is shown that the polarized double differential cross section may be written as the contraction of two tensors namely, the hadronic tensor (describing the projectile and ejectile), and the polarization tensor describing the target nucleus. The basic nucleon-nucleon (NN) interaction is described by the SPVAT or IA1 representation of the NN scattering matrix. Analytical expressions are derived for the polarization tensor using a Fermi gas model for the target nucleus. The nuclear distortion effects on the projectile and ejectile are described using the relativistic eikonal formalism. The expression for the double differential cross section is a nine dimensional oscillatory integral and an efficient procedure is developed to calculate this quantity. Comparison of Gaussian, Monte Carlo and quasi-Monte Carlo numerical integration schemes reveal that for this work, Gaussian quadrature is best suited for this problem. Traditional Gaussian quadrature is used to generate single variable functions whereby these functions are used in combination with modern software such as MATLAB to complete the computation of the full multidimensional integral in a reasonable amount of time. Even though the calculation of the cross section for a single value of the energy transfer is still time consuming, the computational time can be decreased by spreading the calculational burden across a number of nodes in a cluster computing system. A test calculation is performed whereby a proton with incident laboratory energy of 400 MeV is scattered off a 40Ca target nucleus at θcm = 40◦. For this reaction we calculate the unpolarized double differential cross section, as well as a complete set of spin observables namely Ay, Dℓ′,ℓ, Ds′s, Dnn,Ds′ℓ and Dℓ′s. We find that the distortions lead to a reduction of the unpolarized double differential cross section. On the other hand the spin observables are complex entities which show no uniformity in behaviour. However, the differences between the distorted wave spin observables and that of the plane wave observables are minor and we conclude that distortions have little effect on spin observables. AFRIKAANSE OPSOMMING: Hierdie proefskrif bevat, vir die eerste keer, ’n relatiwistiese vervormdegolf impuls benadering formalisme vir die beskrywing van kwasielastiese proton-kern verstrooiing. Daar word aangetoon hoe om stapsgewys te gaan vanaf ’n veel-deeltjie beskrywing van die oorgangsmatriks element na die ekwivalente twee-deeltjie vorm. Hierdie metode laat toe dat die vervormde golwe op ’n duidelike en ondubbelsinnige manier ingevoer kan word. Daar word aangetoon dat die gepolariseerde dubbele differensiële kansvlak geskryf kan word as die kontraksie van twee tensore naamlik, die hadroniese tensor (wat die projektiel en uitgaande nukleon beskryf), sowel as die polarisasie tensor wat die kern beskryf. Die basiese kern-kern (NN) wisselwerking word beskryf deur gebruik te maak van die SPVAT of IA1 daarstelling van die NN verstrooiingsmatriks. Analitiese uitdrukkings word ook afgelei vir die polarisasie tensor binne die Fermi gas model. Die vervormdegolf beskrywing van die projektiel en uitgaande deeltjie word gedoen deur gebruik te maak van die eikonal vervormdegolf benadering. Die uitdrukking vir die ongepolariseerde dubbele differsieële kansvlak bevat ’n nege dimensioneële ossilatoriese integraal en ’n prakties-effektiewe prosedure is ontwikkel om hierdie waarneembare te bereken. Vegelyking van Gauss, Monte Carlo en kwasi-Monte Carlo numeriese integrasie tegnieke het uitgewys dat die Gauss integrasie tegniek die beste geskik is om die probleem op te los. Die gebruik van Gauss integrasie om funksies te bereken wat afhanklik is van net een veranderlike en dit te kombineer met moderne sagteware programme soos MATLAB laat ons toe om die gepolariseerde dubbele differensieële kansvlak te bekeren in ’n redelike tyd. Alhoewel die berekening van die kansvlak vir een waarde van die energie-oordrag nogsteeds tydrowend is, word dit bespoedig deur die berekeningslas te versprei oor ’n aantal nodusse in ’n rekenaarbondel sisteem. ’n Toets berekening word gedoen waarby ’n proton met inkomende laboratoriese energie van 400 MeV vanaf ’n 40Ca kern verstrooi word teen ’n hoek van θcm = 400. Vir hierdie reaksie word die ongepolariseerde dubbele differensieële kansvlak bereken sowel as ’n volledige stel spin waarneembares naamlik Ay, Dℓ′,ℓ, Ds′s, Dnn, Ds′ℓ en Dℓ′s. Daar word gevind dat die versteurings lei tot ’n afname in die differensieële kansvlak. Die spin waarneembares egter, is komplekse hoeveelhede wat geen univorme gedrag toon nie. Die verskil tussen die vervormde golf spin waarneembares en die van vlak golf waarneembares is minimaal en ons lei daarvan af dat spin waarneembares onsensitief is teen oor versteurings. Doctoral 2010-11-18T13:04:11Z 2010-12-15T10:44:43Z 2010-11-18T13:04:11Z 2010-12-15T10:44:43Z 2010-12 Thesis http://hdl.handle.net/10019.1/5427 en University of Stellenbosch 92 p. : ill. application/pdf Stellenbosch : University of Stellenbosch |
| spellingShingle | Relativistic eikonal formalism Quasielastic proton-induced nuclear reactions Dissertations -- Physics Theses -- Physics Theoretical formalism Numerical analysis Titus, Nortin, P-D Relativistic eikonal formalism applied to inclusive quasielastic proton-induced nuclear reactions |
| title | Relativistic eikonal formalism applied to inclusive quasielastic proton-induced nuclear reactions |
| title_full | Relativistic eikonal formalism applied to inclusive quasielastic proton-induced nuclear reactions |
| title_fullStr | Relativistic eikonal formalism applied to inclusive quasielastic proton-induced nuclear reactions |
| title_full_unstemmed | Relativistic eikonal formalism applied to inclusive quasielastic proton-induced nuclear reactions |
| title_short | Relativistic eikonal formalism applied to inclusive quasielastic proton-induced nuclear reactions |
| title_sort | relativistic eikonal formalism applied to inclusive quasielastic proton induced nuclear reactions |
| topic | Relativistic eikonal formalism Quasielastic proton-induced nuclear reactions Dissertations -- Physics Theses -- Physics Theoretical formalism Numerical analysis |
| url | http://hdl.handle.net/10019.1/5427 |
| work_keys_str_mv | AT titusnortinpd relativisticeikonalformalismappliedtoinclusivequasielasticprotoninducednuclearreactions |