Application of the relativistic random-phase and distorted wave impulse approximations to quasielastic proton-nucleus scattering

Van Niekerk, David Douglas (Stellenbosch : University of Stellenbosch, 2010-12)

Thesis (PhD (Physics))--University of Stelllenbosch, 2010.

Thesis

ENGLISH ABSTRACT: In this dissertation a fully relativistic model for polarized inclusive quasielastic proton-nucleus scattering is developed. Using a standard relativistic impulse approximation (RIA) treatment of quasielastic scattering and a two-body SPVAT form of the current operator, it is shown how the behaviour of projectile and target can be decoupled. Subsequently, different models for projectile and target can be adopted and combined to examine a variety of relativistic effects. The most simplistic model of the target is provided by a mean-field nuclear matter approximation to the relativistic meson-nucleon model, quantum hadrodynamics (QHD). Here relativistic effects manifest as an effective mass, which is lower than the free mass, of the constituent nucleons. This model is improved upon by including many-body correlations through medium-modification of meson propagators in the relativistic random-phase approximation (RPA). Since it is generally accepted that the strong nuclear force and the extended range of the nuclear potential lead to distortion effects on the projectile and ejectile (seen as a modulation of the wave functions), our formalism is geared towards the use of relativistic distorted waves (RDWIA). The distorted waves are written as partial wave expansions and are solutions to the Dirac equation with potentials. The inclusion of distortions, however, greatly increases the computational burden and we show how a number of analytical and numerical techniques can be used to facilitate the process of calculation. It is also shown how the standard relativistic plane wave treatment (RPWIA) can, instead, be easily employed to obtain a baseline for determining the impact of distortions. A calculation is performed for the reaction 40Ca(!p, !p !) at a beam energy of 500 MeV. Here it is found that the effect of correlations on the RPWIA calculation can be seen as a quenching of the cross section that is expected to become more pronounced at lower energies or for higher density targets. A RDWIA calculation shows additional reduction and if target correlations are included this effect is enhanced. To our knowledge this is the first calculation that attempts to include both these effects (RPA and RDWIA) in the context of quasielastic proton-nucleus scattering.

AFRIKAANSE OPSOMMING: In hierdie proefskrif word ’n ten volle relatiwistiese model vir die berekening van inklusiewe kwasielastiese proton-kern verstrooiing daargestel. Deur gebruik te maak van ’n standaard relatiwistiese impulsbenadering (RIA) vir kwasi-elastiese verstrooiing asook ’n twee-deeltjie-SPVAT-vorm vir die stroom-operator, word daar gewys hoedat die gedrag van die projektiel en teiken ontkoppel kan word. Verskillende modelle kan dus vir die projektiel en teiken gebruik word om ’n verskeidenheid relatiwistiese effekte te bestudeer. Die mees simplistiese model vir die teiken word verskaf deur ’n gemiddelde-veld kernmateriaalbenadering tot die relatiwistiese meson-nukleon-model, kwantum-hadrodinamika (QHD). In hierdie model manifesteer relatiwistiese effekte as ’n effektiewe massa, wat kleiner is as die vrye massa, van nukleone in die kern. Hierdie model word verbeter deur die inagneming van veeldeeltjie korrelasies deur medium-gewysigde meson-propagators in die relatiwistiese ewekansige-fase-benadering (RPA). Aangesien dit algemeen aanvaar word dat die sterk-wisselwerking en die reikwydte van die kernpotensiaal aanleiding gee tot vervormingseffekte op die projektiel en ejektiel (gesien as die modulasie van golffunksies), is ons model optimaal geformuleer om gebruik te maak van relatiwistiese vervormde golwe (RDWIA). Die vervormde golwe word geskryf as parsi¨elegolf uitbreidings en dien as oplossings vir die Dirac-vergelyking met potensiale. Insluiting van vervormings vermeerder egter die berekeningslas geweldig en ons toon hoedat ’n aantal analitiese en numeriese tegnieke gebruik kan word om die proses te vergemaklik. Daar word ook aangetoon hoe die standaard- relatiwistiese-vlakgolf-benadering (RPWIA), in plaas van vevormde golwe, maklik gebruik kan word om ’n verwysingspunt vir die meting van die effek van vervormings te bepaal. ’n Berekening vir die reaksie 40Ca(!p, !p !) teen ’n projektiel-energie van 500 MeV word getoon. Hier word dit gevind dat die effek van korrelasies op die RPWIA-berekening gesien kan word as ’n verlaging van die kansvlak. Daar word verwag dat hierdie effek duideliker sal word by laer energie¨e en ho¨er kerndigthede. ’n RDWIA-berekening word getoon wat daarop dui dat addisionele verlaging in die kansvlak voorkom en indien korrelasies hier ingesluit word, word hierdie effek vergroot. Sover ons kennis strek, is hierdie die eerste berekening wat poog om beide hierdie effekte (RPA en RDWIA) in die konteks van kwasi-elastiese proton-kern verstrooiing in te sluit.

Please refer to this item in SUNScholar by using the following persistent URL: http://hdl.handle.net/10019.1/5220
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