General Lorentz invariant representation of the NN interaction applied to quasielastic scattering of polarized protons

Van der Ventel, B. I. S.(Brandon Izak Samuel) (1999)

Dissertation (Ph.D.) -- University of Stellenbosch, 1999.

Thesis

ENGLISH ABSTRACT: In this dissertation a general Lorentz invariant representation (referred to as the IA2 representation) of the nucleon-nucleon (NN) scattering matrix, F is applied to the calculation of complete sets of spin observables for quasi elastic (fl, fl ') and (fl, fi) scattering in the context of the Relativistic Plane Wave Impulse Approximation (RPWIA). A complete expansion of the NN scattering matrix eliminates the arbitrariness of the previously used five-term representation (the IAl or SPVAT form of the NN scattering matrix) and allows for a correct incorporation of effective-mass-type medium effects within the RPWIA framework and within the context of the Walecka model. The aim is to investigate how successful the Walecka-model effective nucleon mass concept is in describing quasielastic (fl, fl') and (fl, fi) scattering data and whether it is possible to find a combination of effective projectile and target nucleon masses which can describe a complete set of quasielastic spin observables. Calculations are done for the energy range 200 MeV to 500 MeV and for the following targets: 4°Ca, 12C, 208Pb and 54Fe. Historically the first application of the IAl representation of F within the context of the RPWIA was to the reaction 4°Ca(fl,fl') at 1lab = 500 MeV and ezab = 19°. There it was found that the use of an effective mass for the external nucleons moved the theoretical calculation closer to the analyzing power data and below the free mass calculation. This was referred to as the 'quenching effect' in the analyzing power and was claimed to be a 'relativistic signature'. Employing the correct IA2 representation ofF, however, shows that the quenching effect in Ay is not as large as was initially predicted and in effect becomes negligible as the energy is lowered to 200 MeV for (fl, fl') scattering. The new calculations employing the IA2 representation therefore expose the danger of using an incomplete representation of F. We also extract (individually for (fl, fl') and (fl, fi) scattering) an optimal set of effective projectile and target nucleon masses which is defined as that combination which gives the best fit to all experimental spin observables for a specific reaction and incident laboratory kinetic energy 1/.ab· One finds that the optimal set for (fl, fl') and (fl, fi) scattering are in general fairly the same and constant with 1lab and target nucleus. Numerical results indicate that the optimal set provides an adequate description of Dn, Ds's , Ds'e and De's for the energy range 500 MeV to 200 MeV both at the quasi elastic peak and as a function of energy transfer. The description of Dnn (for both the (fl, fi) and (fl,fl') reaction) and Ay (for the (fl, fl ') reaction only) becomes problematic, however, as the energy is lowered from 500 MeV to 200 MeV.

AFRIKAANSE OPSOMMING: Samevatting Hierdie proefskrif bevat die toepassing van 'n algemene Lorentz invariante daarstelling (bekend as die IA2 daarstelling) van die nukleon-nukleon (NN) verstrooiingsmatriks, F in die berekening van volledige stelle van spin waarneembares vir kwasi-elastiese (p, p') en (p, n) verstrooing binne die raamwerk van die Relatiwistiese Vlakgolf lmpulsbenadering (RVI). 'n Volledige uitbreiding van die NN verstrooiingsmatriks verwyder die dubbelsinnighede wat inherent aan die sogenaamde IAl of SPVAT daarstelling van F is en bemaak sodoende 'n meer korrekte inagneming moontlik van die omringende kernmedium deur middel van effektiewe nukleonmassas volgens die Walecka model. Die doel is om vas te stel hoe suksesvol die konsep van 'n effektiewe nukleonmassa is in die beskrywing van kwasi-elastiese (p, p') en (p, n) verstrooingsdata en of di t moontlik is om 'n kombinasie van effektiewe massas vir die projektiel en teiken nukleone te verkry wat 'n volledige stel van kwasi-elastiese spin waarneembares kan bekryf. Berekeninge is gedoen vir laboratorium energiee tussen 200 MeV en 500 MeV en vir die volgende teikens: 4°Ca, 12C, 208Pb en 54Fe. Histories was die eerste toepassing van die IAl daarstelling van F op die reaksie 4°Ca(p,p') by Tlab = 500 MeV en ()lab = 19°. Daar is toe gevind dat die gebruik van effektiewe mass as die berekende analiseervermoe aansienlik verminder ( relatief tot 'n vrye nukleon massa berekening: die sogenaamde 'quenching effect'.) en dat dit die gemete waardes kan reproduseer. Hierdie situasie is as 'n duidelike relatiwistiese effek geiinterpreteer. Die gebruik van die korrekte IA2 daarstelling van F toon egter dat die dempingseffek nie so groot is as wat oorspronklik voorspel is nie en dat dit eintlik weglaatbaar klein word soos die energie verminder na 200 MeV vir (p,p') verstrooing. Die nuwe berekeninge wat gebruik maak van die IA2 daarstelling wys dus die gevare en beperkings uit verbonde aan die gebruik van 'n onvolledige uitbreiding van F. Verder word 'n optimale stel effektiewe pro j ektiel en teiken mass as ( afsonderlik vir (p, n) en (P, p') verstrooiing) afgelei wat gedefinieer word as daardie stel wat die beste passing gee vir alle eksperimentele spin waarnembares vir 'n spesifieke reaksie en invallende laboratorium energie Tlab· Berekeninge toon aan dat die IA2 daarstelling van F, tesame met die effektiewe nukleonmassa as parameter, bevredigende resultate lewer vir die volgende spin waarneembares: De'e, Ds's, Ds'e en De's vir beide (p,p') en (p, n) verstrooing vir die energiee 200 MeV tot 500 MeV. Die beskrywing van Dnn (vir beide die (p, n) en (p,p') reaksies) en Ay (vir die (p, p') reaksie) word egter pro blematies soos die energie verlaag vanaf 500 MeV na 200 MeV.

Please refer to this item in SUNScholar by using the following persistent URL: http://hdl.handle.net/10019.1/51278
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