D. L. Pham

Comparison of higher order deformations in severals-d shell nuclei obtained through Schrödinger or Dirac coupled-channel analysis of 800 MeV polarized protons inelastic scattering experiments

Cross-sections and analyzing powers data obtained by inelastic scattering of 800 MeV polarized protons from severals-d shell nuclei have been analyzed using the Dirac coupled-channel (CC) formalism putting emphasis in the precise determination of higher order deformation in these nuclei. The superiority of the Dirac formalism compared to the classical Schrödinger CC calculations in the analysis of these data was once more clearly established. The higher order deformations obtained through these calculations are compared to those obtained using the classical Schrödinger equation.

Dirac coupled-channels analysis of inelastic scattering of 800 MeV polarized protons from 16O, 24Mg and 26Mg

Abstract Coupled-channels calculations using the Dirac phenomenology have been performed to analyse cross sections and analyzing power data for inelastic scattering of 800 MeV protons from low-lying states in 16 O, 24 Mg and 26 Mg. Large negative reals scalar potentials, large positive real vector potentials and large negative imaginary vector potentials were obtained. Considerable improvements were obtained using the Dirac equation compared to the classical Schrodinger calculations. These best fits have been found compatible with an imaginary scalar potential equal to zero ( U s i =0) and therefore with less parameters (nine) than usually required in the classical calculations (twelve).

Dirac optical-model analysis of polarized protons elastic scattering from12C,16,18O,20Ne and24,26Mg at 800 MeV

SummaryProton elastic-scattering cross-sections and analysing powers at 800 MeV have been used to derive, within the Dirac formalism, optical-model parameters for six elements from12C to26Mg. The best set of Dirac optical parameters has been obtained by searching on all nine parameters which showed a large negative real scalar potential, a large positive real vector potential and a large negative imaginary vector potential. These calculations have been found to be consistent with an imaginary scalar potential set to zero (Vsi=0). Considerable improvements were obtained by using the Dirac formalism compared to the traditional Schrödinger one with a similar number of parameters.RiassuntoSono state usate le sezioni di urto di diffusione elastica del protone e potenze d’analisi di 800 MeV per dedurre, entro il formalismo di Dirac, parametri del modello ottico per sei elementi dal12C al26Mg. È stato ottenuto il migliore insieme dei parametri ottici di Dirac cercando tra tutti i nove parametri che mostravano un grande potenziale scalare reale negativo, un grande potenziale vettoriale reale positivo e un grande potenziale vettoriale immaginario negativo. Si è trovato che questi calcoli sono coerenti con un potenziale scalare immaginario fissato a zero (Vsi=0). Sono stati ottenuti notevoli miglioramenti usando il formalismo di Dirac in confronto a quello di Schrödinger con ugual numero di parametri.РезюмеИсследуется поперечное сечение упругого рассеяния протонов при энергии 800 МэВ для получения в рамках формализма Дирака параметров оптической модели для шести элементов от12C до26Mg. Наилучшая система оптических параметров Дирака получается при исследовании всех девяти параметров, которые дают большую отрицательную величину для вещественной части скалярного потенциала, больщую положительную величину для вещественной части векторного потенциала и больщую отрицательную величину для мнимой части скалярного потенциала. Эти вычисления согласуются с системой нулей для мнимого скалярного потенциала (Vsi=O). Используя формализм Дирака, получается значительное улучшение по сравнению с традиционным формализмом Шредингера для рассматриваемых параметров.

Inelastic scattering of 40 MeV polarized protons exciting the low-lying 2+ states in 90Zr and 92Zr

Abstract Cross sections and analyzing powers for 40 MeV polarized protons from the low-lying 2 + states in 90 Zr and 92 Zr have been measured. Very good agreement has been obtained with the coupled-channels collective model using the full Thomas deformed spin-orbit term. The microscopic model including core polarization also gives an excellent description of these states, in contrast to the situation at lower energies where this model was unable to reproduce the data.

Optical-model analysis for 30 MeV polarized-proton elastic scattering

SummaryProton clastic-scattering cross-sections and analysing powers at 30 MeV have been used to derive optical-model parameters for ten elements from10B to32S. A set of average geometrical parameters (r0 = 1.10 fm,rLS = 1.0 fm anda1 = 0.60 fm) is found to give good fits to the entire data, the other geometrical parameters beingr1=(1.35 ± 0.15) fm,a0=(0.75 ± 0.10) fm andaLS=(0.55 ± 0.07) fm. The dynamical parameters with fixed geometry are presented.RiassuntoSi sono usate le sezioni d’urto dello scattering inelastico di protoni e le capacità di analisi a 30 MeV per derivare parametri del modello ottico per dieci elementi compresi tra10B e32S. Si trova che un gruppo di parametri geometrici medi (r0 = 1.10 fm,rLS = 1.0 fm ea1 = 0.60 fm) dà buone approssimazioni a tutti i dati, gli altri parametri geometrici essendor1=(1.35 ± 0.15) fm,a0=(0.75 ± 0.10) fm eaLS=(0.55 ± 0.07) fm. Si presentano i parametri dinamici con geometria fissa.РеэюмеАналиэ поперечного сечения упругого рассеяния протонов при 30 МзВ испольэуется для получения параметров оптической модели для десяти злементов от10B до32S. Получается система средних геометрических параметров (ro= 1.10 фм,rLS=1.0 фм иa1=0.60 фм), которая соответствует имеюшимся данным. Получены другие геометрические параметрыr1=(1.35±0.15) фм,a0=(О.75±0.10) фм иaLS=(0.55±0.07) фм. Приводятся динамические параметры в случае фиксированной геометрии.

Macroscopic and microscopic model analysis of inelastic scattering of 30 MeV polarized protons from 90,92Zr and 92Mo

Abstract Angular distributions for 30 MeV polarized proton inelastic scattering and analyzing powers were measured for low-lying 2+, 3−, and 5− states in 90,92Mo. These are compared with coupled channel collective model and microscopic model calculations.

Optical-model analysis for 800 MeV polarized-proton elastic scattering from12C,16,18O,20Ne and24,26Mg

SummaryProton elastic-scattering cross-sections and analysing powers at 800 MeV have been used to derive optical-model parameters for six elements from12C to26Mg. A set of average geometrical parameters for the nuclear radiiro=rI=rVSL=rWSL=0.97 fm is found to give good fits to the entire data except for12C. However, it is not possible to get a unique diffuseness set. Comparisons with low-energy results and with results on heavier nuclei at intermediate energies are made. These calculations show that once more12C is a very special nucleus since requiring a specific treatment.RiassuntoSi usano le sezioni d’urto dello scattering elastico del protone e la potenza di analizzazione a 800 MeV per derivare i parametri del modello ottico per 6 elementi da12C a26Mg. Si trova che un insieme di parametri geometrici medi per i raggi nucleariro=rI=rVSL=rWSL=0.97 fm dà una buona approssimazione di tutti i dati tranne che per12C. Comunque, non è possibile ottenere un unico insieme di diffusione. Si fanno confronti con risultati a bassa energia e con risultati su nuclei piú pesanti ad energie intermedie. Questi calcoli mostrano ancora una volta che12C è un nucleo molto speciale perchè richiede un trattamento specifico.РезюмеАнализ поперечных сечений упругого рассеяния протонов с энергией 800 МэВ и поперечные сечения упругого рассеяния используются для получения параметров оптической модели для шести элементов от12C до26Mg. Получена система средних геометрических параметров для радиуса ядраro=rI=rVSL=rWSL=0.97 фм, которая хорошо согласуется с имеющимися данными, кроме12C. Однако невозможно получить однозначную систему параметров диффузности. Проводятся сравнения с резуьтатами при низких энергиях и результатами, полученными на более тяженых ядрах при промежуточных энергиях. Эти вычисления еще раз показывают, что12C представляет очень специфическое ядро, которое требует специального рассмотрения.

Study of nuclear deformation parameters in the12C(p, p′)12C* reaction between 200 and 800 MeV through dirac coupled-channel calculations

SummaryDirac coupled-channel calculations have been performed to analyse cross-sections and analysing power data for inelastic scatterings of polarized protons between 200 MeV and 800 MeV from the first 2+, 4+ and 3− excited states of12C. No better determination of the deformation parameters could be obtained, although considerable improvements have been obtained using the Dirac equation compared to the classical Schrödinger calculations. The deformation parameters obtained are comparable with those obtained previously and are almost unchanged over this energy range.

New evidences for an imaginary spin‐orbit potential in the inelastic scattering of polarized protons from 12C and 16O

Analyzing powers and cross sections for elastic and inelastic scattering of 20, 30, and 40 MeV polarized protons from 12C and 16O have been analyzed in the coupled‐channels collective model using the full Thomas deformed spin‐orbit term. Evidence is given that there is an imaginary spin‐orbit potential in the proton optical potential for these nuclei.

On the spin-orbit deformation in inelastic scattering of polarized protons at intermediate energy

SummaryCoupled-channel analyses of both cross-sections and analysing-power data have been performed for low-lying states for16,18O(