Faddeev integral-equation treatment of elastic electron-hydrogen scattering

Summary The Faddeev integral equations for the total singlet and triplet amplitude in the elastic e⁻H scattering are studied rigorously in the space of continuous functions at high and intermediate energies. Their solution is first proved to be unique and then evaluated by the method of successive approximations. To improve the convergence rate of the perturbative series obtained, a convergent sequence of Padé approximants is used. The scattering amplitudes are calculated numerically up to the sixth perturbative order.

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Riassunto Le equazioni integrali di Faddeev per l'ampiezza totale di singoletto e di tripletto nello scattering elastico e⁻H sono studiate rigorosamente nello spazio delle funzioni continue ad energie alte ed intermedie. Si dimostra dapprima l'unicità della loro soluzione che è poi calcolata col metodo delle approssimazioni successive. Al fine di migliorare la velocità di convergenza della serie perturbativa ottenuta, si usa una successione convergente di approssimanti di Padé. Le ampiezze di scattering sono calcolate numericamente fino al sesto ordine perturbativo.

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Резюме В пространстве непрерывных функций при высоких и промежуточных энергиях строго исследуются интегральные уравнения Фаддеева для полной синглетной и триплетной амплитуды упругого e⁻-H рассеяния. Сначала докзывается единственность решения этих уравнений. Затем с помощьь метода последовательных приближений вычисляется решение. Для улучшения скорости сходимости полученного пертурбационного разложения используется сходящаяся последовательность Паде приближений. Амплитуды рассеяния вычисляются численно вплоть до шестого порядка теории возмущений.

     

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