UNIVERSIDADE DE BRASÍLIA INSTITUTO DE FÍSICA Tese de Doutorado

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❯◆■❱❊❘❙■❉❆❉❊ ❉❊ ❇❘❆❙❮▲■❆

■◆❙❚■❚❯❚❖ ❉❊ ❋❮❙■❈❆

❚❡s❡ ❞❡ ❉♦✉t♦r❛❞♦

◗✉✐r❛❧✐❞❛❞❡✱ ❙✉♣❡r❢í❝✐❡ ❞❡ ❊♥❡r❣✐❛ P♦t❡♥❝✐❛❧ ❡

❉✐♥â♠✐❝❛ ❞❡ ❈♦♠♣❧❡①♦s ❡♥✈♦❧✈❡♥❞♦ ❍2❖2

✰ ●❛s❡s

◆♦❜r❡s✳

▲✉❝✐❛♥♦ ❆❧♠❡✐❞❛ ▲❡❛❧

❖r✐❡♥t❛❞♦r✿

❘✐❝❛r❞♦ ●❛r❣❛♥♦

❈♦✲♦r✐❡♥t❛❞♦r✿

▲✉✐③ ❋❡r♥❛♥❞♦ ❘♦♥❝❛r❛tt✐

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◗✉✐r❛❧✐❞❛❞❡✱ ❙✉♣❡r❢í❝✐❡ ❞❡ ❊♥❡r❣✐❛ P♦t❡♥❝✐❛❧ ❡ ❉✐♥â♠✐❝❛ ❞❡

❈♦♠♣❧❡①♦s ❡♥✈♦❧✈❡♥❞♦ ❍

2

❖

2

✰ ●❛s❡s ◆♦❜r❡s✳

P♦r

▲✉❝✐❛♥♦ ❆❧♠❡✐❞❛ ▲❡❛❧

❚❡s❡ s✉❜♠❡t✐❞❛ ❛♦ ■♥st✐t✉t♦ ❞❡ ❋ís✐❝❛ ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❞❡ ❇r❛sí❧✐❛ ❝♦♠♦ ♣❛rt❡ ❞♦s r❡q✉✐s✐t♦s ♣❛r❛ ❛ ♦❜t❡♥çã♦ ❞♦ ❣r❛✉ ❞❡ ❞♦✉t♦r ❡♠ ❋ís✐❝❛✳

❈♦❧❛❜♦r❛❞♦r❡s✿

Pr♦❢✳ ❉r✳ ❘✐❝❛r❞♦ ●❛r❣❛♥♦ ✭❖r✐❡♥t❛❞♦r✮ ■❋✲❯♥❇

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✏❍á ✉♠ ❣r❛♥❞❡ ❞❡s❡❥♦ ❡♠ ♠✐♠ ❞❡ s❡♠♣r❡ ♠❡❧❤♦r❛r✳ ▼❡❧❤♦r❛r é ♦ q✉❡ ♠❡ ❢❛③ ❢❡❧✐③✳ ❊ s❡♠♣r❡ q✉❡ s✐♥t♦ q✉❡ ❡st♦✉ ❛♣r❡♥❞❡♥❞♦ ♠❡♥♦s✱ q✉❡ ❛ ❝✉r✈❛ ❞❡ ❛♣r❡♥❞✐③❛❞♦ ❡stá ♥✐✈❡❧❛♥❞♦✱ ♦✉ s❡❥❛ ♦ q✉❡ ❢♦r✱ ❡♥tã♦ ♥ã♦ ✜❝♦ ♠✉✐t♦ ❝♦♥t❡♥t❡✳ ❊ ✐ss♦ s❡ ❛♣❧✐❝❛ ♥ã♦ só ♣r♦✜ss✐♦♥❛❧♠❡♥t❡✱ ❝♦♠♦ ♣✐❧♦t♦✱ ♠❛s ❝♦♠♦ ♣❡ss♦❛✳✑

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❆❣r❛❞❡❝✐♠❡♥t♦s

Pr✐♠❡✐r❛♠❡♥t❡ ❣♦st❛r✐❛ ❞❡ ❛❣r❛❞❡❝❡r ❛♦ ❛✉t♦r ❡ ❣r❛♥❞❡ ❝r✐❛❞♦r ❞♦ ✉♥✐✈❡rs♦✳ ❙❡♠ ❊❧❡✱ ♥❛❞❛ ❞✐ss♦ s❡r✐❛ ♣♦ssí✈❡❧✱ ♥ã♦ ❝♦♥s❡❣✉✐r✐❛ ❛❧❝❛♥ç❛r ❡ss❡ ♦❜❥❡t✐✈♦✳ ❊♠ s❡❣✉♥❞♦ ❧✉❣❛r ❛❣r❛❞❡ç♦ ♠❡✉s ♣❛✐s q✉❡ ❝♦♠ ❣r❛♥❞❡ ❡s❢♦rç♦ ❡ ❛♠♦r ♠❡ ♣r♦♣♦r❝✐♦♥❛r❛♠ ✉♠❛ ❡❞✉❝❛çã♦ ❞❡ q✉❛❧✐❞❛❞❡ ❡ t♦❞❛ ❛ ❜❛s❡ q✉❡ ♣r❡❝✐s❛✈❛ ♣❛r❛ ❝♦♥s❡❣✉✐r ❝❤❡❣❛r ❛té ❛q✉✐✳ ❋❡❧✐③ é ♦ ❤♦♠❡♠ q✉❡ ♣♦ss✉✐ ❣r❛♥❞❡s ♣❛✐s ❡ ❡✉ ❝❡rt❛♠❡♥t❡ s♦✉ ✉♠ ❞❡❧❡s✳ ❆❣r❛❞❡ç♦ ❛♦s ♠❡✉s ❣r❛♥❞❡s ✐r♠ã♦s ▲❡❛♥❞r♦✱ ❆❞r✐❛♥♦ ❡ ❋❛❜✐❛♥♦ q✉❡ s❡♠♣r❡ q✉❡ ♣♦ssí✈❡❧ ♠❡ ❛❥✉❞❛r❛♠ ♥♦ q✉❡ ❡st❛✈❛♠ ❛♦s s❡✉s ❛❧❝❛♥❝❡s s❡♠ ♣❡st❛♥❡❥❛r✱ ❡♠ ❡s♣❡❝✐❛❧ ❛♦ ♠❡✉ ✐r♠ã♦ ❡ ❣r❛♥❞❡ ♣❛r❝❡✐r♦ ❋❛❜✐❛♥♦✳

❆❣r❛❞❡ç♦ ♦ ♣r♦❢❡ss♦r ❘✐❝❛r❞♦ ●❛r❣❛♥♦ q✉❡ à ❡①❡♠♣❧♦ ❞❡ ✉♠ ♣❛✐✱ ♥ã♦ ♠❡❞❡ ❡s❢♦rç♦s ♣❛r❛ ❛❥✉❞❛r s❡✉s ♦r✐❡♥t❛♥❞♦s ❡ ❝♦♠ ❡①í♠✐❛ ❞❡❞✐❝❛çã♦✱ ❝♦♠♣❡tê♥✲ ❝✐❛ ❡ ❛♠✐③❛❞❡ ♥♦s ❝❛♣❛❝✐t❛ ❝♦♠♦ ♣r♦✜ss✐♦♥❛✐s ❝♦♠♣❡t✐t✐✈♦s ♥❡ss❡ ♠❡✐♦ tã♦ ár❞✉♦✳ ❆❣r❛❞❡ç♦ ❛♦s ❞❡♠❛✐s ♣r♦❢❡ss♦r❡s ❞♦ ♥♦ss♦ ❣r✉♣♦ ❞❡ ♣❡sq✉✐s❛✱ q✉❡ à ❡①❡♠♣❧♦ ❞❡ ♣♦✉❝♦s ❡stã♦ s❡♠♣r❡ ❞✐s♣♦♥í✈❡✐s ❛ ❛✉①✐❧✐❛r ♦ ♥ú❝❧❡♦✿ ●❡r❛❧❞♦ ▼❛❣❡❧❛✱ ▲✉✐③ ❋✳ ❘♦♥✲ ❝❛r❛tt✐✱ P❡❞r♦ ❍❡♥r✐q✉❡✱ ❲✐❧✐❛♠ ❈✉♥❤❛✱ ❉❡♠étr✐♦ ❋✐❧❤♦ ❡ ▲✉✐③ ❘✐❜❡✐r♦✳

❆♦s ❛♠✐❣♦s ❞❡ ❣r❛❞✉❛çã♦ ❡ ♣ós✲❣r❛❞✉❛çã♦ q✉❡ s❡♠♣r❡ ♥♦s ❛❥✉❞❛♠♦s ♠✉✲ t✉❛♠❡♥t❡ ❝♦♠ ♦ s✐♠♣❧❡s ✜♠ ❞❡ ❛❥✉❞❛r ♦ ♦✉tr♦ ❛ s❡r ♠❡❧❤♦r✿ ▲✉✐③ ❘✐❜❡✐r♦✱ ▲❡❛♥❞❡r ▼✐❝❤❡❧s✱ ●✉✐❧❤❡r♠❡ ●♦♠✐❞❡✱ ●✐♦✈❛♥♥✐ ●r❛ss✐✱ ❍❡♥r✐q✉❡ ❱✐❡✐r❛✱ ❍❡♥r✐q✉❡ ❆r❛ú❥♦✱ ❘♦❞r✐❣♦ ▼❛✐❛✱ ❙t❡♣❤❛♥✐❡ ▲❛♠♦✉♥✐❡r ❡ ▼❛t❤❡✉s ❍♦r♦✈✐ts✳ ❆♦ ❛♠✐❣♦ ❏♦♥❛t❤❛♥ ❚❡✐①❡✐r❛ ♣❡❧♦ ❝♦♠♣❛♥❤❡✐r✐s♠♦ ♥❛s ✈✐❛❣❡♥s ❞❡ ❝♦♥❣r❡ss♦ ❡ ❛♦ ❛♠✐❣♦ ▲✉✐③ ❘✐❜❡✐r♦ ♣❡❧❛ ❛♠✐③❛❞❡ ❞❡ s❡♠♣r❡ ❡ ❢✉♥❞❛♠❡♥t❛❧ ♣❛♣❡❧ ♣❛r❛ ❛ ❝♦♥t✐♥✉✐❞❛❞❡ ❞❛ ♠✐♥❤❛ ✈✐❞❛ ❛❝❛❞ê♠✐❝❛✳

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♣❡❧♦ ❛♣r❡♥❞✐③❛❞♦ ❛❞q✉✐r✐❞♦ ♥❛ ♠❡❧❤♦r ❡q✉✐♣❡ q✉❡ t✐✈❡ ♦ ♣r❛③❡r ❞❡ tr❛❜❛❧❤❛r✿ ❆❧❡①❛♥✲ ❞r❡ ❊♥✐③✱ ❆❧✈✐r ❏ú♥✐♦r✱ ❈❤r✐s ▲♦✉r❡♥ç♦✱ ❈❤r✐s✱ ❋❡❧✐♣♣❡ ▼❛❝✐❡❧✱ ❋❡❧✐♣❡ ❚♦✉r✐♥❤♦✱ ❋❧á✈✐❛ ▼❛❝✐❡❧✱ ▲✉✐③ ❋❡❧✐♣❡✱ ▲✉✐③❛✱ ▼❛t❤❡✉s ❍♦r♦✈✐ts✱ ◆❡✉③â♥❣❡❧❛✱ ❘❡♥❛t♦ ◆✐❝❛str✐✱ ❘♦❜❡rt ❈✉♥❤❛✱ ❙✐❧❛s ▼✉♥❞✐♠✱ ❚✐❛❣♦ ❇❛❤é ❡ ❚❤✐❛❣♦ ❋r❛♥ç❛✳ ❆♦ ❚❤✐❛❣♦ ❋r❛♥ç❛ ♣❡❧❛ ❝♦♥✜❛♥ç❛ ❡ ♦♣♦rt✉♥✐❞❛❞❡s ♦❢❡r❡❝✐❞❛s✱ ❋❡❧✐♣♣❡ ▼❛❝✐❡❧ ♣❡❧♦ ♠❡s♠♦ ♠♦t✐✈♦✳ ◆❛ ♠❡s♠❛ ✐♥st✐t✉✐çã♦ ❡✉ ♥ã♦ ♣♦❞❡r✐❛ ❞❡✐①❛r ❞❡ ♠❡♥❝✐♦♥❛r t❛♠❜é♠ ♦ ❞✐r❡t♦r ❙ér❣✐♦ ❏♦sé ❉❡✉❞ ❇r✉♠ ♣❡❧❛ ♦♣♦rt✉♥✐❞❛❞❡ ❡ t❛♠❜é♠ ♣❡❧❛ ❝♦♥✜❛♥ç❛ q✉❡ s❡♠♣r❡ t❡✈❡ ♥♦ ♠❡✉ tr❛❜❛❧❤♦ ❡ t❛♠❜é♠ ❛♦s ❛♠✐❣♦s ❞❛s ❞❡♠❛✐s ❡q✉✐♣❡s ❞❡ tr❛❜❛❧❤♦✱ ❛s q✉❛✐s t❡♥❤♦ ❣r❛♥❞❡ ❛❞♠✐r❛çã♦ ❡ r❡s♣❡✐t♦✳

❆♦s ❢✉♥❝✐♦♥ár✐♦s ❞♦ ✐♥st✐t✉t♦ ❲✐❧❧✱ ▲✉✐③✱ ■r✐♦❞❡ ❡ ❞❛ ♣ós✲❣r❛❞✉❛çã♦ ❙❛♥❞r❛ ❡ ❚❤❛❧❡s ♣♦r t♦❞♦ ❛♣♦✐♦✳ ❆ t♦❞♦s ♦s ♣r♦❢❡ss♦r❡s ❞❛ ❣r❛❞✉❛çã♦ ❡ ♣ós✲❣r❛❞✉❛çã♦ q✉❡✱ ♠❡s♠♦ ❝♦♠ ♣♦✉❝♦ ✐♥❝❡♥t✐✈♦✱ ♥ã♦ ♠❡❞✐r❛♠ ❡s❢♦rç♦s ♣❛r❛ ♥♦s ❞❛r ✉♠❛ ❜♦❛ ❢♦r♠❛çã♦ ❡ ♣r♦♣♦r❝✐♦♥❛r ♠♦♠❡♥t♦s ❞❡ ❣r❛♥❞❡ ❛❧❡❣r✐❛ ❝♦♠♦ ❡ss❡ tít✉❧♦ ❞❡ ❞♦✉t♦r✿ ❈❛r❧♦s ●❛❧✈ã♦✱ ◆á❞✐❛ ▼❛r✐❛✱ ❘✐❝❛r❞♦ ●❛r❣❛♥♦✱ ❏ú♥✐♦ ▼ár❝✐♦ ❡ ❖②❛♥❛rt❡ P♦rt✐❧❤♦✱ ♣❡❧❛ ❢♦r♠❛çã♦ ♥❛ ❣r❛❞✉❛çã♦✳ P❡ss♦❛s q✉❡ t❡♥❤♦ ❝♦♠♦ ❡①❡♠♣❧♦ ❞❡ ❡①❝❡❧❡♥t❡s ♣r♦✜ss✐♦♥❛✐s✳

❆♦ ❣r✉♣♦ ❞❡ ♦r❛çã♦ ❙❡❞❡ ❙❛♥t♦s ❡ ❛♦ ❣r✉♣♦ ❊❏❖❈ q✉❡ ♠❡ ❞❡r❛♠ ❢♦rç❛s ♣❛r❛ s❡♠♣r❡ ♣r♦ss❡❣✉✐r ❡ ♥✉♥❝❛ ♣❛r❛r ♦✉ ❞❡s✐st✐r✳ ❆♦s ♠❡✉s ❛♠✐❣♦s q✉❡ ♥❡ss❡s ❣r✉♣♦s ❡❝♦♥tr❡✐ ❡ q✉❡ ♣❛rt✐❝✐♣❛♠ ❥✉♥t❛♠❡♥t♦ ❝♦♠✐❣♦ ❞❡ ♠❛r❛t♦♥❛s q✉❡ ❞❡ ❢❛t♦ t❡♠ s✐❞♦ ♠✐♥❤❛ ✧t❛r❥❛ ♣r❡t❛✏ ❝♦♥tr❛ ❞❡♣r❡ssã♦✿ ❇r✉♥♦✱ ❋❛❜✐❛♥♦✱ ❋á❜✐♦✱ ▲❛♥❞✐♦✱ ▼❛r❝♦s✱ ▼❛r❝❡❧♦✱ P❛✉❧♦✱ ❘❡♥❛♥✱ ❘♦❞r✐❣♦✱ ❞❡♥tr❡ ♦✉tr♦s✳

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❘❡s✉♠♦

◆❡ss❡ tr❛❜❛❧❤♦✱ ❝❛❧❝✉❧❛♠♦s ❛s ❡♥❡r❣✐❛s ❛❜ ✐♥✐t✐♦ ❞♦s s✐st❡♠❛s ❍2❖2✲●◆ ✭●◆ ❂ ❍❡✱ ◆❡✱ ❆r✱ ❑r ❡ ❳❡✮ ❡ ❛s r❡♣r❡s❡♥t❛♠♦s ♣♦r ♠❡✐♦ ❞❡ ❙✉♣❡r❢í❝✐❡s ❞❡ ❊♥❡r❣✐❛ P♦✲ t❡♥❝✐❛❧ ✭❙❊P✮✳ ❆♣ós ❛ ♦❜t❡♥çã♦ ❞❡ t♦❞❛s ❛s ❡♥❡r❣✐❛s ❝♦♥s✐❞❡r❛❞❛s✱ ❛❥✉st❛♠♦s ❛s ❙❊Ps ♣♦r ♠❡✐♦ ❞❛ ❢♦r♠❛ ❛♥❛❧ít✐❝❛ ▲❡♥♥❛r❞ ❏♦♥❡s ❛♣r✐♠♦r❛❞♦ ✭❞♦ ✐♥❣❧ês ■♠♣r♦✈❡❞ ▲❡♥♥❛r❞ ❏♦♥❡s ✭■▲❏✮✮✱ q✉❡ é ✉♠❛ ❞❛s ❢♦r♠❛s q✉❡ ♠❡❧❤♦r ❞❡s❝r❡✈❡ s✐st❡♠❛s ❞❡ ✐♥✲ t❡r❛çã♦ ❞♦ t✐♣♦ ❱❛♥ ❞❡r ❲❛❛❧s✱ ❝♦♠♦ ♦s q✉❡ ❡♥✈♦❧✈❡♠ ❣❛s❡s ♥♦❜r❡s✳ ◆♦ss♦ ❡st✉❞♦ ✐♥✈❡st✐❣❛ ♦ ♣❛♣❡❧ q✉❡ ❛s ❢♦r♠❛s ❡♥❛♥t✐♦♠ér✐❝❛s ❡ ❛ s✐♠❡tr✐❛ ❞❛ ♠♦❧é❝✉❧❛ ❞❡ ❍2❖2 ❞❡✲ s❡♠♣❡♥❤❛♠ ♥❛s ❜❛rr❡✐r❛s r❡s✉❧t❛♥t❡s ❡ ❛s ❝♦rr❡s♣♦♥❞❡♥t❡s ❣❡♦♠❡tr✐❛s ❞❡ ❡q✉✐❧í❜r✐♦✳ ❖ ♠♦❞❡❧♦ t❡ór✐❝♦ ♣r♦♣♦st♦ é út✐❧ ♥♦ ❡st✉❞♦ ❞❛ ❞✐♥â♠✐❝❛ ❞❛ ♠♦❧é❝✉❧❛ ❞❡ ♣❡ró①✐❞♦ ❞❡ ❤✐❞r♦❣ê♥✐♦✱ ♦✉ ♦✉tr♦s s✐st❡♠❛s ❡♥✈♦❧✈❡♥❞♦ ❧✐❣❛çõ❡s ❖✲❖ ❡ ❙✲❙✱ q✉❡ ✐♥t❡r❛❣❡♠ ♣♦r ❢♦rç❛s ♥ã♦ ❝♦✈❛❧❡♥t❡s ❝♦♠ át♦♠♦s ♦✉ ♠♦❧é❝✉❧❛s✳ P❛r❛ ❡♥t❡♥❞❡r ❝♦♠♦ ❛ ♦r✐❡♥t❛çã♦ r❡❧❛t✐✈❛ ❞❛s ❧✐❣❛çõ❡s ❖✲❍ ♠✉❞❛♠ ❛♦ ❧♦♥❣♦ ❞❡ ❡✈❡♥t♦s ❝♦❧✐s✐♦♥❛✐s✱ q✉❡ ♣♦❞❡♠ ❧❡✈❛r ❛ ✉♠❛ ❢♦r♠❛çã♦ ❞❡ ❧✐❣❛çã♦ ❞❡ ❤✐❞r♦❣ê♥✐♦ ♦✉ ♠❡s♠♦ ❛ s❡❧❡t✐✈✐❞❛❞❡ ❡♠ r❡❛çõ❡s q✉í♠✐✲ ❝❛s✳ ❆ ♣❛rt✐r ❞❡ss❛ ❛♥á❧✐s❡ ❡❧❡trô♥✐❝❛ ❧❡✈❛♥❞♦ ❡♠ ❝♦♥s✐❞❡r❛çã♦ ❛s ❢♦r♠❛s ❛♥❛❧ít✐❝❛s ❞♦ t✐♣♦ ■▲❏✱ ❝❛❧❝✉❧❛♠♦s t❛♠❜é♠ ❛s ❡♥❡r❣✐❛s r♦✲✈✐❜r❛❝✐♦♥❛✐s ❞❛ ❞❡♣❡♥❞ê♥❝✐❛ r❛❞✐❛❧ ❞♦s ❝♦♠♣❧❡①♦s ❍2❖2✲●◆✱ ❝♦♥s✐❞❡r❛♥❞♦ s❡♠♣r❡ ❍2❖2 ❡♠ s✉❛ ❣❡♦♠❡tr✐❛ ❞❡ ❡q✉✐❧í❜r✐♦✳ P❛r❛ t♦❞♦s ♦s s✐st❡♠❛s ❝♦♥s✐❞❡r❛❞♦s ❢♦✐ ❡♥❝♦♥tr❛❞♦ q✉❡ ❛ ❝♦❧✐sã♦ ❞♦ ❣ás ♥♦❜r❡ ❝♦♠ ❛ á❣✉❛ ♦①✐❣❡♥❛❞❛ s❡ ❞❛rá ❝♦♠ ♦ ❣ás ♥♦❜r❡ ❝♦❧✐❞✐♥❞♦ ♣❡r♣❡♥❞✐❝✉❧❛r♠❡♥t❡ ❝♦♠ ♦ ❡✐①♦ ❞❛ ❧✐❣❛çã♦ ❖✲❖✳ ◆♦ ❡st❛❞♦ ❢✉♥❞❛♠❡♥t❛❧✱ ♦ s✐st❡♠❛ ❍2❖2✲◆❡ ♥ã♦ é ✉♠ ❡st❛❞♦ ♠✉✐t♦ ♣r♦✈á✈❡❧ ❞❡ s❡r ❡♥❝♦♥tr❛❞♦✱ ♣♦ré♠ ♥♦ ❡st❛❞♦ ❡①❝✐t❛❞♦ é ♣❡r❝❡♣tí✈❡❧ q✉❡ ❡st❛✲ ❞♦s ❡①❝✐t❛❞♦s ❞❡ss❡ s✐st❡♠❛ é ❡①tr❡♠❛♠❡♥t❡ ♣♦ssí✈❡❧ ❞❡ s❡r ❡♥❝♦♥tr❛❞♦✳ ❆❧é♠ ❞✐ss♦✱ ♣❡r❝❡❜❡✲s❡ q✉❡ ♦s ❣❛s❡s ♥♦❜r❡s ♣♦❞❡♠ ✐♥✢✉❡♥❝✐❛r ♦s ♠♦❞♦s t♦r❝✐♦♥❛✐s ❞❛ ♠♦❧é❝✉❧❛ ❞❡ ♣❡ró①✐❞♦ ❞❡ ❤✐❞r♦❣ê♥✐♦✳ ❆♣ós t♦❞❛s ❛s ❛❜♦r❞❛❣❡♥s ❝❛❜✐❞❛s ♥❡st❛ t❡s❡✱ é ♣♦s✲ sí✈❡❧ ♣❡r❝❡❜❡r q✉❡ ♦s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s ❝♦♥❝♦r❞❛♠ ♠✉✐t♦ ❜❡♠ ❝♦♠ ♦s r❡s✉❧t❛❞♦s ❞✐s♣♦♥í✈❡✐s ♥❛ ❧✐t❡r❛t✉r❛✳

(7)

❆❜str❛❝t

■♥ t❤✐s ✇♦r❦✱ ✐t ✐s ❞❡t❡r♠✐♥❡❞ t❤❡ ❛❜ ✐♥✐t✐♦ ❡❧❡❝tr♦♥✐❝ ❡♥❡r❣✐❡s ❢♦r t❤❡ ❍2❖2✲ ◆❣ ❝♦♠♣❧❡①❡s ✭◆❣ ❂ ❍❡✱ ◆❡✱ ❆r✱ ❑r✱ ❛♥❞ ❳❡✮✳ ❚❤❡ ❝❛❧❝✉❧❛t❡❞ ❡♥❡r❣✐❡s ❛r❡ ✜tt❡❞ ✉s✐♥❣ t❤❡ ■♠♣r♦✈❡❞ ▲❡♥♥❛r❞ ❏♦♥❡s ✭■▲❏✮ ❛♥❛❧②t✐❝❛❧ ❢♦r♠✱ ✇❤✐❝❤ ✐s ❛ ❣♦♦❞ ✇❛② ✐♥ ♦r❞❡r t♦ r❡♣r❡s❡♥t s②st❡♠s t❤❛t ♣r❡s❡♥t ❱❛♥ ❞❡r ❲❛❛❧s✬s ✐♥t❡r❛❝t✐♦♥s t②♣❡ ❛s ✐♥ t❤✐s ❝❛s❡ ♦❢ ♥♦❜❧❡ ❣❛s❡s ✐♥t❡r❛❝t✐♦♥✳ ❖✉r st✉❞② ✐♥✈❡st✐❣❛t❡ t❤❡ r♦❧❡ t❤❛t t❤❡ ❡♥❛♥t✐♦♠❡r✐❝ ❢♦r♠s ❛♥❞ t❤❡ s②♠♠❡tr② ♦❢ t❤❡ ❍2❖2 ♠♦❧❡❝✉❧❡ ♣❧❛②s ♦♥ t❤❡ r❡s✉❧t✐♥❣ ❜❛rr✐❡rs ❛♥❞ ❡q✉✐❧✐❜r✐✉♠ ❣❡♦♠❡tr✐❡s✳ ❚❤❡ ♣r♦♣♦s❡❞ t❤❡♦r❡t✐❝❛❧ ❢r❛♠❡✇♦r❦ ✐s ✉s❡❢✉❧ t♦ st✉❞② t❤❡ ❞②♥❛♠✐❝s ♦❢ t❤❡ ❍✷❖✷ ♠♦❧❡❝✉❧❡✱ ♦r ♦t❤❡r s②st❡♠s ✐♥✈♦❧✈✐♥❣ ❖✕❖ ❛♥❞ ❙✕❙ ❜♦♥❞s✱ ✐♥✲ t❡r❛❝t✐♥❣ ❜② ♥♦♥✲❝♦✈❛❧❡♥t ❢♦r❝❡s ✇✐t❤ ❛t♦♠s ♦r ♠♦❧❡❝✉❧❡s ❛♥❞ t♦ ✉♥❞❡rst❛♥❞ ❤♦✇ t❤❡ r❡❧❛t✐✈❡ ♦r✐❡♥t❛t✐♦♥ ♦❢ t❤❡ ❖✕❍ ❜♦♥❞s ❝❤❛♥❣❡s ❛❧♦♥❣ ❝♦❧❧✐s✐♦♥❛❧ ❡✈❡♥ts t❤❛t ♠❛② ❧❡❛❞ t♦ ❛ ❤②❞r♦❣❡♥ ❜♦♥❞ ❢♦r♠❛t✐♦♥ ♦r ❡✈❡♥ t♦ s❡❧❡❝t✐✈✐t② ✐♥ ❝❤❡♠✐❝❛❧ r❡❛❝t✐♦♥s✳ ❋r♦♠ t❤✐s ❛♥❛❧②s✐s✱ t❛❦✐♥❣ ✐♥t♦ ❛❝❝♦✉♥t ■▲❏ ❛♥❛❧②t✐❝❛❧ ❢♦r♠s✱ ✇❡ ❝❛❧❝✉❧❛t❡ t❤❡ r♦✲✈✐❜r❛t✐♦♥❛❧ ❡♥❡r❣✐❡s ♦❢ r❛❞✐❛❧ ❞❡♣❡♥❞❡♥❝❡s ✐♥ ❍2❖2✲◆● ❝♦♠♣❧❡①❡s✱ ❝♦♥s✐❞❡r✐♥❣ ❛❧✇❛②s ❍2❖2 ♦♥ ✐ts ❡q✉✐❧✐❜r✐✉♠ ❣❡♦♠❡tr②✳ ❋♦r ❛❧❧ t❤❡ ❝♦♥s✐❞❡r❡❞ s②st❡♠s ■t ✇❛s ❢♦✉♥❞ t❤❛t t❤❡ ♠♦st ♣r♦❜❛❜❧❡ ❝♦❧❧✐s✐♦♥ ♦❢ t❤❡ ♥♦❜❧❡ ❣❛s ✇✐t❤ ❤②❞r♦❣❡♥ ♣❡r♦①✐❞❡ ✇✐❧❧ ❜❡ ✇✐t❤ t❤❡ ♥♦❜❧❡ ❣❛s ❝♦❧❧✐❞✐♥❣ ♣❡r♣❡♥❞✐❝✉❧❛r t♦ t❤❡ ❛①✐s ❖✲❖ ❜♦♥❞✳ ■♥ t❤❡ ❣r♦✉♥❞ st❛t❡✱ t❤❡ s②st❡♠ ❍2❖2✲◆❡ ✐s ♥♦t ❛ ❧✐❦❡❧② st❛t❡ t♦ ❜❡ ❢♦✉♥❞✱ ❜✉t ✐♥ t❤❡ st❛t❡ ❡①❝✐t❡❞ ✐s ♥♦t✐❝❡❛❜❧❡ t❤❛t ❡①❝✐t❡❞ st❛t❡s ♦❢ t❤✐s s②st❡♠ ✐s ❤✐❣❤❧② ♣♦ss✐❜❧❡ t♦ ❜❡ ❢♦✉♥❞✳ ■♥ ❛❞❞✐t✐♦♥✱ ✐t ✐s ❝❧❡❛r t❤❛t t❤❡ ♥♦❜❧❡ ❣❛s❡s ❝❛♥ ✐♥✢✉❡♥❝❡ t❤❡ t♦rs✐♦♥❛❧ ♠♦❞❡s ♦❢ ❍②❞r♦❣❡♥ ♣❡r♦①✐❞❡ ♠♦❧❡❝✉❧❡✳ ❆♥❛❧②③✐♥❣ ❛❧❧ ♣❛r❛♠❡t❡rs ✐♥✈♦❧✈❡❞ ♦♥ t❤✐s ✇♦r❦✱ ❚❤❡ ♣r❡s❡♥t r❡s✉❧ts ❛r❡ ✐♥ ❛ ❣♦♦❞ ❛❣r❡❡♠❡♥t ✇✐t❤ t❤❡ ❞❛t❛ ❛✈❛✐❧❛❜❧❡ ✐♥ t❤❡ ❧✐t❡r❛t✉r❡✳

(8)

❙✉♠ár✐♦

✶ ■♥tr♦❞✉çã♦ ✶

✶✳✶ ❯♠❛ ❜r❡✈❡ ❍✐stór✐❛ ❡ ✐♠♣♦rtâ♥❝✐❛ ❞♦ ❈á❧❝✉❧♦ ❛❜ ✐♥✐t✐♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻

✷ ❆ ❋✉♥❞❛♠❡♥t❛çã♦ ❚❡ór✐❝❛ ✽

✷✳✶ ❖ Pr♦❜❧❡♠❛ ▼♦❧❡❝✉❧❛r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽ ✷✳✷ ❆ ❆♣r♦①✐♠❛çã♦ ❞❡ ❇♦r♥✲❖♣♣❡♥❤❡✐♠❡r ✭❆❇❖✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵ ✷✳✸ ❖ ▼ét♦❞♦ ❍❛rtr❡❡✲❋♦❝❦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷ ✷✳✹ ❆ ❚❡♦r✐❛ ❞❛ P❡rt✉r❜❛çã♦ ❞❡ ▼♦❧❧❡r✲P❧❡ss❡t ✭▼P✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺ ✷✳✺ ❆s ❋✉♥çõ❡s ❞❡ ❇❛s❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽ ✷✳✺✳✶ ❙♦❧✉çã♦ ❞❛ ❊q✉❛çã♦ ❞❡ ❙❝❤rö❞✐♥❣❡r ◆✉❝❧❡❛r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵

✸ ❖❜t❡♥çã♦ ❞❛s ❙✉♣❡r❢í❝✐❡s ❞❡ ❊♥❡r❣✐❛ P♦t❡♥❝✐❛❧ ❞♦ ❈♦♠♣❧❡①♦ ❍2❖2

✰ ●◆ ✷✼

✸✳✶ ❖ ❉❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞♦ ❙✐st❡♠❛ ❍2❖2 ✰ ●◆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼ ✸✳✷ ❆ ❘❡♣r❡s❡♥t❛çã♦ ●❡♦♠étr✐❝❛ ❞♦ ❙✐st❡♠❛ ❍2❖2 ✰ ●◆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵ ✸✳✷✳✶ ❘❡♣r❡s❡♥t❛çã♦ ❡♠ ✸✲❉ ❞❛ ❣❡♦♠❡tr✐❛ ❞♦ ♣r♦❜❧❡♠❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶ ✸✳✸ ❘❡♣r❡s❡♥t❛çã♦ ❞❛ ❙✉♣❡r❢í❝✐❡ ❞❡ ❊♥❡❣✐❛ P♦t❡♥❝✐❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺ ✸✳✹ ❆ ❛♥á❧✐s❡ ❞❛ ❉✐♥â♠✐❝❛ ❞♦s ❙✐st❡♠❛s ❡♠ ❊st✉❞♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽

✹ ❘❡s✉❧t❛❞♦s ❡ ❉✐s❝✉ssõ❡s ✹✷

✹✳✶ ❖ ❍2❖2 ♣✉r♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷ ✹✳✷ ❖ ❡st✉❞♦ ❡❧❡trô♥✐❝♦ ❞❛ ✐♥t❡r❛çã♦ ❍2❖2 ✰ ●◆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺ ✹✳✷✳✶ ❖s ❈♦♠♣❧❡①♦s ❋r❛❝❛♠❡♥t❡ ▲✐❣❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼

(9)

✹✳✸ ❖ ❊st✉❞♦ ❞❛ ❉✐♥â♠✐❝❛ ❞♦s ❈♦♠♣❧❡①♦s ❍2❖2 ✰ ●◆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶ ✹✳✹ ❖ ❊st✉❞♦ ❞♦s ❊st❛❞♦s ❊①❝✐t❛❞♦s ❞♦s ❈♦♠♣❧❡①♦s ❍2❖2 ✰ ●◆ ✳ ✳ ✳ ✳ ✳ ✻✺ ✹✳✹✳✶ ❚❡♦r✐❛ ❞♦ ❋✉♥❝✐♦♥❛❧ ❞❛ ❉❡♥s✐❞❛❞❡ ❉❡♣❡♥❞❡♥t❡ ❞♦ ❚❡♠♣♦ ✳ ✳ ✳ ✻✺ ✹✳✹✳✷ ❖s ❋✉♥❝✐♦♥❛✐s ❈❆▼✲❇✸▲❨P ❡ ❈❆▼✲◗❚P✲✵✵ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻ ✹✳✹✳✸ ❆s ❈✉r✈❛s ❞❡ ❊♥❡r❣✐❛ P♦t❡♥❝✐❛❧ ♣❛r❛ ♦s ❊st❛❞♦s ❊①❝✐t❛❞♦s ✳ ✳ ✻✼

✺ ❈♦♥❝❧✉sõ❡s ❡ P❡rs♣❡❝t✐✈❛s ✼✼

✻ ❆♣ê♥❞✐❝❡s ✽✼

✻✳✶ ❆♣ê♥❞✐❝❡ ❆✿ Pr♦❣r❛♠❛ ❞❡s❡♥✈♦❧✈✐❞♦ ♣❛r❛ ❣❡r❛r ❛s t♦❞❛s ❛s ❣❡♦♠❡tr✐❛s ❞♦ s✐st❡♠❛ ❍2❖2✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✼ ✻✳✷ ❆♣ê♥❞✐❝❡ ❇✿ Pr♦❣r❛♠❛ ❞❡s❡♥✈♦❧✈✐❞♦ ♣❛r❛ ❣❡r❛r ❛s t♦❞❛s ❛s ❣❡♦♠❡tr✐❛s

❞❛s ✐♥t❡r❛çõ❡s ❞♦ ❝♦♠♣❧❡①♦ ❍2❖2✲❣❛s❡s✲♥♦❜r❡s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✵ ✻✳✸ ❆♣ê♥❞✐❝❡ ❈✿ ❙❝r✐♣t ❝♦♥str✉í❞❛ ♣❛r❛ ❣❡r❛r ❝❛❞❛ ❡♥tr❛❞❛ ✭♣❛r❛ ♦ s✐s✲

t❡♠❛ ✐s♦❧❛❞♦ ❍2❖2✮ ♣❛r❛ ♦ ♣r♦❣r❛♠❛ ❣❛✉ss✐❛♥ ❞❡ ❢♦r♠❛ s❡♣❛r❛❞❛✳ ✳ ✳ ✾✸ ✻✳✹ ❆♣ê♥❞✐❝❡ ❉✿ ❙❝r✐♣t ❝♦♥str✉í❞❛ ♣❛r❛ ❣❡r❛r ❝❛❞❛ ❡♥tr❛❞❛ ✭❝♦♠♣❧❡①♦

❍2❖2✲❣❛s❡s✲♥♦❜r❡s✮ ♣❛r❛ ♦ ♣r♦❣r❛♠❛ ❣❛✉ss✐❛♥ ❞❡ ❢♦r♠❛ s❡♣❛r❛❞❛✳ ✳ ✳ ✾✻ ✻✳✺ ❆♣ê♥❞✐❝❡ ❊✿ ❚❛❜❡❧❛s ❞♦s ❛❥✉st❡s ❞❛s ❈✉r✈❛s ❞❡ ❊♥❡r❣✐❛ P♦t❡♥❝✐❛❧ ❡

❈✉r✈❛s ❞❡ ❊♥❡r❣✐❛ P♦t❡♥❝✐❛❧ ❞♦s ❝♦♠♣❧❡①♦s ❍2❖2✲●❛s❡s✲♥♦❜r❡s ❡♠ ❡st❛❞♦s ❡❧❡trô♥✐❝♦s ❡①❝✐t❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✾ ✻✳✻ ❆♣ê♥❞✐❝❡ ❋✿ ❆rt✐❣♦s ♣✉❜❧✐❝❛❞♦s ❡ ❛❝❡✐t♦ ♣❛r❛ ♣✉❜❧✐❝❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✽

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▲✐st❛ ❞❡ ❋✐❣✉r❛s

✶✳✶ ✭❛✮ ❱✐sã♦ ♣❧❛♥❛r ❞❛s ♠♦❧é❝✉❧❛s ❘✲▲✐♠♦♥❡♥♦ ❡ ❙✲▲✐♠♦♥❡♥♦❀ ✭❜✮ ❱✐sã♦ ❡s♣❛❝✐❛❧ ❞❛ q✉✐r❛❧✐❞❛❞❡ ♣❛r❛ ❛s ♠♦❧é❝✉❧❛s ❘✲▲✐♠♦♥❡♥♦ ❡ ❙✲▲✐♠♦♥❡♥♦✳ ✷ ✶✳✷ ✭❛✮ ❱✐sã♦ ♣❧❛♥❛r ❞❛ q✉✐r❛❧✐❞❛❞❡❀ ✭❜✮ ❱✐sã♦ ❡s♣❛❝✐❛❧ ❞❛ q✉✐r❛❧✐❞❛❞❡✳ ✳ ✳ ✹

✷✳✶ ❘❡♣r❡s❡♥t❛çã♦ ❞❡ ✉♠ s✐st❡♠❛ ♠♦❧❡❝✉❧❛r ❝♦♠M ♥ú❝❧❡♦s ❡N ❡❧étr♦♥s✱

❝♦♠ A ❡ B r❡♣r❡s❡♥t❛♥❞♦ ♦s ♥ú❝❧❡♦s ❛tô♠✐❝♦s ❡ i ❡j ♦s ❡❧étr♦♥s✳ ❆s

❞✐stâ♥❝✐❛s ❡♥✈♦❧✈✐❞❛s sã♦ r❡♣r❡s❡♥t❛❞❛s ♣♦r Rk ❡ rl✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾

✸✳✶ ❘❡♣r❡s❡♥t❛çã♦ ❡sq✉❡♠át✐❝❛ ❞❛s ✐♥t❡r❛çõ❡s ❡♥✈♦❧✈❡♥❞♦ ♦ ❝♦♠♣❧❡①♦ ❍2❖2 ✰ ●◆✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽ ✸✳✷ ❘❡♣r❡s❡♥t❛çã♦ ❡♠ ✸✲❉ ❞♦ s✐st❡♠❛ ❍2❖2 ✰ ●◆✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶ ✸✳✸ ❘❡♣r❡s❡♥t❛çã♦ ❡sq✉❡♠át✐❝❛ ♣❛r❛ ❛ ❛♥á❧✐s❡ ❞❡ γ1✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸ ✸✳✹ ❘❡♣r❡s❡♥t❛çã♦ ❡sq✉❡♠át✐❝❛ ♣❛r❛ ❛ ❛♥á❧✐s❡ ❞❡ γ2✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹

✹✳✶ ❈✉r✈❛ ❞❡ ❡♥❡r❣✐❛ ♣♦t❡♥❝✐❛❧ ♣❛r❛ ♦ s✐st❡♠❛ ❍2❖2 ✰ ❆r ❝♦♠R= 30 ➴✳

θ± r❡♣r❡s❡♥t❛ ♦s â♥❣✉❧♦s ❞❡ ❝♦♥✜❣✉r❛çã♦ ❞❡ ♠í♥✐♠❛ ❡♥❡r❣✐❛ ❡∆Vtrans ❡ ∆Vcis ❛s ❜❛rr❡✐r❛s ❡♥✈♦❧✈✐❞❛s ♥♦ ♣r♦❜❧❡♠❛ t♦r❝✐♦♥❛❧✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸ ✹✳✷ ❋✐❣✉r❛ r❡♣r❡s❡♥t❛t✐✈❛ ❞❛s ❣❡♦♠❡tr✐❛s ❞❡ ❡q✉✐❧í❜r✐♦ ❡①♣r❡ss❛s ♥❛ ❚❛❜❡❧❛

✹✳✸ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵ ✹✳✸ ❊♥❡r❣✐❛ ♣♦t❡♥❝✐❛❧ ❞♦ s✐st❡♠❛ ❍2❖2 ✰ ❳❡ ❝♦♠♦ ✉♠❛ ❢✉♥çã♦ ❞♦ â♥❣✉❧♦

α✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷

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✹✳✹ ❊♥❡r❣✐❛ ♣♦t❡♥❝✐❛❧ ❞♦ ❝♦♠♣❧❡①♦ ❍2❖2 ✰ ❳❡ ❝♦♠♦ ✉♠❛ ❢✉♥çã♦ ❞❛ ❞✐s✲ tâ♥❝✐❛ ✭❘✮ q✉❡ s❡♣❛r❛ ♦ ❳❡ ❞❛ ❧✐❣❛çã♦ ❖✲❖ ❞❛ ♠♦❧é❝✉❧❛ ❍2❖2✳ ◆❡st❡ ❝❛s♦✱ ♦ â♥❣✉❧♦ α ❢♦✐ ✜①❛❞♦ ❡♠ ✶✷✵✱ ✲✻✵ ❡ ✵ ❣r❛✉s ✭✈❡❥❛ ❞✐s❝✉ssã♦ ♥♦

t❡①t♦✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸ ✹✳✺ ❊♥❡r❣✐❛ ♣♦t❡♥❝✐❛❧ ❞♦s s✐st❡♠❛s ❍2❖2✲●◆ ❝♦♠♦ ✉♠❛ ❢✉♥çã♦ ❞♦ â♥❣✉❧♦

α✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹

✹✳✻ ❊♥❡r❣✐❛ ♣♦t❡♥❝✐❛❧ ❞♦s ❝♦♠♣❧❡①♦s ❍2❖2✲●◆ ❝♦♠♦ ✉♠❛ ❢✉♥çã♦ ❞❛ ❞✐s✲ tâ♥❝✐❛Rq✉❡ s❡♣❛r❛ ♦ ❣ás✲♥♦❜r❡ ❞♦ ❝❡♥tr♦ ❞❛ ❧✐❣❛çã♦ ❖✲❖ ❞❛ ♠♦❧é❝✉❧❛

❍2❖2✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺ ✹✳✼ Pr♦❥❡çã♦ ❞❛ ❙✉♣❡r❢í❝✐❡ ❞❡ ❊♥❡r❣✐❛ P♦t❡♥❝✐❛❧ ❞♦ s✐st❡♠❛ ❍2❖2 ✰ ❆r

❝♦♥s✐❞❡r❛♥❞♦ ❛ r❡❣✐ã♦ ❛ss✐♥tót✐❝❛ ❘ ❂ ✸✵ ➴ ✭r❡❣✐ã♦ ♦♥❞❡ ♦ ❣ás✲♥♦❜r❡ ❆r ♥ã♦ ✐♥t❡r❛❣❡ ❝♦♠ ❛ ♠♦❧é❝✉❧❛ ❍2❖2✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼ ✹✳✽ Pr♦❥❡çã♦ ❞❛ ❙✉♣❡r❢í❝✐❡ ❞❡ ❊♥❡r❣✐❛ P♦t❡♥❝✐❛❧ ❞♦ s✐st❡♠❛ ❍2❖2 ✰ ❆r

❝♦♥s✐❞❡r❛♥❞♦ α= 0o _{❡ ❘❂ ✷✳✵ ➴✱ ✷✳✹ ➴✱ ✷✳✽ ➴✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽} ✹✳✾ Pr♦❥❡çã♦ ❞❛ ❙✉♣❡r❢í❝✐❡ ❞❡ ❊♥❡r❣✐❛ P♦t❡♥❝✐❛❧ ❞♦ s✐st❡♠❛ ❍2❖2 ✰ ❆r

❝♦♥s✐❞❡r❛♥❞♦ α = 45o _{❡ ❘❂ ✷✳✹ ➴✱ ✷✳✻ ➴✱ ✸✳✵ ➴ ✭✈❡❥❛ ❞✐s❝✉ssã♦ ♥♦} t❡①t♦✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾ ✹✳✶✵ Pr♦❥❡çã♦ ❞❛ ❙✉♣❡r❢í❝✐❡ ❞❡ ❊♥❡r❣✐❛ P♦t❡♥❝✐❛❧ ❞♦ s✐st❡♠❛ ❍2❖2 ✰ ❆r

❝♦♥s✐❞❡r❛♥❞♦ α = 90o _{❡ ❘❂ ✷✳✷ ➴✱ ✷✳✹ ➴✱ ✷✳✻ ➴ ✭✈❡❥❛ ❞✐s❝✉ssã♦ ♥♦} t❡①t♦✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✵ ✹✳✶✶ ❊♥❡r❣✐❛ ♣♦t❡♥❝✐❛❧ ❞♦ ❝♦♠♣❧❡①♦ ❍2❖2 ✰ ❳❡ ❝♦♠♦ ✉♠❛ ❢✉♥çã♦ ❞♦ â♥✲

❣✉❧♦ φ ❝♦♥s✐❞❡r❛♥❞♦ ❛s ❣❡♦♠❡tr✐❛sR =Req ❡ θ = 113o✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶

✻✳✶ ❈✉r✈❛ ❞❡ ❡♥❡r❣✐❛ ♣♦t❡♥❝✐❛❧ ❞❡ ❱①❘ ♣❛r❛ ♦s ✹ ❡st❛❞♦s ❡①❝✐t❛❞♦s ❞♦ s✐st❡♠❛ ❍2❖2 ✰ ❍❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✹ ✻✳✷ ❈✉r✈❛ ❞❡ ❡♥❡r❣✐❛ ♣♦t❡♥❝✐❛❧ ❞❡ ❱①❘ ♣❛r❛ ♦s ✺ ❡st❛❞♦s ❡①❝✐t❛❞♦s ❞♦

s✐st❡♠❛ ❍2❖2 ✰ ◆❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✺ ✻✳✸ ❈✉r✈❛ ❞❡ ❡♥❡r❣✐❛ ♣♦t❡♥❝✐❛❧ ❞❡ ❱①❘ ♣❛r❛ ♦s ✹ ❡st❛❞♦s ❡①❝✐t❛❞♦s ❞♦

s✐st❡♠❛ ❍2❖2 ✰ ❆r✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✻

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✻✳✹ ❈✉r✈❛ ❞❡ ❡♥❡r❣✐❛ ♣♦t❡♥❝✐❛❧ ❞❡ ❱①❘ ♣❛r❛ ♦s ✺ ❡st❛❞♦s ❡①❝✐t❛❞♦s ❞♦ s✐st❡♠❛ ❍2❖2 ✰ ❑r✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✼

(13)

❈❛♣ít✉❧♦ ✶

■♥tr♦❞✉çã♦

❆ ♠♦❧é❝✉❧❛ ❞❡ ♣❡ró①✐❞♦ ❞❡ ❤✐❞r♦❣ê♥✐♦ ✭❍2❖2✮✱ ♦✉ á❣✉❛ ♦①✐❣❡♥❛❞❛ ❞❡s♣❡rt❛ ❛ ❝✉r✐♦s✐✲ ❞❛❞❡ ♣♦r ❞✐✈❡rs♦s ♠♦t✐✈♦s✱ s❡❥❛ ♣❡❧❛s ❛♣❧✐❝❛çõ❡s ❡♥❝♦♥tr❛❞❛s ♥❛ ❧✐t❡r❛t✉r❛ ♥♦ ❝❛♠♣♦ ❞❛ ❛str♦♥♦♠✐❛✱ ❢ís✐❝❛ ❛♣❧✐❝❛❞❛❬✶✱ ✷✱ ✸❪✱ ♠❡❞✐❝✐♥❛❬✶✱ ✹✱ ✺❪✱ ♦❞♦♥t♦❧♦❣✐❛❬✻❪✱ s❡❥❛ ♣♦r s✉❛s ♣❡❝✉❧✐❛r✐❞❛❞❡s ♠♦❧❡❝✉❧❛r❡s ❛♠♣❧❛♠❡♥t❡ ❡st✉❞❛❞❛s ❛♦ ❧♦♥❣♦ ❞♦s ú❧t✐♠♦s ❛♥♦s❬✼✱ ✽❪✳ ❆s ❛♠♣♦❧❛s ✉t✐❧✐③❛❞❛s ♣❡❧♦s ❞❡♥t✐st❛s ♣❛r❛ ❜r❛♥q✉❡❛♠❡♥t♦ ❞❡ ❞❡♥t❡s ✉t✐❧✐③❛♠ ❝♦♠♦ ♣r✐♥❝✐♣❛❧ ❝♦♠♣♦♥❡♥t❡ ❛ á❣✉❛ ♦①✐❣❡♥❛❞❛✳ ◆❛ ♠❡❞✐❝✐♥❛✱ ♦ ❍2❖2 é ✉s❛❞♦ ❝♦♠♦ ✉♠ ❛♥✲ t✐ssé♣t✐❝♦ ❡ ❡♠ ❡①❝❡ss♦ ♣♦❞❡ ❣❡r❛r sér✐❛s ❞♦❡♥ç❛s ❝♦♠♦ ♦ str❡ss r❡♥❛❧✳ ❱ár✐❛s r❡❛çõ❡s q✉í♠✐❝❛s ✉t✐❧✐③❛♠ ❛ ❡ss❛ ♠♦❧é❝✉❧❛ ♦✉ ❝♦♠♦ ❝❛t❛❧✐s❛❞♦r❛ ♦✉ ❝♦♠♦ ♣❛rt❡ ✐♥t❡❣r❛♥t❡ ❞♦ ♣r♦❝❡ss♦❬✾✱ ✶✵✱ ✶✶✱ ✶✷✱ ✶✸✱ ✶✹❪✳ ▼✉✐t♦s ❡st✉❞♦s t❡ór✐❝♦s ❡ ❡①♣❡r✐♠❡♥t❛✐s ❢♦r❛♠ ❢❡✐t♦s à r❡s♣❡✐t♦ ❛♣❡♥❛s ❞❛ ❍2❖2 ♣✉r♦✱ ♣♦ré♠ ♣♦✉❝♦ s❡ s❛❜❡ s♦❜r❡ ✐♥✢✉ê♥❝✐❛s ❡①t❡r♥❛s ❛ ❡ss❛ ♠♦❧é❝✉❧❛✱ ♣r✐❝✐♣❛❧♠❡♥t❡ ♥♦ q✉❡ t❛♥❣❡ à q✉✐r❛❧✐❞❛❞❡❬✷✱ ✼✱ ✶✺✱ ✶✻✱ ✶✼✱ ✶✽✱ ✶✾✱ ✷✵✱ ✷✶✱ ✷✷✱ ✷✸✱ ✷✹✱ ✷✺✱ ✷✻✱ ✷✼✱ ✷✽✱ ✷✾✱ ✸✵✱ ✸✶✱ ✸✷✱ ✸✸✱ ✸✹✱ ✸✺❪✱ ♣♦✐s ❡ss❛ é ❛ ♠♦❧é❝✉❧❛ ♠❛✐s s✐♠♣❧❡s q✉❡ ❛♣r❡s❡♥t❛ t❛❧ ❝♦♠♣♦rt❛♠❡♥t♦✳

➱ ✐♥t❡r❡ss❛♥t❡ ♦ ❡st✉❞♦ ❞❛ q✉✐r❛❧✐❞❛❞❡✱ ♣♦✐s ❡♠ ❞✐✈❡rs♦s ♣r♦❜❧❡♠❛s ❢ís✐❝♦s ❡ q✉í♠✐❝♦s é ♣❡r❝❡♣tí✈❡❧ q✉❡ ❛ ❛ss✐♠❡tr✐❛ ❞❛ ♠♦❧é❝✉❧❛ ♣♦❞❡ ❣❡r❛r ❡❢❡✐t♦s ❞✐❢❡r❡♥t❡s ❞❡♣❡♥❞❡♥❞♦ ❞♦ ❝♦♥t❡①t♦ ❛❜♦r❞❛❞♦❬✸✻✱ ✸✼✱ ✸✽❪✳ ❖ ❝♦♠♣♦st♦ ❧✐♠♦♥❡♥♦ é ✉♠ ❡①❡♠♣❧♦ ✐♥t❡r❡ss❛♥t❡ ❞❛ ✐♥✢✉ê♥❝✐❛ ❞❛ q✉✐r❛❧✐❞❛❞❡ s♦❜r❡ ❛❧❣✉♥s ♣r♦❝❡ss♦s q✉í♠✐❝♦s ❡ ❢ís✐❝♦s✳ ❊ss❡ ❝♦♠♣♦st♦ ♣♦ss✉✐ ✉♠ ❝❡♥tr♦ q✉✐r❛❧ ❡ ❜❛s✐❝❛♠❡♥t❡ ❞✉❛s r❛♠✐✜❝❛çõ❡s✳ ❊♠ ✉♠❛ ❞❡ss❛s r❛♠✐✜❝❛çõ❡s s❡ ❛ ❞✉♣❧❛ ❧✐❣❛çã♦ ❈❛r❜♦♥♦✲❈❛r❜♦♥♦ ✭❈❂❈✮ ❡st✐✈❡r ♣❛r❛ ✉♠ ❧❛❞♦ s❡ tr❛t❛ ❞♦ ❘✲❧✐♠♦♥❡♥♦✱ ♠❛s s❡ t✐✈❡r ❞♦ ♦✉tr♦ ❧❛❞♦ s❡ tr❛t❛ ❞♦ ❙✲❧✐♠♦♥❡♥♦

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✷

✭✈❡❥❛ ✜❣✉r❛✶✳✶✮✳ ❖ ♣r✐♠❡✐r♦ ♥♦s ❞á ♦ ❛r♦♠❛ ❞❡ ❧❛r❛♥❥❛✱ ❡♥q✉❛♥t♦ ♦ s❡❣✉♥❞♦ ♥♦s ❞á ♦ ❛r♦♠❛ ❞♦ ❧✐♠ã♦✳ ❇❛s❡❛♥❞♦✲s❡ ♥❡ss❛ ❢ór♠✉❧❛ é ♣♦ssí✈❡❧✱ ♣♦r ❡①❡♠♣❧♦✱ ♣r♦❞✉③✐r ✉♠ r❡❢r✐❣❡r❛♥t❡ ♦✉ s✉❝♦ ❝♦♠ ❛r♦♠❛ ❛rt✐✜❝✐❛❧ ❞❡ ❧❛r❛♥❥❛ ♦✉ ❧✐♠ã♦✱ ❡ssê♥❝✐❛s ♣❛r❛ ❛♠❡♥✐③❛r ♦ ❣♦st♦ r✉✐♠ ❞❡ ❞❡t❡r♠✐♥❛❞♦s ♠❡❞✐❝❛♠❡♥t♦s✱ ❞❡♥tr❡ ♦✉tr♦s✳ ❆♣❡s❛r ❞❡ ♣♦ss✉ír❡♠ ❛ ♠❡s♠❛ ❢ór♠✉❧❛ q✉í♠✐❝❛✱ ❣❡r❛♠ ❡❢❡✐t♦s s✉❜st❛♥❝✐❛❧♠❡♥t❡ ❞✐❢❡r❡♥t❡s✳

a)

b)

❋✐❣✉r❡ ✶✳✶✿ ✭❛✮ ❱✐sã♦ ♣❧❛♥❛r ❞❛s ♠♦❧é❝✉❧❛s ❘✲▲✐♠♦♥❡♥♦ ❡ ❙✲▲✐♠♦♥❡♥♦❀ ✭❜✮ ❱✐sã♦ ❡s♣❛❝✐❛❧ ❞❛

(15)

✸

❊ss❛ ❝✉r✐♦s❛ ♣r♦♣r✐❡❞❛❞❡ ❛♣❛r❡❝❡ t❛♠❜é♠ ♥♦ r❛♠♦ ❢❛r♠❛❝ê✉t✐❝♦✱ ♥♦ q✉❛❧ ❞✐✈❡rs♦s ♠❡❞✐❝❛♠❡♥t♦s sã♦ ❡❧❛❜♦r❛❞♦s ❛r❞✉❛♠❡♥t❡ r❡s♣❡✐t❛♥❞♦ ❡ss❛ ♣r♦♣r✐❡❞❛❞❡✱ ❣❡r❛♥❞♦ ❧✉❝r♦s ❛str♦♥ô♠✐❝♦s ♥❡ss❡ r❛♠♦ tã♦ ❝♦♠♣❡t✐t✐✈♦ ✭♣r✐♥❝í♣✐♦s ❛t✐✈♦s ❝♦♠♦ ❈❛♣t♦♣r✐❧✱ ■❜✉♣r♦❢❡♥♦ sã♦ ❣❡r❛❞♦s ✉t✐❧✐③❛♥❞♦ ❛ q✉✐r❛❧✐❞❛❞❡ ❞❡ ❝❡rt♦s ❝♦♠♣♦st♦s q✉í♠✐❝♦s✮❬✸✾❪✳ ◆❡ss❡ ♠❡✐♦✱ é ✐♥t❡r❡ss❛♥t❡ r❡ss❛❧t❛r q✉❡ q✉✐r❛❧✐❞❛❞❡ ❢♦✐ ♣r✐♠❡✐r❛♠❡♥t❡ ❝♦♠♣r❡❡♥❞✐❞❛ ♣❡❧♦ ❢❛♠♦s♦ q✉í♠✐❝♦ ❢r❛♥❝ês ▲♦✉✐s P❛st❡✉r q✉❡ ❝♦♥s❡❣✉✐✉ s❡♣❛r❛r ♠❛♥✉❛❧♠❡♥t❡ ❞✉❛s s✉❜stâ♥❝✐❛s q✉✐r❛✐s q✉❡ ❛♣❡s❛r ❞❡ ♣♦ss✉✐r❡♠ ❛ ♠❡s♠❛ ❢ór♠✉❧❛ q✉í♠✐❝❛ ❣❡r❛♠ ❡❢❡✐t♦s ❝♦♠♣❧❡t❛♠❡♥t❡ ❞✐❢❡r❡♥t❡s❬✸✾❪✳

(16)

✹

CHO

C

OH

CH2OH H

CHO

C

OH CH2OH H

a) b)

(17)

✺

❆♣❡s❛r ❞❡ ♦s ♣r♦❝❡ss♦s q✉í♠✐❝♦s ❡♥✈♦❧✈❡♥❞♦ q✉✐r❛❧✐❞❛❞❡ s❡r❡♠ ❛♠♣❧❛♠❡♥t❡ ✉t✐❧✐③❛❞♦s ❤♦❥❡✱ ♣♦✉❝♦ s❡ s❛❜❡ s♦❜r❡ ❛ ♣❛rt❡ ❢ís✐❝♦✲q✉í♠✐❝❛ ❞❡ss❛ ♣r♦♣r✐❡❞❛❞❡✳ ▼✉✐t♦ s❡ t❡♠ ❢❡✐t♦ ❡①♣❡r✐♠❡♥t❛❧♠❡♥t❡✱ ♣♦ré♠ ♣♦✉❝♦ s❡ ❡①♣❧✐❝❛ t❡♦r✐❝❛♠❡♥t❡ ♦s ❢❛t♦r❡s ❛ ❡❧❛ r❡❧❛❝✐♦♥❛❞♦s✳ ❇❛s❡❛♥❞♦✲s❡ ♥❡ss❡ ♣r❡ss✉♣♦st♦✱ ❝♦♥s✐❞❡r❛♠♦s ♥❡ss❡ tr❛❜❛❧❤♦ ❛ ♠♦❧é❝✉❧❛ ❞❡ ♣❡ró①✐❞♦ ❞❡ ❤✐❞r♦❣ê♥✐♦ q✉❡✱ ❝♦♠♦ ❡①♣♦st♦ ❛❝✐♠❛✱ é ❛ ♠♦❧é❝✉❧❛ ♠❛✐s s✐♠♣❧❡s q✉❡ ❡✈✐❞❡♥❝✐❛ ❛ q✉✐r❛❧✐❞❛❞❡ ❝♦♠♦ ✉♠❛ ❞❡ s✉❛s ♣r♦♣r✐❡❞❛❞❡s❬✸✾❪✳

❆ q✉✐r❛❧✐❞❛❞❡ ❞❡ ✉♠❛ ♠♦❧é❝✉❧❛ s❡ t♦r♥❛ ✐♥t❡r❡ss❛♥t❡ q✉❛♥❞♦ ❛♥❛❧✐s❛♠♦s ❛ ✐♥✢✉ê♥❝✐❛ ❞❡ ✉♠ ❛❣❡♥t❡ ❡①t❡r♥♦ s♦❜r❡ s✉❛ ❝♦♥❢♦r♠❛çã♦❬✽❪✳ ➱ ♥❡ss❡ ♣♦♥t♦ q✉❡ ❡st❡ tr❛❜❛❧❤♦ s❡ ❝♦♥❝❡♥tr♦✉ ❡ s❡ ❞❡s❡♥✈♦❧✈❡✉✳ ▼✉✐t♦s ❡st✉❞♦s ❢♦r❛♠ ❢❡✐t♦s s♦❜r❡ ♦ ❍2❖2 ♣✉r♦✱ ♣♦ré♠ ✐♥✢✉ê♥❝✐❛s ❡①t❡r♥❛s ❛ ❡❧❡ ♠✉✐t♦ ♣♦✉❝♦ s❡ ❡♥❝♦♥tr❛ ♥❛ ❧✐t❡r❛t✉r❛❬✶✺✱ ✶✻❪✳ ❆s ✐♥✢✉ê♥❝✐❛s ❡①t❡r♥❛s sã♦ ❢✉♥❞❛♠❡♥t❛✐s ♣❛r❛ ♣♦❞❡r ❛♥❛❧✐s❛r ♦ q✉❡ ❛❝♦♥t❡❝❡ ❝♦♠ ❧✐❣❛çõ❡s ❝♦✈❛❧❡♥t❡s ❡ ♥ã♦ ❝♦✈❛❧❡♥t❡s ❞❡ ✉♠ s✐st❡♠❛ ❡ ❝♦♠♦ ♦ ❛rr❛♥❥♦ ❞♦s ❡❧étr♦♥s ❡ ❞✐♣♦❧♦s sã♦ ♠♦❞✐✜❝❛❞♦s✳ ◆♦ ♥♦ss♦ ❝❛s♦✱ ❡♥t❡♥❞❡r ❝♦♠♦ s❡ ♣♦❞❡ ❛❧t❡r❛r✱ ♣r✐♥❝✐✲ ♣❛❧♠❡♥t❡ ❛ ❧✐❣❛çã♦ ❖✲❍ ❞❛ ♠♦❧é❝✉❧❛ é ❢✉♥❞❛♠❡♥t❛❧ ♣❛r❛ ✉♠ ♣r✐♠❡✐r♦ ♣❛ss♦ ♥❛ s✉❛ ❞❡s❝r✐çã♦ q✉✐r❛❧❬✼✱ ✶✺✱ ✶✻✱ ✷✹✱ ✷✺✱ ✸✶✱ ✸✸❪✳ ❉✐✈❡rs❛s ♦✉tr❛s ♠♦❧é❝✉❧❛s ♣♦ss✉❡♠ ❝❛r✲ ❛❝t❡ríst✐❝❛s s❡♠❡❧❤❛♥t❡s q✉❛♥t♦ ❛♦s ♣❛r❡s ❧✐❣❛❞♦s ❝♦♠♦ ❍2❙2✱ ❍4◆2✱ ❍3◆❖✱ ❍4P2 ❡ ♣♦❞❡♠ ❣❡r❛r ❞✐✈❡rs♦s ❡st✉❞♦s ✐♥t❡r❡ss❛♥t❡s ❝♦♠ ❝♦♥❝❧✉sõ❡s ♣♦✉❝♦ ❛❜♦r❞❛❞❛s ♥❛ ❧✐t❡r❛t✉r❛ ♥♦ â♠❜✐t♦ ❞♦ q✉❡ ❛❝✐♠❛ ❢♦✐ ❡①♣♦st♦❬✶✺✱ ✶✻❪✳

▼✉✐t❛s sã♦ ❛s ❢♦r♠❛s ❞❡ s❡ ❢❛③❡r ❛ ❛♥á❧✐s❡ ❞❡ t♦❞♦ ❡ss❡ ❝♦♥t❡①t♦ ❞♦ ♣♦♥t♦ ❞❡ ✈✐st❛ ❢ís✐❝♦✳ P♦ré♠✱ ✉♠ ❝❛♠✐♥❤♦ ❜❛st❛♥t❡ ✉t✐❧✐③❛❞♦ ❡♠ ❜♦❛ ♣❛rt❡ ❞❛s ♣❡sq✉✐s❛s é ♣♦r ♠❡✐♦ ❞♦ ❝á❧❝✉❧♦ ❛❜ ✐♥✐t✐♦❬✶✺✱ ✹✵❪✳ ➱ ♣♦ssí✈❡❧ ❛ss✐♠ s✐♠✉❧❛r t❡♦r✐❝❛♠❡♥t❡✱ ✈✐❛ ❝á❧❝✉❧♦s ❝♦♠♣✉t❛❝✐♦♥❛✐s✱ s✐t✉❛çõ❡s ♣ró①✐♠❛s ❞❛ r❡❛❧✐❞❛❞❡ ❞❡ ✐♥t❡r❛çã♦ ♠♦❧❡❝✉❧❛r ❞❡s❝r❡✈❡♥❞♦ ❝❛❞❛ s✐t✉❛çã♦ ❛❜♦r❞❛❞❛✳ ❆ ♣❛rt✐r ❞❡ss❡ ❝♦♥t❡①t♦✱ s❡ t♦r♥❛ ✈✐á✈❡❧ ❛ ❝♦♥str✉çã♦ ❞❡ ✉♠❛ ❙✉♣❡r❢í❝✐❡ ❞❡ ❊♥❡r❣✐❛ P♦t❡♥❝✐❛❧ ✭❙❊P✮✱ ♥❛ q✉❛❧ ✉♠❛ ❢♦r♠❛ ❛♥❛❧ít✐❝❛ ♣♦❞❡ ❞❡s❝r❡✈❡r ❞❡ ❢♦r♠❛ ❝♦❡s❛ ❡ ❝♦❡r❡♥t❡ ❛s ✐♥t❡r❛çõ❡s ❞♦ s✐st❡♠❛✳ ❈♦♠ ❡ss❛ ❞❡s❝r✐çã♦ ♠❛t❡♠át✐❝❛ t♦❞❛ ❛ ♣❛rt❡ ❡❧❡trô♥✐❝❛ ❡ ❞✐♥â♠✐❝❛ ❞♦ s✐st❡♠❛ ♣♦❞❡ s❡r ❞❡s❝r✐t❛ ❡ ❛♥❛❧✐s❛❞❛✳

(18)

✻

❣ás ♥♦❜r❡ s❡♠♣r❡ é ✐♥t❡r❡ss❛♥t❡ ❡♠ s✐st❡♠❛s ♦♥❞❡ s❡ q✉❡r ❛♥❛❧✐s❛r ❛ ❞❡♣❡♥❞ê♥❝✐❛ ❞❡ ❛❣❡♥t❡s ❡①t❡r♥♦s s❡♠ q✉❡ ♦ ♣r♦❝❡ss♦ ❝♦❧✐s✐♦♥❛❧ ❡st❡❥❛ ❡♥✈♦❧✈✐❞♦✳ ❈♦♠♦ ♦ ♣r♦❝❡ss♦ q✉❡ ❜✉s❝❛♠♦s ♥♦ tr❛❜❛❧❤♦ ♥ã♦ é r❡❛t✐✈♦✳ ❛s ✐♥t❡r❛çõ❡s sã♦ ❞❡ ❧♦♥❣♦ ❛❧❝❛♥❝❡ ♦✉ ❞♦ t✐♣♦ ✈❛♥ ❞❡r ❲❛❛❧s ✭✈❞❲✮✱ ❡♥tã♦ ❛ ❢♦r♠❛ ❛♥❛❧ít✐❝❛ ❞❡♥♦♠✐♥❛❞❛ ■♠♣r♦✈❡❞ ▲❡♥♥❛r❞ ❏♦♥❡s ✭■▲❏✮❬✹✶❪ ❛♣❛r❡❝❡ ❝♦♠ ✉♠❛ ❜♦❛ ❝❛♥❞✐❞❛t❛ ♣❛r❛ ❛❥✉st❛r ❛s ❡♥❡r❣✐❛s ❡❧❡trô♥✐❝❛s q✉❡ ❞❡s❝r❡✈❡♠ ❛s ✐♥t❡r❛çõ❡s ❞❡ss❡s s✐st❡♠❛s✳

✶✳✶ ❯♠❛ ❜r❡✈❡ ❍✐stór✐❛ ❡ ✐♠♣♦rtâ♥❝✐❛ ❞♦ ❈á❧❝✉❧♦ ❛❜ ✐♥✐t✐♦

P❛r❛ s❡ ❞❡s❝r❡✈❡r ✉♠ s✐st❡♠❛ ♠♦❧❡❝✉❧❛r r❡❛❧✱ ♠✉✐t❛s ✈❡③❡s s❡ ✉t✐❧✐③❛ r❡❢❡r❡♥❝✐❛✐s t❡ór✐❝♦s q✉❡ ❞❡s❝r❡✈❡♠ ❣❡♦♠❡tr✐❛s ❞❡ ❡q✉✐❧í❜r✐♦✱ ♣r♦♣r✐❡❞❛❞❡s t❡r♠♦❞✐♥â♠✐❝❛s✱ ♣r♦✲ ♣r✐❡❞❛❞❡s ❡s♣❡❝tr♦s❝ó♣✐❝❛s✱ r❡❛çõ❡s ❡①♦tér♠✐❝❛s ❡ ❡♥❞♦tér♠✐❝❛s✱ ❞❡♥tr❡ ♦✉tr♦s✳ ❚♦✲ ❞❛s ❡ss❛s ❝❛r❛❝t❡ríst✐❝❛s só ♣✉❞❡r❛♠ s❡r ❡❢❡t✐✈❛♠❡♥t❡ ❡st✉❞❛❞❛s ❝♦♠ ♦ ❛❞✈❡♥t♦ ❞♦ ❝á❧❝✉❧♦ ❝♦♠♣✉t❛❝✐♦♥❛❧ ❞❡ ▼❡❝â♥✐❝❛ ◗✉â♥t✐❝❛✱ ❝♦♠✉♠❡♥t❡ ❝♦♥❤❡❝✐❞♦s ❝♦♠♦ ❝á❧❝✉❧♦ ❛❜ ✐♥✐t✐♦✳

◆❛ ♣r✐♠❡✐r❛ ♠❡t❛❞❡ ❞♦ sé❝✉❧♦ ♣❛ss❛❞♦✱ ♣♦✉❝♦ s❡ s❛❜✐❛ à r❡s♣❡✐t♦ ❞❛ ♠❡❝â♥✐❝❛ q✉â♥t✐❝❛ ❞❡✈✐❞♦ ❛♦ ❢❛t♦ ❞❡ q✉❡ ❛ s♦❧✉çã♦ ❞❛ ❡q✉❛çã♦ ❞❡ ❙❝rö❞✐♥❣❡r ❡♠ ❣❡r❛❧ ♥ã♦ ❛♣r❡s❡♥t❛ s♦❧✉çã♦ ❛♥❛❧ít✐❝❛❬✹✷❪✳ P❛r❛ t❛♥t♦✱ ♠ét♦❞♦s ❝♦♠♣✉t❛❝✐♦♥❛✐s ❢♦r❛♠ ❞❡s❡♥✲ ✈♦❧✈✐❞♦s ❛ ✜♠ ❞❡ ❞❡s❝r❡✈❡r ♦s ♦r❜✐t❛✐s ♠♦❧❡❝✉❧❛r❡s ❞❡ ❢♦r♠❛ ❝♦❡s❛ ❡ q✉❡ ❢♦ss❡ ♦ ♠❛✐s ✜❡❧ ♣♦ssí✈❡❧ ♥❛ ❞❡s❝r✐çã♦ ❞♦s ♠❛✐s ❞✐✈❡rs♦s s✐st❡♠❛s ♠♦❧❡❝✉❧❛r❡s✳ ❖s ♣r✐♠❡✐r♦s ♣❛s✲ s♦s ♥❡ss❛ ❡♠♣r❡✐t❛❞❛ ❢♦r❛♠ ❥✉st❛♠❡♥t❡ ♦s ❡st✉❞♦s ♣r♦❜❛❜✐❧íst✐❝♦s ❞♦s s✐st❡♠❛s ✉t✐✲ ❧✐③❛♥❞♦ ❢✉♥çõ❡s q✉❡ ❞❡♣❡♥❞✐❛♠ ❞❡ ●❛✉ss✐❛♥❛s ❡ ♣♦❧✐♥ô♠✐♦s q✉❡ r❡♣r❡s❡♥t❛✈❛♠❬✹✸❪ ♦s ❡st❛❞♦s ❞♦s ❡❧étr♦♥s ♣❛r❛ ✉♠❛ ❞❡t❡r♠✐♥❛❞❛ ❝♦♥✜❣✉r❛çã♦ ♣ré✲❞❡t❡r♠✐♥❛❞❛✳ ➚ é♣♦❝❛✱ ❝♦♠♦ s❡ é s❛❜✐❞♦✱ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❝♦♠♣✉t❛❝✐♦♥❛❧ ♥ã♦ ❡st❛✈❛ ♥❛ ♠❡s♠❛ ♣r♦♣♦rçã♦ ❞♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❛ ▼❡❝â♥✐❝❛ ◗✉â♥t✐❝❛✳

(19)

✼

✉t✐❧✐③❛❞❛s ♣❛r❛ r❡♣r❡s❡♥t❛r ♦s ❡st❛❞♦s ❞♦s ❡❧étr♦♥s ❡r❛♠ t❛♠❜é♠ ❧✐♠✐t❛❞❛s✳ P♦r ✐ss♦✱ ❛ ♦t✐♠✐③❛çã♦ ❞❡ss❛s ❢✉♥çõ❡s ❞❡ t❛❧ ❢♦r♠❛ ❛ ❧❡✈❛r ❡♠ ❝♦♥s✐❞❡r❛çã♦ ♦ t❡♠♣♦ ❡ ♠❡♠ór✐❛ ❝♦♠♣✉t❛❝✐♦♥❛❧✳ ▲❡✈❛♥❞♦ ❡♠ ♦♥t❛ ❡ss❡ ❢❛t♦r✱ ❞✉r❛♥t❡ ♦s ❛♥♦s ✶✾✺✵ ❡ ✶✾✻✵✱ ❛ ❝♦♠❜✐♥❛çã♦ ❧✐♥❡❛r ❞❡ ♦r❜✐t❛✐s ❛tô♠✐❝♦s ✭❞♦ ✐♥❣❧ês✿ ▲✐♥❡❛r ❆t♦♠✐❝ ❖❜r✐t❛❧ ❈♦♠❜✐♥❛t✐♦♥ ✭▲❆❖❈✮✮❬✹✹❪ ❢♦✐ ❛♠♣❧❛♠❡♥t❡ ✉t✐❧✐③❛❞❛ ❡ s❡r✈✐✉ ❞❡ ♣r❡ss✉♣♦st♦ ♣❛r❛ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ ❢✉♥çõ❡s ♠❛✐s ❝♦♠♣❧❡①❛s ♣❛r❛ s✐st❡♠❛s ♠♦❧❡❝✉❧❛r❡s ❝❛❞❛ ✈❡③ ♠❛✐s ❝♦♠♣❧❡①♦s✳ ◆❡ss❡ ♣❡rí♦❞♦✱ ❛ ❋ís✐❝❛ ❡ ◗✉í♠✐❝❛ ❡①♣❡r✐♠❡♥t❛❧ s❡r✈✐r❛♠ ❞❡ s✉✲ ♣♦rt❡ ♣❛r❛ t❛❧ ✜♠✱ ♣♦✐s ✈ár✐❛s ❝♦♥st❛♥t❡s ❞❡ ❞✐✈❡rs♦s s✐st❡♠❛s ❢♦r❛♠ ❞❡t❡r♠✐♥❛❞♦s ❡ ✐♥❝r❡♠❡♥t❛❞♦s ♥❡ss❡s ❝á❧❝✉❧♦s ❝♦♠♣✉t❛❝✐♦♥❛✐s✱ t♦r♥❛♥❞♦ ❛ ✈❡r❛❝✐❞❛❞❡ ❞♦s ❝á❧❝✉❧♦s t❡ór✐❝♦s ❝❛❞❛ ✈❡③ ♠❛✐s ❛✢♦r❛❞♦s✳

(20)

❈❛♣ít✉❧♦ ✷

❆ ❋✉♥❞❛♠❡♥t❛çã♦ ❚❡ór✐❝❛

✷✳✶ ❖ Pr♦❜❧❡♠❛ ▼♦❧❡❝✉❧❛r

P❛r❛ tr❛t❛r q✉❛♥t✐❝❛♠❡♥t❡ ✉♠ s✐st❡♠❛ ♠♦❧❡❝✉❧❛r ❝♦♥st✐t✉í❞♦ ♣♦rM ♥ú❝❧❡♦s ✭r❡♣r❡✲

s❡♥t❛❞♦s ♣♦r A ❡ B ♥❛ ❋✐❣✉r❛ ✷✳✶✮ ❡ ◆ ❡❧étr♦♥s ✭r❡♣r❡s❡♥t❛❞♦s ♣♦r i ❡ j ♥❛ ✜❣✉r❛

✷✳✶✮✱ ❞❡✜♥✐♠♦s ♦ s❡❣✉✐♥t❡ ❤❛♠✐❧t♦♥✐❛♥♦ s❡♠ s♣✐♥ ❡ ❝♦rr❡çõ❡s r❡❧❛t✐✈íst✐❝❛s✿

ˆ

H =₋ ~ 2me

N

X

i=1 ∇2i −

M

X

A=1 ~2 2MA∇

2 A− M X A=1 N X i=1

ZAe2

rAi

+

M−1 X

A=1 M

X

B>A

ZAZB

RAB

+

N−1 X i=1 N X j>i e2 rij . ✭✷✳✶✮ ❊ss❡ ♦♣❡r❛❞♦r ❧❡✈❛ ❡♠ ❝♦♥s✐❞❡r❛çã♦ ❛❧❣✉♥s ♣❛râ♠❡tr♦s✿ RA ❂|R~A−R~B|✱

rAi ❂|~rA−~ri |✱ rij ❂|~ri−~rj |✱me é ❛ ♠❛ss❛ ❞♦ ❡❧étr♦♥✱ MA é ❛ ♠❛ss❛ ❞♦ ♥ú❝❧❡♦ ❆✱ e é ❛ ❝❛r❣❛ ❡❧❡♠❡♥t❛r ❞♦ ❡❧étr♦♥✱ ZA ❡ ZB sã♦ ❛ ❝❛r❣❛ ❞♦s ♥ú❝❧❡♦sA ❡ B✱ ~ é ❛ ❝♦♥st❛♥t❡ ❞❡ P❧❛♥❝❦ r❡❞✉③✐❞❛ ✭~₌_h/₂_π✮✳

P♦r ♠♦t✐✈♦s ❞❡ s✐♠♣❧✐✜❝❛çã♦ é ♠❛✐s ❝♦♥✈❡♥✐❡♥t❡ tr❛❜❛❧❤❛r ❝♦♠ ♦ ❍❛♠✐❧✲ t♦♥✐❛♥♦ ❞♦ s✐st❡♠❛ ❡♠ ✉♥✐❞❛❞❡s ❛tô♠✐❝❛s✳ P❛r❛ t❛♥t♦✱ ✉s❛✲s❡ ~ ❂ _m_e ❂ _e ❂ ✶✱ r❡❡s❝r❡✈❡♥❞♦ ♦ ❍❛♠✐❧t♦♥✐❛♥♦ ♣♦❞❡ s❡r ❡s❝r✐t♦ ❞❛ s❡❣✉✐♥t❡ ❢♦r♠❛✿

ˆ

H =₋1 2 N X i=1 ∇2 i − M X A=1 1 2MA∇

2 A− M X A=1 N X i=1 ZA rAi +

M−1 X

A=1 M

X

B>A

ZAZB

RAB

+

(21)

✾

A

B

i

j

= −

= − = −

= −

y z

x

O

❋✐❣✉r❡ ✷✳✶✿ ❘❡♣r❡s❡♥t❛çã♦ ❞❡ ✉♠ s✐st❡♠❛ ♠♦❧❡❝✉❧❛r ❝♦♠ M ♥ú❝❧❡♦s ❡ N ❡❧étr♦♥s✱

❝♦♠ A ❡ B r❡♣r❡s❡♥t❛♥❞♦ ♦s ♥ú❝❧❡♦s ❛tô♠✐❝♦s ❡ i ❡ j ♦s ❡❧étr♦♥s✳ ❆s ❞✐stâ♥❝✐❛s

❡♥✈♦❧✈✐❞❛s sã♦ r❡♣r❡s❡♥t❛❞❛s ♣♦rRk ❡ rl✳

◆❛ ❡q✉❛çã♦ ✭✷✳✷✮✱ ♦s t❡r♠♦s ✭❞❛ ❡sq✉❡r❞❛ ♣❛r❛ ❛ ❞✐r❡✐t❛✮ r❡♣r❡s❡♥t❛♠ ❛ ❡♥❡r❣✐❛ ❝✐♥ét✐❝❛ ❞♦s ❡❧étr♦♥s✱ ❡♥❡r❣✐❛ ❝✐♥ét✐❝❛ ❞♦s ♥ú❝❧❡♦s✱ ❡♥❡r❣✐❛ ♣♦t❡♥❝✐❛❧ ❡♥tr❡ ❡❧étr♦♥s ❡ ♥ú❝❧❡♦s✱ ❡♥❡r❣✐❛ ♣♦t❡♥❝✐❛❧ ❡♥tr❡ ♦s ♥ú❝❧❡♦s ❡ ❡♥❡r❣✐❛ ♣♦t❡♥❝✐❛❧ ❡♥tr❡ ♦s ❡❧étr♦♥s✳

(22)

✶✵

✷✳✷ ❆ ❆♣r♦①✐♠❛çã♦ ❞❡ ❇♦r♥✲❖♣♣❡♥❤❡✐♠❡r ✭❆❇❖✮

❈♦♠♦ s❡ s❛❜❡✱ ❛ ♠❛ss❛ ❞♦s ♥ú❝❧❡♦s é ♠✉✐t♦ s✉♣❡r✐♦r à ❞♦s ❡❧étr♦♥s ✭me ≈ ₁₈₄₀1 mN✮✳ ❇❛s❡❛♥❞♦✲s❡ ♥❡ss❡ ❢❛t♦✱ é q✉❡ ❛ ❆❇❖ s❡ ❝♦♥❝❡♥tr❛ ❡ t♦r♥❛ ♦s ❝á❧❝✉❧♦s ❝♦♠♣✉t❛✲ ❝✐♦♥❛✐s ✈✐á✈❡✐s ❡ ❧❛r❣❛♠❡♥t❡ ✉t✐❧✐③❛❞♦s✳ ❆ ✐♥ér❝✐❛ ❞♦ ♥ú❝❧❡♦ é ♠✉✐t♦ ♠❛✐♦r q✉❡ ❛ ❞♦s ❡❧étr♦♥s✱ ❞❡✈✐❞♦ ❡①❛t❛♠❡♥t❡ ❛♦ ❜❛❧❛♥ç♦ ❞❡ ♠❛ss❛s✳ P♦rt❛♥t♦✱ é ♣❧❛✉sí✈❡❧ ❝♦♥s✐❞❡r❛r q✉❡ ♦ ♠♦✈✐♠❡♥t♦ ❞♦s ♥ú❝❧❡♦s é ♥❡❣❧✐❣❡♥❝✐á✈❡❧ q✉❛♥❞♦ ❝♦♠♣❛r❛❞♦ ❛♦ ♠♦✈✐♠❡♥t♦ ❞♦s ❡❧étr♦♥s❬✺✷❪✳ P♦r ❡ss❡ ♠♦t✐✈♦✱ s❡ ♣♦❞❡ ❞❡s❝♦♥s✐❞❡r❛r ♦s t❡r♠♦s q✉❡ ❧❡✈❛♠ ❡♠ ❝♦♥✲ s✐❞❡r❛çã♦ ❛ ❝✐♥ét✐❝❛ ♥✉❝❧❡❛r❬✺✸❪✳ ❆ ❡q✉❛çã♦ ❞❡ ❙❝❤rö❞✐♥❣❡r ♣♦❞❡ s❡r ❡♥tã♦ r❡s♦❧✈✐❞❛ ✉s❛♥❞♦ ❛ s❡❣✉✐♥t❡ ❡①♣❛♥sã♦ ❛❞✐❛❜át✐❝❛✿

ψ(r, R) =φ(r;R)χ(R), ✭✷✳✸✮

♦♥❞❡ φ(r;R) r❡♣r❡s❡♥t❛ ❛ ❢✉♥çã♦ ❞❡ ♦♥❞❛ ❡❧❡trô♥✐❝❛✱ q✉❡ ❞❡♣❡♥❞❡ ❞❛s ❝♦✲ ♦r❞❡♥❛❞❛s ❞♦s ❡❧étr♦♥s ✭r✮ ❡ ♣❛r❛♠❡tr✐❝❛♠❡♥t❡ ❞❛s ❝♦♦r❞❡♥❛❞❛s ♥✉❝❧❡❛r❡s ✭❘✮✱ ❡♥✲ q✉❛♥t♦ χ(R) ❞❡♣❡♥❞❡ s♦♠❡♥t❡ ❞❛s ❝♦♦r❞❡♥❛❞❛s ♥✉❝❧❡❛r❡s✳ ❆ss✐♠✱ ❛ ❡q✉❛çã♦ ❞❡ ❙❝❤rö❞✐♥❣❡r t♦t❛❧ ♣♦❞❡ s❡r ❡s❝r✐t❛ ❝♦♠♦✿

"

−1₂ N

X

i=1 ∇2i −

M

X

A=1 1 2MA∇

2 A− M X A=1 N X i=1 ZA rAi +

M−1 X

A=1 M

X

B>A

ZAZB

RAB

+

N−1 X i=1 N X j>i 1 rij #

φ(r;R)χ(R)

=Eφ(r;R)χ(R), ✭✷✳✹✮

r❡❡s❝r❡✈❡♥❞♦ ❛ ❡q✉❛çã♦ ✭✷✳✹✮✱ t❡♠♦s✿

−1₂ N

X

i=1

∇2iφ(r;R)χ(R)− M

X

A=1 1 2MA∇

2

Aφ(r;R)χ(R)− M X A=1 N X i=1 ZA rAi

φ(r;R)χ(R)+

M−1 X

A=1 M

X

B>A

ZAZB

RAB

φ(r;R)χ(R) +

N−1 X i=1 N X j>i 1 rij

φ(r;R)χ(R) = Eφ(r;R)χ(R). ✭✷✳✺✮

❉❡s❡♥✈♦❧✈❡♥❞♦ ♦ t❡r♠♦ ∇2

(23)

✶✶

∇2Aφ(r;R)χ(R) =∇A2 (φ(r;R))χ(R)+∇2A(χ(R))φ(r;R)+2.∇A(φ(r;R)).∇A(χ(R)). ✭✷✳✻✮ ❈♦♠♦ ❛ ❢✉♥çã♦ ❞❡ ♦♥❞❛ ❡❧❡trô♥✐❝❛ ❞❡♣❡♥❞❡ ❛❞✐❛❜❛t✐❝❛♠❡♥t❡ ❞❛s ❝♦♦r❞❡✲ ♥❛❞❛s ♥✉❝❧❡❛r❡s✱ ❡♥tã♦ ♦ ♣r✐♠❡✐r♦ ❡ ♦ t❡r❝❡✐r♦ t❡r♠♦ ❞❛ ❡q✉❛çã♦ ✭✷✳✾✮ ♣♦❞❡♠ s❡r ❞❡s♣r❡③❛❞♦s✳ ❈♦♠ ✐ss♦ é ♣♦ssí✈❡❧ ❞❡s❛❝♦♣❧❛r ❛ ❡q✉❛çã♦ ❞❡ ❙❝❤rö❞✐♥❣❡r ♦r✐❣✐♥❛❧ ❡♠ ❞✉❛s ♦✉tr❛s✿ ✉♠❛ ❡❧❡trô♥✐❝❛ ❞❛❞❛ ♣♦r

−₂_φ₍_r1_;_R₎ N

X

i=1

∇2iφ(r;R) + M X A=1 N X i=1 ZA rAi +

N−1 X i=1 N X j>i 1 rij

=₋ǫ(R), ✭✷✳✼✮

❡ ✉♠❛ ♥✉❝❧❡❛r ❞❛❞❛ ♣♦r

E+ 1

χ(R)

M

X

A=1 1 2MA∇

2

Aχ(R) + M−1

X

A=1 M

X

B>A

ZAZB

RAB

=₋ǫ(R). ✭✷✳✽✮

❊ss❡ ❞❡s❛❝♦♣❧❛♠❡♥t♦ é ❝♦♥❤❡❝✐❞♦ ❝♦♠ ❛ ❆❇❖✳ ➱ ✐♠♣♦rt❛♥t❡ r❡ss❛❧t❛r q✉❡✱ ❞❡♥tr♦ ❞❛ ❆❇❖✱ ❛ ❡q✉❛çã♦ ♥✉❝❧❡❛r só ♣♦❞❡ s❡r r❡s♦❧✈✐❞❛ s❡ ❝♦♥❤❡❝❡r♠♦s ❛s s♦❧✉çõ❡s ❞❛ ❡q✉❛çã♦ ❞❡ ❙❝❤rö❞✐♥❣❡r ❡❧❡trô♥✐❝❛ ♣❛r❛ ✉♠ ❛♠♣❧♦ r❡♣r❡s❡♥t❛t✐✈♦ ❝♦♥❥✉♥t♦ ❞❡ ❝♦♥✜❣✉r❛çõ❡s ♥✉❝❧❡❛r❡s✳

◆✉♠❡r✐❝❛♠❡♥t❡✱ t♦r♥❛✲s❡ ✈✐á✈❡❧ ❛ s♦❧✉çã♦ ❞❛ ♣❛rt❡ ❡❧❡trô♥✐❝❛ ❝♦♠ ❛ ♦❜t❡♥çã♦ ❞♦ t❡r♠♦ ǫ(R) ❡ ❛ ♣❛rt✐r ❞❡ ❡♥tã♦ ❛ s✉❜st✐t✉✐çã♦ ❞❡ss❡ t❡r♠♦ ♥❛ ♣❛rt❡ ♥✉❝❧❡❛r ♣❛r❛ ❛ ❞❡s❝r✐çã♦ ❝♦♠♣❧❡t❛ ❞♦ s✐st❡♠❛ ❬✺✸❪✳ ❆ ❡q✉❛çã♦ ♥✉❝❧❡❛r ❛✐♥❞❛ ♣♦❞❡ s❡r ❡s❝r✐t❛ ❞❛ s❡❣✉✐♥t❡ ❢♦r♠❛✿      

−_χ₍1_R₎ M

X

A=1 1 2MA∇

2

Aχ(R)−

X

z }| {

M−1 X

A=1 M

X

B>A

ZAZB

RAB

+ǫ(R)

| {z }

V(R)

     

χ(R) =E(R)χ(R). ✭✷✳✾✮

♦✉✱ ❝♦♠♦ ♣❛r❛ ❝❛❞❛ ❝♦♥✜❣✉r❛çã♦ ♥✉❝❧❡❛r é s✐♠♣❧❡s ❞❡ s❡ ❝❛❧❝✉❧❛r ♦ t❡r♠♦

(24)

✶✷

− M

X

A=1 1 2MA∇

2

Aχ(R) +V(R)χ(R) = Eχ(R), ✭✷✳✶✵✮ ♦♥❞❡ V(R) é ❝♦♥❤❡❝✐❞♦ ❝♦♠♦ ♣♦t❡♥❝✐❛❧ ❡❢❡t✐✈♦ ✭q✉❡ r❡♣r❡s❡♥t❛ ❛ ❙❊P ❞♦ s✐st❡♠❛ ♠♦❧❡❝✉❧❛r✮✱ q✉❡ r❡♣r❡s❡♥t❛ t♦❞♦ ♦ ♣♦t❡♥❝✐❛❧ ❛♦ q✉❛❧ ♦ ♥ú❝❧❡♦ ❞❡ ❢❛t♦ ❡stá s✉❜♠❡t✐❞♦✳ ❆ s❡❣✉✐r✱ ❞❡s❝r❡✈❡♠♦s ♦s ♠ét♦❞♦s ✉s❛❞♦s ♥❡ss❡ tr❛❜❛❧❤♦ ♣❛r❛ r❡s♦❧✈❡r ❛ ❡q✉❛çã♦ ❞❡ ❙❝❤rö❞✐♥❣❡r ❡❧❡trô♥✐❝❛✳

✷✳✸ ❖ ▼ét♦❞♦ ❍❛rtr❡❡✲❋♦❝❦

P❛r❛ r❡s♦❧✈❡r ❛ ❡q✉❛çã♦ ❞❡ ❙❝❤rö❞✐♥❣❡r ❡❧❡trô♥✐❝❛✱ ❞❡✈❡♠♦s ✉s❛r ♠ét♦❞♦s ♥✉♠ér✐❝♦s ❡✜❝❛③❡s✱ ♣♦✐s é ♣r❛t✐❝❛♠❡♥t❡ ✐♠♣♦ssí✈❡❧ r❡s♦❧✈❡r ❛♥❛❧✐t✐❝❛♠❡♥t❡ ❡ss❛ ❡q✉❛çã♦✳ P❛r❛ t❛♥t♦✱ ♥♦ sé❝✉❧♦ ♣❛ss❛❞♦ ❛ ❝♦♠✉♥✐❞❛❞❡ ❝✐❡♥tí✜❝❛ ❝♦♥❝❡♥tr♦✉ ❡s❢♦rç♦s ❡♠ ❡st✉❞♦s ❞❡ ♠ét♦❞♦s ❝♦♠♣✉t❛❝✐♦♥❛✐s q✉❡ ♣❡r♠✐t✐ss❡♠ ❛s s♦❧✉çõ❡s ❞❡ t❛✐s ❡q✉❛çõ❡s✳ ❈♦♠♦ r❡s✉❧✲ t❛❞♦ ❞❡ss❡s ❡s❢♦rç♦s✱ s✉r❣✐✉ ♦ ✐♠♣♦rt❛♥t❡ ♠ét♦❞♦ ❞❡♥♦♠✐♥❛❞♦ ❍❛rtr❡❡ ❡ ❋♦❝❦❬✺✸❪✳ P❛r❛ ❞❡s❝r❡✈❡r ❡ss❡ ♠ét♦❞♦✱ ♣r✐♠❡✐r❛♠❡♥t❡ ❞❡✜♥❡✲s❡ ❛ ❢✉♥çã♦ ❞❡ ♦♥❞❛ ❡❧❡trô♥✐❝❛ ♣❛r❛ ◆ ❡❧étr♦♥s ♣❡❧♦ s❡❣✉✐♥t❡ ♣r♦❞✉t♦✿

ψ(r1, r2, ..., rN) = N

Y

i=1

Φi(ri), ✭✷✳✶✶✮

q✉❡ r❡♣r❡s❡♥t❛ ♦ ♣r♦❞✉t♦ ❞❡ ❢✉♥çõ❡s ❞❡ ✶✲❡❧étr♦♥ ♦✉ ♦r❜✐t❛✐s ♠♦❧❡❝✉❧❛r❡s✱ ❝♦♠✉♠❡♥t❡ ❝♦♥❤❡❝✐❞❛ ❝♦♠♦ ♣r♦❞✉t♦ ❞❡ ❍❛rtr❡❡✳ P♦ré♠✱ ❡ss❛ ❡q✉❛çã♦ ❢❡r❡ ✉♠ ❞♦s ♣r✐♥❝í♣✐♦s ❞❛ ♠❡❝â♥✐❝❛ q✉â♥t✐❝❛✱ ♣♦✐s ❡❧❛ ❝♦♥s✐❞❡r❛ q✉❡ ♦ ❡❧étr♦♥s ♥ã♦ sã♦ ✐♥❞✐s✲ t✐♥❣✉í✈❡✐s ✭Pr✐♥❝í♣✐♦ ❞❡ ❊①❝❧✉sã♦ ❞❡ P❛✉❧✐✮✳ ❆ss✐♠✱ é ♥❡❝❡ssár✐♦ ❝♦rr✐❣✐✲❧❛ ❧❡✈❛♥❞♦ ❡♠ ❝♦♥t❛ ♥ã♦ ♦ ♣r♦❞✉tór✐♦ ❞❛s ❢✉♥çõ❡s ♣✉r❛♠❡♥t❡✱ ♠❛s ❧❡✈❛♥❞♦ ❡♠ ❝♦♥s✐❞❡r❛çã♦ ♦ ♣r♦❞✉tór✐♦ ❞❛s ❝♦♠❜✐♥❛çõ❡s✳ ❙❡ ❝♦♥s✐❞❡ráss❡♠♦s ❞♦✐s ❡❧étr♦♥s✱ ❝♦♠♦ ♣♦r ❡①❡♠♣❧♦ ✉♠ s✐st❡♠❛ ❝♦♠ ♦ ❣ás ❤é❧✐♦ ♣✉r♦✱ ♦ ❝❡rt♦ s❡r✐❛ r❡♣r❡s❡♥t❛r ❛ ❢✉♥çã♦ ❞❡ ♦♥❞❛ ❞❛ s❡❣✉✐♥t❡ ❢♦r♠❛✿

(25)

✶✸

❆ss✐♠✱ ♦ Pr✐♥❝í♣✐♦ ❞❡ ❊①❝❧✉sã♦ ❞❡ P❛✉❧✐ é ❧❡✈❛❞♦ ❡♠ ❝♦♥s✐❞❡r❛çã♦ ❡ ❛ ❞❡✲ s❝r✐çã♦ ❞❛ ❢✉♥çã♦ ❞❡ ♦♥❞❛ ❡stá q✉❛s❡ q✉❡ ♣❡r❢❡✐t❛♠❡♥t❡ ❡①♣❧✐❝✐t❛❞❛✳ P❛r❛ ❞❡s❝r❡✈❡r ❝♦♠♣❧❡t❛♠❡♥t❡ ♦ s✐st❡♠❛ ❞♦ ♣♦♥t♦ ❞❡ ✈✐st❛ q✉â♥t✐❝♦ ❛✐♥❞❛ ❢❛❧t❛ ❝♦♥s✐❞❡r❛r ♦sspins

❞♦s ❡❧étr♦♥s✳ ❖spin❞♦ ❡❧étr♦♥ ♣♦❞❡ s❡r ❞♦ t✐♣♦up♦✉down❝♦♠♦ ❜❡♠ ❝♦♥❤❡❝✐❞♦ ♥❛

❢ís✐❝❛ ❡ ♥❛ q✉í♠✐❝❛✳ P❛r❛ r❡♣r❡s❡♥t❛r ♦ s♣✐♥ ✉♣ ✉t✐❧✐③❛♠♦s α(ω) ❡ ♣❛r❛ r❡♣r❡s❡♥t❛r ♦ s♣✐♥ ❞♦✇♥ ✉t✐❧✐③❛♠♦sβ(ω)✳ ❈♦♠ ✐ss♦✱ ❛ ❡q✉❛çã♦ ✭✷✳✷✶✮ ♣♦❞❡ s❡r ❡s❝r✐t❛ ❝♦♠♦✿

ψ(x1, x2) = τ1(x1)τ2(x2)−τ1(x2)τ2(x1), ✭✷✳✶✸✮ ♦♥❞❡✿

τ1(x1) = Φ1(r1)α(ω) ✭✷✳✶✹✮

❡

τ2(x2) = Φ2(r2)β(ω). ✭✷✳✶✺✮

❊ss❛ ❢♦r♠❛ ❞❡ ❡①♣r❡ss❛r ❛ ❢✉♥çã♦ ❞❡ ♦♥❞❛ ❣❡r❛ ❞✉❛s ❝♦♥❝❧✉sõ❡s✿ ♠❛✐s q✉❡ ❞♦✐s ❡❧étr♦♥s ♥ã♦ ♣♦❞❡♠ ♦❝✉♣❛r ♦ ♠❡s♠♦ ♦r❜✐t❛❧ ❡ ♦s ❡❧étr♦♥s ♥✉♥❝❛ ♣♦❞❡♠ t❡r ♥ú♠❡r♦s q✉â♥t✐❝♦s ✐❞ê♥t✐❝♦s ✭♣r✐♥❝í♣✐♦ ❞❛ ❡①❝❧✉sã♦ ❞❡ P❛✉❧✐✮✱ ♦ q✉❡ ❝♦♥❞✐③ ❝♦♠ t♦❞♦s ♦s ♣r✐♥❝í♣✐♦s ❞❛ ♠❡❝â♥✐❝❛ q✉â♥t✐❝❛✳ ➱ ✐♥t❡r❡ss❛♥t❡ ♥♦t❛r q✉❡ ❜❛s✐❝❛♠❡♥t❡ ❛s ❢✉♥çõ❡s ❞♦ ♦♥❞❛ ❡stã♦ s❡♥❞♦ ❡①♣r❡ss❛s ❝♦♠♦ s❡♥❞♦ ✉♠❛ s♦♠❛ ❞♦ ♣r♦❞✉t♦ ❞❡ ❢✉♥çõ❡s ❛♥t✐ss✐♠étr✐❝❛s✳ ❆ss✐♠✱ ❣❡♥❡r❛❧✐③❛♥❞♦ t♦❞❛ ❛ ❞✐s❝✉ssã♦ ❛♥t❡r✐♦r✱ ❛ r❡♣r❡s❡♥t❛çã♦ ❞❡ss❛s ❢✉♥çõ❡s ❛♥t✐ss✐♠étr✐❝❛s t❡r❡♠♦s✿

ψ(x1, x2, ..., xN) = N

Y

i=1

A_{τi(xi)}, ✭✷✳✶✻✮

(26)

✶✹

ψ(x1, x2, x3) = τ1(x1)τ2(x2)τ3(x3)−τ1(x2)τ2(x1)τ3(x3) +τ1(x2)τ2(x3)τ3(x1)

−τ1(x1)τ2(x3)τ3(x2) +τ1(x3)τ2(x1)τ3(x2)−τ1(x3)τ2(x2)τ3(x1) ✭✷✳✶✼✮

P❛r❛ N ❡❧étr♦♥s✿

ψ(x1, x2, x3, ..., xN) =

τ1(x1) τ2(x1) τ3(x1) · · · τN(x1)

τ1(x2) τ2(x2) τ3(x2) · · · τN(x2)

τ1(x3) τ2(x3) τ3(x3) · · · τN(x3)

✳✳✳ ✳✳✳ ✳✳✳ ✳✳✳ ✳✳✳

τ1(xN) τ2(xN) τ3(xN) · · · τN(xN)

P♦ré♠✱ ❡ss❡ ❞❡t❡r♠✐♥❛♥t❡ ❛✐♥❞❛ ♥ã♦ ❡stá ♥♦r♠❛❧✐③❛❞♦✳ P❛r❛ t❛♥t♦ é ♥❡❝❡ssár✐♦ ♠✉❧t✐♣❧✐❝❛r ♣♦r1/√N!✳ ❊ss❡ ❞❡t❡r♠✐♥❛♥t❡ é ❝♦♥❤❡❝✐❞♦ ❝♦♠♦ ❞❡t❡r♠✐♥❛♥t❡ ❞❡ ❙❧❛t❡r ✭❉❙✮✿

ψ(x1, x2, x3, ..., xN) =

1 √ N!

τ1(x1) τ2(x1) τ3(x1) · · · τN(x1)

τ1(x2) τ2(x2) τ3(x2) · · · τN(x2)

τ1(x3) τ2(x3) τ3(x3) · · · τN(x3)

✳✳✳ ✳✳✳ ✳✳✳ ✳✳✳ ✳✳✳

τ1(xN) τ2(xN) τ3(xN) · · · τN(xN)

❉❡ ❢♦r♠❛ s✉s❝✐♥t❛✱ ❡s❝r❡✈❡♠♦s✿

ψDS(x1, x2, x3, ..., xN) = A{ N

Y

i=1

τi(xi)}, ✭✷✳✶✽✮

♦♥❞❡✿ τi(xi) = Φi(ri)α(ω) ♦✉Φi(ri)β(ω)✱Φi(ri) = PN_j₌₁basescijΦij(ri)✳

❯s❛♥❞♦ ♦ ♠ét♦❞♦ ✈❛r✐❛❝✐♦♥❛❧ ❡ ❛s ❢✉♥çõ❡s ❞❡t❡r♠✐♥❛♥t❛✐s ✭❞❡t❡r♠✐♥❛♥t❡s ❞❡ ❙❧❛t❡r✮✱ ♣♦❞❡♠♦s ❝❤❡❣❛r ♥❛ s❡❣✉✐♥t❡ ❡q✉❛çã♦ ❞❡ ❍❛rtr❡❡✲❋♦❝❦ ❘❡str✐t♦✿

(27)

✶✺

♦♥❞❡ ❢ é ♦ ♦♣❡r❛❞♦r ❞❡ ❋♦❝❦ ❞❛❞♦ ♣♦r✿

f =h(1) +

N

X

b=1

[Jb(1)−Kb(1)], ✭✷✳✷✵✮

❝♦♠ Jb ❡ Kb s❡♥❞♦ ♦s ♦♣❡r❛❞♦r❡s ❞❡ ❝♦✉❧♦♠❜ ❡ tr♦❝❛✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳ ❖ ♠ét♦❞♦ ❍❛rtr❡❡✲❋♦❝❦ ✭❍❋✮ é ❛♠♣❧❛♠❡♥t❡ ✉t✐❧✐③❛❞♦ ❛té ❤♦❥❡✱ ♣♦ré♠ ❡♠ ❛❧❣✉♥s ❝❛s♦s ♥ã♦ ❝♦♥t❡♠♣❧❛ ♣❡r❢❡✐t❛♠❡♥t❡ ❛ ❡♥❡r❣✐❛ ❛ss♦❝✐❛❞❛ ❛♦ s✐st❡♠❛✱ ♣♦✐s ♥ã♦ ❧❡✈❛ ❡♠ ❝♦♥s✐❞❡r❛çã♦ ❛ ❡♥❡r❣✐❛ ❞❡ ❝♦rr❡❧❛çã♦ ❡❧❡trô♥✐❝❛ ❞♦ s✐st❡♠❛✳ P♦r ❡ss❡ ♠♦t✐✈♦✱ ❛♣ós ♦ ❍❋✱ ♦✉tr❛s t❡♦r✐❛s ❢♦r❛♠ ❞❡s❡♥✈♦❧✈✐❞❛s ❛ ✜♠ ❞❡ ❝♦♥t❡♠♣❧❛r ❡ss❛ ❡♥❡r❣✐❛✳ ❯♠❛ ❞❛s t❡♦r✐❛s ❛❞✈✐♥❞❛ ❞❛ ♠❡❝â♥✐❝❛ q✉â♥t✐❝❛ ❡ q✉❡ ❡①♣r❡ss❛ ♠✉✐t♦ ❜❡♠ ❞✐✈❡rs♦s s✐st❡♠❛s ❢ís✐❝♦s é ❛ t❡♦r✐❛ ❞❛ ♣❡rt✉r❜❛çã♦✱ q✉❡ ❧❡✈❛ ❡♠ ❝♦♥s✐❞❡r❛çã♦ ✉♠ s✐st❡♠❛ ♠❛✐s ♣ró①✐♠♦ ❞♦ r❡❛❧✱ ♦✉ s❡❥❛✱ ❡❧❛ ♣♦❞❡ s❡r ✉s❛❞❛ ♣❛r❛ r❡❝✉♣❡r❛r ❛ ❡♥❡r❣✐❛ ❞❡ ❝♦rr❡❧❛çã♦ ❡❧❡trô♥✐❝❛ ❞♦ s✐st❡♠❛✳ ◆❛ ❝♦♠♣✉t❛çã♦ ❞❡ s✐st❡♠❛s ❢ís✐❝♦s✱ ❛ ❚❡♦r✐❛ ❞❛ P❡rt✉r❜❛çã♦ ❞❡ ▼♦❧❧❡r✲P❧❡ss❡t ✭▼P✮ ❝♦rr✐❣✐✉ ❞✐✈❡rs❛s ❞✐✈❡r❣ê♥❝✐❛s q✉❡ ❛♦ ❧♦♥❣♦ ❞♦s ❛♥♦s ❢♦r❛♠ ❛♣❛r❡❝❡♥❞♦ ❛♦ ❢❛③❡r ✉s♦ ❞♦ ♠ét♦❞♦ ❍❋✳ ◆♦ s✐st❡♠❛ ❍2❖2 ✰ ●ás ◆♦❜r❡ ❢♦✐ ♥❡❝❡ssár✐♦ ❡①❛t❛♠❡♥t❡ ♦ ▼P ♣❛r❛ ♣♦❞❡r ❢❛③❡r ♦ ❝á❧❝✉❧♦ ❛❜ ✐♥✐t✐♦ ❞❡ ❢♦r♠❛ ❛ t❡r ✉♠❛ ❝♦❡rê♥❝✐❛ ❡①♣❡r✐♠❡♥t❛❧ ❡ t❡ór✐❝❛✳ ◆❛ ♣ró①✐♠❛ s❡çã♦✱ ♦ ♠ét♦❞♦ ▼P s❡rá ❡①♣❧✐❝❛❞♦✳

✷✳✹ ❆ ❚❡♦r✐❛ ❞❛ P❡rt✉r❜❛çã♦ ❞❡ ▼♦❧❧❡r✲P❧❡ss❡t ✭▼P✮

P❛r❛ ❝♦rr✐❣✐r ❛❧❣✉♥s ❛s♣❡❝t♦s ✭♣r✐♥❝✐♣❛❧♠❡♥t❡ ❛ ❡♥❡r❣✐❛ ❞❡ ❝♦rr❡❧❛çã♦ ❡❧❡trô♥✐❝❛✮ q✉❡ ♦ ♠ét♦❞♦ ❞❡ ❍❛rtr❡❡✲❋♦❝❦ ♥ã♦ ❝♦♥t❡♠♣❧❛✱ ❈❤r✐st✐❛♥ ▼♦❧❧❡r ❡ ▼✐❧t♦♥ ❙✳ P❧❡ss❡t ❞❡s❡♥✈♦❧✈❡r❛♠ ❡♠ ✶✾✸✹ ✉♠ ♠ét♦❞♦ q✉❡ s❡ ❜❛s❡✐❛ ♥♦ ❍❋ ❛❝r❡s❝✐❞♦ ❞❛ ❚❡♦r✐❛ ❞❛ P❡rt✉r❜❛çã♦❬✺✹❪✳ ◆❡ss❡ ♠ét♦❞♦✱ ❝♦♥s✐❞❡r❛✲s❡ ♦ ❍❛♠✐❧t♦♥✐❛♥♦ ❝♦♥❤❡❝✐❞♦ ❛❝r❡s❝✐❞♦ ❞❡ ✉♠❛ ♣❡rt✉r❜❛çã♦ ❡①t❡r♥❛✿

H =H0+λV, ✭✷✳✷✶✮

(28)

✶✻

P❛r❛ s❡ t❡r ✉♠❛ ❝♦♥s✐stê♥❝✐❛ ♠❛t❡♠át✐❝❛✱ ❝♦♥s✐❞❡r❛✲s❡ ♦ ♣♦t❡♥❝✐❛❧V s❡♠♣r❡ ♣❡q✉❡♥♦

♣❛r❛ q✉❡ s❡ ♣♦ss❛ ❡①♣❛♥❞✐r ❛s ❡♥❡r❣✐❛s ❡ ♦s ❛✉t♦❡st❛❞♦s ❞♦ s✐st❡♠❛ ❡♠ ♣♦tê♥❝✐❛s ❞❡

λ✿

H_|ψ_i=E_|ψ_{i →}H_|n_i=E_|n_i, ✭✷✳✷✷✮

En =En(0)+λEn(1)+λ2En(2)+..., ✭✷✳✷✸✮

|n_i=_|n(0)_i+λ_|n(1)_i+λ2_|n(2)_i+... ✭✷✳✷✹✮

❆♣❧✐❝❛♥❞♦ ♦ ❍❛♠✐❧t♦♥✐❛♥♦ ✭✷✳✻✸✮ ♥♦s ❛✉t♦❡st❛❞♦s ✭✷✳✻✻✮ ❡ ✉s❛♥❞♦ ✭✷✳✻✺✮ t❡♠♦s✿

[ ˆH0+λVˆ]|ni=En|ni, ✭✷✳✷✺✮

[ ˆH0+λVˆ][|ni=|n(0)i+λ|n(1)i+λ2|n(2)i+...]

= [En=En(0)+λEn(1)+λ2En(2)+...][|ni=|n(0)i+λ|n(1)i+λ2|n(2)i+...] ✭✷✳✷✻✮

❏✉♥t❛♥❞♦ ♦s t❡r♠♦s ❞❡ ♠❡s♠❛ ♣♦tê♥❝✐❛ ❡♠ λ✿

• λ0_✿ _Hˆ

(0)|n(0)i=En(0)|n(0)i →Hˆ(0)−En(0)|n(0)i= 0❀

• λ1_✿ _H_ˆ

ˆ

V)_|n(0)_i

• λ2_✿ _H_ˆ

(En(1)−Vˆ)|n(1)i+En(2)|n(0)

• λ3_✿ _{( ˆ}_H

(0)−En(0))|n(3)i= (En(1)−Vˆ)|n(2)i+En(2)|n(1)i+En(3)|n(0)i

(29)

✶✼

♥❛ ♦❜t❡♥çã♦ ❞❛ ❡♥❡r❣✐❛ ❡♠ s❡❣✉♥❞❛ ♦r❞❡♠ ✈✐❛ t❡♦r✐❛ ❞❛ ♣❡rt✉r❜❛çã♦✳ ❖s ❛✉t♦❡st❛❞♦s ♣♦❞❡♠ s❡r r❡♣r❡s❡♥t❛❞♦s ❝♦♠♦ ✉♠❛ ❝♦♠❜✐♥❛çã♦ ❧✐♥❡❛r ❞♦s ❡st❛❞♦s ❞♦ ❤❛♠✐❧t♦♥✐❛♥♦ ❝♦♥❤❡❝✐❞♦✿

|n(2)_i=X

m

bm|m(0)i, ✭✷✳✷✼✮

❙✉❜st✐t✉✐♥❞♦ ❡ss❡ ❛✉t♦❡st❛❞♦ ♥❛ ❝♦rr❡çã♦ ❡♠ s❡❣✉♥❞❛ ♦r❞❡♠ ♦❜t❡♠♦s✿

X

m

bm( ˆH(0)−En(0))|m (0)

i=X

m

am(En(1)−Vˆ)|m (0)

i+E_n(2)_|n(0), ✭✷✳✷✽✮

▼✉❧t✐♣❧✐❝❛♥❞♦ ✭✷✳✼✶✮ ♣♦r hk(0)_|_✿

hk(0)_| X m

bm( ˆH(0)−En(0))|m(0)i=

X

m

am(En(1)−Vˆ)|m(0)i+En(2)|n(0)i

!

, ✭✷✳✷✾✮

X

m

bm( ˆH(0)−En(0))hk(0)||m(0)i=

X

m

am(En(1)−Vˆ)hk(0)||m(0)i+

En(2)hk(0)||n(0)i, ✭✷✳✸✵✮

bk(Ek(0)−En(0)) = akEn(1)−

X

m

amVkm+En(2)δkn. ✭✷✳✸✶✮

❆ ❡q✉❛çã♦ ✭✷✳✼✸✮ s✉❣❡r❡ k=n✿

bn(En(0)−En(0)) = anEn(1)−

X

m

amVnm+En(2), ✭✷✳✸✷✮

0 = anEn(1)−

X

m

amVnm+En(2). ✭✷✳✸✸✮

❯♠❛ ❞❛s ♣♦ssí✈❡✐s s♦❧✉çõ❡s é an = 0 ♣❛r❛ ♦s ❝♦❡✜❝✐❡♥t❡s✳ ❈♦♠ ✐ss♦✱ ✉s❛♥❞♦

an= 0✿

En(2) =

X

m6=n

(30)

✶✽

❊♠ ♣r✐♠❡✐r❛ ♦r❞❡♠ ❡♠ t❡♦r✐❛ ❞❛ ♣❡rt✉r❜❛çã♦✱ ✉t✐❧✐③❛♥❞♦ ♦ ♠❡s♠♦ ❝❛♠✐♥❤♦ é ♣♦ssí✈❡❧ ❞❡♠♦♥str❛ q✉❡✿

ak =

Vkn

En(0)−E_k(0)

(k ₆=n), ✭✷✳✸✺✮

❛ss✐♠✿

En(2) =

X

m6=n

|Vnm|2

En(0)−Em(0)

. ✭✷✳✸✻✮

❆ ❡q✉❛çã♦ ✭✷✳✼✽✮ ♣❡r♠✐t❡ ❡♥❝♦♥tr❛r ❛ ❝♦rr❡çã♦ ❞❡ ♣r✐♠❡✐r❛ ♦r❞❡♠ ❞❛ ❡♥❡r❣✐❛ ❞❡ ❝♦rr❡❧❛çã♦ ❡❧❡trô♥✐❝❛ ❞♦ s✐st❡♠❛✳ ❆ ❡♥❡r❣✐❛ ♣❛ss❛ ❛ s❡r ❡♥tã♦✿

Etotal =EHF +EM P2. ✭✷✳✸✼✮

P❛r❛ ❝♦♠♣❧❡t❛r ❛ ❞✐s❝✉ssã♦ s♦❜r❡ ♦s ♠ét♦❞♦s ❞❡ ❝á❧❝✉❧♦s ❞❡ ❡str✉t✉r❛ ❡❧❡trô♥✐❝❛✱ é ✐♠♣♦rt❛♥t❡ ❝♦♥❤❡❝❡r ❝♦♠♦ ❛s ❢✉♥çõ❡s ❞❡ ❜❛s❡ sã♦ ❝♦♥str✉í❞❛s✳ ❆ s❡çã♦ ❛ s❡❣✉✐r s❡rá ❞❡❞✐❝❛❞❛ ❛ ❡ss❡ ❛ss✉♥t♦✳

✷✳✺ ❆s ❋✉♥çõ❡s ❞❡ ❇❛s❡

❊♠ q✉í♠✐❝❛ ♦s ♦r❜✐t❛✐s ♠♦❧❡❝✉❧❛r❡s ♣♦❞❡♠ s❡r ❞❡s❝r✐t♦s ♣♦r ❢✉♥çõ❡s ♠❛t❡♠át✐❝❛s q✉❡ r❡♣r❡s❡♥t❛♠ ❛ ❢✉♥çã♦ ❞❡ ♦♥❞❛ ❞❡ ❝❛❞❛ ❡❧étr♦♥ q✉❡ ❝♦♠♣õ❡ ♦ s✐st❡♠❛✳ ❈♦♠♦ s❡ s❛❜❡✱ ❡♠ ❢ís✐❝❛ q✉â♥t✐❝❛✱ s❡ ❝❛❧❝✉❧❛ ♠✉✐t♦ ♣r♦❜❛❜✐❧✐❞❛❞❡s✳ P♦r ❡ss❡ ♠♦t✐✈♦ ♦s ♦r❜✐t❛✐s ♠♦❧❡❝✉❧❛r❡s ♣♦❞❡♠ ✐♥❝❧✉s✐✈❡ r❡♣r❡s❡♥t❛r ❞❡♥s✐❞❛❞❡ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡✳ ❊♠ ❝♦♥❥✉♥t♦ ❝♦♠ ♦ ♠ét♦❞♦ ❍❛rtr❡❡✲❋♦❝❦ ♦✉ t❡♦r✐❛s ♠❛✐s r❡❝❡♥t❡s✱ ♣r❛t✐❝❛♠❡♥t❡ t♦❞♦s ♦s s✐st❡♠❛s ♠♦❧❡❝✉❧❛r❡s ♣♦❞❡♠ s❡r ❞❡s❝r✐t♦s t❡♦r✐❝❛♠❡♥t❡✳ ❉❛í ♦ ❣r❛♥❞❡ ♣♦❞❡r ❡ ✐♠♣♦rtâ♥❝✐❛ q✉❡ ❡ss❛ ♠❡t♦❞♦❧♦❣✐❛ ♣♦ss✉✐ ♥❛ ❝✐ê♥❝✐❛ ❝♦♥t❡♠♣♦râ♥❡❛✳

❯♠❛ ❞❛s ♣r✐♠❡✐r❛s ❜❛s❡s ✉t✐❧✐③❛❞❛s sã♦ ❝♦♥❤❡❝✐❞❛s ❝♦♠♦ ❙❧❛t❡r✲❚②♣❡ ❖r✲ ❜✐t❛❧s ✭❙❚❖✮✳ ❊♠ ❣❡r❛❧✱ r❡♣r❡s❡♥t❛❞❛ ♥❛ ❧✐t❡r❛t✉r❛ ❝♦♠♦ ❙❚❖✲♥●✱ ♦♥❞❡ n r❡♣r❡✲

s❡♥t❛ ♦ ♥ú♠❡r♦ ❞❡ ♦r❜✐t❛✐s ❣❛✉ss✐❛♥♦s ✭φ✮ ✉t✐❧✐③❛❞♦s ♣❛r❛ ❡①♣❛♥❞✐r ❛ ❢✉♥çã♦ ❞❡ ♦♥❞❛