❯◆■❱❊❘❙■❉❆❉❊ ❋❊❉❊❘❆▲ ❉❖ ❈❊❆❘➪ ❈❊◆❚❘❖ ❉❊ ❈■✃◆❈■❆❙
❉❊P❆❘❚❆▼❊◆❚❖ ❉❊ ❋❮❙■❈❆
P❘❖●❘❆▼❆ ❉❊ PÓ❙✲●❘❆❉❯❆➬➹❖ ❊▼ ❋❮❙■❈❆
❏❖❘●❊ ▲❯■❩ ❇❊❩❊❘❘❆ ❉❊ ❆❘❆Ú❏❖
❆❯❚❖✲❖❘●❆◆■❩❆➬➹❖ ❉❊ P❆❘❚❮❈❯▲❆❙ P❆❚❈❍❨
❈❆❘❘❊●❆❉❆❙
❏❖❘●❊ ▲❯■❩ ❇❊❩❊❘❘❆ ❉❊ ❆❘❆Ú❏❖
❆❯❚❖✲❖❘●❆◆■❩❆➬➹❖ ❉❊ P❆❘❚❮❈❯▲❆❙ P❆❚❈❍❨
❈❆❘❘❊●❆❉❆❙
❉✐ss❡rt❛çã♦ ❞❡ ▼❡str❛❞♦ ❛♣r❡s❡♥t❛❞❛ ❛♦ Pr♦✲ ❣r❛♠❛ ❞❡ Pós✲●r❛❞✉❛çã♦ ❡♠ ❋ís✐❝❛ ❞❛ ❯♥✐✈❡r✲ s✐❞❛❞❡ ❋❡❞❡r❛❧ ❞♦ ❈❡❛rá✱ ❝♦♠♦ r❡q✉✐s✐t♦ ♣❛r❝✐❛❧ ♣❛r❛ ❛ ♦❜t❡♥çã♦ ❞♦ ❚ít✉❧♦ ❞❡ ▼❡str❡ ❡♠ ❋í✲ s✐❝❛✳ ➪r❡❛ ❞❡ ❈♦♥❝❡♥tr❛çã♦✿ ❋ís✐❝❛ ❞❛ ▼❛tér✐❛ ❈♦♥❞❡♥s❛❞❛✳
❖r✐❡♥t❛❞♦r✿ Pr♦❢✳ ❉r✳ ❋❡❧✐♣❡ ❞❡ ❋r❡✐t❛s ▼✉♥❛r✐♥ ❈♦♦r✐❡♥t❛❞♦r✿ Pr♦❢✳ ❉r✳ ❲❛♥❞❡♠❜❡r❣ P❛✐✈❛ ❋❡rr❡✐r❛
❏❖❘●❊ ▲❯■❩ ❇❊❩❊❘❘❆ ❉❊ ❆❘❆Ú❏❖
❆❯❚❖✲❖❘●❆◆■❩❆➬➹❖ ❉❊ P❆❘❚❮❈❯▲❆❙ P❆❚❈❍❨
❈❆❘❘❊●❆❉❆❙
❉✐ss❡rt❛çã♦ ❞❡ ▼❡str❛❞♦ ❛♣r❡s❡♥t❛❞❛ ❛♦ Pr♦✲ ❣r❛♠❛ ❞❡ Pós✲●r❛❞✉❛çã♦ ❡♠ ❋ís✐❝❛ ❞❛ ❯♥✐✈❡r✲ s✐❞❛❞❡ ❋❡❞❡r❛❧ ❞♦ ❈❡❛rá✱ ❝♦♠♦ r❡q✉✐s✐t♦ ♣❛r❝✐❛❧ ♣❛r❛ ❛ ♦❜t❡♥çã♦ ❞♦ ❚ít✉❧♦ ❞❡ ▼❡str❡ ❡♠ ❋í✲ s✐❝❛✳ ➪r❡❛ ❞❡ ❈♦♥❝❡♥tr❛çã♦✿ ❋ís✐❝❛ ❞❛ ▼❛tér✐❛ ❈♦♥❞❡♥s❛❞❛✳
❆♣r♦✈❛❞❛ ❡♠ ✷✶✴✵✶✴✷✵✶✹
❇❆◆❈❆ ❊❳❆▼■◆❆❉❖❘❆
Pr♦❢✳ ❉r✳ ❋❡❧✐♣❡ ❞❡ ❋r❡✐t❛s ▼✉♥❛r✐♥ ✭❖r✐❡♥t❛❞♦r✮ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞♦ ❈❡❛rá ✭❯❋❈✮
Pr♦❢✳ ❉r✳ ❲❛♥❞❡♠❜❡r❣ P❛✐✈❛ ❋❡rr❡✐r❛ ✭❈♦♦r✐❡♥t❛❞♦r✮ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞♦ ❈❡❛rá ✭❯❋❈✮
❉❛❞♦s ■♥t❡r♥❛❝✐♦♥❛✐s ❞❡ ❈❛t❛❧♦❣❛çã♦ ♥❛ P✉❜❧✐❝❛çã♦ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞♦ ❈❡❛rá
❇✐❜❧✐♦t❡❝❛ ❙❡t♦r✐❛❧ ❞❡ ❋ís✐❝❛ ❆✵✵✵♣ ❇❡③❡rr❛✱ ❏♦r❣❡ ▲✉✐③ ✳
❆✉t♦✲❖r❣❛♥✐③❛çã♦ ❞❡ P❛rtí❝✉❧❛s P❛t❝❤② ❈❛rr❡❣❛❞❛s ✴ ❏♦r❣❡ ▲✉✐③ ❇❡③❡rr❛ ❞❡ ❆r❛ú❥♦✳ ✕ ✷✵✶✹✳
✼✺ ♣✳❀✐❧✳
❉✐ss❡rt❛çã♦ ❞❡ ▼❡str❛❞♦ ✲ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞♦ ❈❡❛rá✱ ❉❡♣❛r✲ t❛♠❡♥t♦ ❞❡ ❋ís✐❝❛✱ Pr♦❣r❛♠❛ ❞❡ Pós✲●r❛❞✉❛çã♦ ❡♠ ❋ís✐❝❛✱ ❈❡♥tr♦ ❞❡ ❈✐ê♥❝✐❛s✱ ❋♦rt❛❧❡③❛✱ ✷✵✶✹✳
➪r❡❛ ❞❡ ❈♦♥❝❡♥tr❛çã♦✿ ❋ís✐❝❛ ❞❛ ▼❛tér✐❛ ❈♦♥❞❡♥s❛❞❛ ❖r✐❡♥t❛çã♦✿ Pr♦❢✳ ❉r✳ ❋❡❧✐♣❡ ❞❡ ❋r❡✐t❛s ▼✉♥❛r✐♥
1✳ ❈♦❧♦✐❞❡s✳ 2✳ P❛rtí❝✉❧❛s P❛t❝❤②✳ 3✳ ❉✐❛❣r❛♠❛ ❞❡ ❋❛s❡s✳ 4✳
❆✉t♦✲♦r❣❛♥✐③❛çã♦✳5✳ ❉✐♥â♠✐❝❛ ▼♦❧❡❝✉❧❛r✳ ■✳
❆●❘❆❉❊❈■▼❊◆❚❖❙
• ■♥✐❝✐❛❧♠❡♥t❡ ❛ ❉❡✉s ♣❡❧♦ ❝♦♥❢♦rt♦ ❡s♣✐r✐t✉❛❧ ♥❡❝❡ssár✐♦ ❡♠ t♦❞❛s ❛s ❛t✐✈✐❞❛❞❡s ♥❛ ♠✐♥❤❛ ✈✐❞❛✳
• ❆♦ Pr♦❢❡ss♦r ❉r✳ ❋❡❧✐♣❡ ❞❡ ❋r❡✐t❛s ▼✉♥❛r✐♥✱ ♣❡❧❛ ❣r❛♥❞❡ ❛❥✉❞❛ ♥♦s ú❧t✐♠♦s ❛♥♦s ❞❡ ♠✐♥❤❛ ❝❛rr❡✐r❛ ❛❝❛❞ê♠✐❝❛✳ ❆ s✉❛ ❢♦rç❛ ❞❡ ✈♦♥t❛❞❡ ❞❡ ❛❥✉❞❛r✱ ❥✉♥t❛♠❡♥t❡ ❝♦♠ ❛ ✐♥❝rí✈❡❧ ♣❛❝✐ê♥❝✐❛ ❝♦♠ ❛ ♠✐♥❤❛ ♣❡ss♦❛✱ ✜③❡r❛♠ ❞❡ ♠✐♠ ✉♠ ♣r♦✜ss✐♦♥❛❧ ♠❛✐s ❜❡♠ q✉❛❧✐✜❝❛❞♦✳ ❈♦♠♦ ♦r✐❡♥✲ t❛❞♦r✱ s✉❛s ❞✐s❝✉ssõ❡s ❡ ❡♥s✐♥❛♠❡♥t♦s ❢♦r❛♠ ❢❡rr❛♠❡♥t❛s ❡ss❡♥❝✐❛✐s ♣❛r❛ ❛ ❝♦♥str✉çã♦ ❞❛ ♠✐♥❤❛ ✈✐❞❛ ❛❝❛❞ê♠✐❝❛✳
• ❆♦ Pr♦❢❡ss♦r ❉r✳ ❲❛♥❞❡♠❜❡r❣ P❛✐✈❛ ❋❡rr❡✐r❛ ♣❡❧❛ ❝♦♥tr✐❜✉✐çã♦ ❡ss❡♥❝✐❛❧ ♣❛r❛ ❛ ✐♥s❡rçã♦ ♥❛ ár❡❛ ❞❡ ♣❡sq✉✐s❛ ❛❝❛❞ê♠✐❝❛ ❞❡s❞❡ ❛ ♠✐♥❤❛ ❣r❛❞✉❛çã♦✳ ❙❡✉s ❡♥s✐♥❛♠❡♥t♦s ❢♦r❛♠ ❞❡ ❣r❛♥❞❡ ✈❛❧♦r ♣❛r❛ ❛ ♠✐♥❤❛ ❢♦r♠❛çã♦ t❛♥t♦ ❛❝❛❞ê♠✐❝❛✱ ❝♦♠♦ ♠♦r❛❧✳ ■♥t❡❧✐❣ê♥❝✐❛✱ s❡r✐❡❞❛❞❡ ❡ ♣r♦✜ss✐♦♥❛❧✐s♠♦ sã♦ ❛❧❣✉♠❛s ❞❛s ✈✐rt✉❞❡s ❛s q✉❛✐s ♦ ❝❛r❛t❡r✐③❛✳
• ❆♦ Pr♦❢❡ss♦r ❉r✳ ❋❛❜rí❝✐♦ P♦t✐❣✉❛r ♣❡❧❛ ♣❛rt✐❝✐♣❛çã♦ ♥❛ ❜❛♥❝❛ ❡①❛♠✐♥❛❞♦r❛✳
• ❆♦s ♣r♦❢❡ss♦r❡s ❞♦ ❞❡♣❛rt❛♠❡♥t♦ ❞❡ ❋ís✐❝❛ ❞❛ ❯❋❈ ♣❡❧❛ ❛❥✉❞❛ ♥❛ ♠✐♥❤❛ ❢♦r♠❛çã♦ ❛❝❛❞ê✲ ♠✐❝❛✳ ❊♠ ❞❡st❛q✉❡ ❡stã♦ ♦s ♣r♦❢❡ss♦r❡s ❉r✳ ❘❛✐♠✉♥❞♦✱ ❉r✳ ❆♥❞r❡② ❈❤❛✈❡s✱ ❉r✳ ❆♥❞ré ❆✉t♦✱ ❉r✳ ❊✉❝❧✐♠❛r✱ ❉r✳ ❏♦sé ❙♦❛r❡s✱
• ❆♦s ❣r❛♥❞❡s ❛♠✐❣♦s ❞♦ ●r✉♣♦ ❞❡ ❚❡♦r✐❛ ❞❛ ▼❛tér✐❛ ❈♦♥❞❡♥s❛❞❛ ✭●❚▼❈✮✱ ❉❛✈✐❞ ❋✐✲ ❣✉❡r❡❞♦✱ ❏♦r❣❡ ❉♦♠✐♥❣♦ ✭❈❛♣✉❛♥✮✱ ❉❛✈✐ ❉❛♥t❛s✱ ▲❡✈✐✱ ❏♦ã♦ ❈❧á✉❞✐♦✱ ❋❧♦rê♥❝✐♦✱ ❱❛❣♥❡r✱ ❏❡ssé✱ ▲❡❛♥❞r♦✱ ❆♥❞ré ❇♦r❜❛✱ ❉✐❡❣♦ ▲✉❝❡♥❛✱ ❉✐❡❣♦ ❋r♦t❛✱ ❉✐❡❣♦ ❘❛❜❡❧♦ ♣❡❧❛ ❡♥♦r♠❡ ❛❥✉❞❛ ❡ ❝♦♠♣❛♥❤❡✐r✐s♠♦✳
• ❆♦s ❛♠✐❣♦s ❞♦ ❞❡♣❛rt❛♠❡♥t♦ ❞❡ ❋ís✐❝❛ ❞❛ ❯❋❈✱ ❏♦sé ❊♥❡❞✐❧t♦♥ ✭❉✐❧t♦♥✮✱ ▼❛r❝♦s ❆✉ré❧✐♦✱ ❆♥❝❡❧♠♦✱ ❏♦❡❧✱ ❏♦sé ●❛❞❡❧❤❛✱ ❏♦sé ❇❡③❡rr❛ ✭❘✉✜♥♦✮✱ ❆❧❛♥ ❊❧❦✐♥s♦♥✱ ❈és❛r✱ ▼❛r❝✉s ❱✐♥í✲ ❝✐✉s✱ ❚❤✐❛❣♦ ❙❛♥t✐❛❣♦✱ ■❣♦r✱ ❍❡✐t♦r✱ ❘✐❧❞❡r✱ ❇r✉♥♦ ●♦♥❞✐♠✱ ❆♥❞❡rs♦♥✱ ■♦❧❛♥❞❛✱ ❘❛✈❡♥❛✱ ❆❧❞✐❧❡♥❡✱ ❘❛q✉❡❧ ♣❡❧❛ ❛❥✉❞❛ ✐♥❡st✐♠á✈❡❧ ❡♠ ❣r❛♥❞❡ ♣❛rt❡ ❞❛ ♠✐♥❤❛ ❝❛rr❡✐r❛ ❛❝❛❞ê♠✐❝❛✳ P❡❧♦s ♠♦♠❡♥t♦s ❞❡ ❞❡s❝♦♥tr❛çã♦ ❛♦s q✉❛✐s ❢♦r❛♠ ❞❡ ❣r❛♥❞❡ ✐♠♣♦rtâ♥❝✐❛ ♣❡ss♦❛❧✳
• ❆♦s ♠❡✉s ♣❛ís✱ ▲✉✐③ ❆r❛ú❥♦ ❡ ●❡r❛❧❞❛ ❇❡③❡rr❛ ♣❡❧♦ ❡♥♦r♠❡ ❛♣♦✐♦ ❞✉r❛♥t❡ t♦❞❛ ❛ ♠✐♥❤❛ ✈✐❞❛✳ ❙❡✉s ❡♥s✐♥❛♠❡♥t♦s ❢♦r❛♠ ❛ ❜❛s❡ ❢✉♥❞❛♠❡♥t❛❧ ❞❛ ♠♦r❛❧ ❛♦ q✉❛❧ ❤♦❥❡ ❡✉ ❝♦♠♣r❡❡♥❞♦✱ ❢❛③❡♥❞♦ ❞❡ ♠✐♠ ✉♠ ❝✐❞❛❞ã♦✳
• ❆♦s ♠❡✉s ✐r♠ã♦s ▲✉✐③ ❋❡r♥❛♥❞♦ ✭◆❛♥❞♦✮✱ ❘❡♥❛t❛ ▼✐❦❛❡❧❧❡ ✭❈❛❝á✮ ❡ ●❡ss✐❡❧❡ ❇❡③❡rr❛ ✭●❡ss✐✮ ♣❡❧♦ ❝♦♠♣❛♥❤❡✐r✐s♠♦ ♥❡❝❡ssár✐♦s ♣❛r❛ ♦ ♠❡✉ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ✐♥❢❛♥t✐❧✱ ❥✉✈❡♥✐❧ ❡ ❛❞✉❧t♦✳
• ❆♦s ❢✉♥❝✐♦♥ár✐♦s ❞♦ ❞❡♣❛rt❛♠❡♥t♦ ❞❡ ❋ís✐❝❛✱ ❘❡❥❛♥❡✱ ❏❛í❧s♦♥✱ ❈r❡✉s❛✱ ♣❡❧❛s ❢❛❝✐❧✐❞❛❞❡s ❡ ❛♣♦✐♦✳
• ❆♦s ♠✐❝r♦❡♠♣r❡sár✐♦s ❘❡❣✐♥❛❧❞♦ ✭❇✐❣ ❇r♦t❤❡r✮ ❡ ❏♦s❛ ♣❡❧♦s ♠♦♠❡♥t♦s ❞✐✈❡rsã♦ ❡ ❛♣♦✐♦ ❞✉r❛♥t❡ ♠✐♥❤❛ ❢♦r♠❛çã♦ ❛❝❛❞ê♠✐❝❛✳
✏❆ ✐♠❛❣✐♥❛çã♦ é ♠❛✐s ✐♠♣♦rt❛♥t❡ q✉❡ ❛ ❝✐ê♥❝✐❛✱ ♣♦rq✉❡ ❛ ❝✐ê♥❝✐❛ é ❧✐♠✐t❛❞❛✱
❛♦ ♣❛ss♦ q✉❡ ❛ ✐♠❛❣✐♥❛çã♦ ❛❜r❛♥❣❡ ♦
❘❊❙❯▼❖
❖ ❛t✉❛❧ ❡stá❣✐♦ ❞❡ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ té❝♥✐❝❛s ❡①♣❡r✐♠❡♥t❛✐s ♣❡r♠✐t❡ ❛ sí♥t❡s❡ ❞❡ ♣❛rtí❝✉❧❛s ❝♦❧♦✐❞❛✐s ❝♦♠♣❧❡①❛s✱ ❝✉❥❛ s✉♣❡r❢í❝✐❡ ♣♦❞❡ s❡r ♣r❡❝✐s❛♠❡♥t❡ ✧❞❡❝♦r❛❞❛✧❝♦♠ ♣r♦♣r✐❡❞❛❞❡s ❢ís✐❝❛s ❡✴♦✉ q✉í♠✐❝❛s ❞✐❢❡r❡♥t❡s✳ ❚❛✐s ❝♦❧♦✐❞❡s sã♦ ✉s✉❛❧♠❡♥t❡ ❞❡✜♥✐❞♦s ❝♦♠♦ ♣❛rtí❝✉❧❛s ♣❛t❝❤②✳ ❈♦♠♦ r❡s✉❧t❛❞♦ ❞❛ ♠♦❞✐✜❝❛çã♦ ❞❡ ♣❛rt❡s ❞❛ s✉♣❡r❢í❝✐❡ ❞❡ t❛✐s ♣❛rtí❝✉❧❛s✱ ❛ ✐♥t❡r❛çã♦ ❡♥tr❡ ❛s ♠❡s♠❛s é ❣❡r❛❧♠❡♥t❡ ❝❛r❛❝t❡r✐③❛❞❛ ♣♦r ✉♠ ♣♦t❡♥❝✐❛❧ ❛♥✐s♦tró♣✐❝♦✳ ❊st✉❞❛r ❡ ❝♦♠♣r❡❡♥❞❡r ♦ ♣r♦❝❡ss♦ ❞❡ ❛✉t♦✲♦r❣❛♥✐③❛çã♦ ❞❡ss❡ s✐st❡♠❛ ♣❛rt✐❝✉❧❛r é ❞❡ ❣r❛♥❞❡ ✐♥t❡r❡ss❡ t❛♥t♦ ❞♦ ♣♦♥t♦ ❞❡ ✈✐st❛ ❝✐❡♥tí✜❝♦ ❝♦♠♦ t❡❝♥♦❧ó❣✐❝♦✱ ❞❡✈✐❞♦ s✉❛ ✉t✐❧✐③❛çã♦ ❡♠ ♠❛t❡r✐❛✐s ❢✉♥❝✐♦♥❛✐s✳ ◆❡ss❛ ❞✐ss❡rt❛çã♦✱ ❡st✉❞❛✲ s❡ ♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❞❡ ✉♠ s✐st❡♠❛ ❜✐❞✐♠❡♥s✐♦♥❛❧ ❞❡ ♣❛rtí❝✉❧❛s ♣❛t❝❤② ❝❛rr❡❣❛❞❛s✱ ♥❛s q✉❛✐s ❛ s✉♣❡r❢í❝✐❡ é ❞❡❝♦r❛❞❛ ♣♦♥t✉❛❧♠❡♥t❡ ❝♦♠ ✉♠❛ ❝❛r❣❛ ❞❡ s✐♥❛❧ ❝♦♥trár✐♦ ❛q✉❡❧❛ ❧♦❝❛❧✐③❛❞❛ ♥♦ ❝❡♥tr♦ ❞❛ ♣❛rtí❝✉❧❛✳ ❆ss✐♠ s❡♥❞♦✱ ❝❛❞❛ ♣❛rtí❝✉❧❛ ♣❛t❝❤② ♣♦ss✉✐ ✉♠❛ ❝❛r❣❛ ❧íq✉✐❞❛ ❈✱ q✉❡ é r❡s✉❧t❛❞♦ ❞❛ ❞✐❢❡r❡♥ç❛ ❡♥tr❡ ❛s ❝❛r❣❛s ♣♦♥t✉❛✐s ♥❛ s✉♣❡r❢í❝✐❡ ❡ ❛q✉❡❧❛ ♥♦ ❝❡♥tr♦ ❞❛ ♣❛rtí❝✉❧❛ ♣❛t❝❤②✳ ◆❡st❡ tr❛❜❛❧❤♦✱ ✉t✐❧✐③❛✲s❡ ❛ té❝♥✐❝❛ ❞❡ s✐♠✉❧❛çã♦ ❝♦♠♣✉t❛❝✐♦♥❛❧ ❞❡ ❉✐♥â♠✐❝❛ ▼♦❧❡❝✉❧❛r ♣❛r❛ ❡st✉❞❛r ♦ ♣r♦❝❡ss♦ ❞❡ ❛✉t♦✲♦r❣❛♥✐③❛çã♦ ❞❡ ♣❛rtí❝✉❧❛s ♣❛t❝❤② ❡♠ ❢✉♥çã♦ ❞❛ ❞❡♥s✐❞❛❞❡ ❡ t❡♠♣❡r❛t✉r❛✳ ■♥✐❝✐❛❧♠❡♥t❡✱ ❛♣r❡s❡♥t❛✲s❡ ♦ ♠♦❞❡❧♦ ❞❡ ♣❛rtí❝✉❧❛ ♣❛t❝❤② ❛q✉✐ ❡st✉❞❛❞♦ ❡ ✈❡r✐✜❝❛✲ s❡ ♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❞❛ ❡♥❡r❣✐❛ ❞❡ ✐♥t❡r❛çã♦ ❡♥tr❡ ❞✉❛s ♣❛rtí❝✉❧❛s ❡ s✉❛ ❞❡♣❡♥❞ê♥❝✐❛ ❞❛ ❝❛r❣❛ ❡❢❡t✐✈❛ ❞❛ ♣❛rtí❝✉❧❛ ✭❝❛r❣❛ ❧íq✉✐❞❛✮ ❡ ❞♦ ♥ú♠❡r♦ ❞❡ sít✐♦s ❛t✐✈♦s ✭♣✮ q✉❡ ❞❡❝♦r❛♠ ❛s s✉♣❡r❢í❝✐❡s ❞♦s ❝♦❧♦✐❞❡s✱ ❝❤❛♠❛❞♦s ❞❡ ♣❛t❝❤❡s✳ ❖ ❡st✉❞♦ ❞❡ t❛✐s ♣❛râ♠❡tr♦s é ✐♠♣♦rt❛♥t❡ ♣❛r❛ ♦ ❡♥t❡♥❞✐♠❡♥t♦ ❞❛s ❡str✉t✉r❛s ❛✉t♦✲♦r❣❛♥✐③❛❞❛s ♦❜t✐❞❛s✳ ❆♣r❡s❡♥t❛♠✲s❡ ❛s ❡str✉t✉r❛s ❡stá✈❡✐s ❞❡ ♠í♥✐♠❛ ❡♥❡r❣✐❛ ❞❡ ✉♠ s✐st❡♠❛ ❝♦♠ ♣❂✷ ❡ ❈❂✵ ❡♠ ❢✉♥çã♦ ❞❛ t❡♠♣❡r❛t✉r❛ ❡ ❞❡♥s✐❞❛❞❡✳ ❊♠ ❣❡r❛❧✱ ♦❜s❡r✈❛♠✲s❡ ❞✉❛s ❢❛s❡s ❜❡♠ ❞❡✜♥✐❞❛s q✉❡ ❢♦r❛♠ ❞✐st✐♥❣✉✐❞❛s ❛tr❛✈és ❞❡ ❝á❧❝✉❧♦s ❞❡ ♣r♦♣r✐❡❞❛❞❡s t❡r♠♦❞✐♥â♠✐❝❛s ❞✉r❛♥t❡ ❛ s✐♠✉❧❛çã♦✳ ❘❡s✉❧t❛❞♦s ♣❛r❛ ❞✐❢❡r❡♥t❡s ✈❛❧♦r❡s ❞❡ ♣ ❡ ❈ t❛♠❜é♠ sã♦ ❛♣r❡s❡♥t❛❞♦s ❛ ✜♠ ❞❡ ♠♦str❛r ❛ ✐♥✢✉ê♥❝✐❛ ❞❡ss❡ ♣❛râ♠❡tr♦s ♥❛ ❝♦♥✜❣✉r❛çã♦ ❞♦ s✐st❡♠❛✳ ❊♠ ❣❡r❛❧✱ ♦❜s❡r✈❛✲s❡ q✉❡ ♣❛r❛ ❛❧t♦s ✈❛❧♦r❡s ❞❛ ❝❛r❣❛ ❧íq✉✐❞❛ ❡✴♦✉ ♥ú♠❡r♦ ❞❡ ♣❛t❝❤❡s✱ ♦ ♣♦t❡♥❝✐❛❧ r❡♣✉❧s✐✈♦ ♣r❡✈❛❧❡❝❡ ❢❛③❡♥❞♦ ❝♦♠ q✉❡ ♦ s✐st❡♠❛ s❡ ❡st❛❜✐❧✐③❡ ❡♠ ✉♠❛ ❝♦♥✜❣✉r❛çã♦ ❝r✐st❛❧✐♥❛✳ P♦r ♦✉tr♦ ❧❛❞♦✱ ♣❛r❛ ✉♠ s✐st❡♠❛ ❝♦♠♣♦st♦ ❞❡ ♣❛rtí❝✉❧❛s ❝♦♠ ❜❛✐①♦ ✈❛❧♦r ❞❡ ❝❛r❣❛ ❧íq✉✐❞❛ ❡✴♦✉ ♥ú♠❡r♦ ❞❡ ♣❛t❝❤❡s ♦ ♣♦t❡♥❝✐❛❧ ❞❡ ✐♥t❡r❛çã♦ r❡s✉❧t❛♥t❡ é ♣r❡❞♦♠✐♥❛♥t❡♠❡♥t❡ ❛tr❛t✐✈♦ ✐♥❞✉③✐♥❞♦ ❡str✉t✉r❛s ❝♦♠♣♦st❛s ❞❡ ❛❣❧♦♠❡r❛❞♦s ♥❛ ❢♦r♠❛ ❞❡ ❛♥é✐s ❡ ❧✐♥❤❛s ❞❡ ♣❛rtí❝✉❧❛s✳
❆❇❙❚❘❆❈❚
❚❤❡ ❝✉rr❡♥t st❛❣❡ ♦❢ ❞❡✈❡❧♦♣♠❡♥t ♦❢ ❡①♣❡r✐♠❡♥t❛❧ t❡❝❤♥✐q✉❡s ❛❧❧♦✇ t❤❡ s②♥t❤❡s✐s ♦❢ ♣❛rt✐❝❧❡s ❝♦♠♣❧❡① ❝♦❧❧♦✐❞❛❧✱ ✇❤♦s❡ s✉r❢❛❝❡ ❝❛♥ ❜❡ ♣r❡❝✐s❡❧② ✧❞❡❝♦r❛t❡❞✧✇✐t❤ ♣❤②s✐❝❛❧ ♣r♦♣❡rt✐❡s ❛♥❞✴♦r ❝❤❡♠✐❝❛❧ ❝♦♠❜✐♥❛t✐♦♥s✳ ❙✉❝❤ ❝♦❧❧♦✐❞s ❛r❡ ✉s✉❛❧❧② ❞❡✜♥❡❞ ❛s ♣❛t❝❤② ♣❛rt✐❝❧❡s✳ ❆s r❡s✉❧t ♦❢ t❤❡ ♠♦❞✐✜❝❛t✐♦♥ ♦❢ ♣❛rts ♦❢ t❤❡ s✉r❢❛❝❡ ♦❢ s✉❝❤ ♣❛rt✐❝❧❡s✱ t❤❡ ✐♥t❡r❛❝t✐♦♥ ❜❡t✇❡❡♥ t❤❡♠ ✐s ❣❡♥❡r❛❧❧② ❝❤❛r❛❝t❡r✐③❡❞ ❜② ❛♥ ❛♥✐s♦tr♦♣✐❝ ♣♦t❡♥t✐❛❧✳ ❙t✉❞② ❛♥❞ ✉♥❞❡rst❛♥❞ t❤❡ ♣r♦❝❡ss ♦❢ s❡❧❢✲♦r❣❛♥✐③❛t✐♦♥ ♦❢ t❤✐s ♣❛rt✐❝✉❧❛r s②st❡♠ ✐s ♦❢ ❣r❡❛t ✐♥t❡r❡st ❜♦t❤ ❢r♦♠ t❤❡ s❝✐❡♥t✐✜❝ ♣♦✐♥t ♦❢ ✈✐❡✇ ❛s t❡❝❤♥♦❧♦❣②✱ ❜❡❝❛✉s❡ ♦❢ ✐ts ✉s❡ ✐♥ ❢✉♥❝t✐♦♥❛❧ ♠❛t❡r✐❛❧s✳ ■♥ t❤✐s ❞✐ss❡rt❛t✐♦♥✱ ✇❡ st✉❞②✳ ❚❤❡ ❜❡❤❛✈✐♦r ♦❢ ❛ t✇♦✲❞✐♠❡♥s✐♦♥❛❧ s②st❡♠ ♣❛t❝❤② ❝❤❛r❣❡❞ ♣❛rt✐❝❧❡s✱ ✐♥ ✇❤✐❝❤ t❤❡ s✉r❢❛❝❡ ✐s ❞❡❝♦r❛t❡❞ ✇✐t❤ ❛ t✐♠❡❧② ❝❤❛r❣❡ s✐❣♥ ♦♣♣♦s✐t❡ t❤❛t ❧♦❝❛t❡❞ ✐♥ t❤❡ ♣❛rt✐❝❧❡ ❝❡♥t❡r✳ ❚❤✉s✱ ♣❛t❝❤② ❡❛❝❤ ♣❛rt✐❝❧❡ ❤❛s ❛ ♥❡t ❝❤❛r❣❡ ❈✱ ✇❤✐❝❤ ✐s r❡s✉❧t ♦❢ t❤❡ ❞✐✛❡r❡♥❝❡ ❜❡t✇❡❡♥ t❤❡ ♣♦✐♥t ❝❤❛r❣❡s ♦♥ t❤❡ s✉r❢❛❝❡ ❛♥❞ t❤❛t ✐♥ t❤❡ ♣❛rt✐❝❧❡ ❝❡♥t❡r ♣❛t❝❤②✳ ❚❤✐s st✉❞② ✉s❡s t❤❡ t❡❝❤♥✐q✉❡ ♦❢ ❝♦♠♣✉t❡r s✐♠✉❧❛t✐♦♥ ♦❢ ♠♦❧❡❝✉❧❛r ❞②♥❛♠✐❝s t♦ st✉❞② t❤❡ ♣r♦❝❡ss ♦❢ s❡❧❢✲♦r❣❛♥✐③❛t✐♦♥ ♦❢ ♣❛rt✐❝❧❡s ♣❛t❝❤② ❞❡♣❡♥❞✐♥❣ ♦♥ t❤❡ ❞❡♥s✐t② ❛♥❞ t❡♠♣❡r❛t✉r❡✳ ■♥✐t✐❛❧❧②✱ ✇❡ ♣r❡s❡♥t t❤❡ ♠♦❞❡❧ ♦❢ ♣❛t❝❤② ♣❛rt✐❝❧❡s st✉❞✐❡❞ ❤❡r❡ ❛♥❞ t❤❡r❡ ✐s t❤❡ ❜❡❤❛✈✐♦r ♦❢ t❤❡ ✐♥t❡r❛❝t✐♦♥ ❡♥❡r❣② ❜❡t✇❡❡♥ t✇♦ ♣❛rt✐❝❧❡s ❛♥❞ ✐ts ❞❡♣❡♥❞❡♥❝❡ ♦♥ ❧♦❛❞ ❡✛❡❝t✐✈❡ ♣❛rt✐❝❧❡ ✭❧✐q✉✐❞ ❝❤❛r❣❡✮ ❛♥❞ t❤❡ ♥✉♠❜❡r ♦❢ ❛❝t✐✈❡ s✐t❡s ✭♣✮ t❤❛t ❞❡❝♦r❛t❡ t❤❡ s✉r❢❛❝❡s ♦❢ ❝♦❧❧♦✐❞s✱ ❝❛❧❧❡❞ ♣❛t❝❤❡s ✳ ❚❤❡ st✉❞② ♦❢ t❤❡s❡ ♣❛r❛♠❡t❡rs ✐s ✐♠♣♦rt❛♥t ❢♦r ✉♥❞❡rst❛♥❞✐♥❣ t❤❡ s❡❧❢✲♦r❣❛♥✐③❡❞ str✉❝t✉r❡s ♦❜t❛✐♥❡❞✳ Pr❡s❡♥ts t❤❡ st❛❜❧❡ str✉❝t✉r❡s ♦❢ ♠✐♥✐♠✉♠ ❡♥❡r❣② ❛ s②st❡♠ ✇✐t❤ ♣❂✷ ❛♥❞ ❈❂✵ ❛s ❛ ❢✉♥❝t✐♦♥ ♦❢ t❡♠♣❡r❛t✉r❡ ❛♥❞ ❞❡♥s✐t②✳ ■♥ ❣❡♥❡r❛❧✱ ✇❡ ♦❜s❡r✈❡ t✇♦ ✇❡❧❧ ❞❡✜♥❡❞ ♣❤❛s❡s ✇❡r❡ ❞✐st✐♥❣✉✐s❤❡❞ ❜② ❝❛❧❝✉❧❛t✐♦♥ ♦❢ t❤❡r♠♦❞②♥❛♠✐❝ ♣r♦♣❡rt✐❡s ❞✉r✐♥❣ t❤❡ s✐♠✉❧❛t✐♦♥✳ ❘❡s✉❧ts ❢♦r ❞✐✛❡r❡♥t ✈❛❧✉❡s ♦❢ ♣ ❛♥❞ ❈ ❛r❡ ❛❧s♦ ♣r❡s❡♥t❡❞ ♦r❞❡r t♦ s❤♦✇ t❤❡ ✐♥✢✉❡♥❝❡ ♦❢ t❤✐s ♣❛r❛♠❡t❡r ✐♥ t❤❡ s②st❡♠ ❝♦♥✜❣✉r❛t✐♦♥✳ ■♥ ❣❡♥❡r❛❧✱ ✐t ✐s ♦❜s❡r✈❡❞ t❤❛t ❢♦r ❧❛r❣❡ ✈❛❧✉❡s ♦❢ t❤❡ ❝❤❛r❣❡ ❛♥❞✴♦r ♥✉♠❜❡r ♦❢ ♣❛t❝❤❡s✱ t❤❡ r❡♣✉❧s✐✈❡ ♣♦t❡♥t✐❛❧ ♣r❡✈❛✐❧s ❝❛✉s✐♥❣ t❤❡ s②st❡♠ t♦ st❛❜✐❧✐③❡ ✐♥ ❛ ❝r②st❛❧❧✐♥❡ ❝♦♥✜❣✉r❛t✐♦♥✳ ❖♥ t❤❡ ♦t❤❡r ❤❛♥❞✱ ❢♦r ❛ s②st❡♠ ❝♦♠♣♦s❡❞ ♦❢ ♣❛rt✐❝❧❡s ✇✐t❤ ❛ ❧♦✇ ✈❛❧✉❡ ♦❢ ❝❤❛r❣❡ ❛♥❞✴♦r t❤❡ ♥✉♠❜❡r ♦❞ ♣❛t❝❤❡s ✐♥t❡r❛❝t✐♦♥ ♣♦t❡♥t✐❛❧ ✐s ❛ttr❛❝t✐✈❡ ✐♥❞✉❝✐♥❣ ♣r❡❞♦♠✐♥❛♥t❧② r❡s✉❧t✐♥❣ ❝♦♠♣♦s✐t❡ str✉❝t✉r❡s ✐♥ t❤❡ ❢♦r♠ ♦❢ ❝❧✉st❡rs ♦❢ r✐♥❣ ❛♥❞ ❧✐♥❡s ♣❛rt✐❝❧❡s✳
▲■❙❚❆ ❉❊ ❋■●❯❘❆❙
✶ ▼♦❞❡❧♦s ❞❡ ♣❛rtí❝✉❧❛s ♣❛t❝❤②✳ ❈❧❛ss❡✿ ❆✲ ❈♦❜❡rt✉r❛ s✉♣❡r✜❝✐❛❧❀❇✲ ❘❡❧❛çã♦ ❞❡ ❛s♣❡❝t♦❀ ❈✲ ▼♦❞✐✜❝❛çã♦ ❞❡ ❢❛s❡❀❉✲ ◗✉❛♥t✐③❛çã♦ ♣❛❞rã♦❀ ❊✲❇✐❢✉r❝❛çã♦❀ ❋✲ ❖r✲
❞❡♥❛♠❡♥t♦ q✉í♠✐❝♦❀ ●✲ ●r❛❞✐❡♥t❡ ❞❡ ❢♦r♠❛s✳ ❍✲ ❘✉❣♦s✐❞❛❞❡ ❬✶✹❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✶ ✷ ❋❛❜r✐❝❛çã♦ ❞❡ ♣❛rtí❝✉❧❛s ❏❛♥✉s ❝♦♠ ❛ té❝♥✐❝❛ ●▲❆❉ ♦♥❞❡ ♣❛rtí❝✉❧❛s ❞❡ ♣♦❧✐✲
❡st✐r❡♥♦ sã♦ ✉s❛❞❛s ❝♦♠♦ s✉❜str❛t♦ ♣❛r❛ ❛ ❞❡♣♦s✐çã♦ ❞❡ ♣❛rtí❝✉❧❛s ❞❡ ♦✉r♦✳ ❖ â♥❣✉❧♦ ❞❡ ❡✈❛♣♦r❛çã♦ Θ = 2o ♣❛r❛ ❞✐❢❡r❡♥t❡ â♥❣✉❧♦ ❞❡ ♦r✐❡♥t❛çã♦ ❞♦ ♠♦♥♦❝❛✲
❞❡✐❛✳ ✭❛✮ α= 0o✱ ✭❜✮α= 14o✱ ✭❝✮ α= 28o✱ ✭❞✮α= 38o ❬✶✼❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✷
✸ ■♠❛❣❡♥s ❙❊▼ ❞❡ ❛❣❧♦♠❡r❛❞♦ ❝♦❧♦✐❞❛✐s ❝♦♠ ◆❂✹✲✶✷ ♣❛rtí❝✉❧❛s ❞❡ ♣♦❧✐❡st✐r❡♥♦
❡♠✉❧s✐♦♥❛❞❛s ❡♠ s♦❧✉çã♦ ❞❡ t♦❧✉❡♥♦ ❬✷✸❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✸ ✹ ■♠❛❣❡♥s ❙❊▼ ❞❡ ❛❣❧♦♠❡r❛❞♦ ❝♦❧♦✐❞❛✐s ♦♥❞❡ ◆ r❡♣r❡s❡♥t❛ ♦ ♥ú♠❡r♦ ❞❡ ♣❛t❝❤❡s
❞❛s ♣❛rtí❝✉❧❛s ❞❡ ❊❚P❚❆ ❬✷❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✸ ✺ ❋❧✉①♦❣r❛♠❛ ❞♦ ❛❧❣♦r✐t♠♦ ❞❡ ❉✐♥â♠✐❝❛ ▼♦❧❡❝✉❧❛r ✭❉▼✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✸✼ ✻ ■❧✉str❛çã♦ ❞❛s ✧❝♦♥❞✐çõ❡s ♣❡r✐ó❞✐❝❛s ❞❡ ❝♦♥t♦r♥♦✧✴ ✧❝♦♥✈❡♥sã♦ ❞❡ ♠í♥✐♠❛ ✐♠❛✲
❣❡♠✧✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✵ ✼ ✭❛✮❘❡♣r❡s❡♥t❛çõ❡s ❞❡ ♣❛rtí❝✉❧❛s ♣❛t❝❤② ❝♦♠ ♣❂✷✱✸✱✹ ❡ ✺❀✭❜✮■♠❛❣❡♠ ✐❧✉str❛t✐✈❛
❞❡ ✉♠❛ ♣❛rtí❝✉❧❛ ♣❛t❝❤② ✲ ❝❡♥tr♦ ✭❛♠❛r❡❧♦✮✱ ♣❛t❝❤❡s ✭✈❡r♠❡❧❤♦✮✲♥♦ ❝❛s♦ ♣❂✷✳ ✳ ♣✳ ✹✷ ✽ ✭❛✮■❧✉str❛çã♦ ❣rá✜❝❛ ❞❛ ❝♦♥tr✐❜✉✐çã♦ r❛❞✐❛❧ ❞♦ ♣♦t❡♥❝✐❛❧ ❞❡ ❨✉❦❛✇❛ ✲V = Qe−rkr ♣✳ ✹✸
✾ ❘❡♣r❡s❡♥t❛çã♦ ❣rá✜❝❛ ❞❛ ♠✐♥✐♠❛ ❡♥❡r❣✐❛ ❞❡ ✐♥t❡r❛çã♦ ♣❛r❛ ❞✐✈❡rs♦s ✈❛❧♦r❡s ❞❡ ♣✳ ❖s ❣rá✜❝♦s à ❡sq✉❡r❞❛ ♠♦str❛♠ ❛ ♣♦s✐çã♦ ①② ❞❛ ♣❛rtí❝✉❧❛ ❛✉①✐❧✐❛r ❡♠ r❡❧❛çã♦ ❛ ♦r✐❣❡♠ ❥✉♥t❛♠❡♥t❡ ❝♦♠ ❛ ❡♥❡r❣✐❛ ♠í♥✐♠❛ ♣❛r❛ ❝❛❞❛ ♣♦s✐çã♦✳ ❖s ❣rá✜❝♦s à ❞✐r❡✐t❛ ♠♦str❛♠ ♦ â♥❣✉❧♦ ❞❡ ♦r✐❡♥t❛çã♦ ❞❛ ♣❛rtí❝✉❧❛ ❛✉①✐❧✐❛r ❡♠ r❡❧❛çã♦ ❛♦ ❡✐①♦ ① q✉❡ ♣❛r❛ ❝❛❞❛ ♣♦s✐çã♦ ①② ♦❜t✐❞❛ ♣❛r❛ ♦ ♠❡s♠♦ ♠í♥✐♠♦ ❞❡ ❡♥❡r❣✐❛ ❝♦rr❡s♣♦♥✲ ❞❡♥t❡✳ ❆♦ ❝❡♥tr♦ ❡stá r❡♣r❡s❡♥t❛❞♦ ✉♠ ❡sq✉❡♠❛ ❝♦rr❡s♣♦♥❞❡♥t❡ ❛ ❝♦♥✜❣✉r❛çã♦
✶✵ ❊♥❡r❣✐❛ ❞❡ ✐♥t❡r❛çã♦ ❞❡ ♣❛r❡s ♣❛r❛ ♣❂✷ ❡ ❈❂✵✳ ❯♠❛ ♣❛rtí❝✉❧❛ é ✜①❛ ♥❛ ♦r✐❣❡♠ ❞♦ s✐st❡♠❛ ❝♦♠ s❡✉ ❡✐①♦ ♣r✐♥❝✐♣❛❧ ♣❛r❛❧❡❧♦ ❛♦ ❡✐①♦ ①✳ ❯♠❛ ♦✉tr❛ ♣❛rtí❝✉❧❛ ❛✉①✐❧✐❛r é tr❛♥s❧❛❞❛❞❛ ❞❡ ✉♠❛ ❞✐stâ♥❝✐❛ r ❛♦ ❧♦♥❣♦ ❞♦ ❡✐①♦ ① ♣♦❞❡♥❞♦ ❣✐r❛r ❡♠ t♦r♥♦ ❞♦ s❡✉ ❝❡♥tr♦✳ ❖ â♥❣✉❧♦ ❛♣r❡s❡♥t❛❞♦ r❡❢❡r❡✲s❡ ❛♦ â♥❣✉❧♦ ❡♥tr❡ ♦s ❡✐①♦s
♣r✐♥❝✐♣❛✐s ❞❛s ❞✉❛s ♣❛rtí❝✉❧❛s ♣❛t❝❤②✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✼ ✶✶ ❊♥❡r❣✐❛ ❞❡ ✐♥t❡r❛çã♦ ♣❛r❛ ♣❂✸ ❡ ❈❂✵✳ ❯♠❛ ♣❛rtí❝✉❧❛ é ✜①❛ ♥❛ ♦r✐❣❡♠ ❞♦
s✐st❡♠❛ ❝♦♠ s❡✉ ❡✐①♦ ♣r✐♥❝✐♣❛❧ ♣❛r❛❧❡❧♦ ❛♦ ❡✐①♦ ①✳ ❯♠❛ ♦✉tr❛ ♣❛rtí❝✉❧❛ ❛✉①✐❧✐❛r é tr❛♥s❧❛❞❛❞❛ ❞❡ ✉♠❛ ❞✐stâ♥❝✐❛ r ❛♦ ❧♦♥❣♦ ❞♦ ❡✐①♦ ① ♣♦❞❡♥❞♦ ❣✐r❛r ❡♠ t♦r♥♦ ❞♦ s❡✉ ❝❡♥tr♦✳ ❖ â♥❣✉❧♦ ❛♣r❡s❡♥t❛❞♦ r❡❢❡r❡✲s❡ ❛♦ â♥❣✉❧♦ ❡♥tr❡ ♦s ❡✐①♦s ♣r✐♥❝✐♣❛✐s
❞❛s ❞✉❛s ♣❛rtí❝✉❧❛s ♣❛t❝❤②✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✽ ✶✷ ❊♥❡r❣✐❛ ❞❡ ✐♥t❡r❛çã♦ ♣❛r❛ ♣❂✹ ❡ ❈❂✵✳ ❯♠❛ ♣❛rtí❝✉❧❛ é ✜①❛ ♥❛ ♦r✐❣❡♠ ❞♦
s✐st❡♠❛ ❝♦♠ s❡✉ ❡✐①♦ ♣r✐♥❝✐♣❛❧ ♣❛r❛❧❡❧♦ ❛♦ ❡✐①♦ ①✳ ❯♠❛ ♦✉tr❛ ♣❛rtí❝✉❧❛ ❛✉①✐❧✐❛r é tr❛♥s❧❛❞❛❞❛ ❞❡ ✉♠❛ ❞✐stâ♥❝✐❛ r ❛♦ ❧♦♥❣♦ ❞♦ ❡✐①♦ ① ♣♦❞❡♥❞♦ ❣✐r❛r ❡♠ t♦r♥♦ ❞♦ s❡✉ ❝❡♥tr♦✳ ❖ â♥❣✉❧♦ ❛♣r❡s❡♥t❛❞♦ r❡❢❡r❡✲s❡ ❛♦ â♥❣✉❧♦ ❡♥tr❡ ♦s ❡✐①♦s ♣r✐♥❝✐♣❛✐s
❞❛s ❞✉❛s ♣❛rtí❝✉❧❛s ♣❛t❝❤②✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✾ ✶✸ ❊♥❡r❣✐❛ ❞❡ ✐♥t❡r❛çã♦ ♣❛r❛ ♣❂✺ ❡ ❈❂✵✳ ❯♠❛ ♣❛rtí❝✉❧❛ é ✜①❛ ♥❛ ♦r✐❣❡♠ ❞♦
s✐st❡♠❛ ❝♦♠ s❡✉ ❡✐①♦ ♣r✐♥❝✐♣❛❧ ♣❛r❛❧❡❧♦ ❛♦ ❡✐①♦ ①✳ ❯♠❛ ♦✉tr❛ ♣❛rtí❝✉❧❛ ❛✉①✐❧✐❛r é tr❛♥s❧❛❞❛❞❛ ❞❡ ✉♠❛ ❞✐stâ♥❝✐❛ r ❛♦ ❧♦♥❣♦ ❞♦ ❡✐①♦ ① ♣♦❞❡♥❞♦ ❣✐r❛r ❡♠ t♦r♥♦ ❞♦ s❡✉ ❝❡♥tr♦✳ ❖ â♥❣✉❧♦ ❛♣r❡s❡♥t❛❞♦ r❡❢❡r❡✲s❡ ❛♦ â♥❣✉❧♦ ❡♥tr❡ ♦s ❡✐①♦s ♣r✐♥❝✐♣❛✐s
❞❛s ❞✉❛s ♣❛rtí❝✉❧❛s ♣❛t❝❤②✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✺✵ ✶✹ ❊♥❡r❣✐❛ ❞❡ ✐♥t❡r❛çã♦ ♣❛r❛ ♣❂✷ ❡♠ ❞✐❢❡r❡♥t❡s s✐t✉❛çõ❡s ❞❡ ✐♥t❡r❛çã♦ ✭❡q✉❛t♦r✐❛❧✲
❡q✉❛t♦r✐❛❧✱ ❡q✉❛t♦r✐❛❧✲♣♦❧❛r ❡ ♣♦❧❛r✲♣♦❧❛r✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✺✵ ✶✺ ❈♦♠♣❛r❛çã♦ ❞❛ ❡♥❡r❣✐❛ ❞❡ ✐♥t❡r❛çã♦ ♣❛r❛ ♣❂✷ ❝♦♠ ❞✐❢❡r❡♥t❡s ❝❛r❣❛s ❡❢❡t✐✈❛s
✭δ2 = 90o✮✳ ✭❛✮ P❛rtí❝✉❧❛ ♣❛t❝❤② ❝♦♠ ❝❛r❣❛ ♣♦s✐t✐✈❛✳✭❜✮ P❛rtí❝✉❧❛ ♣❛t❝❤② ❝♦♠
❝❛r❣❛ ♥❡❣❛t✐✈❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✺✷ ✶✻ ❈♦♠♣❛r❛çã♦ ❞❛ ❡♥❡r❣✐❛ ❞❡ ✐♥t❡r❛çã♦ ♣❛r❛ ✭❛✮♣❂✸ ✭δ3= 120o✮✱✭❜✮♣❂✹ ✭δ
4 = 45o✮
❡ ✭❝✮♣❂✺ ✭δ5 = 72o✮ ❝♦♠ ❞✐❢❡r❡♥t❡s ❝❛r❣❛s ❡❢❡t✐✈❛s ❈✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✺✷
✶✼ ■❧✉str❛çã♦ ❞❡ ✉♠❛ ♣❛rtí❝✉❧❛ ♣❛t❝❤② ❝♦♠ ♣❂✹ ♦♥❞❡ r é ✉♠ ✈❡t♦r✱ ♣❡r♣❡♥❞✐❝✉❧❛r
❛ θ✱ ❝❛r❛❝t❡ríst✐❝♦ ❞❛ ♣♦s✐çã♦ ❞❡ ✉♠ ❞♦s ♣❛t❝❤❡s ❝♦♠ r❡s♣❡✐t♦ ❛♦ ❝❡♥tr♦ ❞❡ ♠❛ss❛✳ ♣✳ ✺✹ ✶✽ ❙✐♠✉❧❛çã♦ ❝♦♠ t❡r♠♦st❛t♦ ✭❚✯❂✵✳✵✶✵✮✳ ❘❡s✉❧t❛❞♦ ❞❡ s✐♠✉❧❛çã♦ ❝♦♠ ♣❛rtí❝✉❧❛s
♣❛t❝❤② ✭◆❂✶✵✵✮✱ ✐♥✐❝✐❛❞❛s ❡♠ ♣♦s✐çõ❡s ❛❧❡❛tór✐❛s✱ ❝♦♠ ❝❛r❣❛ ♥❡✉tr❛ ❞♦ t✐♣♦ ♣❂✷✳ ✭❛✮❈♦♠♣♦rt❛♠❡♥t♦ ❞❛s ❡♥❡r❣✐❛s ♣❡❧♦ t❡♠♣♦ ❞❡ s✐♠✉❧❛çã♦ t ✭t0✮✳ ❖♥❞❡ ❑✱ ❯ ❡ ❊ sã♦✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✱ ❛s ❡♥❡r❣✐❛s ❝✐♥ét✐❝❛✱ ♣♦t❡♥❝✐❛❧ ❡ t♦t❛❧ ✭♣♦r ♣❛rtí❝✉❧❛✮✳
✶✾ ❙✐♠✉❧❛çã♦ ❝♦♠ t❡r♠♦st❛t♦✳ ❘❡s✉❧t❛❞♦ ❞❡ s✐♠✉❧❛çã♦ ❝♦♠ ♣❛rtí❝✉❧❛s ♣❛t❝❤② ✭◆❂✶✵✵✮✱ ✐♥✐❝✐❛❞❛s ❡♠ ♣♦s✐çõ❡s ❡ ♦r✐❡♥t❛çõ❡s ❡s♣❡❝í✜❝❛s ♥❛ ❢♦r♠❛ ❡q✉❛t♦r✐❛❧✲♣♦❧❛r ✭❊✲P✮✱ ❝♦♠ ❝❛r❣❛ ♥❡✉tr❛ ❞♦ t✐♣♦ ♣❂✷✳ ✭❛✮❈♦♠♣♦rt❛♠❡♥t♦ ❞❛s ❡♥❡r❣✐❛s ♣❡❧♦ t❡♠♣♦ ❞❡ s✐♠✉❧❛çã♦ t ✭t0✮✳ ❖♥❞❡ ❑✱ ❯ ❡ ❊ sã♦✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✱ ❛s ❡♥❡r❣✐❛s ❝✐♥ét✐❝❛✱
♣♦t❡♥❝✐❛❧ ❡ t♦t❛❧ ✭♣♦r ♣❛rtí❝✉❧❛✮✳ ■❧✉str❛çã♦ ❞❛ ❝♦♥✜❣✉r❛çã♦ ♥♦s ✐♥st❛♥t❡s ✭❜✮
■❧✉str❛çã♦ ❞❛ ❝♦♥✜❣✉r❛çã♦ ❞♦ s✐st❡♠❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✺✾ ✷✵ ❘❡s✉❧t❛❞♦s ❞❛ ❊♥❡r❣✐❛ t♦t❛❧ ✭❡♥❡r❣✐❛ ♣♦r ♣❛rtí❝✉❧❛✮ ♣❡❧♦ t❡♠♣♦ t ✭t0✮ ♣❛r❛ ❞✐❢❡✲
r❡♥t❡s ✈❛❧♦r❡s ❞❡ ❞❡♥s✐❞❛❞❡✿ ✭❛✮ ❉❂✵✳✶✵ ❡ ✭❜✮ ❉❂✵✳✼✵ ❡ ❞✐❢❡r❡♥t❡s t❡♠♣❡r❛t✉r❛s
T∗✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✻✵ ✷✶ ❙✐st❡♠❛ ❞❡ ♣❛rtí❝✉❧❛s ♣❛t❝❤② ❝♦♠ ♣❂✷ ❡ ❝❛r❣❛ ♥❡✉tr❛ ✭❈❂✵✮✳ ❈♦♠♣♦rt❛♠❡♥t♦
❞❛ ❡♥❡r❣✐❛ t♦t❛❧ ♣❡❧❛ t❡♠♣❡r❛t✉r❛ ❡ ✐❧✉str❛çõ❡s ❞♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❡str✉t✉r❛❧ ♣❛r❛ ❛❧❣✉♥s ✈❛❧♦r❡s ❞❡ t❡♠♣❡r❛t✉r❛✳ ❋✉♥çã♦ ❞❡ ❞✐str✐❜✉✐çã♦ r❛❞✐❛❧ ❣✭r✮ ♣❛r❛
❝❛❞❛ t❡♠♣❡r❛t✉r❛ ♠❡♥❝✐♦♥❛❞❛✳ ❉❡♥s✐❞❛❞❡ ❉❂✵✳✶✵✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✻✷ ✷✷ ❈♦♠♣♦rt❛♠❡♥t♦ ❞❛ ❡♥❡r❣✐❛ t♦t❛❧ ✭❡♥❡r❣✐❛ ♣♦r ♣❛rtí❝✉❧❛✮ ❡♠ ❢✉♥çã♦ ❞❛ t❡♠♣❡✲
r❛t✉r❛ ♣❛r❛ ❞❡♥s✐❞❛❞❡s ❉❂✵✳✶✵✱ ❉❂✵✳✶✺✱ ❉❂✵✳✷✵✱ ❉❂✵✳✷✺✱ ❉❂✵✳✸✵ ❡ ❉❂✵✳✹✵ ✳ ♣✳ ✻✸ ✷✸ ❙✐st❡♠❛ ❞❡ ♣❛rtí❝✉❧❛s ♣❛t❝❤② ❝♦♠ ♣❂✷ ❡ ❝❛r❣❛ ♥❡✉tr❛ ✭❈❂✵✮✳ ❈♦♠♣♦rt❛♠❡♥t♦
❞❛ ❡♥❡r❣✐❛ t♦t❛❧ ♣❡❧❛ t❡♠♣❡r❛t✉r❛ ❡ ✐❧✉str❛çõ❡s ❞♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❡str✉t✉r❛❧ ♣❛r❛ ❛❧❣✉♥s ✈❛❧♦r❡s ❞❡ t❡♠♣❡r❛t✉r❛✳ ❋✉♥çã♦ ❞❡ ❞✐str✐❜✉✐çã♦ r❛❞✐❛❧ ❣✭r✮ ♣❛r❛
❝❛❞❛ t❡♠♣❡r❛t✉r❛ ♠❡♥❝✐♦♥❛❞❛✳ ❉❡♥s✐❞❛❞❡ ❉❂✵✳✼✵✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✻✹ ✷✹ ❉✐❛❣r❛♠❛ ❞❡ ❢❛s❡s ♣❛r❛ s✐st❡♠❛s ❞❡ ♣❛rtí❝✉❧❛s ♣❛t❝❤② ❝♦♠ ♣❂✷✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✻✺ ✷✺ ❈♦♠♣♦rt❛♠❡♥t♦ ❞❛ ❡♥❡r❣✐❛ ❞❡ ✐♥t❡r❛çã♦ ♣❛r❛ ♣❛rtí❝✉❧❛s ♣❛t❝❤② ❝♦♠ ♣❂✷✳ ❆
❡sq✉❡r❞❛✱ ♦s ❣rá✜❝♦s q✉❡ r❡♣r❡s❡♥t❛♠ ❛ ❡♥❡r❣✐❛ ❞❡ ✐♥t❡r❛çã♦ ♠í♥✐♠❛ ❡♥tr❡ ❞✉❛s ♣❛rtí❝✉❧❛s ♣❛r❛ ❝❛❞❛ ✈❛❧♦r ❞❡ ❝❛r❣❛✳ ❆ ❞✐r❡✐t❛✱ ❛ ❝♦♥✜❣✉r❛çã♦ ❞♦ s✐st❡♠❛ ♣❛r❛
❝❛❞❛ ✈❛❧♦r ❞❡ ❝❛r❣❛✳ ✭❛✮ ❈❂✵ ✭❉❂✵✳✶✵✮✱✭❜✮❈❂✲✶ ✭❉❂✵✳✶✵✮ ❡ ✭❝✮ ❈❂✷ ✭❉❂✵✳✶✵✮✳ ♣✳ ✻✼ ✷✻ ❈♦♠♣♦rt❛♠❡♥t♦ ❞❛ ❡♥❡r❣✐❛ ❞❡ ✐♥t❡r❛çã♦ ♣❛r❛ ♣❛rtí❝✉❧❛s ♣❛t❝❤② ❝♦♠ ♣❂✸✳ ❆
❡sq✉❡r❞❛✱ ♦s ❣rá✜❝♦s q✉❡ r❡♣r❡s❡♥t❛♠ ❛ ❡♥❡r❣✐❛ ♠í♥✐♠❛ ❞❡ ✐♥t❡r❛çã♦ ❡♥tr❡ ❞✉❛s ♣❛rtí❝✉❧❛s ♣❛r❛ ❝❛❞❛ ✈❛❧♦r ❞❡ ❝❛r❣❛✳ ❆ ❞✐r❡✐t❛✱ ❛ ❝♦♥✜❣✉r❛çã♦ ❞♦ s✐st❡♠❛ ♣❛r❛
❝❛❞❛ ✈❛❧♦r ❞❡ ❝❛r❣❛✳ ✭❛✮ ❈❂✵ ✭❉❂✵✳✸✵✮✱✭❜✮❈❂✶ ✭❉❂✵✳✶✵✮ ❡ ✭❝✮ ❈❂✷ ✭❉❂✵✳✶✵✮✳ ♣✳ ✻✽ ✷✼ ❈♦♠♣♦rt❛♠❡♥t♦ ❞❛ ❡♥❡r❣✐❛ ❞❡ ✐♥t❡r❛çã♦ ♣❛r❛ ♣❛rtí❝✉❧❛s ♣❛t❝❤② ❝♦♠ ♣❂✹✳ ❆
❡sq✉❡r❞❛✱ ♦s ❣rá✜❝♦s q✉❡ r❡♣r❡s❡♥t❛♠ ❛ ❡♥❡r❣✐❛ ♠í♥✐♠❛ ❞❡ ✐♥t❡r❛çã♦ ❡♥tr❡ ❞✉❛s ♣❛rtí❝✉❧❛s ♣❛r❛ ❝❛❞❛ ✈❛❧♦r ❞❡ ❝❛r❣❛✳ ❆ ❞✐r❡✐t❛✱ ❛ ❝♦♥✜❣✉r❛çã♦ ❞♦ s✐st❡♠❛ ♣❛r❛
✷✽ ❈♦♠♣♦rt❛♠❡♥t♦ ❞❛ ❡♥❡r❣✐❛ ❞❡ ✐♥t❡r❛çã♦ ♣❛r❛ ♣❛rtí❝✉❧❛s ♣❛t❝❤② ❝♦♠ ♣❂✺✳ ❆ ❡sq✉❡r❞❛✱ ♦s ❣rá✜❝♦s q✉❡ r❡♣r❡s❡♥t❛♠ ❛ ❡♥❡r❣✐❛ ♠í♥✐♠❛ ❞❡ ✐♥t❡r❛çã♦ ❡♥tr❡ ❞✉❛s ♣❛rtí❝✉❧❛s ♣❛r❛ ❝❛❞❛ ✈❛❧♦r ❞❡ ❝❛r❣❛✳ ❆ ❞✐r❡✐t❛✱ ❛ ❝♦♥✜❣✉r❛çã♦ ❞♦ s✐st❡♠❛ ♣❛r❛
▲■❙❚❆ ❉❊ ❙■●▲❆❙
❉▼ ❉✐♥â♠✐❝❛ ▼♦❧❡❝✉❧❛r
❈P❉ ❈♦♥❞✐çõ❡s P❡r✐ó❞✐❝❛s ❞❡ ❈♦♥t♦r♥♦ ■P❈ ■♥✈❡rs❡ P❛t❝❤② ❈♦❧❧♦✐❞
❈◆Pq ❈♦♥s❡❧❤♦ ◆❛❝✐♦♥❛❧ ❞❡ ❉❡s❡♥✈♦❧✈✐♠❡♥t♦ ❈✐❡♥tí✜❝♦ ❡ ❚❡❝♥♦❧ó❣✐❝♦ ❙❚▼ ❙❝❛♥♥♥✐♥❣ ❚✉♥♥❡❧✐♥❣ ▼✐❝r♦s❝♦♣②
❉❋❚ ❉❡♥s✐t② ❋✉♥❝t✐♦♥❛❧ ❚❤❡♦r② ❈❱❉ ❈❤❡♠✐❝❛❧ ❱❛♣♦r ❉❡♣♦s✐t✐♦♥ ●▲❆❉ ●❧❛♥❝✐♥❣✲❆♥❣❧❡ ❉❡♣♦s✐t✐♦♥ ❙❊▼ ❙❝❛♥♥✐♥❣ ❊❧❡❝tr♦♥ ▼✐❝r♦s❝♦♣②
❙❯▼➪❘■❖
✶ ■◆❚❘❖❉❯➬➹❖ ♣✳ ✶✼
✶✳✶ ❱✐sã♦ ●❡r❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✼ ✶✳✷ P❛rtí❝✉❧❛s P❛t❝❤② ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✵ ✶✳✸ ❚é❝♥✐❝❛s ❞❡ ❋❛❜r✐❝❛çã♦ ❞❡ P❛rtí❝✉❧❛s P❛t❝❤②✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✶
✷ ❋❯◆❉❆▼❊◆❚❖❙ ❚❊Ó❘■❈❖❙ ♣✳ ✷✺
✷✳✶ ▼❡❝â♥✐❝❛ ❊st❛tíst✐❝❛ ❈❧áss✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✺ ✷✳✷ ❋✉♥❞❛♠❡♥t♦s ❞❛ ▼❡❝â♥✐❝❛ ◆❡✇t♦♥✐❛♥❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✽
✸ ❉■◆➶▼■❈❆ ▼❖▲❊❈❯▲❆❘ ♣✳ ✸✷
✸✳✶ ❉❡s❝r✐çã♦ ❞♦ ▼♦❞❡❧♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✸✷ ✸✳✷ ❈á❧❝✉❧♦ ❞❡ ◗✉❛♥t✐❞❛❞❡s ❚❡r♠♦❞✐♥â♠✐❝❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✸✹ ✸✳✸ ❆❧❣♦r✐t♠♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✸✻ ✸✳✸✳✶ ❉▼ ❡♠ ✉♠ ❊♥s❡♠❜❧❡ ▼✐❝r♦❝❛♥ô♥✐❝♦ ✭◆❱❊✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✸✼ ✸✳✸✳✷ ❉▼ ❡♠ ✉♠ ❊♥s❡♠❜❧❡ ❈❛♥ô♥✐❝♦ ✭◆❱❚✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✸✽ ✸✳✹ ❈♦♥❞✐çõ❡s P❡r✐ó❞✐❝❛s ❞❡ ❈♦♥t♦r♥♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✵
✹ ❊◆❊❘●■❆ ❉❊ ■◆❚❊❘❆➬➹❖ ❉❊ P❆❘❊❙ ❊ ▼❖❉❊▲❖ ❉❖ ❙■❙❚❊▼❆ ♣✳ ✹✷
✹✳✶ P❛rtí❝✉❧❛ P❛t❝❤② ❈❛rr❡❣❛❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✷ ✹✳✷ ❊st✉❞♦ ❞❛ ❊♥❡r❣✐❛ ❞❡ ■♥t❡r❛çã♦ ❞❡ P❛r❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✺ ✹✳✸ ❊❢❡✐t♦s ❞❛ ❈❛r❣❛ ❊❢❡t✐✈❛ ❞❛ P❛rtí❝✉❧❛ P❛t❝❤② ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✺✶
✺ ❙■▼❯▲❆➬Õ❊❙ ❊ ❘❊❙❯▲❚❆❉❖❙ ♣✳ ✺✸
✺✳✶✳✷ ❚❡r♠♦st❛t♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✺✻ ✺✳✷ ❉▼ ❡♠ ♣❛rtí❝✉❧❛s ♣❛t❝❤② ❝♦♠ ♣❂✷ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✺✼ ✺✳✷✳✶ ❙✐st❡♠❛s ◆❱❚ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✺✼ ✺✳✸ ❖✉tr❛s ❙✐♠✉❧❛çõ❡s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✻✺
✻ ❈❖◆❈▲❯❙➹❖ ♣✳ ✼✷
✶✼
✶ ■◆❚❘❖❉❯➬➹❖
✶✳✶ ❱✐sã♦ ●❡r❛❧
❆ ❛✉t♦✲♦r❣❛♥✐③❛çã♦ ❡s♣♦♥tâ♥❡❛ ❞❡ s✐st❡♠❛s ❞❡ ❜❛✐①❛s ❞✐♠❡♥s✐♦♥❛❧✐❞❛❞❡s sã♦ ❛♠♣❧❛♠❡♥t❡ ❡st✉❞❛❞❛s ❞❡✈✐❞♦ ❛♦ s❡✉ ❝♦♠♣♦rt❛♠❡♥t♦ ❡str✉t✉r❛❧ ♥❛ s✉❛ ❞❡✈✐❞❛ ❡s❝❛❧❛✳ ❚❛✐s ❡st✉❞♦s sã♦ r❡s✲ ♣♦♥sá✈❡✐s ♣❡❧♦ ❛✈❛♥ç♦ ♥♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ t❡❝♥♦❧ó❣✐❝♦ ❞❡ ❢❛❜r✐❝❛çã♦ ❞❡ ❞✐s♣♦s✐t✐✈♦s ❝❛❞❛ ✈❡③ ♠❡♥♦r❡s ❡ ❝♦♠ ✉♠ ❛❧t♦ ♣♦❞❡r ❞❡ ♣r♦❝❡ss❛♠❡♥t♦✳ ❆ ♦❜s❡r✈❛çã♦ ❡ ❛ ❝❛r❛❝t❡r✐③❛çã♦ ❞♦ ❡st❛❞♦ ❞❡ t❛✐s s✐st❡♠❛s é ❞❡ ❣r❛♥❞❡ ✐♥t❡r❡ss❡ t❛♥t♦ ❞♦ ♣♦♥t♦ ❞❡ ✈✐st❛ ❡①♣❡r✐♠❡♥t❛❧ ❝♦♠♦ t❡ór✐❝♦ ❢❛③❡♥❞♦ ❛s✲ s✐♠ q✉❡ t❛✐s ❡st✉❞♦s t❡♥❤❛♠ ❣r❛♥❞❡ ❛♣❧✐❝❛çã♦ ❡♠ ár❡❛s ❝♦♠♦ ❜✐♦t❡❝♥♦❧♦❣✐❛✱ ♠❡❞✐❝✐♥❛✱ ❡❧❡trô♥✐❝❛✱ ❜✐♦❧♦❣✐❛ ♠♦❧❡❝✉❧❛r✱ ❡t❝✳
❯♠❛ ❞❛s ❝❧❛ss❡s ❜❛st❛♥t❡ ❡st✉❞❛❞❛ ❡♠ s✐st❡♠❛ ❞❡ ❜❛✐①❛ ❞✐♠❡♥s✐♦♥❛❧✐❞❛❞❡ sã♦ ❛q✉❡❧❡s ❝♦♠✲ ♣♦st♦s ❞❡ ♣❛rtí❝✉❧❛s ❝♦❧♦✐❞❛✐s✳ ❚❛✐s s✐st❡♠❛s ❝♦♠❡ç❛r❛♠ ❛ s❡r❡♠ ❢❛❜r✐❝❛❞♦s ♣♦r ✈♦❧t❛ ❞❡ ✶✽✻✵✱ q✉❛♥❞♦ ♦ q✉í♠✐❝♦ ❡s❝♦❝ês ❚❤♦♠❛s ●r❛❤❛♠ ♦❜s❡r✈♦✉ ✐♠♣♦rt❛♥t❡s ❞❡t❛❧❤❡s ❧✐❣❛❞♦s à ❞✐ss♦❧✉çã♦ ❞❡ ❝❡rt❛s s✉❜st❛♥❝✐❛s ❡♠ á❣✉❛✳ ◆❡ss❡ ❡st✉❞♦ ●r❛❤❛♠ ✈❡r✐✜❝♦✉ q✉❡ s✉❜stâ♥❝✐❛s ❝♦♠♦ ❝♦❧❛✱ ❣❡❧❛t✐♥❛✱ ❛♠✐❞♦✱ ❛❧❜✉♠✐♥❛ ❞♦ ♦✈♦✱ ❡♥tr❡ ♦✉tr♦s✱ ❞✐❢❡r❡♥❝✐❛♠✲s❡ ♣❡❧♦s s❡❣✉✐♥t❡s ❛s♣❡❝t♦s❬✸❪✿
• ❞✐❢✉♥❞❡♠✲s❡ ♥❛ á❣✉❛ ♠✉✐t♦ ♠❛✐s ❧❡♥t❛♠❡♥t❡ q✉❡✱ ♣♦r ❡①❡♠♣❧♦✱ ♦ s❛❧ ❡ ♦ ❛çú❝❛r❀ • q✉❛♥❞♦ ❡♠ s♦❧✉çã♦ ❛q✉♦s❛✱ ♣r❛t✐❝❛♠❡♥t❡ ♥ã♦ ❛tr❛✈❡ss❛♠ ❝❡rt❛s ♠❡♠❜r❛♥❛s ♣♦r♦s❛s❀ • ❛♣r❡s❡♥t❛♠ t❡♥❞ê♥❝✐❛ ❛ s❡ ❝r✐st❛❧✐③❛r ❡♠ ❞❡t❡r♠✐♥❛❞♦s ❡st❛❞♦s ❝♦♠ ❞✐❢❡r❡♥t❡s t❡♠♣❡r❛t✉✲
r❛s✱ ❞❡♥s✐❞❛❞❡s✱ ❡t❝✳
❆ ♣❛rt✐r ❞❡ss❛s ♦❜s❡r✈❛çõ❡s✱ s✐st❡♠❛s ❝♦♠ ❝❛r❛❝t❡ríst✐❝❛s ❛❝✐♠❛ ❢♦r❛♠ ❝❤❛♠❛❞❛s ❞❡ ❝♦❧♦✐❞❡s ❡ q✉❛♥❞♦ t❛✐s s✉❜stâ♥❝✐❛s ♣♦ss✉❡♠ ✉♠❛ ❢♦rt❡ t❡♥❞ê♥❝✐❛ à ❝r✐st❛❧✐③❛çã♦ ❡ss❛s sã♦ ❝❤❛♠❛❞♦s ❞❡ ❝r✐st❛❧♦✐❞❡s✳ ❖ ♣r✐♥❝✐♣❛❧ ❝r✐tér✐♦ ♣❛r❛ s❡ ❝❛r❛❝t❡r✐③❛r ✉♠ s✐st❡♠❛ ❝♦❧♦✐❞❛❧ ❜❛s❡✐❛✲s❡ ♥♦ t❛♠❛♥❤♦ ❞❛s ♣❛rtí❝✉❧❛s ❞✐s♣❡rs❛s ♥♦ s♦❧✈❡♥t❡✳ ❆ss✐♠✱ ❞✐③❡♠♦s q✉❡ ✉♠ s✐st❡♠❛ ❝♦❧♦✐❞❛❧ é ✉♠❛ ❞✐s♣❡rsã♦ q✉❛♥❞♦ ❛s ♣❛rtí❝✉❧❛s ♣♦ss✉❡♠ ✉♠ t❛♠❛♥❤♦ ♠é❞✐♦ ❡♥tr❡ ✶ ❡ ✶✵✵✵ ♥❛♥ô♠❡tr♦s ✭♥♠✮✳ ❈♦♠ ❡ss❛ ❞✐♠❡♥sã♦✱ ❛s ♣❛rtí❝✉❧❛s ❝♦❧♦✐❞❛✐s ♥♦r♠❛❧♠❡♥t❡ ♣♦ss✉❡♠ ♠❛ss❛s✱ ❛♣r♦①✐♠❛❞❛♠❡♥t❡✱ ❡♠ t♦r♥♦ ❞❡ ✶✵✳✵✵✵ ❡ ✶✵✵✳✵✵✵ ✉♥✐❞❛❞❡s ❞❡ ♠❛ss❛s ❛tô♠✐❝❛s✳
✶✽
❉✐s♣❡rs♦ ❉✐s♣❡rs❛♥t❡ ◆♦♠❡ ♣❛rt✐❝✉❧❛r ❊①❡♠♣❧♦s
❙ó❧✐❞♦ ❙ó❧✐❞♦ • ❱✐❞r♦ ✈❡r♠❡❧❤♦
❝♦♥t❡♥❞♦ ♦✉r♦ ❝♦❧♦✐❞❛❧ ❙ó❧✐❞♦ ▲íq✉✐❞♦ ❙♦❧✭❤✐❞r♦ss♦❧✱ s❡ ♦ ❧íq✉✐❞♦ ❢♦r ❛ á❣✉❛✮ ●❡❧❛t✐♥❛ ❡♠ á❣✉❛✱
❣♦♠❛✲❛rá❜✐❝❛ ✭❝♦❧❛✮ ❡♠ á❣✉❛✱ ❛r❣✐❧❛ ❡♠ á❣✉❛ ❙ó❧✐❞♦ ●ás ❆❡r♦ss♦❧ ✭s❡ ♦ ❣ás ❢♦r ♦ ❛r✮ ❋✉♠❛ç❛ ❡♠ ❣❡r❛❧
▲íq✉✐❞♦ ❙ó❧✐❞♦ ●❡❧ ●❡❧❡✐❛s ❡♠ ❣❡r❛❧
▲íq✉✐❞♦ ▲íq✉✐❞♦ ❊♠✉❧sã♦ ▲❡✐t❡✱ ♠❛✐♦♥❡s❡
▲íq✉✐❞♦ ●ás ❆❡r♦ss♦❧ ✭s❡ ♦ ❣ás ❢♦r ♦ ❛r✮ ◆❡❜❧✐♥❛✱ s♣r❛② ❞❡
✐♥s❡t✐❝✐❞❛ ♦✉ ♣❡r❢✉r♠❡ ♥♦ ❛r✳
●ás ❙ó❧✐❞♦ • ❆r ♥♦ ✐♥t❡r✐♦r ❞❡
♣❡❞r❛✲ ♣♦♠❡s✱ ♠❛rs❤♠❛❧❧♦✇
●ás ▲íq✉✐❞♦ ❊s♣✉♠❛ ❆r ♥❛ ❡s♣✉♠❛ ❞❡ s❛❜ã♦
♦✉ ♥♦ ❝❤❛♥t✐❧✐✱
CO2 ♥❛ ❡s♣✉♠❛ ❞♦ ❝❤♦♣❡ ●ás ●ás ◆ã♦ ❡①✐st❡✱ ♣♦✐s ♦s ❣❛s❡s ❢♦r♠❛♠ ♠✐st✉r❛s ❤♦♠♦❣ê♥❡❛s
❚❛❜❡❧❛ ✶✿ ❊sq✉❡♠❛ ❞❡ ❞✐s♣❡rs♦s ❝♦❧♦✐❞❛✐s ❡ ❞✐s♣❡rs❛♥t❡s ✭s♦❧✈❡♥t❡s✮ ❡ ❝♦♠ ❛❧❣✉♥s ❡①❡♠♣❧♦s✳
♦s q✉❛✐s ❡stã♦ ❡♠ ✉♠ ♠❡✐♦ ❞❡ ❞✐s♣❡rsã♦✱ ❝❤❛♠❛❞♦ ❞❡ ❞✐s♣❡rs❛♥t❡✳ ❆ t❛❜❡❧❛ ✭✶✮ ❛♣r❡s❡♥t❛ ♦s ❞✐❢❡r❡♥t❡s t✐♣♦s ❞❡ s✐st❡♠❛s ❝♦❧♦✐❞❛✐s✳
❆❧é♠ ❞✐ss♦✱ s❛❜❡✲s❡ q✉❡ ♦s ❝♦❧♦✐❞❡s sã♦ ❝❧❛ss✐✜❝❛❞♦s ❡♠ ❞♦✐s ❣r✉♣♦s✱ ♦s ❧✐ó✜❧♦s ❡ ♦s ❧✐ó❢♦❜♦s✳ ❖s ❧✐ó✜❧♦s ❞✐s♣❡rs❛♠ ❡s♣♦♥t❛♥❡❛♠❡♥t❡ ♥♦ ❞✐s♣❡rs❛♥t❡s ✭❡①❡♠♣❧♦✿ ❣❡❧❛t✐♥❛ ♥❛ á❣✉❛✮ ❡♥q✉❛♥t♦ ♦s ❧✐ó❢♦❜♦s ♥ã♦ ❞✐s♣❡rs❛♠ ✭❡①❡♠♣❧♦s✿ ♠❡t❛✐s✱ ❜❛s❡s✱ s❛✐s✱ ❡t❝✳✮✳ ❱✐st♦ ✐ss♦✱ ♦s ❧✐ó❢♦❜♦s ❡①✐❣❡♠ ♠ét♦❞♦s ❡①♣❡r✐♠❡♥t❛✐s ❡s♣❡❝✐❛✐s ♣❛r❛ s✉❛ ♣r❡♣❛r❛çã♦✳ ❖s ♠ét♦❞♦s ❞❡ ♣r❡♣❛r❛çã♦ ♣♦❞❡♠ s❡r ❞✐✈✐❞✐❞♦s ❡♠ ❞♦✐s ❣r✉♣♦s✿ ❢r❛❣♠❡♥t❛çã♦ ❡ ❛❣❧♦♠❡r❛çã♦ ❬✹❪✳
❆ ❢r❛❣♠❡♥t❛çã♦ é ♦♥❞❡ ♣❛rtí❝✉❧❛s ♠❛✐♦r❡s sã♦ r❡❞✉③✐❞❛s ❛t❡ ❛t✐♥❣✐r ♦ t❛♠❛♥❤♦ ❝❛r❛❝t❡ríst✐❝♦ ❞❡ ✉♠ s✐st❡♠❛ ❝♦❧♦✐❞❛❧✳ ❚é❝♥✐❝❛s ❝♦♠♦ ♠♦✐♥❤♦ ❝♦❧♦✐❞❛❧ ✭tr✐t✉r❛ ❛s ♣❛rtí❝✉❧❛s ❡♠ ❞✐s❝♦s ♠❡✲ tá❧✐❝♦s ❡♠ ❛❧t❛ r♦t❛çã♦✮✱ ♠ét♦❞♦ ❞❡ ❇r❡❞✐❣ ✭♦♥❞❡ ❢❛ís❝❛s ❡❧étr✐❝❛s s❛❧t❛♠ ❡♥tr❡ ❞✉❛s ❝❤❛♣❛s ♠❡tá❧✐❝❛s ♠❡r❣✉❧❤❛❞❛s ❡♠ ✉♠ ❧íq✉✐❞♦❀ ♦ ♣ró♣r✐♦ ♠❡t❛❧ s❡ tr❛♥s❢♦r♠❛ ❡♠ ♣❛rtí❝✉❧❛ ❝♦❧♦✐❞❛❧✮ ❡ ✉❧tr❛ss♦♠ ✭❢r❛❣♠❡♥t❛ ❛ ♣❛rtí❝✉❧❛ ♣♦r ♣✉❧s♦s ❞❡ ♦♥❞❛s s♦♥♦r❛s ❞❡ ❛❧t❛ ❢r❡q✉ê♥❝✐❛✮ sã♦ ❛s ♠❛✐s ✉t✐❧✐③❛❞❛s ♣❛r❛ ❞✐♠✐♥✉✐r ♦ t❛♠❛♥❤♦ ❞❛ ♣❛rtí❝✉❧❛✳
P♦r ♦✉tr♦ ❧❛❞♦✱ ♦ ♠ét♦❞♦ ❞❡ ❛❣❧♦♠❡r❛çã♦ ✉s❛ ♦ ❢❛t♦ ❞❡ ♣❛rtí❝✉❧❛s ♠❡♥♦r❡s ❢♦r♠❛♠ ❣r✉♣♦s ❛té ❛t✐♥❣✐r ♦ t❛♠❛♥❤♦ ❝♦❧♦✐❞❛❧✳ ❚é❝♥✐❝❛s ❝♦♠♦ ♠✉❞❛♥ç❛ ❞♦ s♦❧✈❡♥t❡ ♦✉ r❡❛çõ❡s q✉í♠✐❝❛s ✭♦♥❞❡ ♣♦❞❡rá ❡①✐st✐r ❛ ❢♦r♠❛çã♦ ❞❡ ❛❣❧♦♠❡r❛❞♦ ❝♦❧♦✐❞❛❧ ♥❛ ❢♦r♠❛ ❞❡ ♣r❡❝✐♣✐t❛❞♦✮ sã♦ ✉t✐❧✐③❛❞❛s ♣❛r❛ ♦❜t❡r s✐st❡♠❛s ❝♦❧♦✐❞❛✐s ❬✺❪✳
✶✾
r❡♥t❡s ❢❡♥ô♠❡♥♦s ♥❛ ❢ís✐❝❛ ❞❛ ♠❛tér✐❛ ❝♦♥❞❡♥s❛❞❛ ❬✻✱ ✼✱ ✽❪✳
❆ ❝❛r❛❝t❡r✐③❛çã♦ ❞❡ s✐st❡♠❛s ❝♦❧♦✐❞❛✐s é ❛❜♦r❞❛❞❛ ❝♦♥s✐❞❡r❛♥❞♦ ❛s ❢♦rç❛s ✐♥t❡r♠♦❧❡❝✉❧❛r❡s ❡♥tr❡ ❛s ♣❛rtí❝✉❧❛s ❡ ♦ ♣♦t❡♥❝✐❛❧ ❡①t❡r♥♦✳ ❯♠❛ ✐♠♣♦rt❛♥t❡ ❝❛r❛❝t❡ríst✐❝❛ ❞❡ s✐st❡♠❛ ❝♦❧♦✐❞❛✐s é ❛ ❝❛♣❛❝✐❞❛❞❡ ❞❡ s❡ ✐♥❞✉③✐r ❞✐❢❡r❡♥t❡s t✐♣♦s ❞❡ ✐♥t❡r❛çõ❡s ❡♥tr❡ ❛s ♣❛rtí❝✉❧❛s✳ ❊①✐st❡♠ ✈ár✐❛s ❢♦r♠❛s ❞❡ ✐♥t❡r❛çõ❡s ❡ ✐♥t❡♥s✐❞❛❞❡s ❛♦ q✉❛❧ ❝❛❞❛ ♣❛rt❡ ♣♦❞❡ s❡r ❝♦♥tr♦❧❛❞❛ ❝♦♥t✐♥✉❛♠❡♥t❡✳ ❯♠ ❡①❡♠♣❧♦ é ♦ ♣♦t❡♥❝✐❛❧ ❞❡ ❨✉❦❛✇❛ ❬✶✶✱ ✶✷❪ q✉❡ ♣♦ss✉✐ ❝♦♠♦ ❝❛s♦ ❡s♣❡❝í✜❝♦ ♦ ♣♦t❡♥❝✐❛❧ ❈♦❧♦♠❜✐✲ ❛♥♦✳ ❆ ❛♣r♦①✐♠❛çã♦ ❞❡ ❨✉❦❛✇❛ r❡✢❡t❡ ❡♠ r❡s✉❧t❛❞♦s ❜❛st❛♥t❡s s❛t✐s❢❛tór✐♦s ❞♦ ♣♦♥t♦ ❞❡ ✈✐st❛ ❡①♣❡r✐♠❡♥t❛❧✳ P♦t❡♥❝✐❛✐s ❞❡ ✐♥t❡r❛çã♦ t❡ór✐❝♦s t❛♠❜é♠ sã♦ ❡st✉❞❛❞♦s ♣❛r❛ t❡♥t❛r s✐♠✉❧❛r ❡❢❡✐t♦s ❣❡♦♠étr✐❝♦s ❞❛s ♣❛rtí❝✉❧❛s✱ ❝♦♠♦ ♣♦r ❡①❡♠♣❧♦✱ ♦ ♣♦t❡♥❝✐❛❧ t✐♣♦ ❡s❢❡r❛ ❞✉r❛✳ ❚❛✐s ♣♦t❡♥❝✐❛✐s s❡rã♦ ❝♦♠❡♥t❛❞♦s ♥♦s ❝❛♣ít✉❧♦s s❡❣✉✐♥t❡s✳
❙✐st❡♠❛s ❞❡ ♣❛rtí❝✉❧❛s ❝♦❧♦✐❞❛✐s ♣♦❞❡♠ s❡r ♦❜s❡r✈❛❞❛s ❛tr❛✈és ❞❡ ✉♠ ♠✐❝r♦s❝ó♣✐♦ ❞❡✈✐❞♦ ❛♦ s❡✉ t❛♠❛♥❤♦ ♠❡s♦s❝ó♣✐❝♦✱ ❛tr❛✈és ❞❡ ♠✐❝r♦s❝♦♣✐❛ ❞❡ ❢♦rç❛ ❛tô♠✐❝❛ ♦✉ ♣❡❧♦ ♠✐❝r♦s❝ó♣✐♦ ❞❡ ❝♦rr❡♥t❡ ❞❡ t✉♥❡❧❛♠❡♥t♦✱ ❡♠ ✐♥❣❧ês✱ s❝❛♥♥♥✐♥❣ t✉♥♥❡❧✐♥❣ ♠✐❝r♦s❝♦♣②✭❙❚▼✮✳ ❆❧é♠ ❞✐ss♦✱ ❛s ✐♥t❡✲ r❛çõ❡s ❡♥tr❡ ❝♦❧♦✐❞❡s ♣♦❞❡♠ s❡r ❝♦♥tr♦❧❛❞❛s ❝♦♠ ♣r❡❝✐sã♦ ❛tr❛✈és ❞❡ ♣♦t❡♥❝✐❛✐s ❡①t❡r♥♦s✳ ❉❡✈✐❞♦ ❛♦ s❡✉ t❡♠♣♦ ❞❡ ❛✉t♦❞✐❢✉sã♦ s❡r r❡❧❛t✐✈❛♠❡♥t❡ ❧♦♥❣♦✱ é ♣♦ssí✈❡❧ ❡st✉❞❛r ❛ s✉❛ ❝r✐st❛❧✐③❛çã♦ ❞❡ ❢♦r♠❛ ❞✐♥â♠✐❝❛ ✉t✐❧✐③❛♥❞♦ ❡ss❡s ❡q✉✐♣❛♠❡♥t♦s✳
❯♠ ❝♦♥❥✉♥t♦ ❞❡ ♣❛rtí❝✉❧❛s ❝♦❧♦✐❞❛✐s ♣♦❞❡♠ ❛♣r❡s❡♥t❛r✱ ❡♠ ✉♠ ❞❛❞♦ ❡st❛❞♦ ❞❡ ❡q✉✐❧í❜r✐♦✱ ❢❛✲ s❡s ❡str✉t✉r❛✐s ❞✐st✐♥t❛s✳ ◆♦ r❡❣✐♠❡ ❝❧áss✐❝♦ ♦ ❡st❛❞♦ ❞❡ ❡q✉✐❧í❜r✐♦ t❡r♠♦❞✐♥â♠✐❝♦ ❞❡ ✉♠ s✐st❡♠❛ ❞❡ ♣❛rtí❝✉❧❛s é ❞❡t❡r♠✐♥❛❞♦ ❛♥❛❧✐s❛♥❞♦ ❛ ✐♠♣♦rtâ♥❝✐❛ ❞❛ ❡♥❡r❣✐❛ ❞❡ ✐♥t❡r❛çõ❡s ❡♥tr❡ ♦s ❝♦♥st✐✲ t✉✐♥t❡s ❞♦ s✐st❡♠❛ ❡ ❛ ❡♥❡r❣✐❛ ❝✐♥ét✐❝❛ ❞♦ ♠❡s♠♦✳ ◆♦ ❝❛s♦ ❞❛ ✐♥t❡r❛çã♦ ❈♦❧♦♠❜✐❛♥❛✱ ♦ ❢ís✐❝♦ ❲✐❣♥❡r ❬✶✸❪ ♠♦str♦✉ t❡♦r✐❝❛♠❡♥t❡ q✉❡ ❡❧étr♦♥s ♣♦❞❡♠ ❝r✐st❛❧✐③❛r ♥✉♠❛ ❢♦r♠❛ ♦r❞❡♥❛❞❛ q✉❛♥❞♦ ✈❛❧♦r❡s ❝rít✐❝♦s ❞❡ ❞❡♥s✐❞❛❞❡ ❡ t❡♠♣❡r❛t✉r❛ sã♦ ❛t✐♥❣✐❞♦s ✭❛❧t❛ ❞❡♥s✐❞❛❞❡ ❡ ❜❛✐①❛ t❡♠♣❡r❛t✉r❛✮✳ ❉❡✜♥✐♥❞♦ ♦ ♣❛râ♠❡tr♦ Γ = <V ><K>✱♦♥❞❡ ❱ é ❛ ❡♥❡r❣✐❛ ❞❡ ✐♥t❡r❛çã♦ ❡♥tr❡ ❛s ♣❛rtí❝✉❧❛s ❡ ❑ é ❛
❡♥❡r❣✐❛ ❝✐♥ét✐❝❛✱ r❡❧❛❝✐♦♥❛❞❛ ❝♦♠ ❛ t❡♠♣❡r❛t✉r❛ ❞♦ s✐st❡♠❛✱ ❲✐❣♥❡r ♣r❡✈✐✉ q✉❡✱ ❡♠ ✉♠ s✐st❡♠❛ tr✐❞✐♠❡♥s✐♦♥❛❧✱ ❡❧étr♦♥s ♣♦❞❡♠ ❝r✐st❛❧✐③❛r ❡♠ ❝❡rt❛s ❝♦♥❞✐çõ❡s✳ P❛r❛Γ<1✱ ❛ ❡♥❡r❣✐❛ ❝✐♥ét✐❝❛ é
♠❛✐♦r q✉❡ ❛ ♣♦t❡♥❝✐❛❧✱ ❞❡ss❛ ❢♦r♠❛ é ✈❡r✐✜❝❛❞♦ q✉❡ ♦ ❡❢❡✐t♦ ❞❛ t❡♠♣❡r❛t✉r❛ é ♠✉✐t♦ s✉♣❡r✐♦r ❛ ❢♦rç❛s ✐♥t❡r♠♦❧❡❝✉❧❛r❡s ❡♥tr❡ ❛s ♣❛rtí❝✉❧❛s✳ ◆❡ss❛s ❝♦♥❞✐çõ❡s ♦ s✐st❡♠❛ é ❝❛r❛❝t❡r✐③❛❞♦ ♣♦r ✉♠ ❣ás ❞❡ ❢ér♠✐♦s✳ ◗✉❛♥❞♦1<Γ<100✱ ♦s ❡❧étr♦♥s ❡stã♦ ❢r❛❝❛♠❡♥t❡ ❝♦rr❡❧❛❝✐♦♥❛❞♦s ❡ ❞❡ss❛ ❢♦r♠❛
♦ s✐st❡♠❛ ❝♦♠♣♦rt❛✲s❡ ❝♦♠♦ ✉♠ ❧íq✉✐❞♦✳ P❛r❛Γ >100 ❛ ❡♥❡r❣✐❛ ♣♦t❡♥❝✐❛❧ é tã♦ ✐♥t❡♥s❛ q✉❡ ♦
✷✵
✶✳✷ P❛rtí❝✉❧❛s P❛t❝❤②
▼✉✐t♦s ❡s❢♦rç♦s ❡stã♦ s❡♥❞♦ ❞❡s❡♥✈♦❧✈✐❞♦s ♣❛r❛ ❛ sí♥t❡s❡ ❡ ❝❛r❛❝t❡r✐③❛çã♦ ❞❡ ♣❛rtí❝✉❧❛s ❝♦❧♦✐✲ ❞❛✐s ❞❡ ❞✐✈❡rs❛s ❢♦r♠❛s✳ ❆ ✐♥t❡♥çã♦ é ✈❡r✐✜❝❛r ❛s ♣♦ssí✈❡✐s ❡str✉t✉r❛s q✉❡ ❡ss❡s s✐st❡♠❛s ♣♦❞❡♠ ❢♦r♠❛r✳ ➱ ♥♦tá✈❡❧ q✉❡ ♦ t✐♣♦ ❞❡ ♣♦t❡♥❝✐❛❧ ❞❡ ✐♥t❡r❛çã♦ ✐rá ♠♦❞❡❧❛r✱ ❥✉♥t♦ ❝♦♠ ❛ t❡♠♣❡r❛t✉r❛ ❞♦ s✐st❡♠❛✱ ♦ ❡st❛❞♦ ❢ís✐❝♦ ❞❡ s✐st❡♠❛s ❝♦❧♦✐❞❛✐s✳
❉❡ss❛ ❢♦r♠❛✱ ♣❛rtí❝✉❧❛s ❛♥✐s♦tró♣✐❝❛s ❢♦r♠❛♠ ❞✐✈❡rs❛s ❡str✉t✉r❛s✱ ❢❛③❡♥❞♦ ❝♦♠ q✉❡ ❣❛♥❤❡♠ ✉♠ ✐♥t❡r❡ss❡ ♠❛✐♦r ♦ q✉❡ ♣♦❞❡♠ ✐♥❝❧✉✐r ✉♠ ♠❡❧❤♦r ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❡♠ sí♥t❡s❡s ❞❡ ♣❛rtí❝✉❧❛s ❡ ♥❛ ❛♣❧✐❝❛çã♦ ❢✉♥❝✐♦♥❛❧ ❞❛ ♠❛tér✐❛✳
◆❡ss❡ ❝♦♥t❡①t♦✱ ❢♦✐ ❝r✐❛❞♦ ✉♠❛ ♥♦✈❛ ❝❧❛ss❡ ❞❡ ♣❛rtí❝✉❧❛s ❝♦❧♦✐❞❛✐s ❝❤❛♠❛❞❛s ❞❡ ♣❛rtí❝✉❧❛s ✧♣❛t❝❤②✧✳ ❚❛❧ ❝♦❧♦✐❞❡ ♣♦ss✉✐ ❡ss❡♥❝✐❛❧♠❡♥t❡ ✉♠ ♣♦t❡♥❝✐❛❧ ❛♥✐s♦tró♣✐❝♦ ❛ss♦❝✐❛❞♦ ❛ ❝❛❞❛ ♣❛rtí✲ ❝✉❧❛ ❬✶✵❪✳ ❆ ❢♦r♠❛ ❞♦ ♣♦t❡♥❝✐❛❧ ❞❡ ✐♥t❡r❛çã♦ é ✉♠❛ ❝♦♥s❡q✉ê♥❝✐❛ ❞❛s ♠♦❞✐✜❝❛çõ❡s ❢ís✐❝❛s ❡✴♦✉ q✉í♠✐❝❛s ❛tr✐❜✉í❞❛s ❛s ♣❛rtí❝✉❧❛s✳
❆ ❝♦♠♣❧❡①✐❞❛❞❡ ♥♦ ❡st✉❞♦ ❞❡ ✉♠❛ ♣❛rtí❝✉❧❛ ♣❛t❝❤② ❝♦♠❡ç❛ ♥❛ ✈❛r✐❡❞❛❞❡ ❞❡ ✐♥t❡r❛çõ❡s q✉❡ ❡ss❛s ♣❛rtí❝✉❧❛s ♣♦❞❡♠ ❛♣r❡s❡♥t❛r✳ ❙❡❣✉♥❞♦ ●❧♦t③❡r ❬✶✵❪✱ ♣❛rtí❝✉❧❛ ♣❛t❝❤② é ❞❡✜♥✐❞❛ ❛♣❡♥❛s ♣❡❧♦ ❢❛t♦ ❞❡ q✉❡ ❛ ♣❛rtí❝✉❧❛ ♣♦ss✉❛ ✉♠❛ ✐♥t❡r❛çã♦ ❛♥✐s♦tró♣✐❝❛✳ ▼❛s t❛❧ ❞❡✜♥✐çã♦ ❛❣r❡❣❛ ✉♠❛ q✉❛♥t✐❞❛❞❡ ✐♠❡♥s❛ ❞❡ ♣❛rtí❝✉❧❛s ❝♦♠♦ ♠❛❝r♦♠♦❧é❝✉❧❛s ❜✐♦❧ó❣✐❝❛s✱ ✈ír✉s✱ ♣r♦t❡í♥❛s ❣❧♦❜✉❧❛r❡s ❡ ❞✐♣♦❧♦s✳ ❉❡ss❛ ❢♦r♠❛✱ ❡ss❛ ❞✐ss❡rt❛çã♦ ✐rá s❡ ❝♦♥❝❡♥tr❛r ❡♠ ❛❧❣✉♥s ❡①❡♠♣❧♦s ❞❡ ♣❛rtí❝✉❧❛s ♣❛t❝❤②✱ ♦✉ s❡❥❛✱ ✐r❡♠♦s s❡ ❝♦♥❝❡♥tr❛r ❡♠ s✐st❡♠❛s ♦♥❞❡ ❛s ♣❛rtí❝✉❧❛s sã♦ ❡s❢ér✐❝❛s ❡ ❛ s✉♣❡r❢í❝✐❡ ❞❛ ♠❡s♠❛ ♣♦❞❡ s❡r ♠♦❞❡❧❛❞❛ ❞❡ ❢♦r♠❛ q✉❡ s❡ t❡♥❤❛ ✉♠ ♣♦t❡♥❝✐❛❧ ❞❡ ✐♥t❡r❛çã♦ ❛♥✐s♦tró♣✐❝♦ ♥♦ s✐st❡♠❛✳
Pr✐♠❡✐r❛♠❡♥t❡✱ é ♥❡❝❡ssár✐♦ ♦❜t❡r ✉♠❛ ♥♦♠❡♥❝❧❛t✉r❛ ♣❛r❛ ♣❛rtí❝✉❧❛ ♣❛t❝❤②✳ ❉❡✜♥✐✲s❡ ♥❛ ❋✐❣✉r❛ ✭✶✮ ❛❧❣✉♠❛s ❝❧❛ss❡s ♣❛r❛ ♠❡❧❤♦r r❡♣r❡s❡♥t❛✲❧❛s ❬✶✹❪✳
❆s ♣❛rtí❝✉❧❛s ♣❛t❝❤② ♠❛✐s s✐♠♣❧❡s sã♦ ❛s ♣❛rtí❝✉❧❛s ❏❛♥✉s ✭♦ ♥♦♠❡ é ❞❡❞✐❝❛❞♦ ❛♦ ❞❡✉s r♦♠❛♥♦ ❏❛♥✉s✮❬✶✽✱ ✶✾❪✳ ❊ss❛ ♣❛rtí❝✉❧❛ tí♣✐❝❛ s❡ ❡♥q✉❛❞r❛ ♥❛ ❝❧❛ss❡ ❆ ✭❋✐❣✉r❛ ✭✶✮✮ ❡ ❥á ♣♦ss✉✐ ✉♠❛ ❣r❛♥❞❡ q✉❛♥t✐❞❛❞❡ ❞❡ ❛rt✐❣♦s ❝✐❡♥tí✜❝♦s r❡❧❛❝✐♦♥❛❞❛s ❛♦ s❡✉ ❡st✉❞♦✳ ❆ ♣r✐♥❝✐♣❛❧ ❝❛r❛❝t❡ríst✐❝❛ ❞❡ss❛ ♣❛rtí❝✉❧❛ ♣❛t❝❤② é q✉❡ ❛ ♠❡s♠❛ ♣♦ss✉✐ ❤❡♠✐s❢ér✐♦s ♣r❡❝✐s❛♠❡♥t❡ ✧❞❡❝♦r❛❞♦s✧❝♦♠ ❞✐❢❡r❡♥t❡s ♠❛✲ t❡r✐❛✐s ❡ ❞✐✈❡rs❛s ❢✉♥❝✐♦♥❛❧✐❞❛❞❡s✳ ❖ ♣♦t❡♥❝✐❛❧ ❛♥✐s♦tró♣✐❝♦ s✉r❣✐ ♣❡❧♦ ❢❛t♦ ❡♠ q✉❡ ❤á ❞✉❛s r❡❣✐õ❡s ❞✐st✐♥t❛s ♥❛ s✉♣❡r❢í❝✐❡ ❞❛ ♣❛rtí❝✉❧❛ q✉❡ ♣♦❞❡♠ ♣♦ss✉✐r ♠❛t❡r✐❛✐s ❞✐❢❡r❡♥t❡s ❝♦♠ ❛ ❝♦♠❜✐♥❛çã♦ ❞♦ t✐♣♦ ❤✐❞r♦❢ó❜✐❝♦✴❤✐❞r♦❢í❧✐❝♦✱ ♠❡tá❧✐❝♦✴♣♦❧í♠❡r♦✱ ❝❛rr❡❣❛❞♦✴❞❡s❝❛rr❡❣❛❞♦✱ ♦r❣â♥✐❝♦✴✐♥♦r❣â♥✐❝♦ ♦✉ ❛té ♠❡s♠♦ ✉♠❛ ❝♦♠❜✐♥❛çã♦ ❞❡ ✈ár✐❛s ❞❡ss❛s ❝❛r❛❝t❡ríst✐❝❛s✳
✷✶
❋✐❣✉r❛ ✶✿ ▼♦❞❡❧♦s ❞❡ ♣❛rtí❝✉❧❛s ♣❛t❝❤②✳ ❈❧❛ss❡✿ ❆✲ ❈♦❜❡rt✉r❛ s✉♣❡r✜❝✐❛❧❀❇✲ ❘❡❧❛çã♦ ❞❡ ❛s♣❡❝t♦❀ ❈✲ ▼♦❞✐✜❝❛çã♦ ❞❡ ❢❛s❡❀❉✲ ◗✉❛♥t✐③❛çã♦ ♣❛❞rã♦❀ ❊✲❇✐❢✉r❝❛çã♦❀ ❋✲ ❖r❞❡♥❛♠❡♥t♦ q✉í♠✐❝♦❀ ●✲ ●r❛❞✐❡♥t❡ ❞❡ ❢♦r♠❛s✳ ❍✲ ❘✉❣♦s✐❞❛❞❡ ❬✶✹❪✳
✶✳✸ ❚é❝♥✐❝❛s ❞❡ ❋❛❜r✐❝❛çã♦ ❞❡ P❛rtí❝✉❧❛s P❛t❝❤②✳
❊①✐st❡♠ ✈ár✐❛s té❝♥✐❝❛s ♣❛r❛ ❢❛❜r✐❝❛çã♦ ❡ ♠♦❞✐✜❝❛çã♦ ❞❛ s✉♣❡r❢í❝✐❡ ❞❡ ✉♠❛ ♣❛rtí❝✉❧❛ ♣❛t❝❤②✳ ❆❧❣✉♠❛s ❞❛s té❝♥✐❝❛s sã♦ ❧✐st❛❞❛s ❛❜❛✐①♦✿
✶✳ ▼♦❞❡❧❛❣❡♠ ❝♦❧♦✐❞❛❧❀ ✷✳ ❈❧✉st❡r ❝♦❧♦✐❞❛❧❀
✸✳ ▲✐t♦❣r❛✜❛ ❞❡ ♣❛rtí❝✉❧❛s❀ ✹✳ ❉❡♣♦s✐çã♦ â♥❣✉❧♦✲✈✐s✉❛❧❀ ✺✳ ❋❧✉①♦ ✢✉✐❞♦ ❝❛♣✐❧❛r✳
✷✷
❛♦ ✈❛♣♦r✳ ❚❛❧ ♠ét♦❞♦ é ❜❛st❛♥t❡ ✉t✐❧✐③❛❞♦ ♣❛r❛ ❢❛❜r✐❝❛r ♣❛rtí❝✉❧❛s ❏❛♥✉s ❡♠ ❣r❛♥❞❡ q✉❛♥t✐❞❛❞❡ ❬✶✺✱ ✶✻❪✳
❉♦✐s ❢❛t♦r❡s ❣❡♦♠étr✐❝♦s sã♦ ❡ss❡♥❝✐❛✐s ♣❛r❛ ♦ ❝♦♥tr♦❧❡ ♥❛ ♣r❡♣❛r❛çã♦ ❞❛s ♣❛rtí❝✉❧❛s✳ i)
♦ â♥❣✉❧♦ ❞❡ ❡✈❛♣♦r❛çã♦ ✭Θ✮ ❡ ♦ â♥❣✉❧♦ ❞❡ ♦r✐❡♥t❛çã♦ ❞❛ ♠♦♥♦❝❛❞❡✐❛ ❡♠ r❡❧❛çã♦ ❛ ❢♦♥t❡ ❞❡
❡✈❛♣♦r✐③❛çã♦ ✭α✮✳ ❆ ❞✐✜❝✉❧❞❛❞❡ ❞❛ té❝♥✐❝❛ é ♣r❡✈❡r q✉❛❧ s❡rá ❛ ❢♦r♠❛ ❣❡♦♠étr✐❝❛ ❞❛ r❡❣✐ã♦ ❞❡♣♦s✐t❛❞❛✳ ❆ ❢♦r♠❛ ❞♦s ♣❛t❝❤❡s sã♦ ❜❡♠ ❞❡✜♥✐❞❛s✱ ♠❛s ❛ té❝♥✐❝❛ ❞✐✜❝✉❧t❛ ❛ ❡❧❛❜♦r❛çã♦ ❞❡ ❢❛❜r✐❝❛çã♦ ♣❛r❛ ✉♠❛ ❞❛❞❛ ♣❛rtí❝✉❧❛ ❏❛♥✉s ❡s♣❡❝✐✜❝❛ q✉❡ s❡ ❞❡s❡❥❛ ❢❛❜r✐❝❛r✳
❆ ❋✐❣✉r❛ ✭✷✮ ♠♦str❛ ❛s ✈✐s✉❛❧✐③❛çõ❡s ❡♠ ♠✐❝r♦s❝♦♣✐❛ ❞❡ ✈❛rr❡❞✉r❛ ❡❧❡trô♥✐❝❛✱ ♥♦ ✐♥❣❧ês✱ ❙❝❛♥♥✐♥❣ ❊❧❡❝tr♦♥ ▼✐❝r♦s❝♦♣② ✭❙❊▼✮✱ ♣❛r❛ ✈ár✐♦s ✈❛❧♦r❡s ❞❡α❡♠ ✉♠❛ ♠♦♥♦❝❛❞❡✐❛ ❞❡ ♣❛rtí❝✉❧❛s ❏❛♥✉s ❞❡ ♣♦❧✐❡st✐r❡♥♦ ❝♦♠ ♣❛t❝❤❡s ❞❡ ♦✉r♦✳
P♦r ♦✉tr♦ ❧❛❞♦✱ ❛ té❝♥✐❝❛ ❞❡ ❋❧✉①♦ ❞❡ ❋❧✉✐❞♦ ❈❛♣✐❧❛r ♣♦ss✉✐ ✉♠ ♠❛✐♦r ❝♦♥tr♦❧❡ s♦❜r❡ ❛ r❡❣✐ã♦ ❛♦ q✉❛❧ s❡ ❞❡s❡❥❛r ♠♦❞✐✜❝❛r ❛ ♣❛rtí❝✉❧❛✳ ❖ ♠ét♦❞♦ ❞❡ ❢❛❜r✐❝❛çã♦ s❡ ❞❛ ♣❡❧♦ ✉s♦ ❞❡ ♠✐❝r♦✢✉✐❞♦s ❛♦ q✉❛❧ ❝❛❞❛ ♣❛rtí❝✉❧❛ é ✐♥❞✐✈✐❞✉❛❧♠❡♥t❡ ♠♦❞✐✜❝❛❞❛ ♥❛s r❡❣✐õ❡s ♣r❡❞❡t❡r♠✐♥❛❞❛s✳ ❈❛❞❛ ♣❛rtí❝✉❧❛ é ❡♠✉❧s✐♦♥❛❞❛ ❡♠ s♦❧✉çã♦ ❛q✉♦s❛✱ ❝❛❞❛ ❝❛♣✐❧❛r ❡♥✈♦❧✈❡ ❛ ♣❛rtí❝✉❧❛ ♣♦r ✉♠❛ ❞❛❞❛ r❡❣✐ã♦ ❡ ✉♠❛ ❞❛❞❛ s✉❜stâ♥❝✐❛✳ ❆♦ ✜♥❛❧ ❞♦ ♣r♦❝❡ss♦ s❡ ❢❛③ ♦ ✉s♦ ❞❡ ❧✉③ ✉❧tr❛✈✐♦❧❡t❛ ✭❯❱✮ ♣❛r❛ ♣♦❧✐♠❡r✐③❛r ❛ ♣❛rtí❝✉❧❛✳ ❊ss❛ té❝♥✐❝❛ é ♠✉✐t♦ ✉t✐❧✐③❛❞❛ ♣❛r❛ ❝r✐❛çã♦ ❞❡ ♣❛rtí❝✉❧❛s ❏❛♥✉s ❜❡♠ ❞❡✜♥✐❞❛s✱ ♣♦ré♠ ❛ ♠❡s♠❛ ♣♦ss✉✐ ❞✐✜❝✉❧❞❛❞❡s ♣❛r❛ ♣r♦❞✉③✐r ✉♠❛ q✉❛♥t✐❞❛❞❡ ♠❛✐♦r ❞❡ ♣❛rtí❝✉❧❛s q✉❛♥❞♦ ❝♦♠♣❛r❛❞❛ ❛♦ ●▲❆❉ ❬✶✼❪✳
❋✐❣✉r❛ ✷✿ ❋❛❜r✐❝❛çã♦ ❞❡ ♣❛rtí❝✉❧❛s ❏❛♥✉s ❝♦♠ ❛ té❝♥✐❝❛ ●▲❆❉ ♦♥❞❡ ♣❛rtí❝✉❧❛s ❞❡ ♣♦❧✐❡st✐r❡♥♦ sã♦ ✉s❛❞❛s ❝♦♠♦ s✉❜str❛t♦ ♣❛r❛ ❛ ❞❡♣♦s✐çã♦ ❞❡ ♣❛rtí❝✉❧❛s ❞❡ ♦✉r♦✳ ❖ â♥❣✉❧♦ ❞❡ ❡✈❛♣♦r❛çã♦
Θ = 2o ♣❛r❛ ❞✐❢❡r❡♥t❡ â♥❣✉❧♦ ❞❡ ♦r✐❡♥t❛çã♦ ❞♦ ♠♦♥♦❝❛❞❡✐❛✳ ✭❛✮α= 0o✱ ✭❜✮α= 14o✱ ✭❝✮α= 28o✱
✭❞✮α= 38o ❬✶✼❪✳
✷✸
❝❛r❣❛ ♥❛ s✉♣❡r❢í❝✐❡ ♣r❡✈✐♥❡ ❢♦r♠❛çã♦ ❞❡ ✉♠ ❛❣❧♦♠❡r❛❞♦✳ ❚❛❧ té❝♥✐❝❛ r❡s✉❧t❛ ❡♠ ✉♠❛ ❣r❛♥❞❡ ♣r♦❞✉çã♦ ❞❡ ♣❛rtí❝✉❧❛s✱ ♣♦ré♠ ♥ã♦ s❡ ♣♦❞❡ ❝♦♥tr♦❧❛r✱ ❞❡ ❝❡rt❛ ❢♦r♠❛✱ ♦ t❛♠❛♥❤♦ ❡ ❛ ❢♦r♠❛ ❞♦ ❛❣❧♦♠❡r❛❞♦ r❡s✉❧t❛♥t❡✳ ➱ ♥❛ ❢♦r♠❛ ❣❡♦♠étr✐❝❛ q✉❡ ♣❛rtí❝✉❧❛s ❞❡ss❡ t✐♣♦ s❡ ❡♥q✉❛❞r❛♠ ❝♦♠♦ ♣❛rtí❝✉❧❛s ♣❛t❝❤②✳ ❆ ❋♦r♠❛ ✐rr❡❣✉❧❛r r❡s✉❧t❛ ❡♠ ✉♠❛ ❛♥✐s♦tr♦♣✐❛ ❡str✉t✉r❛❧✳ ❚❛❧ té❝♥✐❝❛ ♣♦❞❡ ❢❛❜r✐❝❛r ♣❛rtí❝✉❧❛s ❞♦ t✐♣♦ ❊ ❡ ❍ ✭❋✐❣✉r❛ ✭✶✮✮✳ ❆ ❋✐❣✉r❛ ✭✸✮ ♠♦str❛ ❛ ✐♠❛❣❡♠ ❡♠ ❙❊▼ ❞❡ ❛❣❧♦♠❡r❛❞♦s ✐rr❡❣✉❧❛r❡s✳
❋✐❣✉r❛ ✸✿ ■♠❛❣❡♥s ❙❊▼ ❞❡ ❛❣❧♦♠❡r❛❞♦ ❝♦❧♦✐❞❛✐s ❝♦♠ ◆❂✹✲✶✷ ♣❛rtí❝✉❧❛s ❞❡ ♣♦❧✐❡st✐r❡♥♦ ❡♠✉❧s✐✲ ♦♥❛❞❛s ❡♠ s♦❧✉çã♦ ❞❡ t♦❧✉❡♥♦ ❬✷✸❪✳
❋✐❣✉r❛ ✹✿ ■♠❛❣❡♥s ❙❊▼ ❞❡ ❛❣❧♦♠❡r❛❞♦ ❝♦❧♦✐❞❛✐s ♦♥❞❡ ◆ r❡♣r❡s❡♥t❛ ♦ ♥ú♠❡r♦ ❞❡ ♣❛t❝❤❡s ❞❛s ♣❛rtí❝✉❧❛s ❞❡ ❊❚P❚❆ ❬✷❪✳
✷✹
✷✺
✷ ❋❯◆❉❆▼❊◆❚❖❙ ❚❊Ó❘■❈❖❙
✷✳✶ ▼❡❝â♥✐❝❛ ❊st❛tíst✐❝❛ ❈❧áss✐❝❛
❊♠ ❣❡r❛❧✱ ❛ ♠❛✐♦r✐❛ ❞❛s ❡q✉❛çõ❡s q✉❡ ❞❡s❝r❡✈❡♠ ♦s ❢❡♥ô♠❡♥♦s ❞❛ ♥❛t✉r❡③❛ ♥ã♦ ♣♦❞❡♠ s❡r r❡s♦❧✈✐❞♦s ❡①❛t❛♠❡♥t❡✱ ❡①❝❡t♦ ❡♠ ❝♦♥❞✐çõ❡s ❜❛st❛♥t❡s ❡s♣❡❝í✜❝❛s✱ ❞❡✈✐❞♦ ❛ ❝♦♠♣❧❡①✐❞❛❞❡ ❞❡ s❡✉s ❝♦♠♣♦♥❡♥t❡s ❡ ❛ ♣r❡s❡♥ç❛ ❞❡ ✈ár✐♦s ❢❛t♦r❡s ❡①t❡r♥♦ q✉❡ ❝♦♠♣❧✐❝❛♠ ❛ ❛♥á❧✐s❡ ❞♦ ❢❡♥ô♠❡♥♦ ❡st✉❞❛❞♦✳ ❉❡ss❛ ❢♦r♠❛ é ❞❡ ❣r❛♥❞❡ ✈❛❧✐❛ ♦ ✉s♦ ❞❡ ❢❡rr❛♠❡♥t❛s ❝♦♠♣✉t❛❝✐♦♥❛✐s q✉❡ ♣♦ss❛♠ ❞❡s❝r❡✈❡r ✉♠ s✐st❡♠❛ ❢ís✐❝♦ ❝♦♠♦ ✉♠ t♦❞♦✳
❈♦♥t✉❞♦✱ ❛ ♠❛✐♦r✐❛ ❞❛s q✉❛♥t✐❞❛❞❡s ❢ís✐❝❛s q✉❡ ♣♦❞❡♠ s❡r ♠❡❞✐❞❛s ❝♦♠♣✉t❛❝✐♦♥❛❧♠❡♥t❡ ♥ã♦ ❝♦rr❡s♣♦♥❞❡♠ às ♣r♦♣r✐❡❞❛❞❡s ❢ís✐❝❛s ♠❡❞✐❞❛s ❡♠ ✉♠ ❡①♣❡r✐♠❡♥t♦ ❬✸✵❪✳ P♦r ❡①❡♠♣❧♦✱ ❡♠ ❉✐♥â♠✐❝❛ ▼♦❧❡❝✉❧❛r ✭❉▼✮✱ ♣♦❞❡✲s❡ ♦❜t❡r ❛ ✐♥❢♦r♠❛çã♦ ❞❛s ♣♦s✐çõ❡s ❡ ❞❛s ✈❡❧♦❝✐❞❛❞❡s ❞❛s ♣❛rtí✲ ❝✉❧❛s✱ ♣♦ré♠✱ t❛❧ ✐♥❢♦r♠❛çã♦ ♥ã♦ é s✉✜❝✐❡♥t❡ ♣❛r❛ ❡♥t❡♥❞❡r ♦s ❢❡♥ô♠❡♥♦s ❝♦♠♣❧❡t❛♠❡♥t❡✳ P❛r❛ ❝❛r❛❝t❡r✐③❛çã♦ ❞♦ s✐st❡♠❛ ❢❛③✲s❡ ✉s♦ ❞❛ ❋ís✐❝❛ ❊st❛tíst✐❝❛ ♣❛r❛ ❝♦♥✈❡rt❡r ❛s ✐♥❢♦r♠❛çõ❡s ❞❡ ♥í✈❡❧ ♠✐❝r♦s❝ó♣✐❝♦✱ ♦❜t✐❞❛s ♣♦r s✐♠✉❧❛çã♦✱ ♣❛r❛ ♠❡❞✐❞❛s q✉❡ ❝❛r❛❝t❡r✐③❛♠ ♦ ❡st❛❞♦ ❢ís✐❝♦ ❞♦ s✐st❡♠❛ ❝♦♠♦ ✉♠ t♦❞♦✳
❆ss✐♠✱ ❛♣r❡s❡♥t❛✲s❡✱ ♥❡ss❛ s❡çã♦✱ ✉♠ ❡st✉❞♦ ❞❛ ❋ís✐❝❛ ❊st❛tíst✐❝❛ ❈❧áss✐❝❛ ❝♦♠ ♦ ✐♥t✉✐t♦ ❞❡ r❡✈❡❧❛r ✐♥❢♦r♠❛çõ❡s ♥❡❝❡ssár✐❛s ♣❛r❛ ❝❛r❛❝t❡r✐③❛çã♦ ❞❡ s✐st❡♠❛s ♠❛❝r♦s❝ó♣✐❝♦s ❛ ♣❛rt✐r ❞❡ ❛♥á❧✐s❡s ❞❡ s❡✉s ❝♦♠♣♦♥❡♥t❡s✳
Pr✐♠❡✐r❛♠❡♥t❡✱ ❝♦♥s✐❞❡r❛✲s❡ ✉♠ ♥ú♠❡r♦ ◆ ❞❡ ❡❧❡♠❡♥t♦s ✐❞ê♥t✐❝♦s ❢♦r♠❛♥❞♦ ❛ss✐♠ ✉♠ ❝♦♥✲ ❥✉♥t♦✳ ❖s ❡❧❡♠❡♥t♦s ♣♦❞❡♠ s❡r ♣❛rtí❝✉❧❛s s✐♠♣❧❡s ♦✉ ❝♦♥❥✉♥t♦s ❞❡ ♣❛rtí❝✉❧❛s ✐❞ê♥t✐❝❛s✱ ❡ ♥❡st❡ ❝❛s♦✱ t❡♠♦s ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ❝♦♥❥✉♥t♦s ❛♦ q✉❛❧ é ❝♦st✉♠❡✐r❛♠❡♥t❡ ❝❤❛♠❛❞♦ ❞❡ ❡♥s❡♠❜❧❡ ❬✷✺❪✳
❙❡ ❛s ♣❛rtí❝✉❧❛s ❞❡ ✉♠ s✐st❡♠❛ ❢♦r❡♠ ✐♥❞✐st✐♥❣✉í✈❡✐s✱ ✉♠❛ ❡s♣❡❝✐✜❝❛çã♦ ❞♦ ♥ú♠❡r♦ t♦t❛❧ ❞❡ ♣❛rtí❝✉❧❛s ❡♠ ❝❛❞❛ ❡st❛❞♦ ❞❡ ❡♥❡r❣✐❛ ❞❡✜♥✐rá ♦ ❝❤❛♠❛❞♦ ♠✐❝r♦❡st❛❞♦ ❞♦ s✐st❡♠❛✳ ❉❡ss❛ ❢♦r♠❛✱ ❞❡✜♥✐✲s❡ Ω(E, V, N, Xi) ❝♦♠♦ s❡♥❞♦ ♦ ♥ú♠❡r♦ ❞❡ ❛✉t♦✲❡st❛❞♦s ❞❡ ✉♠ s✐st❡♠❛ ❝♦♠ ❡♥❡r❣✐❛ ❊✱
✈♦❧✉♠❡ ❱ ❡ ♥ú♠❡r♦ ❞❡ ♣❛rtí❝✉❧❛s ◆✱ ♦♥❞❡Xi r❡♣r❡s❡♥t❛ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ✈í♥❝✉❧♦s✳
