Avaliação da radioatividade natural em algumas rochas graníticas do Estado do Paraná...

❆❯❚❆❘◗❯■❆ ❆❙❙❖❈■❆❉❆ ➚ ❯◆■❱❊❘❙■❉❆❉❊ ❉❊ ❙➹❖ P❆❯▲❖

❆✈❛❧✐❛çã♦ ❞❛ r❛❞✐♦❛t✐✈✐❞❛❞❡ ♥❛t✉r❛❧ ❡♠ ❛❧❣✉♠❛s

r♦❝❤❛s ❣r❛♥ít✐❝❛s ❞♦ ❡st❛❞♦ ❞♦ P❛r❛♥á ❡ s✉❛ ✉t✐❧✐③❛çã♦

♥❛ ❝♦♥str✉çã♦ ❝✐✈✐❧

❆❞❡♠❛r ❞❡ ❖❧✐✈❡✐r❛ ❋❡rr❡✐r❛

❚❡s❡ ❛♣r❡s❡♥t❛❞❛ ❝♦♠♦ ♣❛rt❡ ❞♦s

r❡q✉✐s✐t♦s ♣❛r❛ ❛ ♦❜t❡♥çã♦ ❞♦ ●r❛✉

❞❡ ❉♦✉t♦r ❡♠ ❈✐ê♥❝✐❛s ♥❛ ➪r❡❛ ❞❡

❚❡❝♥♦❧♦❣✐❛ ◆✉❝❧❡❛r✲❆♣❧✐❝❛çõ❡s✳

❖r✐❡♥t❛❞♦r❛✿

Pr♦❢❛✳ ❉r❛✳ ❇r✐❣✐tt❡ ❘♦①❛♥❛ ❙♦r❡❛♥✉

P❡❝❡q✉✐❧♦✳

■◆❙❚■❚❯❚❖ ❉❊ P❊❙◗❯■❙❆❙ ❊◆❊❘●➱❚■❈❆❙ ❊ ◆❯❈▲❊❆❘❊❙ ❆✉t❛rq✉✐❛ ❛ss♦❝✐❛❞❛ à ❯♥✐✈❡rs✐❞❛❞❡ ❞❡ ❙ã♦ P❛✉❧♦

❆✈❛❧✐❛çã♦ ❞❛ r❛❞✐♦❛t✐✈✐❞❛❞❡ ♥❛t✉r❛❧ ❡♠ ❛❧❣✉♠❛s r♦❝❤❛s ❣r❛♥ít✐❝❛s ❞♦ ❡st❛❞♦ ❞♦ P❛r❛♥á ❡ s✉❛ ✉t✐❧✐③❛çã♦ ♥❛ ❝♦♥str✉çã♦ ❝✐✈✐❧

❆❞❡♠❛r ❞❡ ❖❧✐✈❡✐r❛ ❋❡rr❡✐r❛

❚❡s❡ ❛♣r❡s❡♥t❛❞❛ ❝♦♠♦ ♣❛rt❡ ❞♦s

r❡q✉✐s✐t♦s ♣❛r❛ ❛ ♦❜t❡♥çã♦ ❞♦ ●r❛✉

❞❡ ❉♦✉t♦r ❡♠ ❈✐ê♥❝✐❛s ♥❛ ➪r❡❛ ❞❡

❚❡❝♥♦❧♦❣✐❛ ◆✉❝❧❡❛r✲❆♣❧✐❝❛çõ❡s✳

❖r✐❡♥t❛❞♦r❛✿

Pr♦❢❛✳ ❉r❛✳ ❇r✐❣✐tt❡ ❘♦①❛♥❛ ❙♦r❡❛♥✉

P❡❝❡q✉✐❧♦✳

❱❡rsã♦ ❈♦rr✐❣✐❞❛

❱❡rsã♦ ♦r✐❣✐♥❛❧ ❡♥❝♦♥tr❛✲s❡ ❞✐s♣♦♥í✈❡❧ ♥♦ ■P❊◆

❆❣r❛❞❡❝✐♠❡♥t♦s

❆♦ ■♥st✐t✉t♦ ❞❡ P❡sq✉✐s❛s ❊♥❡r❣ét✐❝❛s ❡ ◆✉❝❧❡❛r❡s ♣❡❧❛ ♦♣♦rt✉♥✐❞❛❞❡ ❞❡ r❡❛❧✐③❛r ❡st❡ tr❛❜❛❧❤♦✳

➚ ❈♦♠✐ssã♦ ◆❛❝✐♦♥❛❧ ❞❡ ❊♥❡r❣✐❛ ◆✉❝❧❡❛r ♣❡❧❛ ❇♦❧s❛ ❞❡ ❡st✉❞♦✳

➚ ❉r❛ _{▲✐♥❞❛ ❱✳ ❊✳ ❈❛❧❞❛s ♣❡❧❛ ✐♥❢r❛❡str✉t✉r❛ ❞❛ ●êr❡♥❝✐❛ ❞❡ ▼❡tr♦❧♦❣✐❛ ❞❛s}

❘❛❞✐❛çõ❡s ✳

➚ ❉r❛ _{❇ár❜❛r❛ P❛❝✐ ▼❛③③✐❧❧✐ ♣❡❧❛ ✐♥❢r❛❡str✉t✉r❛ ❞♦ ▲❛❜♦r❛tór✐♦ ❞❡ ❘❛❞✐♦♠❡tr✐❛}

❆♠❜✐❡♥t❛❧ ✭▲❘❆✮✳

➚ Pr♦❢❛ _{❇r✐❣✐tt❡ ♣♦r ✐♥❞✐❝❛r ❛ ❞✐r❡çã♦ ♥♦s ♠♦♠❡♥t♦s ❞❡ ✐♥❝❡rt❡③❛s✱ ♣❡❧♦ ❡①❡♠♣❧♦}

❞❡ ♣r♦✜ss✐♦♥❛❧✐s♠♦ ❡ ❞✐s❝✐♣❧✐♥❛✱ ♣❡❧❛ ♦r✐❡♥t❛çã♦✱ ❛♠✐③❛❞❡✱ s✐♥❝❡r✐❞❛❞❡ ❡ ♣r❡s❡♥ç❛✳

❆♦ ▼✳ ❙❝✳ ▼❛r❝❡❧♦ ❇❡ss❛ ◆✐st✐ ♣❡❧❛ ♣❛rt✐❝✐♣❛çã♦ ❡♠ t♦❞❛s ❛s ❡t❛♣❛s ❞❡st❡ tr❛❜❛❧❤♦✱ ♣♦r ❡st❛r s❡♠♣r❡ ❛❝❡ssí✈❡❧✱ ❝♦♥tr✐❜✉✐♥❞♦ ❝♦♠ s✉❣❡stõ❡s ✈❛❧✐♦s❛s✳

❆♦ ❉r✳ ▼❛r❝❡❧♦ ❋r❛♥❝✐s ▼á❞✉❛r✱ ♣❡❧♦s ❧✐✈r♦s ❡♠♣r❡st❛❞♦s✱ ♣♦r t❡r ❞❡s❡♥✈♦❧✈✐❞♦ ♦ ♠♦❞❡❧♦ ♠❛t❡♠át✐❝♦ ✉t✐❧✐③❛❞♦ ❡ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ♣❡❧❛s ❝♦♥✈❡rs❛s ❞❡s❝♦♥tr❛í❞❛s ♥❛ ❝♦♣❛ ❡ ♥♦ ●r❡✐❝✳

➚ ❉r❛_{▼ár❝✐❛ P✐r❡s ❞❡ ❈❛♠♣♦s ♣❡❧❛s ❞✐s❝✉ssõ❡s s♦❜r❡ ♦ r❛❞ô♥✐♦ q✉❡ ❡s❝❧❛r❡❝❡r❛♠}

♠✉✐t♦s ❛s♣❡❝t♦s ❞❛ té❝♥✐❝❛ ❞❡ ♠❡❞✐❞❛✳

➚ ❉r❛ _{❙❛♥❞r❛ ❘❡❣✐♥❛ ❉❛♠❛tt♦ ♣❡❧❛ ❞✐s♣♦♥✐❜✐❧✐❞❛❞❡ ❡♠ ❛❥✉❞❛r s❡♠♣r❡ q✉❡}

♣r❡❝✐s❡✐✱ ♣❡❧❛s r❡❢❡rê♥❝✐❛s ❜✐❜❧✐♦❣rá✜❝❛s s✉❣❡r✐❞❛s ❡ ♣♦r t♦❞❛s ❛s ❝♦♥tr✐❜✉✐çõ❡s ❞❛❞❛s ❛♦ tr❛❜❛❧❤♦✳

❆♦ ▼✳ ❙❝✳ P❛✉❧♦ ❘❡♥❡ ◆♦❣✉❡✐r❛✱ ♣❡❧❛ ❛❥✉❞❛ ❡♠ ✉♠❛ ❞❛s ❡t❛♣❛s ❞❛ ♣r❡♣❛r❛çã♦ ❞❛s ❛♠♦str❛s ❡ ♣♦r t♦r♥❛r ❞✐s❝✉ssõ❡s té❝♥✐❝❛s ❡♠ ❝♦♥✈❡rs❛s ❛❣r❛❞á✈❡✐s✳

❆♦ ❉r✳ ▼❛r❝♦s ❆♥t♦♥✐♦ ❙❝❛♣✐♥ ❡ à ❉r❛ _{❱❡r❛ ▲✉❝✐❛ ❘✐❜❡✐r♦ ❙❛❧✈❛❞♦r✱ ❞♦ ❈❡♥tr♦}

❞❡ ◗✉í♠✐❝❛ ❡ ▼❡✐♦ ❆♠❜✐❡♥t❡✱ ♣♦r t❡r❡♠ ❝❡❞✐❞♦ ♦ ❧❛❜♦r❛tór✐♦ ♣❛r❛ ♣r❡♣❛r❛çã♦ ❞❛s ❛♠♦str❛s✱ ♣❡❧❛s ❛♥á❧✐s❡s ❞❡ ✢✉♦r❡s❝ê♥❝✐❛ ❞❡ r❛✐♦s ❳ ❡ ♣❡❧❛s ❝♦♥✈❡rs❛s ❡ s✉❣❡stõ❡s ❛ r❡s♣❡✐t♦ ❞♦ tr❛❜❛❧❤♦✳

❆ t♦❞♦s ♦s ❢✉♥❝✐♦♥ár✐♦s ❞♦ ▲❘❆ q✉❡ ♣❛rt✐❝✐♣❛r❛♠ ❞✐r❡t❛ ♦✉ ✐♥❞✐r❡t❛♠❡♥t❡ ❞❡st❡ tr❛❜❛❧❤♦✳

➚ ❞✉♣❧❛ ❞❡ ✐♥s❡♣❛rá✈❡✐s ▲✉❝✐❛ ❍❡❧❡♥❛ ❡ ❙✉❡❧✐ ❞❡ ❏❡s✉s✱ ♣❡❧♦s ❤♦t✲❞♦❣s✱ ♣✐③③❛s ❡ ❝♦♥✈❡rs❛s ❞❡ ❜❛♥❞❡❥ã♦✳

❆ ❆❧✐❝❡ ❈♦st❛✱ ❇r✉♥❛ ❙♦❜r❛❧✱ ❋á❜✐♦ ❙✉ss❛✱ ❋❡r♥❛♥❞❛ ❈❛✈❛❧❝❛♥t❡✱ ❋❧á✈✐❛ ❱❛❧✈❡r❞❡✱ ●✉✐❧❤❡r♠❡ ●r♦♣♣♦✱ ▲í✈✐❛ ❇❛rr♦s✱ ▲✉✐③ ❋❧á✈✐♦✱ ▼❛r❝♦s ▼❡❞r❛❞♦✱ P❛✉❧♦ ❙ér❣✐♦✱ ❘❛q✉❡❧ ❇♦✈♦❧✐♥✐✱ ♣❡❧❛ ❛♠✐③❛❞❡✱ ❡ ♣❡❧♦s ✜♥❛✐s ❞❡ t❛r❞❡ ❡ ❝❤✉rr❛s❝♦s ♥♦ ●r❡✐❝✳

❆ t♦❞♦s ♦s ❜♦❧s✐st❛s✱ ❡st❛❣✐ár✐♦s✱ ❛♠✐❣♦s ❡ ❝♦❧❡❣❛s ❞♦ ▲❘❆✱ ♣❡❧❛ ❝♦♥✈✐✈ê♥❝✐❛ ❡ ♣❡❧♦s ❝❛❢és ♥❛ ❝♦♣❛✳

❆♦s ❛♠✐❣♦s ❞♦ ❈♦♥❥✉♥t♦ ❘❡s✐❞❡♥❝✐❛❧ ❞❛ ❯❙P ✭❈❘❯❙P✮✱ ♣♦r t♦❞❛s ❛s r❡✉♥✐õ❡s s❡♠♣r❡ ♠✉✐t♦ ❜❡♠ ♣❛✉t❛❞❛s ❡ ❞✐✈❡rt✐❞❛s✱ ❛❣❡♥❞❛❞❛s ♣❡❧♦ ✐♥t❡r❢♦♥❡ ❛ q✉❛❧q✉❡r ❤♦r❛ ❡ s❡♠ ♣r♦t♦❝♦❧♦s✳

❆♦s ✐r♠ã♦s ❞♦ ❈❘❯❙P ●❧❡✐❞s♦♥ ●♦♠❡s ❡ ■✈❛♥ ❘♦❝❤❛✱ ♣❡❧♦s ❝♦✛❡❡ ❜r❡❛❦✱ ♣❡❧❛ ❛♠✐③❛❞❡ ❡ ❝✉♠♣❧✐❝✐❞❛❞❡ ❡ ♣♦r ❡♥s✐♥❛r❡♠ q✉❡ ❛ ♠❡❧❤♦r ❢♦r♠❛ ❞❡ s♦♠❛r é ❞✐✈✐❞✐r✳

❆♦ ❘❡❣✐♥❛❧❞♦ ❆q✉✐♥♦✱ ♣❡❧❛s ♣✐③③❛s✱ ♣❡❧❛s ♣✐♠❡♥t❛s✱ ❢❡✐❥♦❛❞❛s✱ ♣❡❧❛s ❛✈❡♥t✉r❛s ♥♦s ❝♦♥❣r❡ss♦s✱ ♣♦r t♦❞♦s ❡ss❡s ❛♥♦s ❞❡ ♣❛rt✐❝✐♣❛çã♦ ♥♦ ❧❛❜♦r❛tór✐♦ ❡ ❢♦r❛ ❞❡❧❡✱ ❡ ♣❡❧❛ ❛♠✐③❛❞❡✳

❆ ❢❛♠í❧✐❛ ●✐✉❧✐ ❞❛ ❙✐❧✈❛✱ ♣♦r t❡r❡♠ ♠❡ r❡❝❡❜✐❞♦ ❡♠ ❙ã♦ P❛✉❧♦✱ ♣❡❧♦ s✉♣♦rt❡✱ ❛♣♦✐♦ ❡ ♣♦r t♦❞♦s ♦s ✜♥❛✐s ❞❡ s❡♠❛♥❛ ❥✉♥t♦s✳

➚ ❏✉❧✐❛♥❛ ■s❛❜❡❧✱ ♣♦r ♣❛rt✐❝✐♣❛r ❞❡ t♦❞♦s ♦s ♠♦♠❡♥t♦s ❛❧❡❣r❡s ❡ t❛♠❜é♠ ❞♦s ♠❡♥♦s ❛❧❡❣r❡s✱ ♣❡❧❛ ❝✉♠♣❧✐❝✐❞❛❞❡✱ ❛♠♦r ❡ ♣❡❧❛ ♣❛❝✐ê♥❝✐❛✳

❆ ♠❡✉s ❢❛♠✐❧✐❛r❡s✱ ♣❡❧♦ ❛♠♦r ❡ ❝❛r✐♥❤♦✱ ❛♣❡s❛r ❞❛ ♠✐♥❤❛ ❛✉sê♥❝✐❛✳

❘❡s✉♠♦

❆✈❛❧✐❛çã♦ ❞❛ r❛❞✐♦❛t✐✈✐❞❛❞❡ ♥❛t✉r❛❧ ❡♠ ❛❧❣✉♠❛s r♦❝❤❛s

❣r❛♥ít✐❝❛s ❞♦ ❡st❛❞♦ ❞♦ P❛r❛♥á ❡ s✉❛ ✉t✐❧✐③❛çã♦ ♥❛

❝♦♥str✉çã♦ ❝✐✈✐❧

❆❞❡♠❛r ❞❡ ❖❧✐✈❡✐r❛ ❋❡rr❡✐r❛

❖s r❛❞✐♦♥✉❝❧í❞❡♦s ♥❛t✉r❛✐s ❞❡ ♦r✐❣❡♠ ♣r✐♠♦r❞✐❛❧✱ ♦✉ t❡rr❡str❡s✱ sã♦ ❡♥❝♦♥tr❛❞♦s ❡♠ q✉❛♥t✐❞❛❞❡s ✈❛r✐❛❞❛s ❡♠ t♦❞♦ ♠❡✐♦ ❛♠❜✐❡♥t❡✳ ◆❛s r❡s✐❞ê♥❝✐❛s✱ ✉♠ ✐♠♣♦rt❛♥t❡ ✐♥❝r❡♠❡♥t♦ ❞❡ ❞♦s❡ ✭■◆❉❖❖❘✮✱ é ❞❡✈✐❞♦ ❛♦s ♠❛t❡r✐❛✐s ❞❡ ❝♦♥str✉çã♦✱ q✉❡ ❝♦♥tr✐❜✉❡♠ t❛♥t♦ ❝♦♠ ❛ ❞♦s❡ ❡①t❡r♥❛ ❣❛♠❛✱ ♣r♦✈❡♥✐❡♥t❡ ❞❛s sér✐❡s ❞♦ 238_❯✱ 235_{❯ ❡} 232_{❚❤ ❡ ❞♦}

r❛❞✐♦♥✉❝❧í❞❡♦ ✐s♦❧❛❞♦ 40_{❑✱ q✉❛♥t♦ ❝♦♠ ❛ ❞♦s❡ ✐♥t❡r♥❛ q✉❡ é ❞❡✈✐❞❛ ♣r✐♥❝✐♣❛❧♠❡♥t❡}

à ✐♥❛❧❛çã♦ ❞♦ 222_{❘♥✳ ❯♠❛ ✈❡③ q✉❡ r♦❝❤❛s ❣r❛♥ít✐❝❛s sã♦ ❛♠♣❧❛♠❡♥t❡ ✉t✐❧✐③❛❞❛s ❝♦♠♦}

♠❛t❡r✐❛✐s ❞❡ ❝♦♥str✉çã♦✱ t❛♥t♦ ❡str✉t✉r❛✐s ❝♦♠♦ ❞❡ r❡✈❡st✐♠❡♥t♦✱ ❡st❛s ♣♦❞❡♠ t♦r♥❛r✲s❡ ✉♠❛ ✐♠♣♦rt❛♥t❡ ❢♦♥t❡ ❞❡ ❞♦s❡✱ ❞❡♣❡♥❞❡♥❞♦ ❞❛s ❝♦♥❝❡♥tr❛çõ❡s ❞❡ r❛❞✐♦❛t✐✈✐❞❛❞❡ q✉❡ ❛♣r❡s❡♥t❡♠✱ ❡ ❞❛ ❢♦r♠❛ ❡ q✉❛♥t✐❞❛❞❡ q✉❡ sã♦ ❛♣❧✐❝❛❞❛s ♥❛s ❝♦♥str✉çõ❡s✳ ◆❡st❡ tr❛❜❛❧❤♦ ❢♦✐ ❣❡r❛❞♦ ✉♠ ❜❛♥❝♦ ❞❡ ❞❛❞♦s ♣❛r❛ r♦❝❤❛s ❣r❛♥ít✐❝❛s ❞♦ ❡s❝✉❞♦ ❝r✐st❛❧✐♥♦ ♣❛r❛♥❛❡♥s❡ ✭♣r✐♥❝✐♣❛❧♠❡♥t❡ ❞❛ ❘❡❣✐ã♦ ▼❡tr♦♣♦❧✐t❛♥❛ ❞❡ ❈✉r✐t✐❜❛✱ ❘▼❈✮✱ q✉❡ sã♦ ✉t✐❧✐③❛❞❛s ♥❛ ❝♦♥str✉çã♦ ❝✐✈✐❧ ❛✈❛❧✐❛♥❞♦ ❡♠ t❡r♠♦s ❞❡ ♣r♦t❡çã♦ r❛❞✐♦❧ó❣✐❝❛ ♦ ✐♥❝r❡♠❡♥t♦ ❞❛ ❞♦s❡✱ ❡①t❡r♥❛ ❡ ✐♥t❡r♥❛✱ ❝❛✉s❛❞❛ ♣❡❧❛ ✉t✐❧✐③❛çã♦ ❞❡st❡s ♠❛t❡r✐❛✐s✳ ❚❛♠❜é♠ ❢♦r❛♠ ❡st✉❞❛❞❛s ❛s ♣♦ssí✈❡✐s ❝♦rr❡❧❛çõ❡s ❡♥tr❡ ❛ ❝♦♥❝❡♥tr❛çã♦ ❞❡ ❛t✐✈✐❞❛❞❡ ❞❡ 226_{❘❛✱ t❛①❛ ❞❡ ❡①❛❧❛çã♦}

❞❡ 222_{❘♥✱ ❞❡♥s✐❞❛❞❡✱ ♣♦r♦s✐❞❛❞❡ ❡ ❝♦♠♣♦s✐çã♦ q✉í♠✐❝❛ ✭t❡♦r ❞❡ ó①✐❞♦s ❝♦♥st✐t✉✐♥t❡s✮}

♥❡st❛s ❛♠♦str❛s✳ ❆ ❞♦s❡ ❡①t❡r♥❛ ❢♦✐ ❛✈❛❧✐❛❞❛ ♣♦r ♠❡✐♦ ❞❛ té❝♥✐❝❛ ❞❡ ❡s♣❡❝tr♦♠❡tr✐❛ ❣❛♠❛ ❝♦♠ ❞❡t❡❝t♦r ❞❡ ❣❡r♠â♥✐♦ ❤✐♣❡r♣✉r♦✱ ♦♥❞❡ ❛s ❝♦♥❝❡♥tr❛çõ❡s ❞❡ ❛t✐✈✐❞❛❞❡ ❞♦s r❛❞✐♦♥✉❝❧í❞❡♦s226_❘❛✱232_{❚❤ ❡}40_{❑ sã♦ ♦s ♣❛râ♠❡tr♦s ✉t✐❧✐③❛❞♦s ❡♠ ♠♦❞❡❧♦s ❞♦s✐♠étr✐❝♦s}

✭❮♥❞✐❝❡s ❉♦s✐♠étr✐❝♦s✮✱ ♦s q✉❛✐s ❡st❛❜❡❧❡❝❡♠ ❧✐♠✐t❡s ♠á①✐♠♦s ♣❡r♠✐t✐❞♦s ❞❡ ❛❝♦r❞♦ ❝♦♠ ❢♦r♠❛✱ q✉❛♥t✐❞❛❞❡ ❡ ❛♣❧✐❝❛çã♦ ❞♦ ♠❛t❡r✐❛❧ ❞❡ ❝♦♥str✉çã♦✳ P❛r❛ ♦ ❝á❧❝✉❧♦ ❞❛ ❞♦s❡ ❡❢❡t✐✈❛ ❛♥✉❛❧ ❡①t❡r♥❛ ❢♦✐ ❛❞♦t❛❞♦ ♦ ♠♦❞❡❧♦ ❞❡ s❛❧❛ ❝♦♠ ❞✐♠❡♥sõ❡s 4♠ ① 5♠ ① 2,8♠

❡ t♦❞❛s ❛s ♣❛r❡❞❡s sã♦ r❡✈❡st✐❞❛s ✐♥t❡r♥❛♠❡♥t❡ ❝♦♠ ❣r❛♥✐t♦s ❞❡ ❡s♣❡ss✉r❛ ❞❡ 2 ❝♠ ❡

❝♦♥s✐❞❡r❛♥❞♦ ♦ t❡♠♣♦ ❞❡ ❡①♣♦s✐çã♦ ❛♥✉❛❧ ❞❡7000 ❤✱ ❝♦♥❢♦r♠❡ s✉❣❡r✐❞♦ ♣❡❧❛ ❈♦♠✐ssã♦

❊✉r♦♣é✐❛ ❞❡ Pr♦t❡çã♦ ❘❛❞✐♦❧ó❣✐❝❛ ♣❛r❛ ♠❛t❡r✐❛✐s ❞❡ r❡✈❡st✐♠❡♥t♦ ✐♥t❡r♥♦ s✉♣❡r✜❝✐❛❧✳ ❆ ❡①♣♦s✐çã♦ ✐♥t❡r♥❛ ❢♦✐ ❛✈❛❧✐❛❞❛ ❛ ♣❛rt✐r ❞❛ ❝♦♥❝❡♥tr❛çã♦ ❞❡ r❛❞ô♥✐♦ ♥♦ ❛r ❞❛ s❛❧❛ ♠♦❞❡❧♦✱ s✐♠✉❧❛❞❛ ❛ ♣❛rt✐r ❞♦ ✈❛❧♦r ❞❛ t❛①❛ ❞❡ ❡①❛❧❛çã♦ s✉♣❡r✜❝✐❛❧ ❞❡222_{❘♥✳ ❆ t❛①❛ ❞❡}

❞❡st❡s ❡st✉❞♦s ♠♦str❛♠ q✉❡ ♦ ✐♥❝r❡♠❡♥t♦ ❞❛ ❞♦s❡ ❡❢❡t✐✈❛ ❛♥✉❛❧ ❡①t❡r♥❛ ✈❛r✐♦✉ ❞❡

(62 _± 3) µ❙✈✳❛−1 ❛ _{(138 ± 1) µ}❙✈✳❛−1 ❡ ♦ ✐♥❝r❡♠❡♥t♦ ❞❛ ❞♦s❡ ❡❢❡t✐✈❛ ❛♥✉❛❧

✐♥t❡r♥❛ ✈❛r✐♦✉ ❞❡ (0,39 _± 0,04) µ❙✈✳❛−1 ❛ _{(70 ± 4) µ}❙✈✳❛−1✳ ❊st❡s ✈❛❧♦r❡s ❡stã♦

❛❜❛✐①♦ ❞♦ ❧✐♠✐t❡ ♠á①✐♠♦ ❞❡1 ♠❙✈✳❛−1 s✉❣❡r✐❞♦ ♣❡❧❛ ❈♦♠✐ssã♦ ❊✉r♦♣é✐❛ ❞❡ Pr♦t❡çã♦

❘❛❞✐♦❧ó❣✐❝❛✱ ♣♦rt❛♥t♦ ♦s ❣r❛♥✐t♦s ❛✈❛❧✐❛❞♦s ♥❡st❡ tr❛❜❛❧❤♦ ♣♦❞❡♠ s❡r ✉t✐❧✐③❛❞♦s s❡♠ ✐♠♣❧✐❝❛çõ❡s r❛❞✐♦❧ó❣✐❝❛s ❞❡s❞❡ q✉❡ ♦❜❡❞❡❝✐❞♦ ♦ ❝❡♥ár✐♦ ❞❡s❝r✐t♦✳ ❖s ✈❛❧♦r❡s ♦❜t✐❞♦s ♣❛r❛ ❛ ❝♦♥tr✐❜✉✐çã♦ ❞❡✈✐❞❛ à ❞♦s❡ ✐♥t❡r♥❛ ✈❛r✐❛r❛♠ ❞❡ 1 % ❛78 % ❞♦s ✈❛❧♦r❡s ♦❜t✐❞♦s ♣❛r❛

❛ r❡s♣❡❝t✐✈❛ ❞♦s❡ ❡①t❡r♥❛✱ ♠♦str❛♥❞♦ q✉❡ ❛ ❝♦♥tr✐❜✉✐çã♦ ❞♦ r❛❞ô♥✐♦ ✈❛r✐❛ ❢♦rt❡♠❡♥t❡ ❝♦♠ ♦ t✐♣♦ ❞❛ r♦❝❤❛✳ ❖s r❡s✉❧t❛❞♦s ❞❛s ❝♦rr❡❧❛çõ❡s ❡♥tr❡ t❛①❛ ❞❡ ❡①❛❧❛çã♦ s✉♣❡r✜❝✐❛❧ ❞❡

222_{❘♥✱ ❝♦♥❝❡♥tr❛çã♦ ❞❡ ❛t✐✈✐❞❛❞❡ ❞❡} 226_{❘❛✱ ❞❡♥s✐❞❛❞❡✱ ♣♦r♦s✐❞❛❞❡ ❡ ♣r✐♥❝✐♣❛✐s ó①✐❞♦s}

❆❜str❛❝t

❊✈❛❧✉❛t✐♦♥ ♦❢ ♥❛t✉r❛❧ r❛❞✐♦❛❝t✐✈✐t② ✐♥ s♦♠❡ ❣r❛♥✐t✐❝

r♦❝❦s ✐♥ t❤❡ st❛t❡ ♦❢ P❛r❛♥á ❛♥❞ ✐ts ✉s❡ ✐♥ ❝✐✈✐❧

❝♦♥str✉❝t✐♦♥

❆❞❡♠❛r ❞❡ ❖❧✐✈❡✐r❛ ❋❡rr❡✐r❛

Pr✐♠♦r❞✐❛❧✱ ♦r t❡rr❡str✐❛❧ ♥❛t✉r❛❧ r❛❞✐♦♥✉❝❧✐❞❡s✱ ❛r❡ ❢♦✉♥❞ ✐♥ ❞✐✛❡r❡♥t ❛♠♦✉♥ts ✐♥ t❤❡ ❡♥✈✐r♦♥♠❡♥t✳ ■♥ ❞✇❡❧❧✐♥❣s✱ ❛♥ ✐♠♣♦rt❛♥t ❞♦s❡ ✐♥❝r❡♠❡♥t ✐s ❞✉❡ t♦ ❜✉✐❧❞✐♥❣ ♠❛t❡r✐❛❧s✱ ✇❤✐❝❤ ❝♦♥tr✐❜✉t❡ ❢♦r ❜♦t❤ t❤❡ ❡①t❡r♥❛❧ ❣❛♠♠❛ ❞♦s❡ ❢r♦♠ t❤❡ r❛❞✐♦♥✉❝❧✐❞❡s ♦❢ t❤❡238_❯✱ 235_{❯ ❛♥❞}232_{❚❤ s❡r✐❡s ❛♥❞ t❤❡ ♥❛t✉r❛❧} 40_{❑ ❛♥❞ t❤❡ ✐♥t❡r♥❛❧ ❞♦s❡✱ ❞✉❡ ♠❛✐♥❧② t♦} 222_❘♥

✐♥❤❛❧❛t✐♦♥✳ ❖♥❝❡ ❣r❛♥✐t✐❝ r♦❝❦s ❛r❡ ✇✐❞❡❧② ✉s❡❞ ❜♦t❤ ❛s ❝♦♥str✉❝t✐♦♥ ♠❛t❡r✐❛❧s ♦r str✉❝t✉r❛❧ ✢♦♦r✐♥❣✱ t❤♦s❡ r♦❝❦s ❝❛♥ ❜❡❝♦♠❡ ❛♥ ✐♠♣♦rt❛♥t ❞♦s❡ s♦✉r❝❡✱ ❞❡♣❡♥❞✐♥❣ ♦♥ t❤❡ ❝♦♥t❡♥t ♦❢ ❝♦♥❝❡♥tr❛t✐♦♥s ♦❢ r❛❞✐♦❛❝t✐✈✐t②✱ ❛♥❞ t❤❡ ❝♦♥str✉❝t✐♦♥ ❛♣♣❧✐❝❛t✐♦♥✳ ■♥ t❤✐s ✇♦r❦✱ ❛ ❞❛t❛❜❛s❡ ❢♦r ❣r❛♥✐t✐❝ r♦❝❦s ♦❢ t❤❡ ❝r②st❛❧❧✐♥❡ s❤✐❡❧❞ ♦❢ P❛r❛♥á ✭♠❛✐♥❧② ✐♥ t❤❡ ▼❡tr♦♣♦❧✐t❛♥ ❘❡❣✐♦♥ ♦❢ ❈✉r✐t✐❜❛✱ ❘▼❈✮✱ ✉s❡❞ ✐♥ ❝✐✈✐❧ ❝♦♥str✉❝t✐♦♥✱ ✇❛s ❣❡♥❡r❛t❡❞✱ ❡✈❛❧✉❛t✐♥❣ ✐♥ t❡r♠s ♦❢ r❛❞✐♦❧♦❣✐❝❛❧ ♣r♦t❡❝t✐♦♥ t❤❡ ❡①t❡r♥❛❧ ❛♥❞ ✐♥t❡r♥❛❧ ❞♦s❡ ✐♥❝r❡♠❡♥ts✱ ❝❛✉s❡❞ ❜② t❤❡ ✉s❡ ♦❢ t❤❡s❡ ♠❛t❡r✐❛❧s✳ ❆❧s♦✱ ♣♦ss✐❜❧❡ ❝♦rr❡❧❛t✐♦♥s ❜❡t✇❡❡♥ t❤❡ 226_❘❛

❛❝t✐✈✐t② ❝♦♥❝❡♥tr❛t✐♦♥✱ t❤❡ 222_{❘♥ ❡①❤❛❧❛t✐♦♥ r❛t❡✱ ❞❡♥s✐t②✱ ♣♦r♦s✐t② ❛♥❞ ❝❤❡♠✐❝❛❧}

❝♦♠♣♦s✐t✐♦♥ ✭♦①✐❞❡ ❝♦♥t❡♥t✮ ✐♥ t❤❡s❡ s❛♠♣❧❡s ❤❛❞ ❜❡❡♥ st✉❞✐❡❞✳ ❚❤❡ ❡①t❡r♥❛❧ ❞♦s❡ ✇❛s ❛ss❡ss❡❞ ❜② ❣❛♠♠❛✲r❛② s♣❡❝tr♦♠❡tr② ✇✐t❤ ❍✐❣❤✲P✉r✐t② ●❡r♠❛♥✐✉♠ ❞❡t❡❝t♦rs✱ ✇❤❡r❡ t❤❡ ❛❝t✐✈✐t② ❝♦♥❝❡♥tr❛t✐♦♥ ♦❢ t❤❡ r❛❞✐♦♥✉❝❧✐❞❡s232_❚❤✱226_{❘❛ ❛♥❞}40_{❑ ❛r❡ t❤❡ ♣❛r❛♠❡t❡rs}

✉s❡❞ ✐♥ ❞♦s✐♠❡tr✐❝ ♠♦❞❡❧s ✭❉♦s✐♠❡tr✐❝ ■♥❞❡①❡s✮✱ ✇❤✐❝❤ ❡st❛❜❧✐s❤❡❞ ❧✐♠✐ts ✐♥ ❛❝❝♦r❞❛♥❝❡ ✇✐t❤ t❤❡ ❢♦r♠✱ ❛♠♦✉♥t ❛♥❞ ❛♣♣❧✐❝❛t✐♦♥ ♦❢ ♠❛t❡r✐❛❧ ♦❢ ❝♦♥str✉❝t✐♦♥✳ ❋♦r t❤❡ ❝❛❧❝✉❧❛t✐♦♥ ♦❢ t❤❡ ❛♥♥✉❛❧ ❡✛❡❝t✐✈❡ ❡①t❡r♥❛❧ ❞♦s❡ ✐t ✇❛s ❛ss✉♠❡❞ ❛ r♦♦♠ ♠♦❞❡❧ ✇✐t❤ ❞✐♠❡♥s✐♦♥s ♦❢ 4 ♠ ① 5 ♠ ① 2.8 ♠ ❛♥❞ ❛❧❧ ✇❛❧❧s ✐♥t❡r♥❛❧❧② ❝♦✈❡r❡❞ ✇✐t❤ 2 ❝♠ t❤✐❝❦♥❡ss ♦❢ ❣r❛♥✐t❡

❛♥❞ ❛♥ ❛♥♥✉❛❧ ❡①♣♦s✉r❡ t✐♠❡ ♦❢ 7000 ❤ ❛s s✉❣❣❡st❡❞ ❜② t❤❡ ❊✉r♦♣❡❛♥ ❈♦♠♠✐ss✐♦♥ ♦❢

❘❛❞✐♦❧♦❣✐❝❛❧ Pr♦t❡❝t✐♦♥ ❢♦r ✐♥t❡r♥❛❧ s✉♣❡r✜❝✐❛❧ ❝♦❛t✐♥❣ ♠❛t❡r✐❛❧s✳ ❚❤❡ ✐♥t❡r♥❛❧ ❡①♣♦s✉r❡ ✇❛s ❛ss❡ss❡❞ ❢r♦♠ t❤❡ r❛❞♦♥ ❝♦♥❝❡♥tr❛t✐♦♥ ✐♥ t❤❡ ❛✐r ♦❢ t❤❡ r♦♦♠ ♠♦❞❡❧✱ s✐♠✉❧❛t❡❞ ❢r♦♠ t❤❡ s✉♣❡r✜❝✐❛❧ ❡①❤❛❧❛t✐♦♥ r❛t❡ ♦❢ 222_{❘♥✳ ❚❤❡ ❡①❤❛❧❛t✐♦♥ r❛t❡ ✇❛s ❞❡t❡r♠✐♥❡❞ ❜②}

t❤❡ ♣❛ss✐✈❡ ❞❡t❡❝t✐♦♥ t❡❝❤♥✐q✉❡ ✇✐t❤ t❤❡ ❙♦❧✐❞ ❙t❛t❡ ◆✉❝❧❡❛r ❚r❛❝❦ ❉❡t❡❝t♦rs ✭❈❘✲39✮

❛♥❞ t❤❡ s❡❛❧❡❞ ❝❛♥ t❡❝❤♥✐q✉❡✱ ❛ss✉♠✐♥❣ ❛ ✈❡♥t✐❧❛t✐♦♥ r❛t❡ ♦❢ 0.5 ❤−1 ❛♥❞ ❛♥ ❛♥♥✉❛❧

❡①♣♦s✉r❡ t✐♠❡ ♦❢ 7000 ❤✳ ❚❤❡ r❡s✉❧ts ❢♦r t❤✐s st✉❞✐❡s s❤♦✇ t❤❛t t❤❡ ❛♥♥✉❛❧ ❡✛❡❝t✐✈❡

❞♦s❡ r❛♥❣❡❞ ❢r♦♠ ✭62 _± 3✮ µ❙✈✳②1 t♦ ✭138 _± 1✮ µ❙✈✳②−1 ❛♥❞ t❤❡ ✐♥t❡r♥❛❧ ❛♥♥✉❛❧

❡✛❡❝t✐✈❡ ❞♦s❡ r❛♥❣❡❞ ❢r♦♠(0,39 _± 0,04) µ❙✈✳②−1 t♦_{(70 ± 4) µ}❙✈✳②−1✳ ❚❤❡s❡ ✈❛❧✉❡s

♦❢ ❘❛❞✐♦❧♦❣✐❝❛❧ Pr♦t❡❝t✐♦♥✱ ♠❡❛♥✐♥❣ t❤❛t t❤❡ ❣r❛♥✐t✐❝ r♦❝❦s ❡✈❛❧✉❛t❡❞ ❝❛♥ ❜❡ ✉s❡❞ ✇✐t❤♦✉t r❛❞✐♦❧♦❣✐❝❛❧ ✐♠♣❧✐❝❛t✐♦♥s s✐♥❝❡ t❤❡ ❝♦♥s✐❞❡r❡❞ s❝❡♥❛r✐♦ ✐s ♦❜❡②❡❞✳ ❚❤❡ ✈❛❧✉❡s ♦❜t❛✐♥❡❞ ❢♦r t❤❡ ❝♦♥tr✐❜✉t✐♦♥ ❞✉❡ t♦ t❤❡ ✐♥t❡r♥❛❧ ❞♦s❡ r❛♥❣❡❞ ❢r♦♠1 % t♦78 % ♦❢ t❤❡

✈❛❧✉❡s ♦❜t❛✐♥❡❞ ❢♦r t❤❡ r❡s♣❡❝t✐✈❡ ❡①t❡r♥❛❧ ❞♦s❡ s❤♦✇✐♥❣ t❤❡ r❛❞♦♥ ❝♦♥tr✐❜✉t✐♦♥ ✈❛r✐❡s str♦♥❣❧② ✇✐t❤ t❤❡ r♦❝❦ t②♣❡✳ ❚❤❡ r❡s✉❧ts ♦❢ t❤❡ ❝♦rr❡❧❛t✐♦♥s ❜❡t✇❡❡♥ 222_{❘♥ s✉♣❡r✜❝✐❛❧}

❡①❤❛❧❛t✐♦♥ r❛t❡✱226_{❘❛ ❛❝t✐✈✐t② ❝♦♥❝❡♥tr❛t✐♦♥✱ ❞❡♥s✐t②✱ ♣♦r♦s✐t② ❛♥❞ ♠❛❥♦r ♦①✐❞❡s ♦❢ t❤❡}

❙✉♠ár✐♦

▲✐st❛ ❞❡ ❚❛❜❡❧❛s

▲✐st❛ ❞❡ ❋✐❣✉r❛s

✶ ■♥tr♦❞✉çã♦ ✶✼

✶✳✶ ❘❛❞✐♦♥✉❝❧í❞❡♦s ♥❛t✉r❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽ ✶✳✷ ❘♦❝❤❛s í❣♥❡❛s ❡ ❛ r❛❞✐♦❛t✐✈✐❞❛❞❡ ♥❛t✉r❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹ ✶✳✸ ■♥t❡r❛çã♦ ❞❛ r❛❞✐❛çã♦ ✐♦♥✐③❛♥t❡ ❝♦♠ ❛ ♠❛tér✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽ ✶✳✸✳✶ ■♥t❡r❛çã♦ ❞❛ r❛❞✐❛çã♦ ✐♦♥✐③❛♥t❡ ❝♦♠ ❛ ♠❛tér✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽ ✶✳✸✳✷ ■♥t❡r❛çã♦ ❞❡ ♣❛rtí❝✉❧❛s ❝❛rr❡❣❛❞❛s ♣❡s❛❞❛s ❝♦♠ ❛ ♠❛tér✐❛ ✳ ✳ ✳ ✳ ✷✾ ✶✳✹ ❆s♣❡❝t♦s ❣❡♦❧ó❣✐❝♦s ❞❛ ár❡❛ ❞❡ ❡st✉❞♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶ ✶✳✺ ❘❡❝✉rs♦s ♠✐♥❡r❛✐s ♥♦ ❡st❛❞♦ ❞♦ P❛r❛♥á ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷ ✶✳✻ ❏✉st✐✜❝❛t✐✈❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸

✷ ❖❜❥❡t✐✈♦s ✸✹

✷✳✶ ❖❜❥❡t✐✈♦ ❣❡r❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹ ✷✳✷ ❖❜❥❡t✐✈♦s ❡s♣❡❝í✜❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹ ✷✳✸ ❖r✐❣✐♥❛❧✐❞❛❞❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺

✸ ❘❡✈✐sã♦ ❞❡ ▲✐t❡r❛t✉r❛ ✸✻

✸✳✶ ❊s♣❡❝tr♦♠❡tr✐❛ ●❛♠❛ ❞❡ ❘❛❞✐♦♥✉❝❧í❞❡♦s ◆❛t✉r❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻ ✸✳✷ ❆♣❧✐❝❛çã♦ ❞❡ ❞❡t❡❝t♦r❡s ✭❙❙◆❚❉✮ ♣❛r❛ ♠❡❞✐❞❛s ❞❡222_{❘♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽}

✸✳✸ ❊st✉❞♦ ❞❛ ❝♦rr❡❧❛çã♦ ❡♥tr❡ ❝♦♥❝❡♥tr❛çã♦ ❞❡ ❯râ♥✐♦ ❡ ❡♠❛♥❛çã♦ ❞❡ ❘❛❞ô♥✐♦ ✸✽

✹ ▼❛t❡r✐❛✐s ❡ ♠ét♦❞♦s ✹✶

✹✳✶ ❆♠♦str❛❣❡♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶ ✹✳✶✳✶ ❊st✉❞♦ ❞❛ ✈❛r✐❛❜✐❧✐❞❛❞❡ ❞❛ ❛♠♦str❛❣❡♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸ ✹✳✷ ❊s♣❡❝tr♦♠❡tr✐❛ ❣❛♠❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹ ✹✳✷✳✶ Pré✲tr❛t❛♠❡♥t♦ ❡ ♣r❡♣❛r♦ ❞❛s ❛♠♦str❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹ ✹✳✷✳✷ ❊st✉❞♦ ❞❛ ❛✉t♦❛t❡♥✉❛çã♦ ❞❛ r❛❞✐❛çã♦ ❣❛♠❛ ♥❛s ❛♠♦str❛s ❡st✉❞❛❞❛s ✹✼ ✹✳✷✳✸ ❈á❧❝✉❧♦ ❞❛ ❝♦♥❝❡♥tr❛çã♦ ❞❡ ❛t✐✈✐❞❛❞❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵ ✹✳✸ ❮♥❞✐❝❡s ❞♦s✐♠étr✐❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸ ✹✳✸✳✶ ❆t✐✈✐❞❛❞❡ ❡q✉✐✈❛❧❡♥t❡ ❡♠ rá❞✐♦ ✭❘❛eq✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸

✹✳✸✳✷ ❮♥❞✐❝❡ ✭❍EX✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸

✹✳✸✳✸ ❮♥❞✐❝❡ ❣❛♠❛ ✭■γ✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹

✹✳✺✳✶ ❚é❝♥✐❝❛ ❞❡ ❞❡t❡❝çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾ ✹✳✺✳✷ ❚❛①❛ ❞❡ ❡①❛❧❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✹ ✹✳✺✳✸ ❊st✐♠❛t✐✈❛ ❞♦ ✐♥❝r❡♠❡♥t♦ ❞❛ ❝♦♥❝❡♥tr❛çã♦ ❞❡ 222_{❘♥ ❞❡✈✐❞♦ ❛♦}

226_{❘❛ ♥♦s ♠❛t❡r✐❛✐s ❞❡ ❝♦♥str✉çã♦ ❡ ❡st✐♠❛t✐✈❛ ❞❛ ❢r❛çã♦ ❞❡}

❡♠❛♥❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✺ ✹✳✻ ❈á❧❝✉❧♦ ❞❛ ❞♦s❡ ❡❢❡t✐✈❛ ❛♥✉❛❧ ❞❡✈✐❞❛ ❛♦ r❛❞ô♥✐♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✼ ✹✳✼ ❆♥á❧✐s❡ ❞♦s ♣r✐♥❝✐♣❛✐s ó①✐❞♦s ❝♦♠♣♦♥❡♥t❡s ♣♦r ✢✉♦r❡s❝ê♥❝✐❛ ❞❡ r❛✐♦s ❳ ✻✼ ✹✳✽ ❊♥s❛✐♦s ❋ís✐❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✽

✺ ❘❡s✉❧t❛❞♦s ✼✵

✺✳✶ ❈♦♥❝❡♥tr❛çã♦ ❞❡ ❛t✐✈✐❞❛❞❡ ♣♦r ❊s♣❡❝tr♦♠❡tr✐❛ ●❛♠❛ ❞❡ ❛❧t❛ r❡s♦❧✉çã♦ ✼✵ ✺✳✶✳✶ ▼❡❞✐❞❛ ❞❛ ❛✉t♦❛t❡♥✉❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✶ ✺✳✶✳✷ ◗✉✐✲q✉❛❞r❛❞♦s ✭χ2✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✹

✺✳✶✳✸ ❈♦♥❝❡♥tr❛çõ❡s ❞❡ ❛t✐✈✐❞❛❞❡s ❞♦40_❑✱232_{❚❤ ❡} 226_{❘❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✺}

✺✳✶✳✹ ❱❛r✐❛❜✐❧✐❞❛❞❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✼ ✺✳✶✳✺ ❮♥❞✐❝❡s ❉♦s✐♠étr✐❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✶ ✺✳✶✳✻ ❚❛①❛ ❞❡ ❉♦s❡ ❛❜s♦r✈✐❞❛ ♥♦ ❛r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✷ ✺✳✷ ❘❛❞ô♥✐♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✻ ✺✳✷✳✶ ❋r❛çã♦ ❞❡ ❊♠❛♥❛çã♦ ❡ ❝♦♥❝❡♥tr❛çã♦ ❞❡ r❛❞ô♥✐♦ ♥❛ s❛❧❛ ♣❛❞rã♦ ✳ ✽✾ ✺✳✷✳✷ ❉♦s❡ ❡❢❡t✐✈❛ ❛♥✉❛❧ ♥❛ s❛❧❛ ♣❛❞rã♦ ❞❡✈✐❞♦ à r❛❞✐❛çã♦ ❣❛♠❛ ❡ ❛♦

r❛❞ô♥✐♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✷ ✺✳✸ ❆♥á❧✐s❡ ❞♦s ♣r✐♥❝✐♣❛✐s ❡❧❡♠❡♥t♦s ❝♦♠♣♦♥❡♥t❡s ♣♦r ✢✉♦r❡s❝ê♥❝✐❛ ❞❡ r❛✐♦s ❳ ✾✸ ✺✳✹ Pr♦♣r✐❡❞❛❞❡s ❢ís✐❝❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✻ ✺✳✺ ❈♦rr❡❧❛çõ❡s ❡♥tr❡ 226_❘❛✱ 222_{❘♥✱ ♣r✐♥❝✐♣❛✐s ó①✐❞♦s ❝♦♠♣♦♥❡♥t❡s ❡}

♣r♦♣r✐❡❞❛❞❡s ❢ís✐❝❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✼ ✺✳✺✳✶ ❘❛❞ô♥✐♦ ✈s ✭❘á❞✐♦✱ ❚ór✐♦ ❡ P♦táss✐♦✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✼ ✺✳✺✳✷ ❈♦rr❡❧❛çõ❡s ❡♥tr❡ ❘á❞✐♦ ❡ ❘❛❞ô♥✐♦ ♥♦r♠❛❧✐③❛❞❛s ♣❡❧❛s ♣r♦♣r✐❡❞❛❞❡s

❢ís✐❝❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✵

✻ ❈♦♥❝❧✉sõ❡s ✶✵✸

✻✳✶ ❙✉❣❡stõ❡s ♣❛r❛ tr❛❜❛❧❤♦s ❢✉t✉r♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✹

❘❡❢❡rê♥❝✐❛s ❇✐❜❧✐♦❣rá✜❝❛s ✶✵✺

✼ ❆♣ê♥❞✐❝❡s ✶✶✷

▲✐st❛ ❞❡ ❚❛❜❡❧❛s

✶✳✶ ■sót♦♣♦s ❞♦ 222_{❘♥✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸}

✶✳✷ ❉❡❝❛✐♠❡♥t♦ r❛❞✐♦❛t✐✈♦ ❞♦ 222_{❘♥✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹}

✶✳✸ ❈❧❛ss✐✜❝❛çã♦ q✉í♠✐❝❛ ❞❛s r♦❝❤❛s✱ ❛ sér✐❡ é ❞❡♥♦♠✐♥❛❞❛ ❞❡ ❛❝♦r❞♦ ❝♦♠ ❛ ♣♦r❝❡♥t❛❣❡♠ ❞❡ ❙✐❖2 ♦❜t✐❞❛ q✉❛♥❞♦ ❛ ✐❣✉❛❧❞❛❞❡(N a2O+K2O) =CaO

é ❛t✐♥❣✐❞❛ ✭❲✐❧❧✐❛♠s ❡t ❛❧✳✱ ✶✾✼✵✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻ ✹✳✶ ❆♠♦str❛s ❞❡ r♦❝❤❛s ❞❛ ❘▼❈✱ ♦❜t✐❞❛s ♥❛ ❢♦r♠❛ ❝♦♠❡r❝✐❛❧ ❡♠ ❢á❜r✐❝❛s

❞❛ r❡❣✐ã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷ ✹✳✷ ❆♠♦str❛s ♦❜t✐❞❛s ❡♠ r❡✈❡♥❞❡❞♦r❛s ❧♦❝❛✐s ❞❛ ❘▼❈ ♣❛r❛ ❡st✉❞♦ ❞❛

✈❛r✐❛❜✐❧✐❞❛❞❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸ ✹✳✹ ❚r❛♥s✐çõ❡s ❣❛♠❛ s❡❧❡❝✐♦♥❛❞❛s ♣❛r❛ ♦ ❡st✉❞♦ ❞❡ ❛✉t♦❛t❡♥✉❛çã♦✳ ✳ ✳ ✳ ✳ ✳ ✹✽ ✹✳✻ ❚r❛♥s✐çõ❡s ❣❛♠❛ ✉t✐❧✐③❛❞❛s ♣❛r❛ ❞❡t❡r♠✐♥❛çã♦ ❞❛s ❝♦♥❝❡♥tr❛çõ❡s ❞❡

❛t✐✈✐❞❛❞❡ ❞♦s r❛❞✐♦♥✉❝❧í❞❡♦s40_❑✱232_{❚❤ ❡ ❞♦} 226_{❘❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶}

✹✳✽ ❋❛t♦r❡s ❞❡ ❝♦♥✈❡rsã♦ ❞❡ ❝♦♥❝❡♥tr❛çã♦ ❞❡ ❛t✐✈✐❞❛❞❡ ❡♠ t❛①❛ ❞❡ ❞♦s❡ ✭❊❈✱ ✶✾✾✾✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹ ✹✳✾ ❈r✐tér✐♦s ❞❡ ❞♦s❡ ♣❛r❛ ♠❛t❡r✐❛✐s ❞❡ ❝♦♥str✉çã♦ ✭❊❈✱ ✶✾✾✾✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺ ✺✳✶ ❘❡s✉❧t❛❞♦s r❡♣♦rt❛❞♦s ♥❛ ❧✐t❡r❛t✉r❛ ❡ ♥❡st❡ tr❛❜❛❧❤♦ ♣❛r❛ ❝♦♥❝❡♥tr❛çõ❡s

▲✐st❛ ❞❡ ❋✐❣✉r❛s

✶✳✶ ❙ér✐❡ r❛❞✐♦❛t✐✈❛ ❞♦ 238_{❯✱ ♠♦❞✐✜❝❛❞♦ ❞❡ ■❆❊❆✲❚❊❈❉❖❈✲✶✸✻✸ ✭✷✵✵✸✮✳ ✳ ✶✾}

✶✳✷ ❙ér✐❡ r❛❞✐♦❛t✐✈❛ ❞♦ 235_{❯✱ ♠♦❞✐✜❝❛❞♦ ❞❡ ■❆❊❆✲❚❊❈❉❖❈✲✶✸✻✸ ✭✷✵✵✸✮✳ ✳ ✷✵}

✶✳✸ ❙ér✐❡ r❛❞✐♦❛t✐✈❛ ❞♦ 232_{❚❤✱ ♠♦❞✐✜❝❛❞♦ ❞❡ ■❆❊❆✲❚❊❈❉❖❈✲✶✸✻✸ ✭✷✵✵✸✮✳ ✷✶}

✶✳✹ ❉✐❛❣r❛♠❛ s✐♠♣❧✐✜❝❛❞♦ ❞♦ ❞❡❝❛✐♠❡♥t♦ ❞♦ 40_{❑ ♠♦❞✐✜❝❛❞♦ ❞❡ ✭❑❛t❤r❡♥✱}

✶✾✾✽❀ ▲◆❍❇✱ ✷✵✶✸✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷ ✶✳✺ P♦ssí✈❡✐s ♠♦❞♦s ❞❡ ❡♠❛♥❛çã♦ ❞♦ r❛❞ô♥✐♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼ ✶✳✻ ■♠♣♦rtâ♥❝✐❛ r❡❧❛t✐✈❛ ❞❛s s❡çõ❡s ❞❡ ❝❤♦q✉❡ ❝♦♠ ❛ ❡♥❡r❣✐❛ ❡ ❝♦♠ ♦ ♥ú♠❡r♦

❛tô♠✐❝♦ ❩ ❞♦ ♠❡✐♦ ❛❜s♦r✈❡❞♦r ♠♦❞✐✜❝❛❞♦ ❞❡ ✭■❆❊❆✲❚❊❈❉❖❈✲✶✸✻✸✱ ✷✵✵✸✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽ ✶✳✼ ●❡♦❧♦❣✐❛ ❞♦ P❛r❛♥á✱ ♠♦❞✐✜❝❛❞♦ ❞❡ ✭▼■◆❊❘❖P❆❘✱ ✷✵✶✵✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷ ✹✳✶ ■❧✉str❛çã♦ ❞❛ ár❡❛ ❞❡ ❡st✉❞♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶ ✹✳✷ Pré✲tr❛t❛♠❡♥t♦ ❞❛s ❛♠♦str❛s ✭❛✮ ❉✐❢❡r❡♥t❡s ❡t❛♣❛s ❞❡ ♣r❡♣❛r❛çã♦✱ ✭❜✮

P✐❧ã♦ ❞❡ ❛ç♦ ❡ ♣❡♥❡✐r❛ ❞❡ 2 ♠♠✱ ✉t✐❧✐③❛❞♦s ♥❛ ♣ré✲❜r✐t❛❣❡♠ ✭❝✮ ❡ ✭❞✮

▼♦✐♥❤♦ ✈✐❜r❛tór✐♦ ❡ r❡s♣❡❝t✐✈❛ ✏♣❛♥❡❧❛✑ ✉t✐❧✐③❛❞♦s ♥❛ ♣✉❧✈❡r✐③❛çã♦✱ ✭❡✮ ❡ ✭❢✮ ❙❡❧❛❣❡♠ ❞❛s ❛♠♦str❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺ ✹✳✸ ✭❛✮ ❙✐st❡♠❛ ❞❡ ♠❡❞✐❞❛ ✭❜✮ ❉❡t❡❝t♦r ❍P●❡ sér✐❡ ●❊▼ ❖rt❡❝ ❝♦♠

r❡s♣❡❝t✐✈❛ ❜❧✐♥❞❛❣❡♠ ❡ ❛♠♦str❛ ♥❛ ❣❡♦♠❡tr✐❛ ❞❡ ♠❡❞✐❞❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✼ ✹✳✹ ❉✐❛❣r❛♠❛ ❞♦ ❛rr❛♥❥♦ ❡①♣❡r✐♠❡♥t❛❧ ❞♦ ♠ét♦❞♦ ❞❡ tr❛♥s♠✐ssã♦ ❣❛♠❛ ♣❛r❛

❛ ❝♦rr❡çã♦ ❞❛ ❛✉t♦❛t❡♥✉❛çã♦ ♥❛s ❛♠♦str❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾ ✹✳✺ ▼♦❞❡❧♦ ❞❡ s❛❧❛ ♣❛❞rã♦ ♣❛r❛ ❡st✐♠❛t✐✈❛ ❞❛ t❛①❛ ❞❡ ❞♦s❡ ❣❛♠❛ ❡①t❡r♥❛

♥♦ ❛r✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻ ✹✳✻ ✭❛✮ ❉✐❛❣r❛♠❛ ✐❧✉str❛t✐✈♦ ❞❛ ❚é❝♥✐❝❛ ❞♦ r❡❝✐♣✐❡♥t❡ s❡❧❛❞♦ ✭❜✮ ❈â♠❛r❛ ❞❡

❞✐❢✉sã♦ ◆❘P❇ ❡ ❞❡t❡❝t♦r ❈❘✲39 ✭❝✮ ❆♠♦str❛ ♥♦ ❢✉♥❞♦ ❞♦ r❡❝✐♣✐❡♥t❡ ❞❡

♠❡❞✐❞❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶ ✹✳✼ ✭❛✮ ❇❛♥❤♦✲♠❛r✐❛ ✉t✐❧✐③❛❞♦ ♣❛r❛ r❡✈❡❧❛çã♦✱ ✭❜✮ ▼✐❝r♦s❝ó♣✐♦ ót✐❝♦ ❩❡✐ss

❆①✐♦❧❛❜ ✶✵✵✱ ✉t✐❧✐③❛❞♦ ♣❛r❛ ❝♦♥t❛❣❡♠ ❞♦s tr❛ç♦s ❡ ♠✐❝r♦❝♦♠♣✉t❛❞♦r✱ ✭❝✮ ❉❡t❛❧❤❡ ❞♦s tr❛ç♦s ❡♠ ✉♠ ❞❡t❡❝t♦r ❈❘✲✸✾ ❛♣ós r❡✈❡❧❛çã♦✱ ❢♦t♦ ❞❡ ✭❆❧❜❡r✐❣✐✱ ✷✵✶✶✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷ ✹✳✽ ✭❛✮ ❈â♠❛r❛ ✉t✐❧✐③❛❞❛ ♣❛r❛ ❝❛❧✐❜r❛çã♦ ❞♦s ❞❡t❡❝t♦r❡s ❈❘✲✸✾ ✭❜✮ ❋♦♥t❡ ❞❡

✢✉①♦ ❝♦♥tí♥✉♦ P②❧♦♥✱ ❘♥✲✶✵✷✺✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✸ ✹✳✾ ✭❛✮ ❉❡t❛❧❤❡ ❞❛ ❜❛❧❛♥ç❛ ❛❞❛♣t❛❞❛ ♣❛r❛ ♣❡s❛❣❡♠ ❤✐❞r♦stát✐❝❛ ✭❜✮ ❈♦r♣♦s

❞❡ ♣r♦✈❛ ❞❡ ✉♠❛ ❞❛s ❛♠♦str❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✾ ✺✳✶ ❊s♣❡❝tr♦ ❞❡ r❛✐♦s ❣❛♠❛ ❞❛ ❛♠♦str❛ 34❡♠ ❝♦♥t❛❣❡♠ ❞❡ 86 ❦s✳ ✳ ✳ ✳ ✳ ✳ ✼✶

✺✳✷ ❋❛t♦r❡s ❞❡ ❛✉t♦❛t❡♥✉❛çã♦ ❡ ❛❥✉st❡ ❞❛ ❝✉r✈❛ ♣❛r❛ ❛ ❛♠♦str❛ ✶✳ ✳ ✳ ✳ ✳ ✳ ✼✷ ✺✳✸ ❋❛t♦r❡s ❞❡ ❛✉t♦❛t❡♥✉❛çã♦ ❡ ❛❥✉st❡ ❞❛ ❝✉r✈❛ ♣❛r❛ ❛ ❛♠♦str❛ ✷✹✳ ✳ ✳ ✳ ✳ ✳ ✼✷ ✺✳✹ ❋❛t♦r❡s ❞❡ ❛✉t♦❛t❡♥✉❛çã♦ ♠❡❞✐❞♦s ❡♠ ❢✉♥çã♦ ❞❛ ❡♥❡r❣✐❛ ♣❛r❛ t♦❞❛s ❛s

✺✳✺ ❆❥✉st❡s ❞♦s ❢❛t♦r❡s ❞❡ ❛✉t♦❛t❡♥✉❛çã♦ ❡♠ ❢✉♥çã♦ ❞❛ ❡♥❡r❣✐❛ ♣❛r❛ t♦❞❛s ❛s ❛♠♦str❛s ❞❡ r♦❝❤❛s ❞❛ ❘▼❈✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✹ ✺✳✻ ❱❛❧♦r❡s ❞❡ ◗✉✐✲q✉❛❞r❛❞♦ ❞❡t❡r♠✐♥❛❞♦s ♣❛r❛ ❛s ❡st✐♠❛t✐✈❛s ❞♦ 226_{❘❛ ❡}

❞♦ 232_{❚❤✱ ❝♦♥s✐❞❡r❛♥❞♦ n = 2✱ ✭❡st❛s ❡st✐♠❛t✐✈❛s ❢♦r❛♠ r❡❛❧✐③❛❞❛s}

❝♦♥s✐❞❡r❛♥❞♦ ❞♦✐s r❛❞✐♦♥✉❝❧í❞❡♦s ❚❆❇✳ ✹✳✻✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✺ ✺✳✼ ❈♦♥❝❡♥tr❛çã♦ ❞❡ ❛t✐✈✐❞❛❞❡s ❞❡ 40_{❑ ♥❛s ❛♠♦str❛s ❞❡ r♦❝❤❛s ♦❜t✐❞❛s ♥❛}

❘▼❈✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✻ ✺✳✽ ❈♦♥❝❡♥tr❛çã♦ ❞❡ ❛t✐✈✐❞❛❞❡s ❞❡ 232_{❚❤ ♥❛s ❛♠♦str❛s ❞❡ r♦❝❤❛s ♦❜t✐❞❛s ♥❛}

❘▼❈✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✻ ✺✳✾ ❈♦♥❝❡♥tr❛çã♦ ❞❡ ❛t✐✈✐❞❛❞❡s ❞❡226_{❘❛ ♥❛s ❛♠♦str❛s ❞❡ r♦❝❤❛s ♦❜t✐❞❛s ♥❛}

❘▼❈✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✼ ✺✳✶✵ ❘❡s✉❧t❛❞♦s ❞♦ ❡st✉❞♦ ❞❛ ✈❛r✐❛❜✐❧✐❞❛❞❡ ♣❛r❛ ❛s5❛♠♦str❛s ❡①tr❛í❞❛s ♣❡❧❛s

❞✉❛s ❢á❜r✐❝❛s ✉t✐❧✐③❛♥❞♦ ♦s r❛❞✐♦✐sót♦♣♦s ✭❛✮40_{❑ ✭❜✮}232_{❚❤ ❡ ✭❝✮} 226_{❘❛✳ ✼✽}

✺✳✶✶ ❘❡s✉❧t❛❞♦s ❞♦ ❡st✉❞♦ ❞❛ ✈❛r✐❛❜✐❧✐❞❛❞❡ ♣❛r❛ ❛s 8 ❛♠♦str❛s ✉t✐❧✐③❛♥❞♦ ♦s

r❛❞✐♦✐sót♦♣♦s ✭❛✮ 40_{❑ ✭❜✮} 232_{❚❤ ❡ ✭❝✮} 226_{❘❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✾}

✺✳✶✷ ❱❛❧♦r❡s ❝❛❧❝✉❧❛❞♦s ♣❛r❛ ♦ ✐♥❞✐❝❡ ❆t✐✈✐❞❛❞❡ ❊q✉✐✈❛❧❡♥t❡ ❡♠ ❘á❞✐♦ ♣❛r❛ ❛s r♦❝❤❛s ❡st✉❞❛❞❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✶ ✺✳✶✸ ❱❛❧♦r❡s ❝❛❧❝✉❧❛❞♦s ♣❛r❛ ♦ ❮♥❞✐❝❡ ❡①t❡r♥♦ ♣❛r❛ ❛s r♦❝❤❛s ❡st✉❞❛❞❛s✳ ✳ ✳ ✳ ✽✶ ✺✳✶✹ ❱❛❧♦r❡s ❝❛❧❝✉❧❛❞♦s ♣❛r❛ ♦ ❮♥❞✐❝❡ ❣❛♠❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✷ ✺✳✶✺ ❚❛①❛ ❞❡ ❞♦s❡ ❆❜s♦r✈✐❞❛ ♥♦ ❛r ❞❡♥tr♦ ❞❛ s❛❧❛ ♣❛❞rã♦ ✭4♠ ①5♠ ①2,8♠✮✱

❞❡❝♦rr❡♥t❡ ❞❛ ✉t✐❧✐③❛çã♦ ❞❛ r♦❝❤❛s ❡st✉❞❛❞❛s ❝♦♠ r❡s✈❡st✐♠❡♥t♦ ✐♥t❡r♥♦✳ ✽✸ ✺✳✶✻ ❘❡s✉❧t❛❞♦s ♣❛r❛ ❚❛①❛ ❞❡ ❞♦s❡ ❆❜s♦r✈✐❞❛ ♥♦ ❛r ❞❡♥tr♦ ❞❛ s❛❧❛ ♣❛❞rã♦

✭4 ♠ ① 5 ♠ ① 2,8 ♠✮✱ ♦❜t✐❞♦s ♣❡❧♦s ♠♦❞❡❧♦s ❞❡s❝r✐t♦s ❡♠ ✭❊❈✱ ✶✾✾✾❀

▼á❞✉❛r✱ ✷✵✵✵✮ ❞❡❝♦rr❡♥t❡ ❞❛ ✉t✐❧✐③❛çã♦ ❞❛s r♦❝❤❛s ❡st✉❞❛❞❛s ❝♦♠♦ r❡✈❡st✐♠❡♥t♦ ✐♥t❡r♥♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✹ ✺✳✶✼ ❈♦♠♣❛r❛çã♦ ❞♦s ✈❛❧♦r❡s ❞❡ t❛①❛ ❞❡ ❞♦s❡ ❝❛❧❝✉❧❛❞♦s ❡♠ três s✐t✉❛çõ❡s

❞✐❢❡r❡♥t❡s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✺ ✺✳✶✽ ❋❛t♦r❡s ❞❡ ❝♦♥✈❡rsã♦ ❞❡ ❞♦s❡ ❡♠ ❢✉♥çã♦ ❞❛ ❡s♣❡ss✉r❛ ❞❛ ♣❛r❡❞❡✱

❝❛❧❝✉❧❛❞♦s ♣❡❧♦ ♣r♦❣r❛♠❛ ❊❉❱❖❙✱ ♣❛r❛ ❛s r♦❝❤❛s ❡st✉❞❛❞❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✻ ✺✳✶✾ ❋❛t♦r ❞❡ ❝❛❧✐❜r❛çã♦ ✭❡✜❝✐ê♥❝✐❛ ❞❡ ❞❡t❡❝çã♦✮ ❞♦s ❞❡t❡❝t♦r❡s ❈❘✲39✱

❞❡t❡r♠✐♥❛❞♦s ❡①♣❡r✐♠❡♥t❛❧♠❡♥t❡ ♣❛r❛ ❛ ❣❡♦♠❡tr✐❛ ❞❡ ♠❡❞✐❞❛✳ ✳ ✳ ✳ ✳ ✳ ✽✻ ✺✳✷✵ ❈♦♥❝❡♥tr❛çã♦ ❞❡ r❛❞ô♥✐♦ ♥❛ ❝â♠❛r❛ s❡❧❛❞❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✼ ✺✳✷✶ ❚❛①❛ ❞❡ ❡①❛❧❛çã♦ s✉♣❡r✜❝✐❛❧ ❞❡ r❛❞ô♥✐♦ ❞❛s ❛♠♦str❛s ❞❡ r♦❝❤❛s ❡st✉❞❛❞❛s✳ ✽✽ ✺✳✷✷ ❚❛①❛ ❞❡ ❡①❛❧❛çã♦ ❞❡ r❛❞ô♥✐♦ ♣♦r ♠❛ss❛ ❞❛s ❛♠♦str❛s ❞❡ r♦❝❤❛s ❡st✉❞❛❞❛s✳ ✽✽ ✺✳✷✸ ❱❛❧♦r❡s t❡ór✐❝♦s ❡ ✈❛❧♦r❡s ❡①♣❡r✐♠❡♥t❛✐s ❞❡ t❛①❛ ❞❡ ❡①❛❧❛çã♦ s✉♣❡r✜❝✐❛❧

❞❡ r❛❞ô♥✐♦ ❞❛s r♦❝❤❛s ❡st✉❞❛❞❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✾ ✺✳✷✹ ❋r❛çã♦ ❞❡ ❡♠❛♥❛çã♦ ✈❛❧♦r❡s t❡ór✐❝♦s ❡ ✈❛❧♦r❡s ♠❡❞✐❞♦s ♣❛r❛ ❛ r♦❝❤❛s

❡st✉❞❛❞❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✵ ✺✳✷✺ ■♥❝r❡♠❡♥t♦ ❞❡ ❝♦♥❝❡♥tr❛çã♦ ❞❡ r❛❞ô♥✐♦ ♥❛ s❛❧❛ ♣❛❞rã♦ ✭✈❛❧♦r t❡ór✐❝♦ ❡

✈❛❧♦r ♠❡❞✐❞♦✮ ❞❡✈✐❞♦ ❛♦ r❡✈❡st✐♠❡♥t♦ ✐♥t❡r♥♦ ❝♦♠ ❛s r♦❝❤❛s ❡st✉❞❛❞❛s✳ ✾✶ ✺✳✷✻ ■♥❝r❡♠❡♥t♦ ❞❛ ❞♦s❡ ❡❢❡t✐✈❛ ❛♥✉❛❧ ❝❛✉s❛❞♦ ♣❡❧♦ r❡✈❡st✐♠❡♥t♦ ✐♥t❡r♥♦ ❞❡

✉♠❛ s❛❧❛ ♣❛❞rã♦ ❞❡✈✐❞♦ ❛ r❛❞✐❛çã♦ ❣❛♠❛ ❡①t❡r♥❛ ❡ ❛ ✐♥❛❧❛çã♦ ❞♦ r❛❞ô♥✐♦✳ ✾✷ ✺✳✷✼ ❆♥á❧✐s❡ ♣♦r ❛❣r✉♣❛♠❡♥t♦ ❞♦s ó①✐❞♦s ♣r✐♥❝✐♣❛✐s ❝♦♥st✐t✉✐♥t❡s ❞❛s

✺✳✷✽ ❚❡♦r ❡♠ ✭✪✮ ❞❡ ó①✐❞♦s ♥❛s ❛♠♦str❛s1✱4✱20❡35❡①tr❡♠♦s ❞♦ ❞❡♥❞♦❣r❛♠❛✳ ✾✺

✺✳✷✾ ❉❡♥s✐❞❛❞❡ ❛♣❛r❡♥t❡ ❞❛s ❛♠♦str❛s ♠❡❞✐❞❛s ❝♦♥❢♦r♠❡ ♥♦r♠❛ ❆❇◆❚ ✭✷✵✶✵✮✳ ✾✻ ✺✳✸✵ P♦r♦s✐❞❛❞❡ ❛♣❛r❡♥t❡ ❞❛s ❛♠♦str❛s ♠❡❞✐❞❛s ❝♦♥❢♦r♠❡ ♥♦r♠❛ ❆❇◆❚ ✭✷✵✶✵✮✳ ✾✻ ✺✳✸✶ ❈♦♥❝❡♥tr❛çã♦ ❞❡ 222_{❘♥ ♥❛ ❝â♠❛r❛ ❡♠ ❢✉♥çã♦ ❞❛ ❝♦♥❝❡♥tr❛çã♦ ❞❡}

❛t✐✈✐❞❛❞❡ ❞♦226_{❘❛ ♥❛s ❛♠♦str❛s ❞❡ r♦❝❤❛ ❡st✉❞❛❞❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✼}

✺✳✸✷ ❚❛①❛ ❞❡ ❡①❛❧❛çã♦ s✉♣❡r✜❝✐❛❧ ❞❡ 222_{❘♥ ❡♠ ❢✉♥çã♦ ❞❛ ❝♦♥❝❡♥tr❛çã♦ ❞❡}

❛t✐✈✐❞❛❞❡ ❞♦226_{❘❛ ♥❛s ❛♠♦str❛s ❞❡ r♦❝❤❛s ❡st✉❞❛❞❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✽}

✺✳✸✸ ❚❛①❛ ❞❡ ❡①❛❧❛çã♦ ♣♦r ♠❛ss❛ ❞❡ 222_{❘♥ ❡♠ ❢✉♥çã♦ ❞❛ ❝♦♥❝❡♥tr❛çã♦ ❞❡}

❛t✐✈✐❞❛❞❡ ❞♦226_{❘❛ ♥❛s ❛♠♦str❛s ❞❡ r♦❝❤❛s ❡st✉❞❛❞❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✽}

✺✳✸✹ ❚❛①❛ ❞❡ ❡①❛❧❛çã♦ s✉♣❡r✜❝✐❛❧ ❞❡ 222_{❘♥ ❡♠ ❢✉♥çã♦ ❞❛ ❝♦♥❝❡♥tr❛çã♦ ❞❡}

❛t✐✈✐❞❛❞❡ ❞❡232_{❚❤ ♥❛s ❛♠♦str❛s ❞❡ r♦❝❤❛s ❡st✉❞❛❞❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✾}

✺✳✸✺ ❚❛①❛ ❞❡ ❡①❛❧❛çã♦ s✉♣❡r✜❝✐❛❧ ❞❡ 222_{❘♥ ❡♠ ❢✉♥çã♦ ❞❛ ❝♦♥❝❡♥tr❛çã♦ ❞❡}

❛t✐✈✐❞❛❞❡ ❞❡40_{❑ ♥❛s ❛♠♦str❛s ❞❡ r♦❝❤❛s ❡st✉❞❛❞❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✾}

✺✳✸✻ ❈♦♥❝❡♥tr❛çã♦ ❞❡ ❛t✐✈✐❞❛❞❡ ❞❡ 232_{❚❤ ❡♠ ❢✉♥çã♦ ❞❛ ❝♦♥❝❡♥tr❛çã♦ ❞❡}

❛t✐✈✐❞❛❞❡ ❞♦226_{❘❛ ♥❛s ❛♠♦str❛s ❞❡ r♦❝❤❛s ❡st✉❞❛❞❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✵}

✺✳✸✼ ❚❛①❛ ❞❡ ❡①❛❧❛çã♦ s✉♣❡r✜❝✐❛❧ ❞❡222_{❘♥ ❡♠ ❢✉♥çã♦ ❞❛ r❛③ã♦ ✭❝♦♥❝❡♥tr❛çã♦}

❞❡ ❛t✐✈✐❞❛❞❡ ❞❡226_{❘❛✴❞❡♥s✐❞❛❞❡✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✶}

✺✳✸✽ ❚❛①❛ ❞❡ ❡①❛❧❛çã♦ s✉♣❡r✜❝✐❛❧ ❞❡222_{❘♥ ❡♠ ❢✉♥çã♦ ❞❛ r❛③ã♦ ✭❝♦♥❝❡♥tr❛çã♦}

❞❡ ❛t✐✈✐❞❛❞❡ ❞❡226_{❘❛✴♣♦r♦s✐❞❛❞❡✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✶}

✺✳✸✾ ❘❛③ã♦ ✭❚❛①❛ ❞❡ ❡①❛❧❛çã♦ s✉♣❡r✜❝✐❛❧ ❞❡ 222_{❘♥ ✴ ❉❡♥s✐❞❛❞❡✮ ❡♠ ❢✉♥çã♦}

❞❛ ❝♦♥❝❡♥tr❛çã♦ ❞❡ ❛t✐✈✐❞❛❞❡ ❞❡226_{❘❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✷}

✺✳✹✵ ❘❛③ã♦ ✭❚❛①❛ ❞❡ ❡①❛❧❛çã♦ s✉♣❡r✜❝✐❛❧ ❞❡ 222_{❘♥ ✴ P♦r♦s✐❞❛❞❡✮ ❡♠ ❢✉♥çã♦}

❈❛♣ít✉❧♦

1

■♥tr♦❞✉çã♦

❖s r❛❞✐♦♥✉❝❧í❞❡♦s ♥❛t✉r❛✐s ❞❡ ♦r✐❣❡♠ ♣r✐♠♦r❞✐❛❧✱ ♦✉ t❡rr❡str❡s✱ sã♦ ❡♥❝♦♥tr❛❞♦s ❡♠ q✉❛♥t✐❞❛❞❡s ✈❛r✐❛❞❛s ❡♠ t♦❞♦ ♠❡✐♦ ❛♠❜✐❡♥t❡✿ ♦r❣❛♥✐s♠♦s ✈✐✈♦s✱ r♦❝❤❛s✱ s♦❧♦s✱ á❣✉❛✱ ❛t♠♦s❢❡r❛✳ ❆ss✐♠✱ ❡❧❡s ❝♦♥tr✐❜✉❡♠ ♥❛ ❞♦s❡ ❛ s❡r❡s ❤✉♠❛♥♦s t❛♥t♦ ❡①t❡r♥❛♠❡♥t❡ ✭♠❛t❡r✐❛✐s ❞❡ ❝♦♥str✉çã♦ ❡ s♦❧♦ ♣✳❡①✳✮✱ ❝♦♠♦ ✐♥t❡r♥❛♠❡♥t❡ ✭s❡♥❞♦ ✐♥❝♦r♣♦r❛❞♦s ♣♦r ♠❡✐♦ ❞❛ ✐♥❣❡stã♦ ❞❡ ❛❧✐♠❡♥t♦s ❡ ✐♥❛❧❛çã♦ ❞♦ ❛r ❝♦♥t❛♠✐♥❛❞♦✮✭❯◆❙❈❊❆❘✱ ✷✵✵✵✮✳

❊♠ r❡s✐❞ê♥❝✐❛s✱ ♦ ♣r✐♥❝✐♣❛❧ ✐♥❝r❡♠❡♥t♦ ❞❛ ❞♦s❡ ❝❛✉s❛❞♦ ♣♦r r❛❞✐♦♥✉❝❧í❞❡♦s ♥❛t✉r❛✐s é ♦r✐❣✐♥❛❞♦ ❞♦s ♠❛t❡r✐❛✐s ❞❡ ❝♦♥str✉çã♦✳ ❆ ❞♦s❡ ❡①t❡r♥❛ ❣❛♠❛ t❡♠ ♦r✐❣❡♠ ♥❛ ❡①♣♦s✐çã♦ ❞❡✈✐❞❛ ❛ r❛❞✐♦♥✉❝❧í❞❡♦s ♥❛t✉r❛✐s q✉❡ ♣♦❞❡♠ ♦❝♦rr❡r ❞❡ ❢♦r♠❛ ✐s♦❧❛❞❛ ♦✉ ❡♠ sér✐❡s r❛❞✐♦❛t✐✈❛s ✭❛s sér✐❡s ❞♦ 238_❯✱ 235_{❯ ❡} 232_{❚❤ ❡ ♦ r❛❞✐♦♥✉❝❧í❞❡♦ ✐s♦❧❛❞♦} 40_❑

r❡♣r❡s❡♥t❛♠ ✶✻✱✾✼ ✪ ❞❛ ❞♦s❡ ❡❢❡t✐✈❛ ♠é❞✐❛ ❛♥✉❛❧ ♠✉♥❞✐❛❧✮✳ ❆ ❞♦s❡ ✐♥t❡r♥❛ é ❞❡❝♦rr❡♥t❡ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ❞❛ ✐♥❛❧❛çã♦ ❞♦ ✐sót♦♣♦ ❞♦ r❛❞ô♥✐♦✱222_{❘♥✱ q✉❡ é ✉♠ ❣ás ♥♦❜r❡ ♦r✐❣✐♥❛❞♦}

♣♦r ♠❡✐♦ ❞❡ ❡♠✐ssã♦ ❞❡ ♣❛rtí❝✉❧❛s ❛❧❢❛ ❞✉r❛♥t❡ ❛ ❞❡s✐♥t❡❣r❛çã♦ r❛❞✐♦❛t✐✈❛ ❞♦ 226_❘❛✱

q✉❡ ♣♦r s✉❛ ✈❡③✱ é ♣r♦❞✉t♦ ❞❡ ❞❡❝❛✐♠❡♥t♦ ❞❛ sér✐❡ ❞♦ 238_{❯✳ ❆ ✐♥❛❧❛çã♦ ❞♦ r❛❞ô♥✐♦}

r❡♣r❡s❡♥t❛ ✹✼✱✻ ✪ ❞❛ ❞♦s❡ ❡❢❡t✐✈❛ ♠é❞✐❛ ❛♥✉❛❧ ♠✉♥❞✐❛❧ ❞❡✈✐❞♦ ❛ r❛❞✐♦♥✉❝❧í❞❡♦s ♥❛t✉r❛✐s ✭❯◆❙❈❊❆❘✱ ✷✵✵✵✮✳

❯♠❛ ✈❡③ q✉❡ r♦❝❤❛s sã♦ ❛♠♣❧❛♠❡♥t❡ ✉t✐❧✐③❛❞❛s ❝♦♠♦ ♠❛t❡r✐❛✐s ❞❡ ❝♦♥str✉çã♦✱ t❛♥t♦ ❡str✉t✉r❛✐s ❝♦♠♦ ❞❡ r❡✈❡st✐♠❡♥t♦✱ ❡❧❛s ♣♦❞❡♠ t♦r♥❛r✲s❡ ✉♠❛ ✐♠♣♦rt❛♥t❡ ❢♦♥t❡ ❞❡ ❞♦s❡ s❡ ❛s ❝♦♥❝❡♥tr❛çõ❡s ❞❡ r❛❞✐♦❛t✐✈✐❞❛❞❡ ❢♦r❡♠ ❛❧t❛s✱ ❡ ❞❡♣❡♥❞❡♥❞♦ ❞❛ ❢♦r♠❛ ❡ q✉❛♥t✐❞❛❞❡ ❝♦♠ q✉❡ sã♦ ❛♣❧✐❝❛❞❛s✳ ❆ r❛❞✐♦❛t✐✈✐❞❛❞❡ ♥❛t✉r❛❧ ❞❛s r♦❝❤❛s✱ ♣♦r s✉❛ ✈❡③✱ ✈❛r✐❛ ❞❡ ❛❝♦r❞♦ ❝♦♠ s✉❛ ♥❛t✉r❡③❛✱ ❡♠ ❣❡r❛❧ ❝♦♥❝❡♥tr❛çõ❡s ♠❛✐s ❛❧t❛s sã♦ ❝♦♠✉♥s ❡♠ r♦❝❤❛s í❣♥❡❛s ✭❣r❛♥ít✐❝❛s✮ ❡♠ r❡❧❛çã♦ às s❡❞✐♠❡♥t❛r❡s ❡ ♠❡t❛♠ór✜❝❛s✳ ❆ss✐♠✱ t♦r♥❛✲s❡ ✐♠♣♦rt❛♥t❡✱ ❡♠ t❡r♠♦s r❛❞✐♦❧ó❣✐❝♦s✱ ❢❛③❡r❡♠✲s❡ ❡st✉❞♦s ❞❛ ❛♣❧✐❝❛çã♦ ❞❡ r♦❝❤❛s ❣r❛♥ít✐❝❛s ❝♦♠♦ ♠❛t❡r✐❛✐s ❞❡ ❝♦♥str✉çã♦✱ ❝♦♠ ♦ ♦❜❥❡t✐✈♦ ❞❡ ❛✈❛❧✐❛r ♦ ❛✉♠❡♥t♦ ❞❛ ❞♦s❡ q✉❡ ❡st❛ ❛♣❧✐❝❛çã♦ ♣♦❞❡ ❝❛✉s❛r às ♣❡ss♦❛s✳

❊st✉❞♦s ❞❡ r❛❞✐♦t✐✈✐❞❛❞❡ ♥❛t✉r❛❧ ❡♠ r♦❝❤❛s✱ ♣❛r❛ ❡st❡ ✜♠✱ tê♠ s✐❞♦ ❢❡✐t♦s✱ ❡♠ ✈ár✐♦s ♣❛ís❡s ✭❚✉r❤❛♥✱ ✷✵✵✽❀ ❋❛❤❡❡♠ ❡t ❛❧✳✱ ✷✵✵✽❀ ▼❛r♦❝❝❤✐ ❡t ❛❧✳✱ ✷✵✶✶✮✱ ❡♠ s✉❛ ♠❛✐♦r✐❛✱ ♥♦ q✉❡ ❞✐③ r❡s♣❡✐t♦ ❛ ❣r❛♥✐t♦s ✭✉t✐❧✐③❛❞♦s ❝♦♠♦ ♠❛t❡r✐❛✐s ❞❡ ❝♦♥str✉çã♦✮✱ ❞❡t❡r♠✐♥❛♥❞♦ ❛ ❝♦♥❝❡♥tr❛çã♦ ❞❡ ❛t✐✈✐❞❛❞❡ ❞❡ 226_❘❛✱ 232_{❚❤ ❡} 40_{❑✱ ♣♦r ♠❡✐♦ ❞❛ té❝♥✐❝❛}

❞❡ ❡s♣❡❝tr♦♠❡tr✐❛ ❣❛♠❛✱ ❡ ❡st❡s ✈❛❧♦r❡s s❡r✈❡♠ ❡♥tã♦ ❞❡ ♣❛râ♠❡tr♦s ❡♠ ♠♦❞❡❧♦s ❞♦s✐♠étr✐❝♦s✱ ❜✉s❝❛♥❞♦ ❧✐♠✐t❛r ❛ ❞♦s❡ ❛ ✉♠ ❝❡rt♦ ♥í✈❡❧ ❛❜❛✐①♦ ❞♦ q✉❛❧ ♥ã♦ s❡ ❡s♣❡r❛ ❞❛♥♦s ♣❛r❛ ♦ ✐♥❞✐✈í❞✉♦ ❞♦ ♣ú❜❧✐❝♦✳ ◆❡st❡ tr❛❜❛❧❤♦ ❢♦r❛♠ ❝❛❧❝✉❧❛❞♦s ♦s três í♥❞✐❝❡s ❞♦s✐♠étr✐❝♦s✱ q✉❡ sã♦ ❛♠♣❧❛♠❡♥t❡ ✉t✐❧✐③❛❞♦s ♥❛ ❧✐t❡r❛t✉r❛✱ ❛t✐✈✐❞❛❞❡ ❡q✉✐✈❛❧❡♥t❡ ❡♠ rá❞✐♦ ❘❛eq✱ ❡ ♦s í♥❞✐❝❡s ❞❡ ❞♦s❡ ❣❛♠❛ ❡①t❡r♥❛✱ ❍EX ❡ ■γ ✭✐t❡♠ ✹✳✸✮✳ ❆❧❣✉♥s ❞❡st❡s

✶✳✶ ✲ ❘❛❞✐♦♥✉❝❧í❞❡♦s ♥❛t✉r❛✐s ✶✽

♠♦❞❡❧♦s s✉♣õ❡♠ q✉❡ ✉♠❛ ❞❛❞❛ ❝♦♥❝❡♥tr❛çã♦ ❞❡226_{❘❛ ✭❧✐♠✐t❡ ♠á①✐♠♦ ♣❡r♠✐t✐❞♦✮ ♥ã♦}

❣❡r❡ ❝♦♥❝❡♥tr❛çõ❡s ❞❡ r❛❞ô♥✐♦ s✉♣❡r✐♦r❡s ❛200 ❇q✳♠−3 ✭❊❈✱ ✶✾✾✾✮✳

✶✳✶ ❘❛❞✐♦♥✉❝❧í❞❡♦s ♥❛t✉r❛✐s

❆ ❞♦s❡ ❡①t❡r♥❛ ❣❛♠❛ ❞❡✈✐❞❛ ❛ r❛❞✐♦♥✉❝❧í❞❡♦s ♥❛t✉r❛✐s ♣♦❞❡ s❡r ❝❛✉s❛❞❛ ♣♦r r❛❞✐♦♥✉❝❧í❞❡♦s ❞❛s sér✐❡s r❛❞✐♦❛t✐✈❛s ♦✉ ♣♦r r❛❞✐♦♥✉❝❧í❞❡♦s q✉❡ ♦❝♦rr❡♠ ❞❡ ❢♦r♠❛ ✐s♦❧❛❞❛✳

❚rês sér✐❡s r❛❞✐♦❛t✐✈❛s sã♦ ❡♥❝♦♥tr❛❞❛s ♥❛ ♥❛t✉r❡③❛✱ sã♦ ❡❧❛s✿ 238_{❯ ✭❛❜✉♥❞â♥❝✐❛}

✐s♦tó♣✐❝❛ ❞❡ ✾✾✱✷✼ ✪✱ ❡ t1/2 ❂4,46①109 ❛♥♦s✮✱ 235❯ ✭❛❜✉♥❞â♥❝✐❛ ✐s♦tó♣✐❝❛ ❞❡ ✵✱✼ ✪✱ ❡

t1/2 ❂ 7,13①108 ❛♥♦s✮ ❡ 232❚❤ ✭❛❜✉♥❞â♥❝✐❛ ✐s♦tó♣✐❝❛ ✶✵✵ ✪✱ ❡ t1/2 ❂ 1,39①1010 ❛♥♦s✮

✶✳✶ ✲ ❘❛❞✐♦♥✉❝❧í❞❡♦s ♥❛t✉r❛✐s ✶✾

✶✳✶ ✲ ❘❛❞✐♦♥✉❝❧í❞❡♦s ♥❛t✉r❛✐s ✷✵

✶✳✶ ✲ ❘❛❞✐♦♥✉❝❧í❞❡♦s ♥❛t✉r❛✐s ✷✶

✶✳✶ ✲ ❘❛❞✐♦♥✉❝❧í❞❡♦s ♥❛t✉r❛✐s ✷✷

❉♦ ♣♦♥t♦ ❞❡ ✈✐st❛ ❜✐♦❧ó❣✐❝♦✲❛♠❜✐❡♥t❛❧✱ s♦♠❡♥t❡ ❞♦✐s r❛❞✐♦♥✉❝❧í❞❡♦s ✐s♦❧❛❞♦s q✉❡ ♦❝♦rr❡♠ ♥❛t✉r❛❧♠❡♥t❡ sã♦ r❡❧❡✈❛♥t❡s✿ 40_{❑ ❡ ♦} 87_{❘❜✱ s❡♥❞♦ ♦} 40_{❑ ♦ ♠❛✐s ✐♠♣♦rt❛♥t❡✱}

❞♦ ♣♦♥t♦ ❞❡ ✈✐st❛ ❜✐♦❧ó❣✐❝♦ ✭❑❛t❤r❡♥✱ ✶✾✾✽✮✳ ❉♦s três ✐sót♦♣♦s ♥❛t✉r❛✐s ❞♦ ♣♦táss✐♦✱ ♦

40_{❑ é ♦ ú♥✐❝♦ r❛❞✐♦❛t✐✈♦✱ ❝♦♠ ♠❡✐❛✲✈✐❞❛ ❞❡ ✶✱✷✽ ①10}9 _{❛♥♦s ❡ ✉♠❛ ❛❜✉♥❞â♥❝✐❛ ✐s♦tó♣✐❝❛}

❞❡ ✵✱✵✶✶✽ ✪✳ ◆❛ ❋■●✳ ✶✳✹ é ❛♣r❡s❡♥t❛❞♦ ♦ ❞✐❛❣r❛♠❛ s✐♠♣❧✐✜❝❛❞♦ ❞♦ ❞❡❝❛✐♠❡♥t♦ ❞♦40_❑✳

❋✐❣✉r❛ ✶✳✹✿ ❉✐❛❣r❛♠❛ s✐♠♣❧✐✜❝❛❞♦ ❞♦ ❞❡❝❛✐♠❡♥t♦ ❞♦ 40_{❑ ♠♦❞✐✜❝❛❞♦ ❞❡ ✭❑❛t❤r❡♥✱ ✶✾✾✽❀}

▲◆❍❇✱ ✷✵✶✸✮✳

❖ 40_{❑ ❞❡❝❛✐ ♣❛r❛ ♦} 40_{❈❛✱ ♣♦r ❡♠✐ssã♦ β}− ❝♦♠ ✽✾✱✷✺ ✪ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡✱ ✉♠❛

♣❡q✉❡♥❛ ❢r❛çã♦ ✭✶ ①10−3 ✪✮ q✉❡ ❞❡❝❛✐ ♣♦r_β+♣❛r❛ ♦40❆r ♥♦ ❡st❛❞♦ ❢✉♥❞❛♠❡♥t❛❧✱ ✵✱✷ ✪

❞❡❝❛❡♠ ♣♦r ❝❛♣t✉r❛ ❡❧❡trô♥✐❝❛ ♣❛r❛ ♦40_{❆r ♥♦ ❡st❛❞♦ ❢✉♥❞❛♠❡♥t❛❧ ❡ ♦s ✶✵✱✺✺ ✪ r❡st❛♥t❡s}

❞♦ 40_{❑ ❞❡❝❛❡♠ ♣♦r ❝❛♣t✉r❛ ❡❧❡trô♥✐❝❛ ♣❛r❛ ♦} 40_{❆r ❡♠ ✉♠ ❡st❛❞♦ ❡①❝✐t❛❞♦✱ q✉❡ ❡♠✐t❡}

✉♠ ❢ót♦♥ ❝❛r❛❝t❡ríst✐❝♦ ❞❡ ✶✹✻✵ ❦❡❱✱ q✉❡ é ✉t✐❧✐③❛❞♦ ♣❛r❛ ❛ ✐❞❡♥t✐✜❝❛çã♦ ❡ q✉❛♥t✐✜❝❛çã♦ ❞♦ 40_{❑ ♣♦r ❡s♣❡❝tr♦♠❡tr✐❛ ❣❛♠❛✱ ❛❧é♠ ❞❡ ❢♦r♥❡❝❡r ✉♠ ❡①❝❡❧❡♥t❡ ♣♦♥t♦ ❞❡ ❝❛❧✐❜r❛çã♦✱}

✉♠❛ ✈❡③ q✉❡ ♦ ♣♦táss✐♦ ❡stá ♣r❡s❡♥t❡ ❡♠ q✉❛s❡ t♦❞❛s ❛s ❛♠♦str❛s ❛♠❜✐❡♥t❛✐s✳

❆ ❞♦s❡ ✐♥t❡r♥❛ ❞❡✈❡✲s❡ ♣r✐♥❝✐♣❛❧♠❡♥t❡ à ✐♥❛❧❛çã♦ ❞♦ ✐sót♦♣♦ ❞♦ r❛❞ô♥✐♦✱222_❘♥

♣r♦✈❡♥✐❡♥t❡ ❞❛ sér✐❡ ❞♦ 238_{❯✱ ♣♦ré♠✱ ❛❧é♠ ❞❡st❡✱ ❡①✐st❡♠ ♦✉tr♦s ❞♦✐s ✐sót♦♣♦s ♥❛t✉r❛✐s}

❞♦ r❛❞ô♥✐♦✱ ♣r♦✈❡♥✐❡♥t❡s ❞❛s sér✐❡s ❞♦ 235_{❯ ❡ ❞♦} 232_{❚❤✱ t♦❞♦s ❡♠✐ss♦r❡s ❞❡ ♣❛rtí❝✉❧❛s}

✶✳✶ ✲ ❘❛❞✐♦♥✉❝❧í❞❡♦s ♥❛t✉r❛✐s ✷✸

❚❛❜❡❧❛ ✶✳✶✿ ■sót♦♣♦s ❞♦ 222_❘♥✳

❙ér✐❡ ■sót♦♣♦ ▼❡✐❛ ✈✐❞❛

238_❯ 222_{❘♥ ✸✱✽ ❞} 235_❯ 219_{❘♥ ✸✱✾✻ s} 232_❚❤ 220_{❘♥ ✺✺✱✻ s}

❉❡✈✐❞♦ às ♠❡✐❛s✲✈✐❞❛s ❝✉rt❛s ❞♦s ✐sót♦♣♦s220_{❘♥ ❡} 219_{❘♥ ❡ à ❜❛✐①❛ ❛❜✉♥❞â♥❝✐❛}

✐s♦tó♣✐❝❛ ❞♦ 235_{❯ ✭❛♣❡♥❛s ✵✱✼✶ ✪ ❞♦ ✉râ♥✐♦ ♥❛t✉r❛❧✮✱ ❡♠ s✐t✉❛çõ❡s ♥♦r♠❛✐s ♦♥❞❡ ❛}

❝♦♥❝❡♥tr❛çã♦ ❞❡ tór✐♦ ♥ã♦ é ♠✉✐t♦ ❛❧t❛✱ ❛ ♠❛✐♦r ♣r❡♦❝✉♣❛çã♦ r❛❞✐♦❧ó❣✐❝❛ ❝♦♥❝❡♥tr❛✲s❡ ♥❛ ❞❡t❡r♠✐♥❛çã♦ ❞♦ 222_{❘♥✱ q✉❡ ❛♣r❡s❡♥t❛ ❛ ♠❛✐♦r ♠❡✐❛✲✈✐❞❛ ✭✸✱✽ ❞✐❛s✮✳}

❆ ❡①♣♦s✐çã♦ ❛♦ 222_{❘♥ é r❡❝♦♥❤❡❝✐❞❛ ❝♦♠♦ ✉♠ ✐♠♣♦rt❛♥t❡ r✐s❝♦ ❛♦ s✐st❡♠❛}

r❡s♣✐r❛tór✐♦✱ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ♣❡❧❛ ✐♥❝♦r♣♦r❛çã♦ ❞♦s s❡✉s ❞❡s❝❡♥❞❡♥t❡s ❞❡ ♠❡✐❛✲✈✐❞❛ ❝✉rt❛ ✭❚❆❇✳ ✶✳✷✮✱ s❡♥❞♦ q✉❡ ♦ 218_{P♦ ❡} 214_{P♦ sã♦ ❡♠✐ss♦r❡s ❛❧❢❛✱ r❛❞✐❛çã♦ ❝♦♠ ♠❛✐♦r}

tr❛♥s❢❡rê♥❝✐❛ ❧✐♥❡❛r ❞❡ ❡♥❡r❣✐❛ ❡ r❡s♣♦♥sá✈❡❧ ♣❡❧♦ ❛✉♠❡♥t♦ ♥❛ ✐♥❝✐❞ê♥❝✐❛ ❞❡ ❝â♥❝❡r ♥♦ ♣✉❧♠ã♦ ✭❯◆❙❈❊❆❘✱ ✷✵✵✵✮✳ ❖s ✜❧❤♦s✱ ❞✐❢❡r❡♥t❡♠❡♥t❡ ❞♦ ♣❛✐✱ ♣♦❞❡♠ s❡ ❛ss♦❝✐❛r ❢❛❝✐❧♠❡♥t❡ ❛ ♣❛rtí❝✉❧❛s ❞❡ ❛❡r♦ssó✐s✱ ♦✉ q✉❛❧q✉❡r ♦✉tr♦ t✐♣♦ ❞❡ s✉♣❡r❢í❝✐❡✱ ❢❡♥ô♠❡♥♦ ❝♦♥❤❡❝✐❞♦ ❝♦♠♦ ♣❧❛t❡✲♦✉t✳ ❆ss♦❝✐❛❞♦s ♦✉ ♥ã♦ ❛ ❛❡r♦ssó✐s ♦s ✜❧❤♦s ♣♦❞❡♠ s❡r ✐♥❛❧❛❞♦s✱ ❞❡♣♦s✐t❛♥❞♦✲s❡ ♥♦s ♣✉❧♠õ❡s ✭❙❘❙✸✸✱ ✷✵✵✸✮✳ ❙❡❣✉♥❞♦ ❛ ❖r❣❛♥✐③❛çã♦ ▼✉♥❞✐❛❧ ❞❡ ❙❛ú❞❡ ✭❲❍❖✱ ✷✵✵✼✮✱ ♦ 222_{❘♥ ❡ s✉❛ ♣r♦❣ê♥✐❡ sã♦ ♦s ♠❛✐♦r❡s ❝♦♥tr✐❜✉✐♥t❡s ♣❛r❛ ❛ ❞♦s❡ ❞❡}

✶✳✷ ✲ ❘♦❝❤❛s í❣♥❡❛s ❡ ❛ r❛❞✐♦❛t✐✈✐❞❛❞❡ ♥❛t✉r❛❧ ✷✹

❚❛❜❡❧❛ ✶✳✷✿ ❉❡❝❛✐♠❡♥t♦ r❛❞✐♦❛t✐✈♦ ❞♦ 222_❘♥✳

■sót♦♣♦ M eia₋vida Eα(M eV) Eβmax(M eV)

222_{❘♥ 3,823 ❞ 5,49 ✲} 218_{P♦ 3,05♠✐♥ 6,00 ✲} 214_{P❜ 26,8♠✐♥ ✲ 0,72}

214_{❇✐ 19,7♠✐♥ ✲ 1,78} 214_{P♦ 164 ♠s 7,69 ✲} 210_{P❜ 21❛ ✲ 0,02}

210_{❇✐ 5,01❞ ✲ 1,16} 210_{P♦ 138,4 ❞ 5,31 ✲}

206_{P❜ ❡stá✈❡❧ ✲ ✲}

❖ 222_{❘♥ é ✉♠ ❣ás ♥♦❜r❡ q✉❡ s❡ ♦r✐❣✐♥❛ ♣♦r ♠❡✐♦ ❞❡ ❡♠✐ssã♦ ❞❡ ♣❛rtí❝✉❧❛s ❛❧❢❛}

❞✉r❛♥t❡ ❛ ❞❡s✐♥t❡❣r❛çã♦ r❛❞✐♦❛t✐✈❛ ❞♦226_{❘❛✱ q✉❡✱ ♣♦r s✉❛ ✈❡③✱ é ♣r♦❞✉t♦ ❞❡ ❞❡❝❛✐♠❡♥t♦}

❞❛ sér✐❡ ❞♦238_{❯✳ P♦r s❡r ❡❧❡♠❡♥t♦ ❞❛ ❢❛♠í❧✐❛ ❞♦s ❣❛s❡s ♥♦❜r❡s✱ ♥ã♦ ✐♥t❡r❛❣❡ ❝♦♠ ♦✉tr♦s}

❡❧❡♠❡♥t♦s ❡✱ ♣♦r s✉❛ ♥❛t✉r❡③❛ ❣❛s♦s❛✱ ♣♦ss✉✐ ❝❛♣❛❝✐❞❛❞❡ ❞❡ ❡①❛❧❛r ❞♦ s♦❧♦ ♦✉ r♦❝❤❛ ❝♦♠ ❡①tr❡♠❛ ❢❛❝✐❧✐❞❛❞❡ ❡ ❞❡ s❡ ❝♦♥❝❡♥tr❛r ❡♠ ❛♠❜✐❡♥t❡s ❢❡❝❤❛❞♦s ✭❊✐s❡♥❜✉❞✱ ✶✾✽✼✮✳

❈♦♠♦ ✉râ♥✐♦ ❡ rá❞✐♦ ❡stã♦ ♣r❡s❡♥t❡s ♥♦ s♦❧♦✱ r♦❝❤❛s✱ á❣✉❛✱ ♠❛t❡r✐❛✐s ❞❡ ❝♦♥str✉çã♦✱ é ♥❛t✉r❛❧ ❛ ❡①✐stê♥❝✐❛ ❞❡ r❛❞ô♥✐♦ ♥♦ ❛r✱ s❡♥❞♦ s✉❛ ❝♦♥❝❡♥tr❛çã♦ ❞❡t❡r♠✐♥❛❞❛ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ♣❡❧♦s s❡❣✉✐♥t❡s ❢❛t♦r❡s✿ r❡✈❡st✐♠❡♥t♦ ❞♦ s♦❧♦ ✭♣♦r ❡①❡♠♣❧♦✱ ♣❛✈✐♠❡♥t❛çã♦✱ ❝♦♥str✉çõ❡s ❡ ✈❡❣❡t❛çã♦✮✱ ♣♦r♦s✐❞❛❞❡ ❡ ❣r❛♥✉❧♦♠❡tr✐❛ ❞♦ s♦❧♦✱ t❡♠♣❡r❛t✉r❛✱ ♣r❡ssã♦ ❛t♠♦s❢ér✐❝❛✱ ❛❧t✐t✉❞❡✱ t❡♦r ❞❡ ✉♠✐❞❛❞❡ ❞♦ s♦❧♦✱ ❝♦♥❞✐çõ❡s ❛t♠♦s❢ér✐❝❛s ❡ ❡st❛çõ❡s ❞♦ ❛♥♦✳ ❉♦ t♦t❛❧ ❞❡ 222_{❘♥ ❧✐❜❡r❛❞♦ ♥♦ ❛r✱ ❡st✐♠❛❞♦ ❡♠}

❛♣r♦①✐♠❛❞❛♠❡♥t❡9①1019 ❇q ♣♦r ❛♥♦✱ ❞♦✐s t❡rç♦s sã♦ ♣r♦✈❡♥✐❡♥t❡s ❞♦ s♦❧♦ ❡ ❛ ♠❛✐♦r✐❛

❞♦ r❡st❛♥t❡ ❞❛ á❣✉❛ ❞♦❝❡✱ ❛ ❝♦♥tr✐❜✉✐çã♦ ❞♦s ♦❝❡❛♥♦s é ❞❡ ❝❡r❝❛ ❞❡ ✶ ✪ ❞♦ t♦t❛❧✱ ❝♦♠ ❛✐♥❞❛ ♠❡♥♦r ❝♦♥tr✐❜✉✐çã♦ ❞❡ ❢♦♥t❡s✱ t❛✐s ❝♦♠♦ ❞❡♣ós✐t♦s ❞❡ ❢♦s❢❛t♦ ❡ ♣✐❧❤❛s ❞❡ r❡❥❡✐t♦s ❞❡ ✉râ♥✐♦ ✭❑❛t❤r❡♥✱ ✶✾✾✽✮✳ ❆ ✐♥❛❧❛çã♦ ❞♦ r❛❞ô♥✐♦ r❡♣r❡s❡♥t❛ ✹✼✱✻ ✪ ❞❛ ❞♦s❡ ❡❢❡t✐✈❛ ♠é❞✐❛ ❛♥✉❛❧ ♠✉♥❞✐❛❧ ❞❡✈✐❞♦ à r❛❞✐♦♥✉❝❧í❞❡♦s ♥❛t✉r❛✐s ✭❯◆❙❈❊❆❘✱ ✷✵✵✵✮✳

✶✳✷ ❘♦❝❤❛s í❣♥❡❛s ❡ ❛ r❛❞✐♦❛t✐✈✐❞❛❞❡ ♥❛t✉r❛❧

✶✳✷ ✲ ❘♦❝❤❛s í❣♥❡❛s ❡ ❛ r❛❞✐♦❛t✐✈✐❞❛❞❡ ♥❛t✉r❛❧ ✷✺

❆ ❞✐❢❡r❡♥❝✐❛çã♦ é ♦ ♣r♦❝❡ss♦ ♥♦ q✉❛❧ ♦ ♠❛❣♠❛ ✐♥✐❝✐❛❧♠❡♥t❡ ❤♦♠♦❣ê♥❡♦ ❞❡s❞♦❜r❛✲s❡ ❡♠ ❢r❛çõ❡s ❞❡ ❝♦♠♣♦s✐çã♦ ❞✐❢❡r❡♥t❡✱ ♦ ♣r♦❝❡ss♦ ❞❡ ❞✐❢❡r❡♥❝✐❛çã♦ ♠❛✐s ✐♠♣♦rt❛♥t❡ é ♦ ❢r❛❝✐♦♥❛♠❡♥t♦ r❡s✉❧t❛♥t❡ ❞❛ ❝r✐st❛❧✐③❛çã♦✱ ❛ss✐♠ ❝❡rt♦s ♠✐♥❡r❛✐s ❡stã♦ s❡♠♣r❡ ❛ss♦❝✐❛❞♦s ♣♦rq✉❡ ❝r✐st❛❧✐③❛♠ ❛♣r♦①✐♠❛❞❛♠❡♥t❡ ♥❛ ♠❡s♠❛ t❡♠♣❡r❛t✉r❛✳

◗✉❛♥❞♦ ❛ ❝r✐st❛❧✐③❛çã♦ ♣r♦❣r✐❞❡✱ ❡①✐st❡ ✉♠❛ t❡♥❞ê♥❝✐❛ ♣❛r❛ ❛ ♠❛♥✉t❡♥çã♦ ❞♦ ❡q✉✐❧í❜r✐♦ ❡♥tr❡ ❛ ❢❛s❡ só❧✐❞❛ ❡ ❛ ❧íq✉✐❞❛✳ P❛r❛ ♠❛♥t❡r ❡st❡ ❡q✉✐❧í❜r✐♦✱ q✉❛♥❞♦ ❛ t❡♠♣❡r❛t✉r❛ ❞✐♠✐♥✉✐✱ ♦s ❝r✐st❛✐s ♣r❡❝♦❝❡s r❡❛❣❡♠ ❝♦♠ ♦ ❧íq✉✐❞♦ ♠✉❞❛♥❞♦ ❞❡ ❝♦♠♣♦s✐çã♦✳ ❊st❛ r❡❛çã♦ ♣♦❞❡ s❡r ♣r♦❣r❡ss✐✈❛ ❞❡ ♠♦❞♦ q✉❡ s❡ ♣r♦❞✉③ ✉♠❛ sér✐❡ ❝♦♥tí♥✉❛ ❞❡ s♦❧✉çõ❡s só❧✐❞❛s ❤♦♠♦❣ê♥❡❛s ✭sér✐❡ ❞❡ r❡❛çã♦ ❝♦♥tí♥✉❛✮✳ ❈❡rt♦s ♠✐♥❡r❛✐s ♣♦r ♦✉tr♦ ❧❛❞♦✱ tr❛♥s❢♦r♠❛♠✲s❡ ❛ t❡♠♣❡r❛t✉r❛s ❞❡✜♥✐❞❛s✱ ❡♠ ♦✉tr♦s ♠✐♥❡r❛✐s ❞❡ ❡str✉t✉r❛ ❝r✐st❛❧✐♥❛ ❞✐❢❡r❡♥t❡ ✭sér✐❡ ❞❡ r❡❛çã♦ ❞❡s❝♦♥tí♥✉❛✮✳ ◗✉❛♥❞♦ ❛ r❡❛çã♦ t❡r♠✐♥❛✱ ♦s ♠✐♥❡r❛✐s ❞❛ r♦❝❤❛ ✜♥❛❧ sã♦ ♦s ú❧t✐♠♦s ❢♦r♠❛❞♦s✳ P♦ré♠✱ s❡ ❛ r❡❛çã♦ ♥ã♦ ❢♦r ❝♦♠♣❧❡t❛✱ ❞❡✈✐❞♦ ❛ r❡s❢r✐❛♠❡♥t♦ ♠✉✐t♦ rá♣✐❞♦ ♦✉ ❛ ♦✉tr❛s r❛③õ❡s✱ ♦s ♠❡♠❜r♦s ♣r❡❝♦❝❡s ❞❡ ❛♠❜❛s ❛s sér✐❡s ♣♦❞❡♠ ♣❡rs✐st✐r ❝♦♠♦ r❡sí❞✉♦s ♥❛ r♦❝❤❛ ✜♥❛❧ ✭❲✐❧❧✐❛♠s ❡t ❛❧✳✱ ✶✾✼✵✮✳ ❆ ❡✈♦❧✉çã♦ ❞♦ ♠❛❣♠❛ ♣♦❞❡ s❡r ✐♥✢✉❡♥❝✐❛❞❛ t❛♠❜é♠ ♣❡❧❛ r❡❛çã♦ ❝♦♠ ❛s r♦❝❤❛s ❞❛s ♣❛r❡❞❡s✱ s❡ ❛ t❡♠♣❡r❛t✉r❛ ❞♦ ♠❛❣♠❛ ❢♦r ♠❛✐♦r q✉❡ ❛ t❡♠♣❡r❛t✉r❛ ❞❡ ❢✉sã♦ ❞❛s ♣❛r❡❞❡s ❞♦ r❡s❡r✈❛tór✐♦✳