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❖♥ t❤❡ st❛❜✐❧✐t② ♦❢ Λ(✶✹✵✺)✲♠❛tt❡r

❏✳ ❍rtá♥❦♦✈á✶✱ ◆✳ ❇❛r♥❡❛✷✱ ❊✳ ❋r✐❡❞♠❛♥✷✱ ❆✳ ●❛❧✷✱ ❏✳ ▼❛r❡➨✶✱ ❛♥❞ ▼✳ ❙❝❤ä❢❡r✶

✶◆✉❝❧❡❛r P❤②s✐❝s ■♥st✐t✉t❡ ♦❢ t❤❡ ❈③❡❝❤ ❆❝❛❞❡♠② ♦❢ ❙❝✐❡♥❝❡s✱ ➄❡➸✱ ❈③❡❝❤ ❘❡♣✉❜❧✐❝ ✷❘❛❝❛❤ ■♥st✐t✉t❡ ♦❢ P❤②s✐❝s✱ ❚❤❡ ❍❡❜r❡✇ ❯♥✐✈❡rs✐t②✱ ❏❡r✉s❛❧❡♠✱ ■sr❛❡❧ ✶

■♥tr♦❞✉❝t✐♦♥

▼♦t✐✈❛t✐♦♥

❢♦r♠❛t✐♦♥ ♦❢ st❛❜❧❡ ❤❛❞r♦♥✐❝ ♠❛tt❡r ❝♦♠♣♦s❡❞ ♦❢ Λ∗ [Λ(✶✹✵✺)] ❜❛r②♦♥s

❨✳ ❆❦❛✐s❤✐✱ ❚✳ ❨❛♠❛③❛❦✐✱ P❤②s✳ ▲❡tt✳ ❇ ✼✼✹ ✭✷✵✶✼✮ ✺✷✷

str♦♥❣ ❡♥❡r❣②✲✐♥❞❡♣❡♥❞❡♥t ¯ KN ♣♦t❡♥t✐❛❧ ♣r♦❞✉❝✐♥❣ ( ¯ KN)I=✵ q✉❛s✐❜♦✉♥❞ st❛t❡ [Λ(✶✹✵✺)] ✷✼ ▼❡❱ ❜❡❧♦✇ t❤❡ K −p t❤r❡s❤♦❧❞

❙✳ ▼❛❡❞❛✱ ❨✳ ❆❦❛✐s❤✐✱ ❚✳ ❨❛♠❛③❛❦✐✱ Pr♦❝✳ ❏♣♥✳ ❆❝❛❞✳ ❙❡r✳ ❇ ✽✾ ✭✷✵✶✸✮ ✹✶✽

✐♠♣❧✐❝❛t✐♦♥s ❢♦r st❛❜❧❡ Λ∗✲♠❛tt❡r ❜❛s❡❞ ♦♥ ❢❡✇✲❜♦❞② ❝❛❧❝✉❧❛t✐♦♥s✱ ♥♦ r❡❧✐❛❜❧❡ ♠❛♥②✲❜♦❞② ❝❛❧❝✉❧❛t✐♦♥s ❤❛✈❡ ❜❡❡♥ ❞♦♥❡

⇓

✇❡ ❤❛✈❡ ♣❡r❢♦r♠❡❞ ♠❛♥②✲❜♦❞② ❝❛❧❝✉❧❛t✐♦♥s ♦❢ Λ∗ ♥✉❝❧❡✐ ✇✐t❤✐♥ t❤❡ ❘❡❧❛t✐✈✐st✐❝ ▼❡❛♥✲❋✐❡❧❞ ❛♣♣r♦❛❝❤

❏✳ ❍rt❛♥❦♦✈❛ ❡t ❛❧✳✱ P❤②s✳ ▲❡tt✳ ❇ ✼✽✺ ✭✷✵✶✽✮ ✾✵✳

✷

¯ KN ✐♥t❡r❛❝t✐♦♥

¯ KN ✐♥t❡r❛❝t✐♦♥ ♠♦❞❡❧s

1350 1400 1450 1500 s

1/2 (MeV)

• 1.0

0.0 1.0 2.0 3.0 4.0 Real K

• p amplitude (fm)

KM P B2 B4 M1 M2 YA 1350 1400 1450 1500 s

1/2 (MeV)

• 1.0

0.0 1.0 2.0 3.0 4.0 Imaginary K

• p amplitude (fm)

B2 B4 M1 M2 P KM YA

❨❛♠❛③❛❦✐✲❆❦❛✐s❤✐ ✭❨❆✮

❚✳ ❨❛♠❛③❛❦✐✱ ❨✳ ❆❦❛✐s❤✐✱ P❤②s✳ ❘❡✈✳ ❈ ✼✻ ✭✷✵✵✼✮ ✵✹✺✷✵✶

Pr❛❣✉❡ ✭P✮

❆✳ ❈✐❡♣❧②✱ ❏✳ ❙♠❡❥❦❛❧✱ ◆✉❝❧✳ P❤②s✳ ❆ ✽✽✶ ✭✷✵✶✷✮ ✶✶✺

❑②♦t♦✲▼✉♥✐❝❤ ✭❑▼✮

❨✳ ■❦❡❞❛✱ ❚✳ ❍②♦❞♦✱ ❲✳ ❲❡✐s❡✱ ◆✉❝❧✳ P❤②s✳ ❆ ✽✽✶ ✭✷✵✶✷✮ ✾✽

▼✉r❝✐❛ ✭▼✶ ❛♥❞ ▼✷✮

❩✳ ❍✳ ●✉♦✱ ❏✳ ❆✳ ❖❧❧❡r✱ P❤②s✳ ❘❡✈✳ ❈ ✽✼✱ ✵✸✺✷✵✷ ✭✷✵✶✸✮

❇♦♥♥ ✭❇✷ ❛♥❞ ❇✹✮

▼✳ ▼❛✐✱ ❯✳✲●✳ ▼❡✐ÿ♥❡r✱ ◆✉❝❧✳ P❤②s✳ ❆ ✾✵✵ ✭✷✵✶✸✮ ✺✶

✸

¯ KN ✐♥t❡r❛❝t✐♦♥

¯ KN ✐♥t❡r❛❝t✐♦♥ ♠♦❞❡❧s

1350 1400 1450 1500 s

1/2 (MeV)

• 0.5

0.0 0.5 1.0 Real K

• n amplitude (fm)

B2 B4 M1 M2 P KM YA 1350 1400 1450 1500 s

1/2 (MeV)

• 0.5

0.0 0.5 1.0 Imaginary K

• n amplitude (fm)

B2 B4 M1 M2 P KM YA

✹

¯ KN ✐♥t❡r❛❝t✐♦♥

❑❛♦♥✐❝ ❛t♦♠s t❡st

→ ❡♥❡r❣②✲✐♥❞❡♣❡♥❞❡♥t ¯ KN ♣♦t❡♥t✐❛❧ ✭❆❨✮ ❝♦♥❢r♦♥t❡❞ ✇✐t❤ ❦❛♦♥✐❝ ❛t♦♠ ❞❛t❛✿ ♦♣t✐❝❛❧ ♣♦t❡♥t✐❛❧ ❝♦♥str✉❝t❡❞ ❢r♦♠ ❝♦rr❡s♣♦♥❞✐♥❣ ¯ KN ❛♠♣❧✐t✉❞❡s s✉♣♣❧❡♠❡♥t❡❞ ❜② ♣❤❡♥♦♠❡♥♦❧♦❣✐❝❛❧ K − ♠✉❧t✐♥✉❝❧❡♦♥ ♣♦t❡♥t✐❛❧ ♠♦❞❡❧ ❇✷ ❇✹ ▼✶ ▼✷ P ❑▼ ❆❨ χ✷(✻✺) ✶✶✶ ✶✵✺ ✶✷✶ ✶✵✾ ✶✷✺ ✶✷✸ ✶✺✵ ❝❛❧❝✉❧❛t❡❞ K − s✐♥❣❧❡✲♥✉❝❧❡♦♥ ❛❜s♦r♣t✐♦♥ ❢r❛❝t✐♦♥s ❛t t❤r❡s❤♦❧❞ ❛♥❞ ❝♦♠♣❛r❡❞ ✇✐t❤ ❡①♣❡r✐♠❡♥t❛❧ ❞❛t❛

✺

¯ KN ✐♥t❡r❛❝t✐♦♥

❑❛♦♥✐❝ ❛t♦♠s t❡st

20 40 60 80 100 Z 0.2 0.4 0.6 0.8 1.0 1N absorption fraction

EXP KM upper M1 lower YA Kaonic atoms &P

❋✐❣✳✶✿ ❈❛❧❝✉❧❛t❡❞ K − s✐♥❣❧❡✲♥✉❝❧❡♦♥ ❛❜s♦r♣t✐♦♥ ❢r❛❝t✐♦♥s ✐♥ t❤❡ ❆❨ ♠♦❞❡❧ ✭❞❡♥♦t❡❞ ❜② ❨❆✮ ❝♦♠♣❛r❡❞ ✇✐t❤ ❑▼✱ P✱ ❛♥❞ ▼✶ ❝❤✐r❛❧ ♠♦❞❡❧s✳ ❚❤❡ r❛♥❣❡ ♦❢ ❡①♣❡r✐♠❡♥t❛❧❧② ❞❡❞✉❝❡❞ ❢r❛❝t✐♦♥s ✐s ♠❛r❦❡❞ ❜② t❤❡ t✇♦ ❤♦r✐③♦♥t❛❧ ❞❛s❤❡❞ ❧✐♥❡s✳

✻

¯ KN ✐♥t❡r❛❝t✐♦♥

¯ KN ✐♥t❡r❛❝t✐♦♥ ✫ q✉❛s✐❜♦✉♥❞ st❛t❡s

❚❛❜❧❡✿ ( ¯ KN)I=✵✱ ( ¯ KNN)I=✶/✷ ❛♥❞ ( ¯ K ¯ KNN)I=✵ ❜✐♥❞✐♥❣ ❡♥❡r❣✐❡s B ❝❛❧❝✉❧❛t❡❞ ✉s✐♥❣ ❡♥❡r❣② ❞❡♣❡♥❞❡♥t ✭❊✲❞❡♣✳✮ ❛♥❞ ❡♥❡r❣② ✐♥❞❡♣❡♥❞❡♥t ✭❊✲✐♥❞❡♣✳✮ ¯ KN ♣♦t❡♥t✐❛❧s✳ ❚❤❡ ❜✐♥❞✐♥❣ ❡♥❡r❣✐❡s ❧✐st❡❞ ❢♦r ( ¯ K ¯ KNN)I=✵ ❛r❡ tr❛♥s❢♦r♠❡❞ ✐♥ t❤❡ ❧❛st r♦✇ t♦ BΛ∗Λ∗ = B( ¯ K ¯ KNN)I=✵ − ✷B( ¯ KN)I=✵✳

B ✭▼❡❱✮ ✭❊✲❞❡♣✳✮ ❬✶❪ ✭❊✲✐♥❞❡♣✳ ❆✮ ❬✷❪ ✭❊✲✐♥❞❡♣✳ ❇✮ ❬✷❪ ( ¯ KN)I=✵ ✶✶✳✹ ✷✻✳✻ ✻✹✳✷ ( ¯ KNN)I=✶/✷ ✶✺✳✼ ✺✶✳✺ ✶✵✷ ❬✸❪ ( ¯ K ¯ KNN)I=✵ ✸✷✳✶ ✾✸ ✶✾✵ Λ∗Λ∗ ✾✳✸ ✹✵ ✻✷

❬✶❪ ◆✳ ❇❛r♥❡❛✱ ❆✳ ●❛❧✱ ❊✳❩✳ ▲✐✈❡rts✱ P❤②s✳ ▲❡tt✳ ❇ ✼✶✷ ✭✷✵✶✷✮ ✶✸✷ ❬✷❪ ❙✳ ▼❛❡❞❛✱ ❨✳ ❆❦❛✐s❤✐✱ ❚✳ ❨❛♠❛③❛❦✐✱ Pr♦❝✳ ❏♣♥✳ ❆❝❛❞✳ ❙❡r✳ ❇ ✽✾ ✭✷✵✶✸✮ ✹✶✽ ❬✸❪ ❚✳ ❨❛♠❛③❛❦✐ ❡t ❛❧✳✱ P❤②s✳ ❘❡✈✳ ▲❡tt✳ ✶✵✹ ✭✷✵✶✵✮ ✶✸✷✺✵✷

✼

Λ∗ ♥✉❝❧❡✐

Λ∗Λ∗ ✐♥t❡r❛❝t✐♦♥

Λ∗Λ∗ ✐♥t❡r❛❝t✐♦♥ ❞❡s❝r✐❜❡❞ ❜② ❨✉❦❛✇❛ ♠❡s♦♥✲❡①❝❤❛♥❣❡ ♣♦t❡♥t✐❛❧s✿ ✶✮ ❉♦✈❡r✲●❛❧ ❈✳❇✳ ❉♦✈❡r✱ ❆✳ ●❛❧✱ Pr♦❣✳ P❛rt✳ ◆✉❝❧✳ P❤②s✳ ✶✷ ✭✶✾✽✹✮ ✶✼✶ VΛ∗Λ∗(r) =α✷

ωg✷ ωΛ∗ (✶ − ✶

✽ m✷

ω

M✷

Λ∗

) Yω(r) − α✷

σg✷ σΛ∗ (✶ − ✶

✽ m✷

σ

M✷

Λ∗

) Yσ(r) + α✷

ωg✷ ωΛ∗ ✶

✻ mω MΛ∗

• Yω(r)(

σ✶ · σ✷) , ✷✮ ▼❛❝❤❧❡✐❞t ❘✳ ▼❛❝❤❧❡✐❞t✱ ❆❞✈✳ ◆✉❝❧✳ P❤②s✳ ✶✾ ✭✶✾✽✾✮ ✶✽✾ VΛ∗Λ∗(r) =α✷

ωg✷ ωΛ∗(✶ − ✶

✷ m✷

ω

M✷

Λ∗

) Yω(r) − α✷

σg✷ σΛ∗ (✶ − ✶

✹ m✷

σ

M✷

Λ∗

) Yσ(r) + α✷

ωg✷ ωΛ∗ ✶

✻ mω MΛ∗

• Yω(r)(

σ✶ · σ✷) , ✇❤❡r❡ Yi=σ,ω(r) = ❡①♣(−mir)/(✹πr) ❛♥❞ MΛ∗ = ✶✹✵✺ ▼❡❱

✽

Λ∗ ♥✉❝❧❡✐

Λ∗Λ∗ ✐♥t❡r❛❝t✐♦♥

s❝❛❧✐♥❣ ❡✐t❤❡r gσΛ∗ ♦r gωΛ∗ ✐♥ ♦r❞❡r t♦ ❣❡t BΛ∗Λ∗ = ✹✵ ▼❡❱ ❢❡✇✲❜♦❞② ❝❛❧❝✉❧❛t✐♦♥s ✭A ≤ ✻✮ ♣❡r❢♦r♠❡❞ ✉s✐♥❣ ❙t♦❝❤❛st✐❝ ❱❛r✐❛t✐♦♥❛❧ ▼❡t❤♦❞ ✭❙❱▼✮ ✇✐t❤ ▼❛❝❤❧❡✐❞t ❛♥❞ ❉♦✈❡r✲●❛❧ ♣♦t❡♥t✐❛❧s s✐♠✐❧❛r ❙❱▼ ❝❛❧❝✉❧❛t✐♦♥s ❞♦♥❡ ❜② ❆❦❛✐s❤✐ ❛♥❞ ❨❛♠❛③❛❦✐ ✉s✐♥❣ ▼❛❝❤❧❡✐❞t ♣♦t❡♥t✐❛❧ ❜✉t ♥❡❣❧❡❝t✐♥❣ t❤❡ s♣✐♥✲s♣✐♥ ✐♥t❡r❛❝t✐♦♥

❨✳ ❆❦❛✐s❤✐✱ ❚✳ ❨❛♠❛③❛❦✐✱ ❛r❳✐✈✿✶✾✵✸✳✶✵✻✽✼ ❬♥✉❝❧✲t❤❪

❚❛❜❧❡✿ ❚❤❡ ✈❛❧✉❡s ♦❢ t❤❡ s❝❛❧✐♥❣ ♣❛r❛♠❡t❡rs ασ ❛♥❞ αω ❢♦r σ ❛♥❞ ω ✜❡❧❞s✱ r❡s♣❡❝t✐✈❡❧②✳

VΛ∗Λ∗ ασ αω ▼❛❝❤❧❡✐❞t ✶✳✵✾✶✸ ✵✳✽✽✽✾ ❉♦✈❡r✲●❛❧ ✶✳✵✸✸✷ ✵✳✾✼✺✵

✾

Λ∗ ♥✉❝❧❡✐

❋❡✇✲❜♦❞② ❙❱▼ ❝❛❧❝✉❧❛t✐♦♥s

❚❤❡ ❡✛❡❝t ♦❢ s♣✐♥✲s♣✐♥ ✐♥t❡r❛❝t✐♦♥ ✐s s✐③❛❜❧❡✦

2 3 4 5 6 A 20 40 60 80 100 120 140 B/A (MeV) no mass corr. mass corr. mass corr. + spin 2 3 4 5 6 A 0.5 0.6 0.7 0.8 0.9 rrms (fm) Machleidt

ασ=1.0725 ασ=1.1513 ασ=1.0913 ασ=1.1513 ασ=1.0725 ασ=1.0913

❋✐❣✳✷✿ ❇✐♥❞✐♥❣ ❡♥❡r❣② ♣❡r Λ∗ ✭❧❡❢t✮✱ B/A✱ ❛♥❞ ❘▼❙ r❛❞✐✉s ✭r✐❣❤t✮✱ rr♠s✱ ❛s ❛ ❢✉♥❝t✐♦♥ ♦❢ ♠❛ss ♥✉♠❜❡r✱ ❝❛❧❝✉❧❛t❡❞ ✇✐t❤✐♥ t❤❡ ❙❱▼ ♠❡t❤♦❞ ✉s✐♥❣ t❤❡ ▼❛❝❤❧❡✐❞t t②♣❡ ♣♦t❡♥t✐❛❧ ❛♥❞ s❝❛❧✐♥❣ ♦❢ σ ❝♦✉♣❧✐♥❣ ❝♦♥st❛♥t✳

✶✵

Λ∗ ♥✉❝❧❡✐

❘▼❋ ❝❛❧❝✉❧❛t✐♦♥s ♦❢ Λ∗ ♥✉❝❧❡✐

♠❛♥②✲❜♦❞② s②st❡♠s ❝♦♠♣♦s❡❞ ♦❢ Λ∗ ❤②♣❡r♦♥s ✭♥❡✉tr❛❧✱ I = ✵✮ ❝❛❧❝✉❧❛t❡❞ ✇✐t❤✐♥ t❤❡ ❘❡❧❛t✐✈✐st✐❝ ▼❡❛♥✲❋✐❡❧❞ ✭❘▼❋✮ ❛♣♣r♦❛❝❤

❏✳ ❍rt❛♥❦♦✈❛ ❡t ❛❧✳✱ P❤②s✳ ▲❡tt✳ ❇ ✼✽✺ ✭✷✵✶✽✮ ✾✵✳

L = ¯ Λ∗ [ ✐γµDµ − (MΛ∗ − gσΛ∗σ) ] Λ∗ + (σ, ωµ ❢r❡❡✲✜❡❧❞ t❡r♠s)

✇❤❡r❡ Dµ = ∂µ + ✐ gωΛ∗ ωµ✱ MΛ∗ ✲ ♠❛ss ♦❢ Λ∗✱ giΛ∗ ✲ ❝♦✉♣❧✐♥❣ ❝♦♥st❛♥ts

❝♦✉♣❧✐♥❣ ❝♦♥st❛♥ts giΛ∗ ❛♥❞ ♠❡s♦♥ ♠❛ss❡s mi ✭i = σ, ω✮ t❛❦❡♥ ❢r♦♠ t❤❡ ❍❙ ♠♦❞❡❧ ❈✳❏✳ ❍♦r♦✇✐t③✱ ❇✳❉✳ ❙❡r♦t✱ ◆✉❝❧✳ P❤②s✳ ❆ ✸✻✽ ✭✶✾✽✶✮ ✺✵✸ mω = ✼✽✸ ▼❡❱, mσ = ✺✷✵ ▼❡❱, gωΛ∗ = ✶✸.✽✵, gσΛ∗ = ✶✵.✹✼ s❡❧❢✲❝♦♥s✐st❡♥t s♦❧✉t✐♦♥ ♦❢ ❝♦✉♣❧❡❞ ❉✐r❛❝ ❛♥❞ ❑❧❡✐♥✲●♦r❞♦♥ ❡q✉❛t✐♦♥s ❝❛❧❝✉❧❛t✐♦♥s ✇✐t❤ t❤❡ ◆▲✲❙❍ ♠♦❞❡❧ ❢♦r ❝♦♠♣❛r✐s♦♥

▼✳▼✳ ❙❤❛r♠❛✱ ▼✳❆✳ ◆❛❣❛r❛❥❛♥✱ P✳ ❘✐♥❣✱ P❤②s✳ ▲❡tt✳ ❇ ✸✶✷ ✭✶✾✾✸✮ ✸✼✼

✶✶

Λ∗ ♥✉❝❧❡✐

❇✐♥❞✐♥❣ ❡♥❡r❣② ♣❡r Λ∗

40 80 120 160 200 A 10 20 30 40 50 60 70 80 90 B/A (MeV)

NL-SH nuclei Λ* αω = 0.9570 ασ = 1.0913 αω = 0.8889 ασ = 1.0332 NL-SH ασ = 1.026

❋✐❣✳✸✿ ❇✐♥❞✐♥❣ ❡♥❡r❣② ♦❢ Λ∗ ♥✉❝❧❡✐ ♣❡r Λ∗✱ B/A✱ ❛s ❛ ❢✉♥❝t✐♦♥ ♦❢ ♠❛ss ♥✉♠❜❡r A✱ ❝❛❧❝✉❧❛t❡❞ ✇✐t❤✐♥ t❤❡ ❍❙ ❛♥❞ ◆▲✲❙❍ ❘▼❋ ♠♦❞❡❧s ❢♦r ✈❛r✐♦✉s str❡♥❣t❤s ♦❢ s❝❛❧❛r ❛♥❞ ✈❡❝t♦r ✜❡❧❞s✳ ❚❤❡ ❜✐♥❞✐♥❣ ❡♥❡r❣② ♣❡r ♥✉❝❧❡♦♥ ✐♥ ❛t♦♠✐❝ ♥✉❝❧❡✐ ✐s s❤♦✇♥ ❢♦r ❝♦♠♣❛r✐s♦♥ ✭◆▲✲❙❍ ♥✉❝❧❡✐✮✳

✶✷

Λ∗ ♥✉❝❧❡✐

Λ∗ ♥✉❝❧❡✐ ❞❡♥s✐t② ❞✐str✐❜✉t✐♦♥ ❛♥❞ r❛❞✐✐

1 2 3 4 5 6 7 r (fm) 0.1 0.2 0.3 0.4 0.5 ρ (fm

• 3)

20 Λ

∗

82 Λ

∗

126 Λ

∗

168 Λ

∗

ασ=1.026 NL-SH 40 80 120 160 200 A 0.6 0.8 1 r0 (fm) NL-SH nuclei Λ

∗

ασ = 1.0332 ασ = 1.026 αω = 0.8889

❋✐❣✳✹✿ ▲❡❢t✿ Λ∗ ❞❡♥s✐t② ❞✐str✐❜✉t✐♦♥ ✐♥ ✈❛r✐♦✉s s②st❡♠s ❝❛❧❝✉❧❛t❡❞ ✇✐t❤✐♥ t❤❡ ◆▲✲❙❍ ♠♦❞❡❧✳ ❘✐❣❤t✿ ❱❛❧✉❡s ♦❢ r♠s r❛❞✐✉s ♣❛r❛♠❡t❡r r✵✱ rr♠s = r✵A✶/✸✱ ✐♥ Λ∗ ♥✉❝❧❡✐ ❢♦r ✈❛r✐♦✉s ✐♥t❡r❛❝t✐♦♥ str❡♥❣t❤s✳ ❱❛❧✉❡s ♦❢ r✵ ✐♥ ❛t♦♠✐❝ ♥✉❝❧❡✐ ✭◆▲✲❙❍ ♥✉❝❧❡✐✮ ❛r❡ s❤♦✇♥ ❢♦r ❝♦♠♣❛r✐s♦♥✳

✶✸

Λ∗ ♥✉❝❧❡✐

Λ∗ ❞❡❝❛②

♥♦♥♠❡s♦♥✐❝ ❞❡❝❛② ❝❤❛♥♥❡❧ Λ∗Λ∗ → YY (Y = Σ, Λ) ❞❡❝❛② ♦❢ Λ∗Λ∗ → ΛΛ ✐♥ ✶s st❛t❡ ❞❡s❝r✐❜❡❞ ❜② ✐♠❛❣✐♥❛r② ♣♦t❡♥t✐❛❧ ■♠V♦♣t = − ✹π ✷EΛ∗ √s MΛ∗ ■♠b✵ fs✉♣♣ ρ ✇❤❡r❡ EΛ∗ = MΛ∗ − BΛ∗✱ √s =

• (EΛ∗ + EΛ∗)✷ − (

pΛ∗ + pΛ∗)✷✱ ■♠b✵ = ✵.✽✺ ❢♠ ✭✜tt❡❞ t♦ ΓΛ∗Λ∗ = ✶✵✵ ▼❡❱ ❛t t❤r❡s❤♦❧❞✮✱ ❛♥❞ fs✉♣♣ ✐s ♣❤❛s❡ s♣❛❝❡ s✉♣♣r❡ss✐♦♥ ❢❛❝t♦r

❚❛❜❧❡✿ ✶s s✐♥❣❧❡✲♣❛rt✐❝❧❡ ❡♥❡r❣② ǫΛ∗ ❛♥❞ ✇✐❞t❤ ΓΛ∗Λ∗ ✭✐♥ ▼❡❱✮ ♦❢ Λ∗ ✐♥ s②st❡♠s ❝♦♠♣♦s❡❞ ♦❢ ✽ ❛♥❞ ✶✻✽ Λ∗ ❜❛r②♦♥s✱ ❝❛❧❝✉❧❛t❡❞ ✉s✐♥❣ t❤❡ ❍❙ ♠♦❞❡❧ ✇✐t❤ ασ = ✶.✵✾✶✸✳

✽ Λ∗ ✶✻✽ Λ∗ ǫΛ∗ ✲✶✸✸✳✽ ✲✷✵✷✳✻ ΓΛ∗Λ∗ ✼✷✳✶ ✾✾✳✾

✶✹

Λ∗ ♥✉❝❧❡✐

❙❛t✉r❛t✐♦♥ ♠❡❝❤❛♥✐s♠ ✐♥ ❘▼❋

❞❡❝✐s✐✈❡ r♦❧❡ ♦❢ ▲♦r❡♥t③ ❝♦✈❛r✐❛♥❝❡ ✐♥ ♣r♦❞✉❝✐♥❣ s❛t✉r❛t✐♦♥ ✇✐t❤✐♥ t❤❡ ❘▼❋ ♠♦❞❡❧ ❑❧❡✐♥✲●♦r❞♦♥ ❡q✉❛t✐♦♥s ❢♦r ♠❡s♦♥ ✜❡❧❞s (−△ + m✷

σ)σ = −gσBρs

(−△ + m✷

ω)ω✵ = gωBρ✈

s❝❛❧❛r ❞❡♥s✐t② ρs = ¯ BB ❞❡❝r❡❛s❡ ✐♥ ❞❡♥s❡ ♠❛tt❡r ✇✐t❤ r❡s♣❡❝t t♦ ✈❡❝t♦r ✭❜❛r②♦♥✮ ❞❡♥s✐t② ρ✈ = B†B ρs ∼ M∗ E ∗ ρ✈ ✇❤❡r❡ M∗ E ∗ < ✶ ❛♥❞ M∗ = M − gσBσ ✐s ❜❛r②♦♥ ❡✛❡❝t✐✈❡ ♠❛ss

✶✺

Λ∗ ♥✉❝❧❡✐

❙❛t✉r❛t✐♦♥ ♠❡❝❤❛♥✐s♠ ✐♥ ❘▼❋

40 80 120 160 A 50 100 150 200 250 B/A (MeV)

SVM RMF

Machleidt (ρS = 0.97ρV) Machleidt (SVM)

Λ* NUCLEI

Machleidt

❋✐❣✳✺✿ ❇✐♥❞✐♥❣ ❡♥❡r❣② ♦❢ Λ∗ ♥✉❝❧❡✐ ♣❡r Λ∗✱ B/A ❛s ❛ ❢✉♥❝t✐♦♥ ♦❢ ♠❛ss ♥✉♠❜❡r A✱ ❝❛❧❝✉❧❛t❡❞ ✇✐t❤✐♥ t❤❡ ❘▼❋ ❛♥❞ ❙❱▼ ❛♣♣r♦❛❝❤❡s ❢♦r ασ = ✶.✵✾✶✸ ✭▼❛❝❤❧❡✐❞t✮✳

✶✻

Λ∗ ♥✉❝❧❡✐

❈♦♥❝❧✉s✐♦♥s

✇❡ ❡①♣❧♦r❡❞ t❤❡ ♣♦ss✐❜✐❧✐t② ♦❢ ❡①✐st❡♥❝❡ ♦❢ st❛❜❧❡ Λ∗ ♠❛tt❡r ❜❛s❡❞ ♦♥ ❡♥❡r❣② ✐♥❞❡♣❡♥❞❡♥t ¯ KN ✐♥t❡r❛❝t✐♦♥ ♠♦❞❡❧ ✭❆❨✮ t❤❡ ❆❨ ♠♦❞❡❧ ✇❛s ❝♦♥❢r♦♥t❡❞ ✇✐t❤ ❦❛♦♥✐❝ ❛t♦♠ ❞❛t❛ − → ✐t ❞♦❡s ♥♦t r❡♣r♦❞✉❝❡ ❡①♣❡r✐♠❡♥t❛❧ ✈❛❧✉❡s ♦❢ s✐♥❣❧❡✲♥✉❝❧❡♦♥ ❛❜s♦r♣t✐♦♥ ❢r❛❝t✐♦♥s ✇❡ ♣❡r❢♦r♠❡❞ ❘▼❋ ❝❛❧❝✉❧❛t✐♦♥s ♦❢ Λ∗ ♥✉❝❧❡✐ ✇✐t❤ ✈❛r✐♦✉s Λ∗ ✐♥t❡r❛❝t✐♦♥ str❡♥❣t❤s ❝♦♠♣❛t✐❜❧❡ ✇✐t❤ BΛ∗Λ∗ = ✹✵ ▼❡❱ ❜✐♥❞✐♥❣ ❡♥❡r❣② ♣❡r Λ∗ ✐♥ ♠❛♥②✲❜♦❞② s②st❡♠s s❛t✉r❛t❡s ❜❡❧♦✇ ✶✵✵ ▼❡❱ ❢♦r A ≥ ✶✷✵ ❧❡❛✈✐♥❣ Λ∗ ❛❣❣r❡❣❛t❡s ✉♥st❛❜❧❡ ❛❣❛✐♥st str♦♥❣ ✐♥t❡r❛❝t✐♦♥ ❞❡❝❛②

✶✼

Λ∗ ♥✉❝❧❡✐

❇❛❝❦✉♣ s❧✐❞❡s

✶✽

Λ∗ ♥✉❝❧❡✐

❇❛❝❦✉♣ s❧✐❞❡s

❡♥❡r❣②✲✐♥❞❡♣❡♥❞❡♥t ¯ KN ♣♦t❡♥t✐❛❧s ❜② ❨❛♠❛③❛❦✐ ❛♥❞ ❆❦❛✐s❤✐

❚✳ ❨❛♠❛③❛❦✐✱ ❨✳ ❆❦❛✐s❤✐✱ P❤②s✳ ❘❡✈✳ ❈ ✼✻ ✭✷✵✵✼✮ ✵✹✺✷✵✶

V I=✵

¯ KN (r) =(−✺✾✺ − i✽✸) ❡①♣[−(r/✵.✻✻ ❢♠)✷] ,

V I=✶

¯ KN (r) =(−✶✼✺ − i✶✵✺) ❡①♣[−(r/✵.✻✻ ❢♠)✷] .

✶✾