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ATOMIC AND NUCLEAR PHYSICS PLEASE ANSWER ALL QUESTIONS Let us consider that the two particles interact via an attractive square well potential, i.e -Uo TSR V(r)= 0 r> R, where R = 1.2 fm(4/³+A), with A1 and A2, the particles' atomic masses. For the s-wave state (= 0), the above equation has the following form Csin(Kr) T≤R to(k,r) == sin(kr +80) r> R₁ where C is a normalization constant, K² = √(k+Uo), and do the scattering phase shift. Using the continuity of the wave function and its derivative at r= R, i.e Csin(KR) = sin(kR+ 8), d dR Csin(KR) = sin(kR+60), d dR (a) show that the phase phift is given by

ATOMIC AND NUCLEAR PHYSICS PLEASE ANSWER ALL QUESTIONS Let us consider that the two particles interact via an attractive square well potential, i.e -Uo TSR V(r)= 0 r> R, where R = 1.2 fm(4/³+A), with A1 and A2, the particles' atomic masses. For the s-wave state (= 0), the above equation has the following form Csin(Kr) T≤R to(k,r) == sin(kr +80) r> R₁ where C is a normalization constant, K² = √(k+Uo), and do the scattering phase shift. Using the continuity of the wave function and its derivative at r= R, i.e Csin(KR) = sin(kR+ 8), d dR Csin(KR) = sin(kR+60), d dR (a) show that the phase phift is given by

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| W 07:37 PM 2022-05-24 W File 70 Paste 14+1+13+1+12+|+11·10 ·9·1·8·1·7·1·6·1·5·1·4·1·3·1·2·1·1····1·1·20 Home Insert Cut Copy Format Painter Clipboard Page: 1 of 1 Words: 8 Document1 - Microsoft Word (Product Activation Failed) Page Layout References Review View T 14 T Α Α΄ B-B-S ## T AaBbCcDc AaBbCcDc AaBbC AaBbCc AaBl AaBbCcl abe X, X² A ab T 트플 1 Normal No Spaci... Heading 1 Heading 2 Title Subtitle Font Paragraph G Styles ··2·1·1·1···1·1·2·1·3·1·4·1·5· 1 · 6 · 1 · 7 · 1 · 8 · 1 · 9 · 1 · 10 · |··11· |·12·|·13°||·14° | ・15° |-·\\ · |·17· |-•· 18 · | I I I I I ATOMIC AND NUCLEAR PHYSICS PLEASE ANSWER ALL QUESTIONS Let us consider that the two particles interact via an attractive square well potential, i.e -Uo r≤R V(r) = { 0 r> R, 1/3 where R = 1.2 fm(4/³ + A/³), with A₁ and A2, the particles' atomic masses. For the s-wave state (l=0), the above equation has the following form uo(k,r): Csin(Kr) sin(kr + 8) T≤R r> R, where C is a normalization constant, K² = √(k+Uo), and do the scattering phase shift. Using the continuity of the wave function and its derivative at r = R, i.e d Csin(KR) = sin(kR+ 5), d dR -Csin(KR)= dR sin(kR+60), (a) show that the phase phift is given by tan d = k tan(KR) - K tan(kR) K+ k tan(kR) tan(KR) (b) Calculate the phase shift 6 for 160+208 Pb reaction at an incident energy E = 20.0 MeV, consider Uo 102.0 MeV. Calibri (Body) BIU I U abe X₂ X² Mailings Aal Aa יד Ef Find A Час Replace Change Styles Select G Editing R 90% Ⓒ @? E OG
Transcribed Image Text:| W 07:37 PM 2022-05-24 W File 70 Paste 14+1+13+1+12+|+11·10 ·9·1·8·1·7·1·6·1·5·1·4·1·3·1·2·1·1····1·1·20 Home Insert Cut Copy Format Painter Clipboard Page: 1 of 1 Words: 8 Document1 - Microsoft Word (Product Activation Failed) Page Layout References Review View T 14 T Α Α΄ B-B-S ## T AaBbCcDc AaBbCcDc AaBbC AaBbCc AaBl AaBbCcl abe X, X² A ab T 트플 1 Normal No Spaci... Heading 1 Heading 2 Title Subtitle Font Paragraph G Styles ··2·1·1·1···1·1·2·1·3·1·4·1·5· 1 · 6 · 1 · 7 · 1 · 8 · 1 · 9 · 1 · 10 · |··11· |·12·|·13°||·14° | ・15° |-·\\ · |·17· |-•· 18 · | I I I I I ATOMIC AND NUCLEAR PHYSICS PLEASE ANSWER ALL QUESTIONS Let us consider that the two particles interact via an attractive square well potential, i.e -Uo r≤R V(r) = { 0 r> R, 1/3 where R = 1.2 fm(4/³ + A/³), with A₁ and A2, the particles' atomic masses. For the s-wave state (l=0), the above equation has the following form uo(k,r): Csin(Kr) sin(kr + 8) T≤R r> R, where C is a normalization constant, K² = √(k+Uo), and do the scattering phase shift. Using the continuity of the wave function and its derivative at r = R, i.e d Csin(KR) = sin(kR+ 5), d dR -Csin(KR)= dR sin(kR+60), (a) show that the phase phift is given by tan d = k tan(KR) - K tan(kR) K+ k tan(kR) tan(KR) (b) Calculate the phase shift 6 for 160+208 Pb reaction at an incident energy E = 20.0 MeV, consider Uo 102.0 MeV. Calibri (Body) BIU I U abe X₂ X² Mailings Aal Aa יד Ef Find A Час Replace Change Styles Select G Editing R 90% Ⓒ @? E OG
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