Symmetry Energy in Surface
|
|
- Alexandrina Thompson
- 6 years ago
- Views:
Transcription
1 Symmetry Energy in Nuclear Surface Natl Superconducting Cyclotron Lab, Michigan State U Workshop on Nuclear Symmetry Energy at Medium Energies Catania & Militello V.C., May 28-29, 2008
2 Charge Symmetry & Charge Invariance Charge symmetry: invariance of nuclear interactions under n p interchange n isoscalar quantity F does not change under n p interchange. Example: nuclear energy. Expansion in η = (N Z )/ for smooth F, has even terms only: F(η) = F 0 + F 2 η 2 + F 4 η n isovector quantity G changes sign. Example: ρ np (r) = ρ n (r) ρ p (r). Expansion with odd terms only: G(η) = G 1 η + G 3 η Note: G/η = G 1 + G 3 η Charge invariance: invariance of nuclear interactions under rotations in n-p space
3 Charge Symmetry & Charge Invariance Charge symmetry: invariance of nuclear interactions under n p interchange n isoscalar quantity F does not change under n p interchange. Example: nuclear energy. Expansion in η = (N Z )/ for smooth F, has even terms only: F(η) = F 0 + F 2 η 2 + F 4 η n isovector quantity G changes sign. Example: ρ np (r) = ρ n (r) ρ p (r). Expansion with odd terms only: G(η) = G 1 η + G 3 η Note: G/η = G 1 + G 3 η Charge invariance: invariance of nuclear interactions under rotations in n-p space
4 Charge Symmetry & Charge Invariance Charge symmetry: invariance of nuclear interactions under n p interchange n isoscalar quantity F does not change under n p interchange. Example: nuclear energy. Expansion in η = (N Z )/ for smooth F, has even terms only: F(η) = F 0 + F 2 η 2 + F 4 η n isovector quantity G changes sign. Example: ρ np (r) = ρ n (r) ρ p (r). Expansion with odd terms only: G(η) = G 1 η + G 3 η Note: G/η = G 1 + G 3 η Charge invariance: invariance of nuclear interactions under rotations in n-p space
5 Symmetry Energy: From Finite to System Skyrme Interactions η = (ρ n ρ p )/ρ expansion under n p symmetry ( ρn ρ p E(ρ n, ρ p ) = E 0 (ρ)+s(ρ) ρ S(ρ) = aa V + L ρ ρ ρ 0 Finite Nucleus Nucleon densities ρ p (r) & ρ n (r) Bethe-Weizsäcker formula: E = a V + a S 2/3 Z 2 + a C 1/3 +a (N Z )2 a() +E mic a a? = a V a a a = a V a + 2/3 a S a a a () =? half-infinite matter ) 2
6 Symmetry Energy: From Finite to System Skyrme Interactions η = (ρ n ρ p )/ρ expansion under n p symmetry ( ρn ρ p E(ρ n, ρ p ) = E 0 (ρ)+s(ρ) ρ S(ρ) = aa V + L ρ ρ ρ 0 Finite Nucleus Nucleon densities ρ p (r) & ρ n (r) Bethe-Weizsäcker formula: E = a V + a S 2/3 Z 2 + a C 1/3 +a (N Z )2 a() +E mic a a? = a V a a a = a V a + 2/3 a S a a a () =? half-infinite matter ) 2
7 Symmetry Energy: From Finite to System Skyrme Interactions η = (ρ n ρ p )/ρ expansion under n p symmetry ( ρn ρ p E(ρ n, ρ p ) = E 0 (ρ)+s(ρ) ρ S(ρ) = aa V + L ρ ρ ρ 0 Finite Nucleus Nucleon densities ρ p (r) & ρ n (r) Bethe-Weizsäcker formula: E = a V + a S 2/3 Z 2 + a C 1/3 +a (N Z )2 a() +E mic a a? = a V a a a = a V a + 2/3 a S a a a () =? half-infinite matter ) 2
8 Symmetry Energy: From Finite to System Skyrme Interactions η = (ρ n ρ p )/ρ expansion under n p symmetry ( ρn ρ p E(ρ n, ρ p ) = E 0 (ρ)+s(ρ) ρ S(ρ) = aa V + L ρ ρ ρ 0 Finite Nucleus Nucleon densities ρ p (r) & ρ n (r) Bethe-Weizsäcker formula: E = a V + a S 2/3 Z 2 + a C 1/3 +a (N Z )2 a() +E mic a a? = a V a a a = a V a + 2/3 a S a a a () =? half-infinite matter ) 2
9 Symmetry Energy: From Finite to System Skyrme Interactions η = (ρ n ρ p )/ρ expansion under n p symmetry ( ρn ρ p E(ρ n, ρ p ) = E 0 (ρ)+s(ρ) ρ S(ρ) = aa V + L ρ ρ ρ 0 Finite Nucleus Nucleon densities ρ p (r) & ρ n (r) Bethe-Weizsäcker formula: E = a V + a S 2/3 Z 2 + a C 1/3 +a (N Z )2 a() +E mic a a? = a V a a a = a V a + 2/3 a S a a a () =? half-infinite matter ) 2
10 Nucleus as Capacitor for symmetry E = a v + a s 2/3 + a a (N Z )2 = E 0 () + a a() (N Z )2 Capacitor analogy Q N Z E = E 0 + Q2 2C C 2a a () symmetry chemical potential nalogy µ a = E (N Z ) = 2a a() (N Z ) V = Q C V µ a
11 Nucleus as Capacitor for symmetry E = a v + a s 2/3 + a a (N Z )2 = E 0 () + a a() (N Z )2 Capacitor analogy Q N Z E = E 0 + Q2 2C C 2a a () symmetry chemical potential nalogy µ a = E (N Z ) = 2a a() (N Z ) V = Q C V µ a
12 Nucleus as Capacitor for symmetry E = a v + a s 2/3 + a a (N Z )2 = E 0 () + a a() (N Z )2 Capacitor analogy Q N Z E = E 0 + Q2 2C C 2a a () symmetry chemical potential nalogy µ a = E (N Z ) = 2a a() (N Z ) V = Q C V µ a
13 Invariant Densities Net density ρ(r) = ρ n (r) + ρ p (r) is isoscalar weakly depends on (N Z ) for given. (Coulomb suppressed... ) ρ np (r) = ρ n (r) ρ p (r) isovector but ρ np (r)/(n Z ) isoscalar! /(N Z ) normalizing factor global... Similar local normalizing factor, in terms of intense quantities, 2a V a /µ a, where a V a S(ρ 0 ) symmetric density (formfactor for isovector density) defined: ρ a (r) = 2aV a µ a [ρ n (r) ρ p (r)] Normal matter ρ a = ρ 0. Both ρ(r) & ρ a (r) weakly depend on η! In any nucleus ρ n,p (r) = 1 2 [ µ a ρ(r) ± 2aa V ρ a (r) ] where ρ(r) & ρ a (r) have universal features!
14 Invariant Densities Net density ρ(r) = ρ n (r) + ρ p (r) is isoscalar weakly depends on (N Z ) for given. (Coulomb suppressed... ) ρ np (r) = ρ n (r) ρ p (r) isovector but ρ np (r)/(n Z ) isoscalar! /(N Z ) normalizing factor global... Similar local normalizing factor, in terms of intense quantities, 2a V a /µ a, where a V a S(ρ 0 ) symmetric density (formfactor for isovector density) defined: ρ a (r) = 2aV a µ a [ρ n (r) ρ p (r)] Normal matter ρ a = ρ 0. Both ρ(r) & ρ a (r) weakly depend on η! In any nucleus ρ n,p (r) = 1 2 [ µ a ρ(r) ± 2aa V ρ a (r) ] where ρ(r) & ρ a (r) have universal features!
15 Invariant Densities Net density ρ(r) = ρ n (r) + ρ p (r) is isoscalar weakly depends on (N Z ) for given. (Coulomb suppressed... ) ρ np (r) = ρ n (r) ρ p (r) isovector but ρ np (r)/(n Z ) isoscalar! /(N Z ) normalizing factor global... Similar local normalizing factor, in terms of intense quantities, 2a V a /µ a, where a V a S(ρ 0 ) symmetric density (formfactor for isovector density) defined: ρ a (r) = 2aV a µ a [ρ n (r) ρ p (r)] Normal matter ρ a = ρ 0. Both ρ(r) & ρ a (r) weakly depend on η! In any nucleus ρ n,p (r) = 1 2 [ µ a ρ(r) ± 2aa V ρ a (r) ] where ρ(r) & ρ a (r) have universal features!
16 Invariant Densities Net density ρ(r) = ρ n (r) + ρ p (r) is isoscalar weakly depends on (N Z ) for given. (Coulomb suppressed... ) ρ np (r) = ρ n (r) ρ p (r) isovector but ρ np (r)/(n Z ) isoscalar! /(N Z ) normalizing factor global... Similar local normalizing factor, in terms of intense quantities, 2a V a /µ a, where a V a S(ρ 0 ) symmetric density (formfactor for isovector density) defined: ρ a (r) = 2aV a µ a [ρ n (r) ρ p (r)] Normal matter ρ a = ρ 0. Both ρ(r) & ρ a (r) weakly depend on η! In any nucleus ρ n,p (r) = 1 2 [ µ a ρ(r) ± 2aa V ρ a (r) ] where ρ(r) & ρ a (r) have universal features!
17 Nuclear Densities ρ n,p (r) = 1 2 [ µ a ρ(r) ± 2aa V ρ a (r) ] Net isoscalar density ρ usually parameterized w/fermi function 1 ρ(r) = 1 + exp ( ) with R = r r R 0 1/3 d Isovector density ρ a?? Related to a a () & to S(ρ)! a a () = 2(N Z ) = 2 dr ρ np = 1 µ a µ a aa V dr ρ a (r) In uniform matter µ a = E (N Z ) = [S(ρ) ρ2 np/ρ] = 2 S(ρ) ρ np ρ ρ np ρ a = 2aV a ρ np = av a ρ µ a S(ρ) = Hartree-Fock calculations of half-infinite nuclear matter
18 Nuclear Densities ρ n,p (r) = 1 2 [ µ a ρ(r) ± 2aa V ρ a (r) ] Net isoscalar density ρ usually parameterized w/fermi function 1 ρ(r) = 1 + exp ( ) with R = r r R 0 1/3 d Isovector density ρ a?? Related to a a () & to S(ρ)! a a () = 2(N Z ) = 2 dr ρ np = 1 µ a µ a aa V dr ρ a (r) In uniform matter µ a = E (N Z ) = [S(ρ) ρ2 np/ρ] = 2 S(ρ) ρ np ρ ρ np ρ a = 2aV a ρ np = av a ρ µ a S(ρ) = Hartree-Fock calculations of half-infinite nuclear matter
19 Nuclear Densities ρ n,p (r) = 1 2 [ µ a ρ(r) ± 2aa V ρ a (r) ] Net isoscalar density ρ usually parameterized w/fermi function 1 ρ(r) = 1 + exp ( ) with R = r r R 0 1/3 d Isovector density ρ a?? Related to a a () & to S(ρ)! a a () = 2(N Z ) = 2 dr ρ np = 1 µ a µ a aa V dr ρ a (r) In uniform matter µ a = E (N Z ) = [S(ρ) ρ2 np/ρ] = 2 S(ρ) ρ np ρ ρ np ρ a = 2aV a ρ np = av a ρ µ a S(ρ) = Hartree-Fock calculations of half-infinite nuclear matter
20 Nuclear Densities ρ n,p (r) = 1 2 [ µ a ρ(r) ± 2aa V ρ a (r) ] Net isoscalar density ρ usually parameterized w/fermi function 1 ρ(r) = 1 + exp ( ) with R = r r R 0 1/3 d Isovector density ρ a?? Related to a a () & to S(ρ)! a a () = 2(N Z ) = 2 dr ρ np = 1 µ a µ a aa V dr ρ a (r) In uniform matter µ a = E (N Z ) = [S(ρ) ρ2 np/ρ] = 2 S(ρ) ρ np ρ ρ np ρ a = 2aV a ρ np = av a ρ µ a S(ρ) = Hartree-Fock calculations of half-infinite nuclear matter
21 Half-Infinite Matter in Skyrme-Hartree-Fock To one side infinite uniform matter & vacuum to the other Wavefunctions: Φ(r) = φ(z) e ik r matter interior/exterior: φ(z) sin (k z z + δ(k)) φ(z) e κ(k)z Discretization in k-space. Set of 1D HF eqs solved using Numerov s method until self-consistency: d dz B(z) d ( ) dz φ(z) + B(z) k 2 + U(z) φ(z) = ɛ(k) φ(z) Before: Farine et al, NP338(80)86
22 Net & symmetric Densities from SHF Results for different Skyrme interactions in half-infinite matter. Net & asymmetric densities displaced relative to each other. s symmetry energy changes gradually, so does the displacement.
23 symmetry Dependence of Net Density Results for different asymmetries
24 symmetry Dependence of symmetric Density ρ a = 2aV a µ a (ρ n ρ p ) Results for different asymmetries
25 Sensitivity to S(ρ) For weakly nonuniform matter, expected asymmetric density ρ a = ρ a V a /S(ρ) symmetric density ρ a oscillates around the expectation down to ρ ρ 0 /4
26 WKB nalysis Semiclassical sin ( z 0 k z (z ) dz ) allowed z < z 0 wavefunction φ z k (z) exp ( z κ z (z ) dz ) forbidden z > z 0 z 0 Density from ρ α (z) = dk φ k α(z) 2 Findings: t z < z 0 ρ a (z) av a ρ ( ρ 2/3 1 + S(ρ) S(ρ) F) where F(z) sin (2k F (z 0 z)), describing Friedel oscillations around ρ/s, up to the classical return point z 0. t z < z 0 ρ α (z) exp ( 2m ɛ F α z ) Fall-off governed by separation energy ɛ F α
27 WKB nalysis Semiclassical sin ( z 0 k z (z ) dz ) allowed z < z 0 wavefunction φ z k (z) exp ( z κ z (z ) dz ) forbidden z > z 0 z 0 Density from ρ α (z) = dk φ k α(z) 2 Findings: t z < z 0 ρ a (z) av a ρ ( ρ 2/3 1 + S(ρ) S(ρ) F) where F(z) sin (2k F (z 0 z)), describing Friedel oscillations around ρ/s, up to the classical return point z 0. t z < z 0 ρ α (z) exp ( 2m ɛ F α z ) Fall-off governed by separation energy ɛ F α
28 WKB nalysis Semiclassical sin ( z 0 k z (z ) dz ) allowed z < z 0 wavefunction φ z k (z) exp ( z κ z (z ) dz ) forbidden z > z 0 z 0 Density from ρ α (z) = dk φ k α(z) 2 Findings: t z < z 0 ρ a (z) av a ρ ( ρ 2/3 1 + S(ρ) S(ρ) F) where F(z) sin (2k F (z 0 z)), describing Friedel oscillations around ρ/s, up to the classical return point z 0. t z < z 0 ρ α (z) exp ( 2m ɛ F α z ) Fall-off governed by separation energy ɛ F α
29 Density Tails Two Skyrme interactions + different asymmetries
30 a a () = 1 aa V where a S a a V a Symmetry Coefficient dr ρ a (r) = 1 a V a r 0 3 R a and R a is displacement of isovector and isoscalar surfaces. a V a dr ρ(r) + 1 a V a surface region dr (ρ a ρ)(r) + 2/3 aa S L aa S Correlation f/shf 1 a a () = 1 a V a + 1/3 a S a
31 Charge Invariance?a a ()? Conclusions on sym-energy details, following E-formula fits, interrelated with conclusions on other terms in the formula: asymmetry-dependent Coulomb, Wigner & pairing + asymmetry-independent, due to (N Z )/ - correlations along stability line (PD NP727(03)233)! Best would be to study the symmetry energy in isolation from the rest of E-formula! bsurd?! Charge invariance to rescue: lowest nuclear states characterized by different isospin values (T,T z ), T z = (Z N)/2. Nuclear energy scalar in isospin space: sym energy E a = a a () (N Z )2 = 4 a a () T 2 z E a = 4 a a () T 2 = 4 a a() T (T + 1)
32 Charge Invariance?a a ()? Conclusions on sym-energy details, following E-formula fits, interrelated with conclusions on other terms in the formula: asymmetry-dependent Coulomb, Wigner & pairing + asymmetry-independent, due to (N Z )/ - correlations along stability line (PD NP727(03)233)! Best would be to study the symmetry energy in isolation from the rest of E-formula! bsurd?! Charge invariance to rescue: lowest nuclear states characterized by different isospin values (T,T z ), T z = (Z N)/2. Nuclear energy scalar in isospin space: sym energy E a = a a () (N Z )2 = 4 a a () T 2 z E a = 4 a a () T 2 = 4 a a() T (T + 1)
33 Charge Invariance?a a ()? Conclusions on sym-energy details, following E-formula fits, interrelated with conclusions on other terms in the formula: asymmetry-dependent Coulomb, Wigner & pairing + asymmetry-independent, due to (N Z )/ - correlations along stability line (PD NP727(03)233)! Best would be to study the symmetry energy in isolation from the rest of E-formula! bsurd?! Charge invariance to rescue: lowest nuclear states characterized by different isospin values (T,T z ), T z = (Z N)/2. Nuclear energy scalar in isospin space: sym energy E a = a a () (N Z )2 = 4 a a () T 2 z E a = 4 a a () T 2 = 4 a a() T (T + 1)
34 a a () Nucleus-by-Nucleus T (T + 1) E a = 4 a a () In the ground state T takes on the lowest possible value T = T z = N Z /2. Through +1 most of the Wigner term absorbed. Formula generalized to the lowest state of a given T (e.g. Jänecke et al., NP728(03)23). Pairing depends on evenness of T.?Lowest state of a given T : isobaric analogue state (IS) of some neighboring nucleus ground-state. T z =-1 T z =0 T z =1 Study of changes in the symmetry term possible nucleus by nucleus T=1 T=0
35 IS Data nalysis In the same nucleus: E 2 (T 2 ) E 1 (T 1 ) = 4 a a { T2 (T 2 + 1) T 1 (T 1 + 1) } +E mic (T 2, T z ) E mic (T 2, T z ) a 1 a () = 4 T 2 E? = (a V a ) 1 + (a S a ) 1 1/3 Data: ntony et al. DNDT66(97)1 E mic : Koura et al., ProTheoPhys113(05)305 v Groote et al., tdatnucdattab17(76)418 Moller et al., tdatnucdattab59(95)185
36 a a vs Line: best fit at > 20.
37 Best a()-descriptions... some problems w/extracting a a() from SHF for finite nuclei
38 Symmetry-Energy Parameters a V a = ( ) MeV, a S a = (9.5 12) MeV, L 95 MeV
39 Modified Binding Formula E = a V + a S 2/3 Z 2 + a C 1/3 + aa V 1 + 1/3 aa V /aa S Energy Formula Performance: Fit residuals f/light asymmetric nuclei, either following the Bethe-Weizsäcker formula (open symbols) or the modified formula with a V a /a S a = 2.8 imposed (closed), i.e. the same parameter No. (N Z ) 2
40 Conclusions In bulk limit, ρ n & ρ p describable in terms of isoscalar ρ & isovector ρ a, η-independent. Surfaces for ρ & ρ a displaced by fixed distance R a ; different diffusenesses. side from the Friedel (shell) oscillations, ρ a (ρ n ρ p ) ρ/s(ρ) at ρ ρ 0 /4; separation-energy fall-off at ρ ρ 0 /4. -variation of the symmetry coefficient a a () tied to the difference between ρ a and ρ. Modified E-formula. Mass-dependence of a a determined from IS. Parameter values: a V a = ( ) MeV, a S a = (9.5 12) MeV, L 95 MeV; stiff symmetry energy. Outlook: finite nuclei - Coulomb & shell effects, learning on finer S(ρ)-details from ρ p (r) Thanks: Jenny Lee
41 Conclusions In bulk limit, ρ n & ρ p describable in terms of isoscalar ρ & isovector ρ a, η-independent. Surfaces for ρ & ρ a displaced by fixed distance R a ; different diffusenesses. side from the Friedel (shell) oscillations, ρ a (ρ n ρ p ) ρ/s(ρ) at ρ ρ 0 /4; separation-energy fall-off at ρ ρ 0 /4. -variation of the symmetry coefficient a a () tied to the difference between ρ a and ρ. Modified E-formula. Mass-dependence of a a determined from IS. Parameter values: a V a = ( ) MeV, a S a = (9.5 12) MeV, L 95 MeV; stiff symmetry energy. Outlook: finite nuclei - Coulomb & shell effects, learning on finer S(ρ)-details from ρ p (r) Thanks: Jenny Lee
42 Conclusions In bulk limit, ρ n & ρ p describable in terms of isoscalar ρ & isovector ρ a, η-independent. Surfaces for ρ & ρ a displaced by fixed distance R a ; different diffusenesses. side from the Friedel (shell) oscillations, ρ a (ρ n ρ p ) ρ/s(ρ) at ρ ρ 0 /4; separation-energy fall-off at ρ ρ 0 /4. -variation of the symmetry coefficient a a () tied to the difference between ρ a and ρ. Modified E-formula. Mass-dependence of a a determined from IS. Parameter values: a V a = ( ) MeV, a S a = (9.5 12) MeV, L 95 MeV; stiff symmetry energy. Outlook: finite nuclei - Coulomb & shell effects, learning on finer S(ρ)-details from ρ p (r) Thanks: Jenny Lee
43 Conclusions In bulk limit, ρ n & ρ p describable in terms of isoscalar ρ & isovector ρ a, η-independent. Surfaces for ρ & ρ a displaced by fixed distance R a ; different diffusenesses. side from the Friedel (shell) oscillations, ρ a (ρ n ρ p ) ρ/s(ρ) at ρ ρ 0 /4; separation-energy fall-off at ρ ρ 0 /4. -variation of the symmetry coefficient a a () tied to the difference between ρ a and ρ. Modified E-formula. Mass-dependence of a a determined from IS. Parameter values: a V a = ( ) MeV, a S a = (9.5 12) MeV, L 95 MeV; stiff symmetry energy. Outlook: finite nuclei - Coulomb & shell effects, learning on finer S(ρ)-details from ρ p (r) Thanks: Jenny Lee
44 Conclusions In bulk limit, ρ n & ρ p describable in terms of isoscalar ρ & isovector ρ a, η-independent. Surfaces for ρ & ρ a displaced by fixed distance R a ; different diffusenesses. side from the Friedel (shell) oscillations, ρ a (ρ n ρ p ) ρ/s(ρ) at ρ ρ 0 /4; separation-energy fall-off at ρ ρ 0 /4. -variation of the symmetry coefficient a a () tied to the difference between ρ a and ρ. Modified E-formula. Mass-dependence of a a determined from IS. Parameter values: a V a = ( ) MeV, a S a = (9.5 12) MeV, L 95 MeV; stiff symmetry energy. Outlook: finite nuclei - Coulomb & shell effects, learning on finer S(ρ)-details from ρ p (r) Thanks: Jenny Lee
45 Conclusions In bulk limit, ρ n & ρ p describable in terms of isoscalar ρ & isovector ρ a, η-independent. Surfaces for ρ & ρ a displaced by fixed distance R a ; different diffusenesses. side from the Friedel (shell) oscillations, ρ a (ρ n ρ p ) ρ/s(ρ) at ρ ρ 0 /4; separation-energy fall-off at ρ ρ 0 /4. -variation of the symmetry coefficient a a () tied to the difference between ρ a and ρ. Modified E-formula. Mass-dependence of a a determined from IS. Parameter values: a V a = ( ) MeV, a S a = (9.5 12) MeV, L 95 MeV; stiff symmetry energy. Outlook: finite nuclei - Coulomb & shell effects, learning on finer S(ρ)-details from ρ p (r) Thanks: Jenny Lee
46 Conclusions In bulk limit, ρ n & ρ p describable in terms of isoscalar ρ & isovector ρ a, η-independent. Surfaces for ρ & ρ a displaced by fixed distance R a ; different diffusenesses. side from the Friedel (shell) oscillations, ρ a (ρ n ρ p ) ρ/s(ρ) at ρ ρ 0 /4; separation-energy fall-off at ρ ρ 0 /4. -variation of the symmetry coefficient a a () tied to the difference between ρ a and ρ. Modified E-formula. Mass-dependence of a a determined from IS. Parameter values: a V a = ( ) MeV, a S a = (9.5 12) MeV, L 95 MeV; stiff symmetry energy. Outlook: finite nuclei - Coulomb & shell effects, learning on finer S(ρ)-details from ρ p (r) Thanks: Jenny Lee
47 nalytic Skin Size r 2 1/2 n r 2 1/2 p r 2 1/2 = 6NZ nalytic Expression for Skin Size symmetry energy only Coulomb correction N Z 1 + 1/3 a S a /a V a a C 168aa V 5/3 N /3 a S a /a V a 1 + 1/3 a S a /a V a Formula (lines) vs Typel & Brown results (symbols) from nonrelativistic & relativistic mean-field calculations, PRC64(01)027302
48 nalytic Skin Size Skin Sizes for Sn & Pb Isotopes Lines - formula predictions, PD NP727(03)233 Favored ratio a V a /a S a 32.5/
IAS and Skin Constraints. Symmetry Energy
IS and Skin Constraints on the Pawel Natl Superconducting Cyclotron Lab, US 32 nd International Workshop on Nuclear July, 2013, East Lansing, Michigan ρ in Nuclear Mass Formula Textbook Bethe-Weizsäcker
More informationSymmetry Energy. in Structure and in Central and Direct Reactions
: in Structure and in Central and Direct Reactions Pawel Natl Superconducting Cyclotron Lab, US The 12 th International Conference on Nucleus-Nucleus Collisions June 21-26, 2015, Catania, Italy Bulk Properties
More informationarxiv: v1 [nucl-th] 21 Aug 2007
Symmetry Energy as a Function of Density and Mass Pawel Danielewicz and Jenny Lee arxiv:0708.2830v1 [nucl-th] 21 ug 2007 National Superconducting Cyclotron Laboratory and Department of Physics and stronomy,
More informationSymmetry energy, masses and T=0 np-pairing
Symmetry energy, masses and T=0 np-pairing Can we measure the T=0 pair gap? Do the moments of inertia depend on T=0 pairing? Do masses evolve like T(T+1) or T^2 (N-Z)^2? Origin of the linear term in mean
More informationAn extended liquid drop approach
An extended liquid drop approach Symmetry energy, charge radii and neutron skins Lex Dieperink 1 Piet van Isacker 2 1 Kernfysisch Versneller Instituut University of Groningen 2 GANIL, Caen, France ECT,
More informationThe role of isospin symmetry in collective nuclear structure. Symposium in honour of David Warner
The role of isospin symmetry in collective nuclear structure Symposium in honour of David Warner The role of isospin symmetry in collective nuclear structure Summary: 1. Coulomb energy differences as
More informationJoint ICTP-IAEA Workshop on Nuclear Structure Decay Data: Theory and Evaluation August Introduction to Nuclear Physics - 1
2358-19 Joint ICTP-IAEA Workshop on Nuclear Structure Decay Data: Theory and Evaluation 6-17 August 2012 Introduction to Nuclear Physics - 1 P. Van Isacker GANIL, Grand Accelerateur National d'ions Lourds
More informationExtracting symmetry energy information with transport models
Extracting symmetry energy information with transport models Yingxun Zhang China Institute of Atomic Energy Collaborator: Zhuxia Li (CIAE) M.B.Tsang, P. Danielewicz, W.G. Lynch (MSU/NSCL) Fei Lu (PKU)
More informationThe Nuclear Many-Body Problem
The Nuclear Many-Body Problem relativistic heavy ions vacuum electron scattering quarks gluons radioactive beams heavy few nuclei body quark-gluon soup QCD nucleon QCD few body systems many body systems
More informationNeutron Rich Nuclei in Heaven and Earth
First Prev Next Last Go Back Neutron Rich Nuclei in Heaven and Earth Jorge Piekarewicz with Bonnie Todd-Rutel Tallahassee, Florida, USA Page 1 of 15 Cassiopeia A: Chandra 08/23/04 Workshop on Nuclear Incompressibility
More informationStatistical analysis in nuclear DFT: central depression as example
Statistical analysis in nuclear DFT: central depression as example P. G. Reinhard 1 1 Institut für Theoretische Physik II, Universität Erlangen-Nürnberg ISNET17, York (UK), 8. November 217 Statistical
More informationHeavy-ion reactions and the Nuclear Equation of State
Heavy-ion reactions and the Nuclear Equation of State S. J. Yennello Texas A&M University D. Shetty, G. Souliotis, S. Soisson, Chen, M. Veselsky, A. Keksis, E. Bell, M. Jandel Studying Nuclear Equation
More informationNuclear symmetry energy deduced from dipole excitations: comparison with other constraints
Nuclear symmetry energy deduced from dipole excitations: a comparison with other constraints G. Colò June 15th, 2010 This work is part of a longer-term research plan. The goal is: understanding which are
More informationNuclear symmetry energy: from nuclear extremes to neutron-star matter
1 Nuclear symmetry energy: from nuclear extremes to neutron-star matter Pawel Danielewicz National Superconducting Cyclotron Laboratory and Department of Physics and stronomy, Michigan State University,
More informationRelativistic versus Non Relativistic Mean Field Models in Comparison
Relativistic versus Non Relativistic Mean Field Models in Comparison 1) Sampling Importance Formal structure of nuclear energy density functionals local density approximation and gradient terms, overall
More informationSome new developments in relativistic point-coupling models
Some new developments in relativistic point-coupling models T. J. Buervenich 1, D. G. Madland 1, J. A. Maruhn 2, and P.-G. Reinhard 3 1 Los Alamos National Laboratory 2 University of Frankfurt 3 University
More informationNucelon self-energy in nuclear matter and how to probe ot with RIBs
Nucelon self-energy in nuclear matter and how to probe ot with RIBs Christian Fuchs University of Tübingen Germany Christian Fuchs - Uni Tübingen p.1/?? Outline relativistic dynamics E/A [MeV] 6 5 4 3
More informationVolume and Surface Components of the Nuclear Symmetry Energy
NUCLEAR THEORY, Vol. 35 (2016) eds. M. Gaidarov, N. Minkov, Heron Press, Sofia Volume and Surface Components of the Nuclear Symmetry Energy A.N. Antonov 1, M.K. Gaidarov 1, P. Sarriguren 2, E. Moya de
More informationRelativistic point-coupling models for finite nuclei
Relativistic point-coupling models for finite nuclei T. J. Buervenich 1, D. G. Madland 1, J. A. Maruhn 2, and P.-G. Reinhard 3 1 Los Alamos National Laboratory 2 University of Frankfurt 3 University of
More informationInterpretation of the Wigner Energy as due to RPA Correlations
Interpretation of the Wigner Energy as due to RPA Correlations arxiv:nucl-th/001009v1 5 Jan 00 Kai Neergård Næstved Gymnasium og HF Nygårdsvej 43, DK-4700 Næstved, Denmark neergard@inet.uni.dk Abstract
More informationNuclear structure III: Nuclear and neutron matter. National Nuclear Physics Summer School Massachusetts Institute of Technology (MIT) July 18-29, 2016
Nuclear structure III: Nuclear and neutron matter Stefano Gandolfi Los Alamos National Laboratory (LANL) National Nuclear Physics Summer School Massachusetts Institute of Technology (MIT) July 18-29, 2016
More informationReactions of neutron-rich Sn isotopes investigated at relativistic energies at R 3 B
investigated at relativistic energies at R 3 B for the R 3 B collaboration Technische Universität Darmstadt E-mail: fa.schindler@gsi.de Reactions of neutron-rich Sn isotopes have been measured in inverse
More informationDipole Response of Exotic Nuclei and Symmetry Energy Experiments at the LAND R 3 B Setup
Dipole Response of Exotic Nuclei and Symmetry Energy Experiments at the LAND R 3 B Setup Dominic Rossi for the LAND collaboration GSI Helmholtzzentrum für Schwerionenforschung GmbH D 64291 Darmstadt, Germany
More informationNuclear Symmetry Energy in Relativistic Mean Field Theory. Abstract
Nuclear Symmetry Energy in Relativistic Mean Field Theory Shufang Ban, 1, Jie Meng, 1, 3, 4, Wojciech Satu la, 5,, and Ramon A. Wyss 1 School of Physics, Peking University, Beijing 1871, China Royal Institute
More informationDensity dependence of the nuclear symmetry energy estimated from neutron skin thickness in finite nuclei
Density dependence of the nuclear symmetry energy estimated from neutron skin thickness in finite nuclei X. Roca-Maza a,c X. Viñas a M. Centelles a M. Warda a,b a Departament d Estructura i Constituents
More informationThe isospin dependence of the nuclear force and its impact on the many-body system
Journal of Physics: Conference Series OPEN ACCESS The isospin dependence of the nuclear force and its impact on the many-body system To cite this article: F Sammarruca et al 2015 J. Phys.: Conf. Ser. 580
More informationProbing the Nuclear Symmetry Energy and Neutron Skin from Collective Excitations. N. Paar
Calcium Radius Experiment (CREX) Workshop at Jefferson Lab, March 17-19, 2013 Probing the Nuclear Symmetry Energy and Neutron Skin from Collective Excitations N. Paar Physics Department Faculty of Science
More informationTheory of neutron-rich nuclei and nuclear radii Witold Nazarewicz (with Paul-Gerhard Reinhard) PREX Workshop, JLab, August 17-19, 2008
Theory of neutron-rich nuclei and nuclear radii Witold Nazarewicz (with Paul-Gerhard Reinhard) PREX Workshop, JLab, August 17-19, 2008 Introduction to neutron-rich nuclei Radii, skins, and halos From finite
More informationSelf-Consistent Equation of State for Hot Dense Matter: A Work in Progress
Self-Consistent Equation of State for Hot Dense Matter: A Work in Progress W.G.Newton 1, J.R.Stone 1,2 1 University of Oxford, UK 2 Physics Division, ORNL, Oak Ridge, TN Outline Aim Self-consistent EOS
More informationSymmetry Energy within the Brueckner-Hartree-Fock approximation
Symmetry Energy within the Brueckner-Hartree-Fock approximation Isaac Vidaña CFC, University of Coimbra International Symposium on Nuclear Symmetry Energy Smith College, Northampton ( Massachusetts) June
More informationarxiv:nucl-th/ v3 8 Sep 2003
MSUCL-1251 Surface Symmetry Energy arxiv:nucl-th/0301050v3 8 Sep 2003 Pawe l Danielewicz National Superconducting Cyclotron Laboratory and Department of Physics and Astronomy, Michigan State University,
More informationQRPA Calculations of Charge Exchange Reactions and Weak Interaction Rates. N. Paar
Strong, Weak and Electromagnetic Interactions to probe Spin-Isospin Excitations ECT*, Trento, 28 September - 2 October 2009 QRPA Calculations of Charge Exchange Reactions and Weak Interaction Rates N.
More informationDensity dependence of the symmetry energy and the nuclear equation of state : A dynamical and statistical model perspective
Density dependence of the symmetry energy and the nuclear equation of state : A dynamical and statistical model perspective D. V. Shetty, S. J. Yennello, and G. A. Souliotis The density dependence of the
More informationThe Nuclear Equation of State
The Nuclear Equation of State Theoretical models for nuclear structure studies Xavier Roca-Maza Università degli Studi di Milano e INFN, sezione di Milano Terzo Incontro Nazionale di Fisica Nucleare LNF,
More informationMean-field concept. (Ref: Isotope Science Facility at Michigan State University, MSUCL-1345, p. 41, Nov. 2006) 1/5/16 Volker Oberacker, Vanderbilt 1
Mean-field concept (Ref: Isotope Science Facility at Michigan State University, MSUCL-1345, p. 41, Nov. 2006) 1/5/16 Volker Oberacker, Vanderbilt 1 Static Hartree-Fock (HF) theory Fundamental puzzle: The
More informationEquation of State of Dense Matter
Department of Physics & Astronomy 449 ESS Bldg. Stony Brook University April 25, 2017 Nuclear Astrophysics James.Lattimer@Stonybrook.edu Zero Temperature Nuclear Matter Expansions Cold, bulk, symmetric
More informationProperties of Nuclei deduced from the Nuclear Mass
Properties of Nuclei deduced from the Nuclear Mass -the 2nd lecture- @Milano March 16-20, 2015 Yoshitaka Fujita Osaka University Image of Nuclei Our simple image for Nuclei!? Nuclear Physics by Bohr and
More informationATOMIC PARITY VIOLATION
ATOMIC PARITY VIOLATION OUTLINE Overview of the Atomic Parity Violation Theory: How to calculate APV amplitude? Analysis of Cs experiment and implications for search for physics beyond the Standard Model
More informationLiquid Drop Model From the definition of Binding Energy we can write the mass of a nucleus X Z
Our first model of nuclei. The motivation is to describe the masses and binding energy of nuclei. It is called the Liquid Drop Model because nuclei are assumed to behave in a similar way to a liquid (at
More informationNuclear Matter Incompressibility and Giant Monopole Resonances
Nuclear Matter Incompressibility and Giant Monopole Resonances C.A. Bertulani Department of Physics and Astronomy Texas A&M University-Commerce Collaborator: Paolo Avogadro 27th Texas Symposium on Relativistic
More informationSummary Int n ro r d o u d c u tion o Th T e h o e r o e r t e ical a fra r m a ew e o w r o k r Re R s e ul u ts Co C n o c n lus u ion o s n
Isospin mixing and parity- violating electron scattering O. Moreno, P. Sarriguren, E. Moya de Guerra and J. M. Udías (IEM-CSIC Madrid and UCM Madrid) T. W. Donnelly (M.I.T.),.), I. Sick (Univ. Basel) Summary
More informationPhysics Letters B 695 (2011) Contents lists available at ScienceDirect. Physics Letters B.
Physics Letters B 695 (2011) 507 511 Contents lists available at ScienceDirect Physics Letters B www.elsevier.com/locate/physletb Configuration interactions constrained by energy density functionals B.
More informationAn improved nuclear mass formula: WS3
Journal of Physics: Conference Series An improved nuclear mass formula: WS3 To cite this article: Ning Wang and Min Liu 2013 J. Phys.: Conf. Ser. 420 012057 View the article online for updates and enhancements.
More informationShape of Lambda Hypernuclei within the Relativistic Mean-Field Approach
Universities Research Journal 2011, Vol. 4, No. 4 Shape of Lambda Hypernuclei within the Relativistic Mean-Field Approach Myaing Thi Win 1 and Kouichi Hagino 2 Abstract Self-consistent mean-field theory
More informationIntroduction to nuclear structure
Introduction to nuclear structure A. Pastore 1 Department of Physics, University of York, Heslington, York, YO10 5DD, UK August 8, 2017 Introduction [C. Diget, A.P, et al Physics Education 52 (2), 024001
More informationarxiv:nucl-th/ v4 9 May 2002
Interpretation of the Wigner Energy as due to RPA Correlations Kai Neergård arxiv:nucl-th/001009v4 9 May 00 Næstved Gymnasium og HF, Nygårdsvej 43, DK-4700 Næstved, Denmark, neergard@inet.uni.dk Abstract
More informationWhat did you learn in the last lecture?
What did you learn in the last lecture? Charge density distribution of a nucleus from electron scattering SLAC: 21 GeV e s ; λ ~ 0.1 fm (to first order assume that this is also the matter distribution
More informationNuclear matter inspired Energy density functional for finite nuc
Nuclear matter inspired Energy density functional for finite nuclei: the BCP EDF M. Baldo a, L.M. Robledo b, P. Schuck c, X. Vinyes d a Instituto Nazionale di Fisica Nucleare, Sezione di Catania, Catania,
More informationModeling the EOS. Christian Fuchs 1 & Hermann Wolter 2. 1 University of Tübingen/Germany. 2 University of München/Germany
Modeling the EOS Christian Fuchs 1 & Hermann Wolter 2 1 University of Tübingen/Germany 2 University of München/Germany Christian Fuchs - Uni Tübingen p.1/20 Outline Christian Fuchs - Uni Tübingen p.2/20
More informationNeutron Skins with α-clusters
Neutron Skins with α-clusters GSI Helmholtzzentrum für Schwerionenforschung, Darmstadt Nuclear Astrophysics Virtual Institute Hirschegg 2015 Nuclear Structure and Reactions: Weak, Strange and Exotic International
More informationCollective excitations in nuclei away from the valley of stability
Collective excitations in nuclei away from the valley of stability A. Horvat 1, N. Paar 16.7.14, CSSP 14, Sinaia, Romania 1 Institut für Kernphysik, TU Darmstadt, Germany (for the R3B-LAND collaboration)
More informationNuclear Equation of State from ground and collective excited state properties of nuclei
Nuclear Equation of State from ground and collective excited state properties of nuclei arxiv:1804.06256v1 [nucl-th] 17 Apr 2018 X. Roca-Maza 1 and N. Paar 2 1 Dipartimento di Fisica, Università degli
More informationBeyond mean-field study on collective vibrations and beta-decay
Advanced many-body and statistical methods in mesoscopic systems III September 4 th 8 th, 2017, Busteni, Romania Beyond mean-field study on collective vibrations and beta-decay Yifei Niu Collaborators:
More informationNuclear Structure V: Application to Time-Reversal Violation (and Atomic Electric Dipole Moments)
T Symmetry EDM s Octupole Deformation Other Nuclei Nuclear Structure V: Application to Time-Reversal Violation (and Atomic Electric Dipole Moments) J. Engel University of North Carolina June 16, 2005 T
More informationGianluca Colò. Density Functional Theory for isovector observables: from nuclear excitations to neutron stars. Università degli Studi and INFN, MIlano
Density Functional Theory for isovector observables: from nuclear excitations to neutron stars Gianluca Colò NSMAT2016, Tohoku University, Sendai 1 Outline Energy density functionals (EDFs): a short introduction
More informationarxiv: v1 [nucl-th] 1 Sep 2017
EoS constraints from nuclear masses and radii in a meta-modeling approach D. Chatterjee 1, F. Gulminelli, 1 Ad. R. Raduta, 2 and J. Margueron 3,4 1 LPC, UMR6534, ENSICAEN, F-145 Caen, France 2 IFIN-HH,
More informationCalculations for Asymmetric Nuclear matter and many-body correlations in Semi-classical Molecular Dynamics
Calculations for Asymmetric Nuclear matter and many-body correlations in Semi-classical Molecular Dynamics M. Papa Istituto Nazionale di Fisica Nucleare Sezione di Catania V. S.Sofia 64 9513 Catania Italy
More informationLow-lying dipole response in stable and unstable nuclei
Low-lying dipole response in stable and unstable nuclei Marco Brenna Xavier Roca-Maza, Giacomo Pozzi Kazuhito Mizuyama, Gianluca Colò and Pier Francesco Bortignon X. Roca-Maza, G. Pozzi, M.B., K. Mizuyama,
More informationDensity dependence of the nuclear symmetry energy estimated from neutron skin thickness in finite nuclei
Density dependence of the nuclear symmetry energy estimated from neutron skin thickness in finite nuclei X. Viñas a M. Centelles a M. Warda a,b X. Roca-Maza a,c a Departament d Estructura i Constituents
More informationNuclear Symmetry Energy and its Density Dependence. Chang Xu Department of Physics, Nanjing University. Wako, Japan
Nuclear Symmetry Energy and its Density Dependence Chang Xu Department of Physics, Nanjing University 2016.8.17-21@RIKEN, Wako, Japan Outline 1. Brief Review: Nuclear symmetry energy 2. What determines
More informationTemperature Dependence of the Symmetry Energy and Neutron Skins in Ni, Sn, and Pb Isotopic Chains
Bulg. J. Phys. 44 (2017) S27 S38 Temperature Dependence of the Symmetry Energy and Neutron Skins in Ni, Sn, and Pb Isotopic Chains A.N. Antonov 1, D.N. Kadrev 1, M.K. Gaidarov 1, P. Sarriguren 2, E. Moya
More informationRelativistic Hartree-Bogoliubov description of sizes and shapes of A = 20 isobars
Relativistic Hartree-Bogoliubov description of sizes and shapes of A = 20 isobars G.A. Lalazissis 1,2, D. Vretenar 1,3, and P. Ring 1 arxiv:nucl-th/0009047v1 18 Sep 2000 1 Physik-Department der Technischen
More informationCoupled-cluster theory for medium-mass nuclei
Coupled-cluster theory for medium-mass nuclei Thomas Papenbrock and G. Hagen (ORNL) D. J. Dean (ORNL) M. Hjorth-Jensen (Oslo) A. Nogga (Juelich) A. Schwenk (TRIUMF) P. Piecuch (MSU) M. Wloch (MSU) Seattle,
More informationSymmetry energy and the neutron star core-crust transition with Gogny forces
Symmetry energy and the neutron star core-crust transition with Gogny forces Claudia Gonzalez-Boquera, 1 M. Centelles, 1 X. Viñas 1 and A. Rios 2 1 Departament de Física Quàntica i Astrofísica and Institut
More informationStochastic Mean Field (SMF) description TRANSPORT Maria Colonna INFN - Laboratori Nazionali del Sud (Catania)
Stochastic Mean Field (SMF) description TRANSPORT 2017 March 27-30, 2017 FRIB-MSU, East Lansing, Michigan, USA Maria Colonna INFN - Laboratori Nazionali del Sud (Catania) Dynamics of many-body system I
More informationNucleon Pair Approximation to the nuclear Shell Model
Nucleon Pair Approximation to the nuclear Shell Model Yu-Min Zhao (Speaker: Yi-Yuan Cheng) 2 nd International Workshop & 12 th RIBF Discussion on Neutron-Proton Correlations, Hong Kong July 6-9, 2015 Outline
More information8 Nuclei. introduc)on to Astrophysics, C. Bertulani, Texas A&M-Commerce 1
8 Nuclei introduc)on to Astrophysics, C. Bertulani, Texas A&M-Commerce 1 8.1 - The nucleus The atomic nucleus consists of protons and neutrons. Protons and neutrons are called nucleons. A nucleus is characterized
More informationNuclear Symmetry Energy Constrained by Cluster Radioactivity. Chang Xu ( 许昌 ) Department of Physics, Nanjing University
Nuclear Symmetry Energy Constrained by Cluster Radioactivity Chang Xu ( 许昌 ) Department of Physics, Nanjing University 2016.6.13-18@NuSym2016 Outline 1. Cluster radioactivity: brief review and our recent
More informationNuclear Binding Energy in Terms of a Redefined (A)symmetry Energy
Nuclear Binding Energy in Terms of a Redefined (A)symmetry Energy Author: Paul Andrew Taylor Persistent link: http://hdl.handle.net/345/460 This work is posted on escholarship@bc, Boston College University
More informationIsospin asymmetry in stable and exotic nuclei
Isospin asymmetry in stable and exotic nuclei Xavier Roca Maza 6 May 2010 Advisors: Xavier Viñas i Gausí and Mario Centelles i Aixalà Motivation: Nuclear Chart Relative Neutron excess I (N Z )/(N + Z )
More informationNeutron star structure explored with a family of unified equations of state of neutron star matter
Neutron star structure explored with a family of unified equations of state of neutron star matter Department of Human Informatics, ichi Shukutoku University, 2-9 Katahira, Nagakute, 48-1197, Japan E-mail:
More informationNuclear symmetry energy and Neutron star cooling
Nuclear symmetry energy and Neutron star cooling Yeunhwan Lim 1 1 Daegu University. July 26, 2013 In Collaboration with J.M. Lattimer (SBU), C.H. Hyun (Daegu), C-H Lee (PNU), and T-S Park (SKKU) NuSYM13
More informationc E If photon Mass particle 8-1
Nuclear Force, Structure and Models Readings: Nuclear and Radiochemistry: Chapter 10 (Nuclear Models) Modern Nuclear Chemistry: Chapter 5 (Nuclear Forces) and Chapter 6 (Nuclear Structure) Characterization
More informationExcitations in light deformed nuclei investigated by self consistent quasiparticle random phase approximation
Excitations in light deformed nuclei investigated by self consistent quasiparticle random phase approximation C. Losa, A. Pastore, T. Døssing, E. Vigezzi, R. A. Broglia SISSA, Trieste Trento, December
More informationRFSS: Lecture 8 Nuclear Force, Structure and Models Part 1 Readings: Nuclear Force Nuclear and Radiochemistry:
RFSS: Lecture 8 Nuclear Force, Structure and Models Part 1 Readings: Nuclear and Radiochemistry: Chapter 10 (Nuclear Models) Modern Nuclear Chemistry: Chapter 5 (Nuclear Forces) and Chapter 6 (Nuclear
More informationA new approach to detect hypernuclei and isotopes in the QMD phase space distribution at relativistic energies
A new approach to detect hypernuclei and isotopes in the QMD phase space distribution at relativistic energies A. Le Fèvre 1, J. Aichelin 2, Ch. Hartnack 2 and Y. Leifels 1 1 GSI Darmstadt, Germany 2 Subatech
More informationTamara Nikšić University of Zagreb
CONFIGURATION MIXING WITH RELATIVISTIC SCMF MODELS Tamara Nikšić University of Zagreb Supported by the Croatian Foundation for Science Tamara Nikšić (UniZg) Primošten 11 9.6.11. 1 / 3 Contents Outline
More informationEvolution Of Shell Structure, Shapes & Collective Modes. Dario Vretenar
Evolution Of Shell Structure, Shapes & Collective Modes Dario Vretenar vretenar@phy.hr 1. Evolution of shell structure with N and Z A. Modification of the effective single-nucleon potential Relativistic
More informationClusters in Dense Matter and the Equation of State
Clusters in Dense Matter and the Equation of State Excellence Cluster Universe, Technische Universität München GSI Helmholtzzentrum für Schwerionenforschung, Darmstadt in collaboration with Gerd Röpke
More informationPairing Interaction in N=Z Nuclei with Half-filled High-j Shell
Pairing Interaction in N=Z Nuclei with Half-filled High-j Shell arxiv:nucl-th/45v1 21 Apr 2 A.Juodagalvis Mathematical Physics Division, Lund Institute of Technology, S-221 Lund, Sweden Abstract The role
More informationPygmy dipole resonances in stable and unstable nuclei
Pygmy dipole resonances in stable and unstable nuclei Xavier Roca-Maza INFN, Sezione di Milano, Via Celoria 16, I-2133, Milano (Italy) Collaborators: Giacomo Pozzi, Marco Brenna, Kazhuito Mizuyama and
More informationTemperature Dependence of the Symmetry Energy and Neutron Skins in Ni, Sn, and Pb Isotopic Chains
NUCLEAR THEORY, Vol. 36 (17) eds. M. Gaidarov, N. Minkov, Heron Press, Sofia Temperature Dependence of the Symmetry Energy and Neutron Skins in Ni, Sn, and Pb Isotopic Chains A.N. Antonov 1, D.N. Kadrev
More informationA MICROSCOPIC MODEL FOR THE COLLECTIVE RESPONSE IN ODD NUCLEI
Corso di Laurea Magistrale in Fisica A MICROSCOPIC MODEL FOR THE COLLECTIVE RESPONSE IN ODD NUCLEI Relatore: Prof. Gianluca COLÒ Correlatore: Prof.ssa Angela BRACCO Correlatore: Dott. Xavier ROCA-MAZA
More informationNuclear and Coulomb excitations of the pygmy dipole resonances
SPES Legnaro, 5-7 ovember uclear and oulomb excitations of the pygmy dipole resonances M. V. Andrés a), F. tara b), D. Gambacurta b), A. Vitturi c), E. G. Lanza b) a)departamento de FAM, Universidad de
More informationNucleon Pairing in Atomic Nuclei
ISSN 7-39, Moscow University Physics Bulletin,, Vol. 69, No., pp.. Allerton Press, Inc.,. Original Russian Text B.S. Ishkhanov, M.E. Stepanov, T.Yu. Tretyakova,, published in Vestnik Moskovskogo Universiteta.
More informationLaboratory, Michigan State University, East Lansing, MI 48824, USA. East Lansing, MI 48824, USA. Abstract
Constraints on the density dependence of the symmetry energy M.B. Tsang( 曾敏兒 ) 1,2*, Yingxun Zhang( 张英逊 ) 1,3, P. Danielewicz 1,2, M. Famiano 4, Zhuxia Li( 李祝霞 ) 3, W.G. Lynch( 連致標 ) 1,2, A. W. Steiner
More informationQuantum Theory of Many-Particle Systems, Phys. 540
Quantum Theory of Many-Particle Systems, Phys. 540 Questions about organization Second quantization Questions about last class? Comments? Similar strategy N-particles Consider Two-body operators in Fock
More informationNuclear Structure for the Crust of Neutron Stars
Nuclear Structure for the Crust of Neutron Stars Peter Gögelein with Prof. H. Müther Institut for Theoretical Physics University of Tübingen, Germany September 11th, 2007 Outline Neutron Stars Pasta in
More informationarxiv:nucl-th/ v1 6 Dec 2003
Observable effects of symmetry energy in heavy-ion collisions at RIA energies Bao-An Li arxiv:nucl-th/322v 6 Dec 23 Department of Chemistry and Physics P.O. Box 49, Arkansas State University State University,
More informationarxiv: v1 [nucl-th] 21 Sep 2007
Parameterization of the Woods-Saxon Potential for Shell-Model Calculations arxiv:79.3525v1 [nucl-th] 21 Sep 27 N.Schwierz, I. Wiedenhöver, and A. Volya Florida State University, Physics Department, Tallahassee,
More informationCorrelations between Saturation Properties of Isospin Symmetric and Asymmetric Nuclear Matter in a Nonlinear σ-ω-ρ Mean-field Approximation
Adv. Studies Theor. Phys., Vol. 2, 2008, no. 11, 519-548 Correlations between Saturation Properties of Isospin Symmetric and Asymmetric Nuclear Matter in a Nonlinear σ-ω-ρ Mean-field Approximation Hiroshi
More informationNuclear physics around the unitarity limit
Nuclear physics around the unitarity limit Sebastian König Nuclear Theory Workshop TRIUMF, Vancouver, BC February 28, 2017 SK, H.W. Grießhammer, H.-W. Hammer, U. van Kolck, arxiv:1607.04623 [nucl-th] SK,
More informationDirect reactions methodologies for use at fragmentation beam energies
1 Direct reactions methodologies for use at fragmentation beam energies TU Munich, February 14 th 2008 Jeff Tostevin, Department of Physics Faculty of Engineering and Physical Sciences University of Surrey,
More informationThe search for the nuclear symmetry energy in reaction dynamics
The search for the nuclear symmetry energy in reaction dynamics Giuseppe Verde INFN, Sezione di Catania, 64 Via Santa Sofia, I-95123, Catania, Italy E-mail: verde@ct.infn.it ABSTRACT This lecture is devoted
More informationFine structure of nuclear spin-dipole excitations in covariant density functional theory
1 o3iø(œ April 12 16, 2012, Huzhou, China Fine structure of nuclear spin-dipole excitations in covariant density functional theory ùíî (Haozhao Liang) ŒÆÔnÆ 2012 c 4 13 F ÜŠöµ Š # Ç!Nguyen Van Giai Ç!ë+
More informationThe liquid drop model
The liquid drop model Introduction to Nuclear Science Simon Fraser University Spring 2011 NUCS 342 January 10, 2011 NUCS 342 (Tutorial 0) January 10, 2011 1 / 33 Outline 1 Total binding energy NUCS 342
More information1 Introduction. 2 The hadronic many body problem
Models Lecture 18 1 Introduction In the next series of lectures we discuss various models, in particluar models that are used to describe strong interaction problems. We introduce this by discussing the
More informationBao-An Li. Collaborators: Bao-Jun Cai, Lie-Wen Chen, Chang Xu, Jun Xu, Zhi-Gang Xiao and Gao-Chan Yong
Probing High-Density Symmetry Energy with Heavy-Ion Reactions Bao-An Li Collaborators: Bao-Jun Cai, Lie-Wen Chen, Chang Xu, Jun Xu, Zhi-Gang Xiao and Gao-Chan Yong Outline What is symmetry energy? Why
More informationCoefficients and terms of the liquid drop model and mass formula
Coefficients and terms of the liquid drop model and mass formula G. Royer, Christian Gautier To cite this version: G. Royer, Christian Gautier. Coefficients and terms of the liquid drop model and mass
More informationNature of low-energy dipole states in exotic nuclei
Nature of low-energy dipole states in exotic nuclei Xavier Roca-Maza Università degli Studi di Milano, Via Celoria 16, I-133, Milano SPES One-day Workshop on "Collective Excitations of Exotic Nuclei" December
More information