Short- and long-range correlations in nuclear pairing phenomena

Transcription

1 Short- and long-range correlations in nuclear pairing phenomena Ding, Rios, et al., Phys Rev C (26) Arnau Rios Huguet Lecturer in Nuclear Theory Department of Physics University of Surrey ECT Superfluids Workshop, 23 March 27

2 Summary. Neutron star motivation 2. Reminder of nuclear BCS 3. Beyond-BCS with SCGF methods 4. Dineutrons 2

3 Neutron star modeling Input # EoS Observable # Mass-Radius relation Input #2 Pairing gap Observable #2 Cooling curve superfluid Input #3 Crust-core Observable #3 Glitching Frequency crust spindown Time 3

4 Neutron star modeling Observable # Mass-Radius relation Input Consistent many-body theory Observable #2 Cooling curve superfluid Observable #3 Glitching Frequency crust spindown Time 3

5 Cooling of Car A Cas A data Ho, et al., PRC (25) Page, et al., PRL 6 8 (2) Ingredients (a) Mass of pulsar (b) EoS (determines radius) (c) Internal composition (d) Pairing gaps ( S & 3 PF2 channels) (e) Atmosphere composition Ho, Elshamouty, Heinke, Potekhin PRC (25) 4

6 Bayesian inversion is coming Beloin, Han, Steiner & Page, arxiv: Ingredients (a) Mass of pulsar (b) EoS (determines radius) (c) Internal composition (d) Pairing gaps ( S & 3 PF2 channels) < Bayesian inversion from data (e) Atmosphere composition 5

7 Summary. Neutron star motivation 2. Reminder of nuclear BCS 3. Beyond-BCS with SCGF methods 4. Dineutrons 6

8 Bardeen-Cooper-Schrieffer pairing 3. S Neutron matter BCS gaps 3 PF2 Pairing gap, F [MeV] Fermi momentum, k F [fm - ] BCS equation Fermi momentum, k F [fm - ] CDBONN AV8 N3LO Dean & Hjorth-Jensen, Rev. Mod. Phys (23) + Single-particle spectrum choice: Angular gap dependence: " k = k2 2m + U(k) µ k 2 = X L k 2 L Maurizio, Holt & Finelli, Phys. Rev. C 9, 443 (24) 7

9 Bardeen-Cooper-Schrieffer pairing 3. S Neutron matter BCS gaps 3 PF2 Pairing gap, F [MeV] Fermi momentum, k F [fm - ] BCS equation Fermi momentum, k F [fm - ] CDBONN AV8 N3LO Dean & Hjorth-Jensen, Rev. Mod. Phys (23) + Single-particle spectrum choice: Angular gap dependence: " k = k2 2m + U(k) µ k 2 = X L k 2 L Maurizio, Holt & Finelli, Phys. Rev. C 9, 443 (24) 7

10 Bardeen-Cooper-Schrieffer pairing 3. S Neutron matter BCS gaps 3 PF2 Pairing gap, F [MeV] Fermi momentum, k F [fm - ] BCS equation Fermi momentum, k F [fm - ] CDBONN AV8 N3LO Dean & Hjorth-Jensen, Rev. Mod. Phys (23) + Single-particle spectrum choice: Angular gap dependence: " k = k2 2m + U(k) µ k 2 = X L k 2 L L k 2 Maurizio, Holt & Finelli, Phys. Rev. C 9, 443 (24) 7

11 Triplet pairing: phase shift equivalence Momentum, q 2 [fm - ] Momentum, q 2 [fm - ] Momentum, q 2 [fm - ] P2 CDBonn 3 P2 Av8 3 P2 N3LO Momentum, q [fm - ] δ [deg] δ [deg] δ [deg] NN phase shifts 3 P2 3 F2 Nij par SAID Nij data CDBonn Av8 N3LO ε q bin [fm - ] Pairing gap, [MeV].. Neutron matter BCS gaps 3 PF2 CDBonn Av8 N3LO Fermi momentum, k F [fm - ] Srinivias & Ramanan, PRC (26) 8

12 NN forces from EFTs of QCD c i c i π O ˆQ GeV Chiral perturbation theory π and N as dof Systematic expansion 2N at N 3 LO - LECs from πn, NN 3N at N 2 LO - 2 more LECs (Often further renormalized) c i Weinberg, Phys. Lett. B (99), NPB (99) Entem & Machleidt, PRC 68, 4(R) (23) Tews, Schwenk et al., PRL, 3254 (23) Epelbaum, Frebs & Meissner, PRL 5, 223 (25) 9

13 NN forces from EFTs of QCD c i c i π O ˆQ GeV Chiral perturbation theory π and N as dof Systematic expansion 2N at N 3 LO - LECs from πn, NN 3N at N 2 LO - 2 more LECs (Often further renormalized) c i Weinberg, Phys. Lett. B (99), NPB (99) Entem & Machleidt, PRC 68, 4(R) (23) Tews, Schwenk et al., PRL, 3254 (23) Epelbaum, Frebs & Meissner, PRL 5, 223 (25) 9

14 Uncertainties at the BCS + HF level Hard R=.9 fm R=. fm R=. fm R=.2 fm Soft Drischler, Kruger, Hebler, Schwenk, PRC (27)

15 Uncertainties at the BCS + HF level Hard R=.9 fm R=. fm Srinivias & Ramanan, PRC (26) R=. fm R=.2 fm Soft Drischler, Kruger, Hebler, Schwenk, PRC (27)

16 Summary. Neutron star motivation 2. Reminder of nuclear BCS 3. Beyond-BCS with SCGF methods 4. Dineutrons

17 Why short-range correlations? Deuteron momentum distribution n d (k) [GeV 3 ] Av8 CDBONN N3LO Av4 θ=8 o, <Q 2 >=2.7 θ=22 o, <Q 2 >=3.8 θ=26 o, <Q 2 >=4.8 θ=32 o, <Q 2 >= k [MeV] Fomin et al., PRL (22) Inclusive quasi-elastic e - scattering vs NN potential theory 2

18 Why short-range correlations? Deuteron momentum distribution n d (k) [GeV 3 ] Tensor Av8 CDBONN N3LO Av4 θ=8 o, <Q 2 >=2.7 θ=22 o, <Q 2 >=3.8 θ=26 o, <Q 2 >=4.8 θ=32 o, <Q 2 >= k [MeV] Fomin et al., PRL (22) Inclusive quasi-elastic e - scattering vs NN potential theory 2

19 Why short-range correlations? Deuteron momentum distribution n d (k) [GeV 3 ] Tensor k [MeV] Av8 CDBONN N3LO Av4 θ=8 o, <Q 2 >=2.7 θ=22 o, <Q 2 >=3.8 θ=26 o, <Q 2 >=4.8 θ=32 o, <Q 2 >=6.4 SRC Fomin et al., PRL (22) Inclusive quasi-elastic e - scattering vs NN potential theory 2

20 SCGF Ladder approximation In-medium interaction Ladder self-energy Self-consistent resummation Energy and momentum T (Matsubara) pp & hh Pauli blocking Dyson equation T-matrix at T=5 MeV Re T(Ω + ; P,q=) [MeV fm3] One-body properties Momentum distribution Thermodynamics & EoS Transport Spectral function 4 P [MeV] 2 2 Ramos, Polls & Dickhoff, NPA 53 (989) Alm et al., PRC (996) Dewulf et al., PRL (23) Frick & Muther, PRC (23) Rios, PhD Thesis, U. Barcelona (27) Soma & Bozek, PRC (28) Rios & Soma PRL 8 25 (22) 3 Ω 2µ [MeV] 2

21 Advantages All kinds of NN interactions 3N interactions Short-range & tensor correlations Density & isospin dependence Access to off-shell spectral function Thermodynamically consistent Limitations Non-relativistic Missing diagrams? No nuclear surface 4

22 Quantitative SRC Av8 - k= (a) N3LO+SRG+3NF k= (d) - Energy weighted sum rules A(k,ω) [MeV - ] A(k,ω) [MeV - ] A(k,ω) [MeV - ] k=k F (b) k=2k F (c) Energy, ω µ [MeV] k=k F (e) k=2k F (f) Energy, ω µ [MeV] m () k = m () k = m (2) k = Z Z Z sf variance 2 k = 2 k = Z + d! 2 A k(!) = d! 2!A k(!) = ~2 k 2 2m + k h i 2 + Z + d! 2!2 A k (!) = d! 2 [! m () k 2 k m() k ]2 A k (!) d! Im k(!) Rios, Carbone, Polls, arxiv:

23 Quantitative SRC m (2) k moment [MeV2 ] 5x 4 4x 4 3x 4 2x 4 x 4 N3LO+SRG+3NF Sum rule [m k () ] 2 σ k 2 Av8 (d) Energy weighted sum rules m () k = m () k = m (2) k = Z Z Z d! 2 A k(!) = d! 2!A k(!) = ~2 k 2 2m + k h i 2 + d! 2!2 A k (!) = m () k 2 k m (2) k moment [MeV2 ] 3x 5 2x 5 x 5 (f) Momentum, k [MeV] sf variance 2 k = 2 k = Z + Z + d! 2 [! m() k ]2 A k (!) d! Im k(!) Rios, Carbone, Polls, arxiv:

24 Momentum distribution Single-particle occupation Momentum distribution, n(k) npkq A a : k a k Momentum, k/k F E ρ=.6 fm -3, T= MeV Av8 CD-Bonn N3LO FFG ª d 3 k npkq p2 q3 ρ=.6 fm -3, T= MeV Neutron matter Momentum, k/k F Momentum distribution, n(k) SNM: -3% depletion at low k, population at high k Dependence on NN interaction under control PNM: 4-5% depletion at low k 6

25 T= extrapolations Spectral function, A(k,ω) k= Av8 k F =.33 fm - k=k F T= MeV T=4 MeV T=5 MeV T=6 MeV T=8 MeV T=9 MeV T= MeV T= MeV T=2 MeV T=4 MeV T=5 MeV T=6 MeV T=8 MeV T=2 MeV k=2k F ω µ [MeV] ω µ [MeV] ω µ [MeV] 2 26 Temperature, T [MeV] E/A [MeV]... Density, ρ [fm -3 ] T [MeV] 2 7

26 Available data Av8 2 Temperature, T [MeV] Density, ρ [fm -3 ] Self-energy, spectral function & thermodynamics 8

27 Neutron matter Pressure [MeV fm -3 ] EoS for neutron matter: SRG Density, ρ [fm -3 ] Tolman-Oppenheimer-Volkov dp G pm`4 pr 3 qp ` pq dr c 2 rpr 2Gm{c 2 q dm dr 4 c 2 r2 Error band from fits in ChPT c, c 3 parameters Finite temperature & higher densities available Mass, M (Solar Masses) Radius, R (km) Carbone, Polls & Rios, PRC (24) A. Carbone, Drischler, Hebeler, Schwenk, PRC (26) GR P < Causality 9

28 Neutron matter Pressure [MeV fm -3 ] EoS for neutron matter: SRG Density, ρ [fm -3 ] Tolman-Oppenheimer-Volkov dp G pm`4 pr 3 qp ` pq dr c 2 rpr 2Gm{c 2 q dm dr 4 c 2 r2 Error band from fits in ChPT c, c 3 parameters Finite temperature & higher densities available Hebeler, Lattimer, Pethick, Schwenk ApJ 773 (23) Carbone, Polls & Rios, PRC (24) A. Carbone, Drischler, Hebeler, Schwenk, PRC (26) 9

29 Beyond BCS : SRC BCS is lowest order in Gorkov Green s function expansion T-matrix can be extended to paired systems Bozek, Phys. Rev. C (2); Muether & Dickhoff, Phys. Rev. C (25) 2

30 Beyond BCS : SRC Normal state BCS is lowest order in Gorkov Green s function expansion T-matrix can be extended to paired systems Bozek, Phys. Rev. C (2); Muether & Dickhoff, Phys. Rev. C (25) 2

31 Beyond BCS : SRC Normal state Superfluid Δ(kF) BCS is lowest order in Gorkov Green s function expansion T-matrix can be extended to paired systems Bozek, Phys. Rev. C (2); Muether & Dickhoff, Phys. Rev. C (25) 2

32 Beyond BCS : SRC Normal state? Superfluid Δ(kF) BCS is lowest order in Gorkov Green s function expansion T-matrix can be extended to paired systems Bozek, Phys. Rev. C (2); Muether & Dickhoff, Phys. Rev. C (25) 2

33 BCS gap equation + BCS+SRC gap equation L k = X Z L k hk V LL nn k i 2 p 2k L + k 2 2 k = Z! Z k +! f(!) f(! )! +! A(k,!)A s (k,! ) Gorkov gap equation L k = X Z L k hk V LL nn 2 k 2 k = k i Z! Z L k +! f(!) f(! )! +! A(k,!)A s (k,! ) Muether & Dickhoff, Phys. Rev. C (25) 2

34 BCS gap equation + BCS+SRC gap equation L k = X Z L k hk V LL nn k i 2 p 2k L + k 2 2 k = Z! Z k +! f(!) f(! )! +! A(k,!)A s (k,! ) Gorkov gap equation L k = X Z L k hk V LL nn 2 k 2 k = k i Z! Z L k +! f(!) f(! )! +! A(k,!)A s (k,! ) Muether & Dickhoff, Phys. Rev. C (25) 2

35 Beyond BCS : SRC 2 k = Z! Z Full off-shell! f(!) f(! )! +! A(k,!)A(k,! ) Quasi-particle BCS 2 k = 2 " k µ Denominator, χ(k) [MeV] Momentum, k/k F T= MeV T=4 MeV T=5 MeV T=6 MeV T=8 MeV T=9 MeV T= MeV T= MeV T=2 MeV T=4 MeV T=5 MeV T=6 MeV T=8 MeV T=2 MeV qp denominator, χ qp (k) [MeV] Av8 k F =.33 fm Momentum, k/k F 22

36 Beyond BCS : 3 SD Symmetric matter 3 SD pairing gap Pairing gap, [MeV] BCS CDBonn BCS Av8 SRC CDBonn SRC Av Fermi momentum, k F [fm - ] Massive gaps 3 SD channel but No evidence of strong np nuclear pairing Short-range correlations deplete gap 3BF effect? Short-range effects? Muether & Dickhoff, PRC (25) Maurizio, Holt & Finelli, PRC 9, 443 (24) 23

37 Beyond BCS : SRC Neutron matter CDBonn Av8 N3LO 3 S S S Pairing gap, [MeV] S BCS SRC Fermi momentum, k F [fm - ].5..5 Fermi momentum, k F [fm - ].5..5 Fermi momentum, k F [fm - ] PF2 BCS SRC CDBonn Av8 N3LO Pairing gap, [MeV] PF2 3 PF2 3 PF2. BCS+SRC Fermi momentum, k F [fm - ] L k = X Z L k hk V LL nn k i 2 p 2k L + k Fermi momentum, k F [fm - ] k + 2 k = Z! Z Fermi momentum, k F [fm - ]! f(!) f(! )! +! A(k,!)A s (k,! ) 24

38 Beyond BCS 2: LRC? ph recoupled G-matrix Effective Landau parameters V pair = h V i = 4 X 2,2 X ( ) S (2S + )h2 G ph ST 2 ph i A h2 G ST 2 i A (22 ) S,T ST (q) = ST (q) ST (q) F ST Bare NN potential only is not the only possible interaction Diagram (a): nuclear interaction Diagram (b): in-medium interaction, density and spin fluctuations Diagram (c): included by Landau parameters Cao, Lombardo & Schuck, Phys Rev C (26) 25

39 Landau parameters Landau parameters.6 F.4 G F.2 /(+F )+G /(+G ) Fermi momentum, k F [fm - ] Diagonal V [MeVfm -3 ] Diagonal V [MeVfm -3 ] 3 S Bare (a) P (b) Momentum, k [fm - ] Effective V S= LRC V S= LRC (c) (d) Momentum, k [fm - ] 26

40 Landau parameters Landau parameters.6 F.4 G F.2 /(+F )+G /(+G ) Fermi momentum, k F [fm - ] Diagonal V [MeVfm -3 ] Diagonal V [MeVfm -3 ] 3 S Bare (a) P (b) Momentum, k [fm - ] Effective V S= LRC V S= LRC (c) (d) Momentum, k [fm - ] 26

41 Beyond BCS 2: results S Neutron matter CDBonn Av8 N3LO 3 S S S Pairing gap, [MeV] S BCS SRC SRC+LRC Fermi momentum, k F [fm - ].5..5 Fermi momentum, k F [fm - ].5..5 Fermi momentum, k F [fm - ] Pairing gap, [MeV] PF2 BCS SRC SRC+LRC 3 PF2 CDBonn 3 PF2 Av8 3 PF2 N3LO Fermi momentum, k F [fm - ] Fermi momentum, k F [fm - ] Fermi momentum, k F [fm - ] LRC S ( 3 PF2) produces (anti-)screening 27

42 Summary Pairing gap, [MeV] N3LO (c) S Pairing gap, [MeV]... N3LO 3 PF2 (c) BCS BCS+LRC SRC SRC+LRC Fermi momentum, k F [fm - ] Fermi momentum, k F [fm - ] JST pk F k q 2 pk F k 2 q 2 L pk F q pk F k q 2 ` k pk F k 2 q 2 ` k 3 Δ k k k2 k3 CDBonn Singlet Av N3LO CDBonn Triplet Av N3LO

43 Ladder approximation with 3BF Two-body interaction Effective interactions 2 In-medium T-matrix = + In-medium T-matrix = + Self-energy Self-energy Dyson equation 2 Carbone et al., PRC (23) A. Carbone, PhD Thesis 29

44 Ladder approximation with 3BF Two-body interaction Effective interactions 2 In-medium T-matrix = + In-medium T-matrix = + Self-energy Self-energy Dyson equation 2 Carbone et al., PRC (23) A. Carbone, PhD Thesis 29

45 3BF effect: estimate Pairing gap, [MeV] S (a) BCS NN SRC NN BCS NN+3NF SRC NN+3NF spectrum 2 NN forces Pairing gap, [MeV]. 3 PF2 (b) Singlet gap: 3NF reduce closure Triplet gap: 3NF increase gap Model dependence to be explored SRG dependence for systematics Fermi momentum, k F [fm - ] 3

46 BCS+HF level Singlet gaps with 3NF Triplet gaps with 3NF Drischler, Kruger, Hebler, Schwenk, PRC (27) 3

47 Beyond BCS pairing: overview S 3 PF2 Pairing gap, F [MeV] BCS N3LO BCS CDBONN BCS AV8 N3LO CDBONN AV8 CCDK GIPSF CLS MSH SFB SCLBL BCS N3LO BCS CDBONN BCS AV8 N3LO CDBONN AV8 SYHHP EEHOr EEHO AO Fermi momentum, k F [fm - ] Fermi momentum, k F [fm - ] Effect is robust: independent of NN potential 3NF effect not included in SRC, BCS indicates small Singlet results very close to Cao+Lombardo+Schuck Triplet results are significantly different 32

48 Beyond BCS pairing: overview S 3 PF2 Pairing gap, F [MeV] BCS N3LO BCS CDBONN BCS AV8 N3LO CDBONN AV8 CCDK GIPSF CLS MSH SFB SCLBL BCS N3LO BCS CDBONN BCS AV8 N3LO CDBONN AV8 SYHHP EEHOr EEHO AO Fermi momentum, k F [fm - ] Fermi momentum, k F [fm - ] Effect is robust: independent of NN potential 3NF effect not included in SRC, BCS indicates small Singlet results very close to Cao+Lombardo+Schuck Triplet results are significantly different 32

49 Summary. Neutron star motivation 2. Reminder of nuclear BCS 3. Beyond-BCS with SCGF methods 4. Dineutrons 33

50 Dineutrons BHF G-matrix.2 bnn [ MeV ] AV8 Paris N3LO 2N N3LO 2N +N2LO 3N Poles kf=.6 fm - <r> [ fm ] 2 8 AV8 Paris N3LO 2N N3LO 2N +N2LO 3N r 2 Ψ 2 [ fm - ].2. Deuteron (free space) AV8 Paris N3LO 2N N3LO 2N +N2LO 3N k F [ fm - ] 2 3 r [ fm ] Isaule, Arellano, Rios, in preparation 34

51 Collaborators +A. Carbone +D. Ding, W. H. Dickhoff +A. Polls UNIVERSITAT DE BARCELONA U B +C. Barbieri +V. Somà +H. Arellano, F. Isaule 35

52 Conclusions Ab initio nuclear theory to treat correlations Talk to us if you need quantitative predictions! Different NN forces provide robust predictions Challenges ahead Full self-consistent Gorkov Consistent treatment of LRC Pairing in isospin asymmetric 36