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Sonja Orrigo

Sonja Orrigo. Correlation effects and continuum spectroscopy in light exotic nuclei. Unbound Nuclei Workshop, Pisa, Italy, November 3-5, 2008. Contents. Physical scenario: light exotic nuclei Correlations effects and continuum spectroscopy DCP correlations: Fano resonances

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Sonja Orrigo

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  1. Sonja Orrigo Correlation effects and continuum spectroscopy in light exotic nuclei Unbound Nuclei Workshop, Pisa, Italy, November 3-5, 2008

  2. Contents • Physical scenario: light exotic nuclei • Correlations effects and continuum spectroscopy • DCP correlations: Fano resonances • Experimental results on 11Be and 15C via CEX reactions • Pairing correlations in the continuum • Transfer reactions to unbound states: 9Li(d,p)10Li • Summary and conclusions

  3. Why correlation effects in light exotic nuclei? Peculiar conditions: • Large charge asymmetry • Weak binding of valence n • Proximity of s.p. continuum isovector interaction low density (halos) open quantum systems • Dissolution of shell structures • Influence of correlation dynamics light n-rich nuclei

  4. Continuum spectroscopy of light exotic nuclei • Two topics: • 15C: weakly-bound Sn = 1218 keV • effects due to the DCP correlation dynamics Fano Resonances • 10Li: n-unbound by 25 keV • effects due to pairing correlations • continuum spectroscopy by one-neutron transfer s.p. excitations • Dynamical Core Polarization • (DCP) correlations • Pairing correlations • Important to investigate their effects in the low-energy continuum

  5. Contents • Physical scenario: light exotic nuclei • Correlations effects and continuum spectroscopy • DCP correlations: Fano resonances • Experimental results on 11Be and 15C via CEX reactions • Pairing correlations in the continuum • Transfer reactions to unbound states: 9Li(d,p)10Li • Summary and conclusions

  6. Fano Resonances General phenomenon observed in many different areas of physics Atomic physics • H.Feshbach, Ann. of Phys.5 p. 357 (1958), Ann. of Phys.19 p. 287 (1962), Ann. of Phys. 43 p. 410 (1967) • F.H.Mies, Phys. Rev.175 p. 164 (1968) • A.F.Starace, Phys. Rev. B5 p. 1773 (1972) • A.K.Bhatia and A.Temkin, Phys. Rev. A29 p. 1895 (1984) • J.P.Connerade and A.M.Lane, Rep. on Progr. in Phys.51 p. 1439 (1988) Solid-state physics • S.Glutsch, Phys. Rev. B 66 p. 075310 (2002) Hadron physics N.E.Ligterink, PiN Newslett.16 p. 400 nucl-th/0203054 (2002) Nuclear physics G.Baur and H.Lenske, Nucl. Phys. A282 p. 201 (1977) Fano Resonances are investigated as a new continuum excitation mode in exotic nuclei

  7. Fano interference Fano interference quantum-mechanical interaction between discrete and continuous configurations asymmetric line shape • Originally detected in atomic spectra • 1960’s, Fano: first model for atomic states excited in theinelastic scattering e--atoms Typical for interacting many-body systems at all scales !

  8. Fano Resonances in nuclear physics Bound States Embedded in the Continuum (BSEC) • BSEC: narrow resonances in the continuum (Ex > Sn) • DCP model: BSEC as quasi-bound core-excited configurations • Experimental signature of the DCP correlations G.Baur and H.Lenske, Nucl. Phys. A 282(1977)201; H.Lenske et al., Jour. Progr. Part. Nucl. Phys.46(2001)187 • Predicted theoretically by Mahaux and Weidenmüller (1969) • C.Mahaux and H.A.Weidenmüller, Shell Model Approach to Nuclear Reactions, North-Holland, Amsterdam (1969) • 1st observed BSEC (1980): 13C (stable), Ex = 7.677 MeV (Jp = 3/2+) • H.Fuchs et al., Nucl. Phys. A 343(1980)133 And in exotic nuclei?

  9. In exotic nuclei • n-dripline nuclei: easily polarizable core BSEC at low-energy • C-isotopes: presence of low-energy 2+ core states good candidates • Importance of a systematic study H. Lenske, from HFB & QRPA calculations

  10. Fano Resonances in exotic nuclei 35 30 25 20 15 10 5 0 8.50 Single particle regime qlab = 14°, 55 keV/ch Counts 0.77 7.30 qL=8° 109 keV/ch Counts 8.50* 0.77* DCP regime 8.50 7.30 6.77 8.50* ]6.4 g.s.* 7.30* g.s. 15C Excitation energy [MeV] Sn 0 2 4 6 8 10 12 15C Excitation energy [MeV] 15N(7Li,7Be)15C @ 55 MeV Fano interference: BSEC – s.p. continuum S.E.A. Orrigo et al., Proceedings Varenna122 p. 147 (2003) F.Cappuzzello, S.E.A. Orrigo et al., EuroPhys. Lett.65 p. 766 (2004)

  11. 15N(7Li,7Be)15C @ 55 MeV Single particle regime 35 30 25 20 15 10 5 0 Counts 0.77 qlab = 14° 55 keV/ch 0.77* DCP regime 8.50 7.30 6.77 8.50* ]6.4 7.30* g.s.* g.s. Sn 0 2 4 6 8 10 12 15C Excitation energy [MeV] 10 2 10 1 10 2 10 1 dQRPA(w) [MeV -1] s. p. a) level density natural paritytransitions Results of microscopic QRPA calculations • 15C: Fano Resonances • Strong competition of mean-field and correlation dynamics • mean-field approaches are no longer appropriate • Enhanced correlation effects (Dynamical Core Polarization DCP) • new excitation modes involving core-excited configurations (BSEC) 0 2 4 6 8 10 12 14 15C Excitation energy [MeV] Sn dQRPA(w) [MeV -1] b) level density unnatural parity transitions s. p. Sn 0 2 4 6 8 10 12 14 15C Excitation energy [MeV] • Strength well reproduced for single particle transitions (1/2+ g.s., 5/2+ state at 0.77 MeV) • Observed fragmentation for Ex > 2 MeV not reproduced S.E.A. Orrigo et al., Proceedings Varenna122 p. 147 (2003); F.Cappuzzello, S.E.A. Orrigo et al., EuroPhys. Lett.65 p. 766 (2004)

  12. 11B(7Li,7Be)11Be @ 57 MeV Counts Single particle DCP regime Sn 0 1 2 3 4 5 6 7 8 11Be Excitation energy [MeV] dQRPA(w) [MeV -1] s. p. a) level density natural paritytransitions 0 2 4 6 8 10 12 14 11Be Excitation energy [MeV] dQRPA(w) [MeV -1] b) level density unnatural parity transitions s. p. 0 2 4 6 8 10 12 14 11Be Excitation energy [MeV] 7Be detected with the IPN-Orsay Split-Pole magnetic spectrometer QRPA calculations • Strength well reproduced for single particle transitions (1/2+ g.s., 1/2- state at 0.32 MeV and 5/2+ state at 1.77 MeV) • Observed fragmentation for Ex > 2 MeV not reproduced F.Cappuzzello, H.Lenske et al., Phys. Lett B 516(2001)21

  13. The QPC model Strength fragmentation not reproduced by QRPA DCP effects • QPC Hamiltonian of the odd-masssystem: coupled by V13 1QP 3QP 1QP states 3QP states • Core excitations: 2QP exc. given by QRPA • Quasiparticle-core coupling (QPC) model(Bohr & Mottelson) • DCP correlations described by coupling 1QP to the core-excited configurations H.Lenske, J. Phys. G: Nucl. Part. Phys.24 (1998) 1429 H.Lenske, C.M.Keil, N.Tsoneva, Progr.in Part. and Nucl.Phys. 53 (2004) 153

  14. Theoretical model QPC eigenstates: 1QP 3QP s.p. mixing E < 0 bound states E> 0 continuum BSEC (EC) Bound core-excited states (E – EC < 0) To study resonances in the low-energy continuum and their line shapes S.E.A.Orrigo, H.Lenske et al., Phys. Lett. B633 (2006) 469

  15. Theoretical model By projecting the Schrödinger equation onto the 1-QP and 3-QP components N coupled equations 1QP Channel 1 3QP Channels i = 2, …, N Ch. 11QP continuum Ch. i = 2, …, N 3QP states Coupling of a single particle elastic channel to closed core-excited channels S.E.A.Orrigo, H.Lenske et al., Phys. Lett. B633 (2006) 469

  16. Numerical methods 1QP Channel 1 (open) 3QP Channels i = 2, …, N (closed) r < RA r >> RA • Potentials Ui from HFB calculations • Transition form factors from QRPA calculations & data The coupled channels problem is solved in coordinate space N coupled equations for the radial wave functions S.E.A.Orrigo, H.Lenske et al., Phys. Lett. B633 (2006) 469

  17. Numerical methods 1) Internal w.f. by solving the NxN eigenvalue problem r < RA i = 1, …, N 2) Asymptotic w.f. r >> RA i = 1, …, N • Matching 2N equations with complex coefficients bm, C1i i = 1, …, N S.E.A.Orrigo, H.Lenske et al., Phys. Lett. B633 (2006) 469

  18. Results for 15C s-, p-, d-waves s11 [mb] 12 s - wave V13 0 p - wave 10 d - wave 8 Fano interference 6 4 2 0 0 5 10 15 20 25 30 15C excitation energy [MeV] s11 [mb] 12 s - wave V13= 0 p - wave 10 d - wave 8 6 4 2 0 0 5 10 15 20 25 30 15C excitation energy [MeV] • Elastic scattering cross section • Analytic calculation for 2 ch. • A single excited state of the 14C core: EC = 8.317 MeV • Ui from HFB • V13 is the only free parameter S.E.A.Orrigo, H.Lenske et al., Phys. Lett. B633 (2006) 469

  19. Results for 15C • Full 5-channels calculation • 4 14C states: EC(Jp) = 6.094(1–), • 6.728(3–), 7.012(2+), 8.317(2+) MeV • Ui from HFB • V13 weighted by b(i) of 14C(a,a’) JC   15C theo. (s11 d-wave) • V13 is the only free parameter 15C exp. from (7Li,7Be) • Qualitative comparison: • Eth. = 6.67, 7.36, 7.70, 8.92 MeV • Gth.= 66, 80, 141, 85 keV • Eexp. = (6.77, 7.30, 8.50)  0.06 MeV • Gexp. ≤ 160, 70, 140 keV • V13affectsG of the resonances (here V13 = 5 MeV) S.E.A.Orrigo, H.Lenske et al., Phys. Lett. B633 (2006) 469

  20. Results for 17C and 19C 70 d-wave 60 50 40 30 s11 [mb] s11 [mb] 20 10 17CSn = 0.73 MeV 19CSn = 0.16 MeV 0 0 2 4 6 8 10 12 100 d-wave 90 80 70 60 50 19C excitation energy [MeV] 17C excitation energy [MeV] 40 Increased effect of the correlations 30 BSEC structures move towards lower energies with increasing the neutron excess 20 10 0 0 2 4 6 8 10 12 • Systematic study of the evolution of the phenomenon when going towards more n-rich nuclei V13 is the only free parameter (here 5 MeV) State parameters by QRPA 16C states: EC(Jp) = 1.766(2+), 3.986(2+), 4.142(4+) MeV 18C states: EC(Jp) = 1.620(2+), 2.967(4+), 3.313(2+), 5.502(1–) MeV S.E.A. Orrigo, H.Lenske et al., Proceedings INPC07, Tokyo

  21. The (7Li,7Be) CEX reaction N a + 3 n • Structural properties: • Single particle isovector excitations • BSEC and Fano resonances • in the continuum • Reaction dynamics: • One-step / two-step contributions • Spin transfer probabilities • N = 1 7He • N = 2 11Be • N = 3 15C • N = 4 19O • N = 5 23Ne • N = 6 27Mg • … IPN-Orsay MAGNEX References: S.E.A. Orrigo et al.,Core excited Fano-resonances in exotic nuclei, Phis.Lett. B 633(2006)469 F.Cappuzzello, S.E.A. Orrigo et al., Excited states of 15C, EuroPhys.Lett.65(2004)766 F.Cappuzzello et al., Analysis of the 11B(7Li,7Be)11Be reaction at 57 MeV in a Microscopic Approach,Nucl.Phys. A 739(2004)30 S.E.A. Orrigo et al., Spectroscopy of 15C by (7Li,7Be) Charge Exchange Reaction, Proc. “10th Int. Conf. on Nuclear Reaction Mechanisms” , Varenna, Italy, 122(2003)147 C.Nociforo et al., Investigation of light neutron-rich nuclei via the (7Li,7Be) reaction, Acta Physica Polonica, B 34(2003)2387 F.Cappuzzello et al., Excited states of 11Be, Phys.Lett B 516(2001)21

  22. MAGNEX Upper bent limits E < 30 AMeV 2 < A < 40 E < 25 AMeV 40 < A < 93 A.Cunsolo et al., NIMA 481 (2002) 48 A.Cunsolo et al., NIMA 484 (2002) 56

  23. 19F(7Li,7Be)19O @ 52.4 MeV g.s. E/DE ~ 1000 96 keV 19O qlab = 7° - 19.5° W = 50 msr Energy byte = ± 27% PRELIMINARY Counts 19.8 keV/ch Xfoc [m] Sn = 3.9 MeV

  24. Contents • Physical scenario: light exotic nuclei • Correlations effects and continuum spectroscopy • DCP correlations: Fano resonances • Experimental results on 11Be and 15C via CEX reactions • Pairing correlations in the continuum • Transfer reactions to unbound states: 9Li(d,p)10Li • Summary and conclusions • Single particle dynamics: the relevant energy scale is Sn-l-D • Stable nuclei: Sn~10MeV • → static MF in the p-h channel + paring for the p-p correlations • Weakly-bound n-rich nuclei: Sn~few keV-MeV • → pairing correlations in the p-h channel are also important

  25. Theory of Pairing in the Continuum • Similarity between the Pairing and DCP approaches • Particle-stable system: lq<0 • ea-<0 , hole w.f. va decaying exponentially for r»RA • In the continuum ea+>0, particle w.f. ua like a scattering wave: • Extended MF approach for pairing in weakly-bound or unbound nuclei • 2x2 coupled channel problem described by the Gorkov equations • H.Lenske, F.Hofmann, C.M.Keil, J. Progr. Part. Nucl. Phys.46(2001)187 • Particle channel (open) • Hole channel (closed)

  26. Theory of Pairing in the Continuum Relationship scattering observables – pairing strength • Continuum level density: spectral distribution of particle strength per energy E • = Density of states • Partial wave elastic scattering cross section: Resonances in resonances in sℓj • Observables involving the states ua will show a characteristic energy dependence • (e.g., transfer cross sections through Sa(E)) • The same type of effects is produced by any types of correlations (e.g., DCP → Fano) S.E.A. Orrigo and H. Lenske, submitted to PLB (2008)

  27. Neutron s.p. spectral functions in 9Li E<0 hole sector E>0 particle sector • Effects of the dynamical correlations (particle-hole coupling) due to the pairing field • The widths of the hole distributions (E<0) are due to the bound-continuum coupling • The deeper-lying s-wave levels are coupled more efficiently to the particle continuum • The 5/2+d-wave strength is lowered into the bound state sector (intruder component) • A small amount of 1/2+ and 3/2+ strengths is above the p½ peak • Dramatic change in dynamics at the n-dripline: the level ordering is not determined by simple MF S.E.A. Orrigo and H. Lenske, submitted to PLB (2008)

  28. Partial wave cross sections for elastic scattering 9Li+n The structure results are used as input for transfer reaction calculations • Comparison: full HFB Gorkov-pairing – bare MF calculations • Pairing gives an attractive self-energy in the p-wave channels • → 1/2– and 3/2– resonances at very low energy (E<<3MeV ~ threshold for DCP correlations) • Slight attraction in the 1/2+ channel and repulsion for the d-waves S.E.A. Orrigo and H. Lenske, submitted to PLB (2008)

  29. Continuum spectroscopy of 10Li by transfer reactions • Transfer reactions well established tool for structural studies of bound and exotic nuclei • Weakly-bound final state: prevalence of small momentum components the cross section maximum is at much lower incident energies H. Lenske and G. Schrieder, Eur. Phys. J2 (1998) 41 • Single-nucleon transfer reactions as a tool for continuum spectroscopy in exotic nuclei • Study of the low-energy s.p. resonances in unbound systems also • Method based on a DWBA approach.Main innovations: to treat the case of unbound final states and to calculate the double differential cross section for one-neutron transfer • The model is applied to the 9Li(d,p)10Li reaction to explore the structure of 10Li 10Li is neutron-unbound by 25 ± 15 keV

  30. Why 10Li? • Crucial for the comprehension of the structure of 11Li as a three body system • (11Li is a Borromean 2-n-halo nucleus) • Information on the n-9Li interaction, important for the theoretical models of 11Li • Interest in the structure of 10Li itself: low-lying states are not yet well known • Ground state: p-wave or s1/2 virtual state at the n+9Li threshold? • 4 states are expected at low energy with Jp = 1−, 2− and 1+, 2+ • (neutron in 2s1/2 or 1p1/2unpaired 1p3/2 proton of the 9Li core) • Two resonances seen at Ex~ 250 and 500 keV; several resonances at higher Ex D.R. Tilley et al., Nucl. Phys. A 745 (2004) 155 and refs. therein • Interest in the 9Li(d,p)10Li reaction in inverse kinematics: • experiments at MSU @ 20 AMeV (P. Santi at al., Phys. Rev. C 67 (2003) 024606) resonance at ~ 350 keV with G~ 300 keV • experiments at REX-ISOLDE @ 2.36 AMeV (H.B. Jeppesen et al., Phys. Lett. B642 (2006) 449) resonance at ~ 380 keV with G~ 200 keV

  31. Theory for transfer reactions -36.14 • Transfer reaction A(a,b)B (a = b+x, B = A+x) in a DWBA approach [Satchler] • Optical model Hamiltonians and DW Schroedinger equations: • Ha = HA + Ha + Ka + Ua + Va (a = a+A) ; Hb = HB + Hb + Kb + Ub + Vb (b = b+B) • (Kg + Ug – Eg) cg(±) (rg, kg) = 0 (g = a, b) • The optical model wave functionscg(±) (rg, kg) describe the elastic scattering determined • by the optical potentials Ug at the channel energies Eg = E – eA – ea Hinterberger Menet d-potentials p-potentials NPA111(1968) PRC4(1971) Residual interaction Vb (post) chosen according to effective self-energy (full HFB Gorkov-pairing), it reproduces B.E., rM, rC of 9Li

  32. Theory for transfer reactions • for a fixed energy • In the post representation for a stripping reaction in which x is transferred from a to B: • Fba = JB MB sb mb | V | JA MA sa ma = • =Sjl (Sjl)½ Rjl(rxA)(l s m m – m | j m)(sb s mb ma – mb | sa ma)(JA j MA MB – MA | JB MB)D(rxb) Ylm*( ) • spectroscopic amplitude radial wave function for the transferred particle x • projectile internal function times x-b interaction potential • Zero-Range Approximation: • D(rxb) = D0d(rx – rb)Tba = D0 (Sb)½cb(–) | R(rx)Y*( ) d(rx – rb) | ca(+) • which contains dynamics and structure information ˆ r xA • First order DWBA transition amplitude: • Tba = cb(–) | Fba | ca(+) • Fba = bB|V|aAform factor

  33. Theory for transfer reactions to unbound states Double differential cross section for one-nucleon transfer to unbound final states Momentum distribution (Dynamics: Fourier transform of the wave function) Spectral function (Structure: probability per energy for finding the particle in state ℓj at energy E) • Transfer into the continuum: • The B = A+x final states are unbound against the reemission of the nucleon x (ex< 0) • the overlap form factor oscillates at large distances • the DWBA radial integrals converge very slowly • Vincent and Fortune: • powerful method of contour integration in the complex radius plane to overcome the convergence problem C.M. Vincent and H.T. Fortune, PRC2(1970); PRC7(1973); PRC8(1973) S.E.A. Orrigo and H.Lenske, submitted to PLB (2008)

  34. Spectroscopy of 10Li = 9Li+n at the continuum threshold ds[mb/MeV] dE 16 Angle-integrated cross sectiond(9Li,10Li)p @ 2.36 AMeV Total d(9Li,10Li)p qcm = [98°,134°] data 14 1/2+ 3/2- 1/2- 12 5/2+ 3/2+ 10 S.E.A. Orrigo and H. Lenske, submitted to PLB (2008) 8 H.B. Jeppesen et al., PLB 642(2006)449 ER~ 380 keV, G~ 200 keV 6 4 2 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 E [MeV] • p1/2 resonance at ER = 400 keV Mainly a potential resonance • p3/2 resonance at ER = 850 keV Coupled-channels pairing resonance • New feature essential to describe data • obtained by adding a polarization repulsive surface potential (acting in DE~250keV around ER) to reproduce the full HFB Gorkov-pairing results • The theoretical results include the experimental energy resolution GFWHM~250keV • Good agreement with data (shape and resonances position)

  35. Angular distributions Angular distributionsd(9Li,10Li)p @ 2.36 AMeV 100 Total ds [mb/sr] dW data d(9Li,10Li)p 1/2+ 3/2- 1/2- 5/2+ 10 3/2+ S.E.A. Orrigo and H. Lenske, submitted to PLB (2008) H.B. Jeppesen et al., PLB 642(2006)449 ER~ 380 keV, G~ 200 keV 1 0.1 0 20 40 60 80 100 120 140 160 180 qcm [deg.] • Good agreement with data (no scaling) • The p1/2-wave is dominant • As expected, transfer is favoured at low incident energies: • calculations @ 20 AMeV (MSU exp.) →stransfer at ER(p1/2) is lowered by a factor of 26 • The measurement of angular distributions is important to identify the 10Li states (ℓp values)

  36. Transfer 9Li(d,p)10Li @ 2.36 AMeV, before folding, qcm =[98°,134°] dsR[mb/MeV] dE 12 • Same structure for selastic and stransfer: a physical resonance appears in both dℓj(E) [°]→ Sℓj(E) Access to the spectroscopic information by transfer • However, in stransfer there can be not physical resonances also, due only to the reaction dynamics part p1/2 p3/2 10 8 6 4 140 2 120 0 0 0.2 0.4 0.6 0.8 1 100 E [MeV] dsE[mb/MeV] dE 80 8000 p1/2 E [MeV] 60 p3/2 7000 40 6000 5000 20 4000 0 0 0.2 0.4 0.6 0.8 1 3000 2000 1000 0 0 0.2 0.4 0.6 0.8 1 E [MeV] • Elastic scattering n+9Li (p-wave) S.E.A. Orrigo and H. Lenske, submitted to PLB (2008)

  37. Spectral distribution ↔ properties of n-9Li interaction 18000 Elastic scattering n+9Li (p1/2-wave) 16000 dsE[mb/MeV] dE c, R c + 10% c – 10% R + 10% R – 10% 14000 12000 10000 8000 E [MeV] 6000 Information on the residual n-9Li interaction 4000 2000 0 0 0.2 0.4 0.6 0.8 1 • Variations by ±10% of the potential • diffuseness c and radius R • IVol = 486.62 (AMeV)·fm3 = constant • p1/2-wave:ER, G strongly sensitive to c • (asymptotic shape of potential, halo tail) • Scattering length as = 1.69 fm • (c+10%)=1.68 fm, (c-10%)=1.72 fm • (R+10%)=2.21 fm, (R-10%)=1.06 fm • s1/2-wave: larger sensitivity to R • (no centrifugal barrier) S.E.A. Orrigo and H. Lenske, submitted to PLB (2008)

  38. Summary • Fano resonancescan be expected to be of particular importance for the continuum dynamics of exotic nuclei • The coupled channels model extends the QPC into the continuum: the interference between open 1-QP and closed 3-QP ch. gives sharp and asymmetric resonances (G→V13) • The calculations performed for 15C, 17C, 19C show increased effects of correlations • Exp. evidence of DCP correlations in the 15C spectra, qualitatively reproduced by theoretical calculations, and in the 11Be and 19O spectra • Transfer reactions are a powerful tool to do continuum spectroscopy in exotic nuclei • Innovations of the DWBA approach: to treat unbound final states and to calculate d2s/dWdE • Calculations performed for the d(9Li,10Li)p reaction at ELi = 2.36 and 20 AMeV • 10Li continuum: p1/2-resonance at ~400 keV and p3/2-pairing resonance at~850 keV in very good agreement with experimental data • Same behaviour of selastic and stransfer: same structure Sa(E) • Correlation: spectral distributions ↔ n-9Li interaction (sensitivity to the halo tail)

  39. Summary • Pairing in unbound nuclear states explored in terms of an extended MF approach • Paring effects may introduce pronounced structures and shifts in the low-energy continuum of all the channels • Configuration mixing acts at the MF level, but mechanisms similar to the mixing due to dynamical correlations Analogy: Configuration Mixing due to 15C continuum = n+14C, BSEC = n+14C* core polarization (DCP) 10Li continuum = n+9Li unbound, (particle-hole) pairing correlations (MF-level) ☺ Thank you for your attention ☺

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