1. Jose Javier Valiente Dobón (INFN-LNL, Italy) Lifetime measurements around the doubly-magic 48 Ca nucleus

2. Overview Lifetime measurements of neutron-rich nuclei via MNT: RDDS + CLARA +PRISMA Results for N=30 isotones ( 50 Ca, 51 Sc) Result for the N=28 46 Ar Summary

3. Grazing reactions Tool to populate neutron-rich nuclei Target Beam Grazing Target-like Grazing Beam-like LAB. Substantial kinetic energy damping and mass exchange while retaining partial memory and entrance-channel masses and charges 82 Se + 238 U, E=505 MeV Fission 238 U G.de Angelis, G.Duchêne

4. PRISMA The CLARA-PRISMA setup Gamma spectrometer CLARA Magnetic spectrometer PRISMA CLARA Laboratori Nazionali di Legnaro (INFN), Italy

5. The CLARA spectrometer 23 Euroball Clover detectors with anti-Compton (Eff. ~ 3.0 %) FWHM = 0.9% (for β=10%)  spectrum CLARA spectrometer

6. The PRISMA spectrometer Formed by 1 Quadrupole, 1 Dipole and detectors (MCP, MWPPAC, IC) to track the ions. ΔΩ = 80 msr, ΔZ/Z  1/60, ΔA/A  1/190, Bρ = 1.2 T.m Identifies nuclei produced in the reaction (A,Z,β) event by event PRISMA spectrometer Large-acceptance magnetic spectrometer

7. Target-Degrader setup Degrader Target Beam Plunger setup Ta:1mg/cm 2 208 Pb:1mg/cm 2 nat Mg: 4mg/cm 2 Pictures of the fixed Plunger Distances set by metallic rings

8. Experimental setup Beam 48 Ca 208 Pb nat Mg PRISMA β≈10.0% β’≈8.0% E beam =310MeV d DegraderTarget Eγ’Eγ’ EγEγ CLARA Recoil Distance Doppler Shift method (RDDS) EγEγ Eγ’Eγ’ E γ’ : Doppler corrected Good Mass Resolution Multi-nucleon transfer reactions Placed at the θ grazing for BLF

9. Around the doubly-magic 48 Ca The Z=18 isotopes The N=30 isotones

10. Nuclei in the fp shell The case of 50 Ca- 51 Sc and 51 Mn- 51 Fe N=Z 51 Fe 51 Mn 50 Ca 51 Sc

11. Experimental RDDS spectra IsIs IuIu Gamma spectra of the 2 + and 11/2 - in 50 Ca and 51 Sc (mass gate in PRISMA) Mass spectrum from PRISMA Rection: 48 Ca onto 208 Pb at 310 MeV

12. Lifetimes of first excited states The velocity required is the velocity before the degrader. PRISMA measures the velocity after the degrader Velocity PRISMA CLARA ring

13. B(E2) and Eff. charges of N=30 Calcium systematics E and B(E2) Experimental and theoretical effective charges. E2+E2+ B(E2) 50 Ca wave function of the 2 + → vp 2 3/2 51 Sc wave function of the 11/2 - → vp 2 3/2, πf 7/2 Shell-model calculations in the full fp shell 40 Ca core (KB3G & GXPF1A):

14. Effective charge ISOSCALAR + ISOVECTOR: (e eff ) p E2 =1.15e (e eff ) n E2 =0.8e Neutron deficient A=51 mirror nuclei 51 Fe and 51 Mn

15. Ductu Naturae N=Z 51 Fe 51 Mn 50 Ca 51 Sc (e eff ) p E2 =1.15e (e eff ) n E2 =0.80e (e eff ) p E2 =1.50e (e eff ) n E2 =0.50e Full fp shell with a 40 Ca core. A HO potential and separable (IS and IV) QQ interactions → Effective charges are constant for a given core and valence space.

16. The N=28 isotope: 46 Ar Simulations performed in order to deduce the lifetime of the 2 + state in 46 Ar Full GEANT4 simulations : CLARA PRISMA Realistic velocity distributions Energy loss degrader τ=0.8(0.3)ps

17. B(E2) value of 46 Ar Collectivity arises from proton (sd) neutron (fp) interaction Increased collectivity with respect to 44 Ar A. Gade et al., Phys. Rev. C68 (2003) 014302., H. Scheit et al., Phys. Rev. Lett 77 (1996) 3967.

18. AGATA + PRISMA: Lifetimes CLARA vs. AGATA CLARA AGATA Lifetime τ=100ps Degrader nat Mg 4 mg/cm 2

19. Novel method that combines the traditional RDDS method with the CLARA-PRISMA spectrometers, allowing to measure lifetimes of neutron-rich nuclei. Complementarity of this method with Coulex with radioactivy beams Results on the lifetime of the first excited states in the N=30 isotones 50 Ca and 51 Sc. Determination of the effective charges in the fp shell. Indication of an orbital dependence of the effective charges in the fp shell. Need of more experimental data of selected nuclei to fully understand the question. Measured lifetime of 46 Ar, increased collectivity. Future: AGATA at LNL Summary

20. Collaborators

21. Harmonic Oscillator & Woods-Saxon Spherical Woods-Saxon potential Spherical Harmonic Oscillator potential ‹ r 2 › (p3/2) = ‹ r 2 › (f7/2) ‹ r 2 › (p3/2) ≈ 1.2 ‹ r 2 › (f7/2) (e eff ) n E2 =0.42e ↓

22. Effective charges The E2-polarization effect gives rise to an effective charge e eff associated with the quadrupole processes: Proton Neutron As a reference the effective charges e eff associated to a free nucleon: (e eff ) p =1.0e (e eff ) n =0.0e Proton Neutron A HO potential and separable (IS and IV) QQ interactions → Effective charges are constant for a given core and valence space.

23. The IS+IV effective charges A. Poves et al., Phys. Rev. C 72, 047302 (2005) Possible explanation for the staggering in B(E2) for Ti N=28 N=30 N=32

24. What are effective charges. Effective charges take into account the core polarization, that can be understood in terms of the coupling between the particles and the collective oscillations associated with deformations of the core. GQR (IS)GQR (IV) f 7/2 p 3/2 p 1/2 f 5/2 fp 40 Ca CORE Full fp shell with a 40 Ca core. Nuclear Structure, Bohr and Mottelson. For a pure configuration: B(E2: ν(p 3/2 ) 2 ) ~ (e ν eff ) 2 ‹r 2 › 2 (p3/2)

25. N=30 isotones Well known from multi-nucleon and deep-inelastic reactions (thin and thick target). R. Broda et al., Acta Phys. Pol. B36 (2005) 1343. Neutron-rich 50 Ca and 51 Sc isotopes 20

26. The CLARA spectrometer 23 Euroball Clover detectors with anti-Compton (Eff. ~ 3.0 %) Not used detectors around 90 o → Doppler shift ≈ 0 (Eff. ~ 1.2 %) FWHM = 0.6% (for β=10%)  spectrum CLARA spectrometer

27. The PRISMA spectrometer Formed by 1 Quadrupole, 1 Dipole and detectors (MCP, MWPPAC, IC) to track the ions. ΔΩ = 80 msr, ΔZ/Z  1/60, ΔA/A  1/190, Bρ = 1.2 T.m Identifies nuclei produced in the reaction (A,Z,β) event by event PRISMA spectrometer Large-acceptance magnetic spectrometer

28. Target-Degrader setup Degrader Target Beam Plunger setup Ta:1mg/cm 2 208 Pb:1mg/cm 2 nat Mg: 4mg/cm 2 Pictures of the fixed Plunger Distances set by metallic rings

29. Control of the feeding 4+4+ 0+0+ 2+2+ C1C1 C2C2 46 Ca Total Kinetic Energy Loss TKEL = -Q value 2 + →0 + 4 + →2 + 2 + →0 + τ≈9.02±2.16 ps τ≈5.50±2.17 ps M. Bini et al., Nuovo Cimento Lett. 5 913 (1972). Coulex: τ= 5.24±0.54 ps

30. Future at LNL: AGATA D. & PRISMA Degrader Target Beam PRISMA Lifetime measurements AGATA 0 o – 45 ° ε AD ≈ 6% Cologne Plunger γ-γ coincidences CLARA does not exist anymore...

31. Effective charges & B(E2) values The relation between the effective charges and the B(E2) value for a pure configuration can be given: B(E2: ν(p 3/2 ) 2 ) ~ (e ν eff ) 2 ‹ r 2 › 2 (p3/2) If we consider a Harmonic Oscillator potential, the ‹r 2 › is the same for any give orbital of the same quantum number N. Therefore in our valence space: ‹ r 2 › (p3/2) = ‹ r 2 › (f7/2) If we consider a simple model with a HO potential and separable (IS and IV) QQ interactions → The effective charges are the same for a given core and valence space for all nuclei.

32. Energies and B(E2) values Indication of shell gaps B(E2) valuesEnergy N=28 N=32 Energies and B(E2) values are complementary to study in detail shell evolution. 34 KB3G: A. Poves, et al., Nucl. Phys. A (2001). GXPF1A: M. Honma et al., Phys. Rev. C (2002); Eur. Phys. J. A (2004). 50 Ca 52 Ca 54 Ca Energy