1 Nuclear reactions as probes of exotic nuclei

1 Nuclear reactions as probes of exotic nuclei International Conference on Nuclear Physics, INPC 2007, Tokyo, 3 rd – 8 th June 2007 Jeffrey Tostevin, Department of Physics Faculty of Engineering and Physical Sciences University of Surrey, United Kingdom

2 Exotic nuclei – presence of two Fermi surfaces n p Spherical Hartree Fock density (Sk. X) 38 Si

3 Otsuka: the np tensor correlation n p Spherical Hartree Fock density (Sk. X) 38 Si

4 Outline 1. Advances in theoretical approaches to reaction dynamics (heard also Fonseca) 2. Transfer reactions 3. Single nucleon removal from fast beams – single particle strengths in asymmetric matter 4. Two nucleon removal - lessons to date, correlations and momentum distributions

5 Advances in theoretical approaches to reaction dynamics

6 Dynamics studies: halos in the light nuclei N=8 Borromean halo nuclei Few-body (three- and now four-body methods) are restricted to the light loosely bound sector of the chart – 9 C, 8 B, 11 Be, 11 Li, 14 Be …

7 Reaction dynamics: four-body methods Four-body Continuum-Discretized Coupled-Channels (CDCC) Kyushu University – to date, elastic scattering only GEM and resulting pseudostates basis Ogata (Invited), G 5 -1 Egami (Poster), QW Matsumoto (Poster), QW T. Matsumoto et al. Phys. Rev. C 70, 061601(R) (2004), C 73, 051602(R) (2006) Figures: T. Matsumoto

8 Reaction dynamics: four-body methods Lisboa-Sevilla-Surrey (Rodrıguez-Gallardo) Pseudo-state Expansion of the three body (projectile) system in Hyperspherical Harmonics (HH) M. Rodrıguez-Gallardo et al. , Phys. Rev. C 72, 024007 (2005), RNB 7 proceedings, DREB 2007 Energy bins

9 Reaction dynamics: other methods/developments Time dependent: Lagrange mesh (for two-body projectile) Dynamical Eikonal method (Baye, Brussels) PRL 95, 082502 Capel G 5 -3 Time-dependent Schrodinger equation solutions (Tsukuba) Yabana G 2 -3 Ab-initio developments (David Dean’s talk) Navratil (LLNL), Phys. Rev. C 73, 065801 (2006) Nollett (Argonne) (VMC), Phys. Rev. C 63, 054002 (2001) Continuum shell model Tennessee/GANIL (Michel, Nazarewicz, and Płoszajczak) – Gamow. SM Florida/Michigan (Volya, Zelevinsky) To cover the chart of nuclides – and do spectroscopy - we must adopt less microscopic (more pragmatic and approximate but robust) direct reactions methods – using effective interactions, shell model, Hartree Fock, etc.

10 Transfer reactions

11 Spectroscopy: Transfer reactions are now being carried out with significant precision using novel detection systems – DWBA, CRC, Johnson. Soper adiabatic (breakup) and CDCC are being used and appear fit for purpose. 1. Spectroscopic factors (with intrinsic uncertainties from assumed optical potentials and formfactors) 2. By energy of kinematic conditions for peripherality, the ANC, with greater precision Relatationships of ANCs for mirror systems, e. g. N. K. Timofeyuk, R. C. Johnson and A. M. Mukhamedzhanov, PRL 91, 0232501 (2003)

12 Single nucleon removal from fast beams – single particle strengths in asymmetric matter

13 One and two nucleon knockout, ~ 100 Me. V/u 9 Be 1 2 c light nuclear target [fast] spectator Experiments are inclusive (with respect to the target final states). Core final state measured – using gamma rays – whenever possible – and the momenta of the residues. Cross sections are large and they include both: Break-up (elastic) and stripping (inelastic/absorptive) interactions of the removed nucleon(s) with the target More exclusive -1 N measurements: Bazin G 1 -2

14 Sudden removal – eikonal model cross sections 1 9 Be A At any given facility, and a programme of measurements (with an essentially fixed energy per nucleon) and given target then only two things change for different exotic beams (1) the core target interaction (2) the nuclear structure *** J. A. Tostevin, G. Podolyák et al. , PRC 70 (2004) 064602.

15 Reaction description is very robust and quantitative Core/residue-target interaction is highly absorptive at 100 Me. V/u. The range of this absorption is determined by the core and target sizes which is encoded within the double folding model and can be cross referenced to These interactions and the rquired S-matrices can be calculated reliably using Glauber methods – using, e. g. Hartree-Fock densities. B. A. Brown et al. , Phys. Rev. C 65 (2001) 014612

16 Geometry considerations: Hartree Fock for ‘sizes’ The rms radii of single particle formfactors are the sole requirement for determining the cross section calculations – to high precision. We constrain these to Hartree-Fock or other theoretetical values Reaction description between different exotic systems is very ‘robust’

17 Sampling the single-nucleon wave function Interaction with the target probes wave functions at surface A target Overlap function determines SF for residue in state JM z

18 Residue parallel momentum distribution 1 p 3/2 2 s 1/2

19 Strengths from e-induced knockout – stable nuclei W. Dickhoff and C. Barbieri, Progress in Particle and Nuclear Physics 52 377 (2004)

20 Removal strengths at the Fermi surface (2007) +Shell M)

21 Increased correlations from pn pairs? Asymmetric nuclear matter: We observe a depletion of the proton occupancies for momenta below the Fermi momentum, which increases significantly with neutron fraction. This can be explained by the strong correlations induced from proton neutron interactions. T. Frick, et al. , PRC 71, 014313 (2005) proton occupation Dispersive optical potential: Thus a preponderance of one type of particle reduces the occupancies of valence hole states for the other type. This indicates that correlations are stronger for these valence nucleons. R. J. Charity, et al. , PRL 97, 162503 (2006) 40 Ca 48 Ca 60 Ca

22 Two nucleon removal, lessons to date, correlations and momentum distributions

23 Two nucleon knockout – direct reaction set Z 34 Ar 32 Ar 54 Ti 44 S 30 S 28 S 52 Ca 26 P 24 Si 2 n from neutron deficient 28 P 26 Si 32 Al 28 Mg 30 Mg 28 Na 26 Ne 42 Si 34 Al 32 Mg 30 Na 28 Ne 32 Na 30 Ne 2 p from neutron rich N

24 Sudden removal – eikonal model cross sections 1 2 A J. A. Tostevin et al. , PRC 70 (2004) 064602 and PRC 74 (2006) 064604.

25 Sampling the two-nucleon wave function Interaction with the target probes wave functions at surface and beyond A target z Shell model overlaps – for 0+ heavy residue in state JM

26 Two-neutron removal – g. s. branching ratios Sigma (0+) / Sigma(inclusive) 32 Ar uncorrelated 34 Ar 30 S 26 Si Yoneda et al. , POSTER QW 298

27 Rs (2 N) Two-nucleon removal – suppression - Rs(2 N) 28 Mg -2 p 26 Si 30 S 34 Ar -2 n (Yoneda et al. ) 54 Ti(gs) -2 p J. A. Tostevin and B. A. Brown, PRC 74 064604 (2006), PRC 70 064602 (2004)

28 Knockout cross sections – correlated case 26 Ne(0+, 2+, 4+ , 22+) 82. 3 Me. V/u Sigma (mb) 28 Mg 0+ 2+ 1 4+ J. A. Tostevin et al. , PRC 70 (2004) 064602, PRC 74 064604 (2006 22+

29 Example: Island of Inversion extends to 36 Mg? 1) Insufficient yield for, e. g. secondary beam inelastic scattering 2) Parent for beta decay, 37 Na, is particle unbound 3) can use 2 p removal from n-rich (sd-shell) parent, 38 Si + p n p n

30 Asymmetry dependence yet to be established 38 Si J. A. Tostevin and B. A. Brown, PRC 74 064604 (2006), PRC 70 064602 (2004) Figure: A. Gade, and submitted

31 The Island of Inversion extends to 36 Mg? 38 Si + p n Measured cross sections and those calculated assuming population of the 0 hw components of the final states by the direct 2 p knockout reaction mechanism p n Monte-Carlo shell model calculations: SDPF-M interaction of Utsono, Otsuka et al.

32 Look at momentum content of sampled volume 2 z 1 Probability of a residue with parallel momentum K J. A. Tostevin, EPJ A, in press, and Acta Physica Polonica B 38 (2007) 1195

33 Two proton knockout from 38 Si 36 Mg(0+, 2+) Residue momentum probability 38 Si ( 2 p) 83 A Me. V uncorrelated 0+ 38 Si 36 Mg 0+ 2+ residue parallel momentum (Me. V/c) 2+

34 Residue momentum distribution Two proton knockout from 38 Si 36 Mg(0+, 2+) 38 Si 0+ 2+ ( 2 p) 83 A Me. V Theory Expt. 0+ 56% 58(7)% 2+ 44% 42(7)% dp/p=1. 66% A. Gade et al. , to be published

35 Summary 1. With fast fragmentation beams (> 50 Me. V/u) reaction theory is rather accurate and is capable of providing quantitative tests of structure model predictions far from stability. 2. Single nucleon knockout analyses indicate a systematic dependence of suppression of shell model single-particle strength on the asymmetry of the Fermi surfaces. 3. The 2 N knockout reaction mechanism can be very clean the combination of N and 2 N removal reactions can help to elucidate structures, shell gaps, and level ordering. 4. Six data sets are now consistent with shell model spectroscopy and a suppression [~0. 50(5)] of 2 N shell model strength – analog of 1 N removal suppression. Direct cases studied all have similar Fermi surface asymmetries so any asymmetry dependence is not yet evident. 5. Spectroscopic information (J assignment) will be available from final-state-exclusive residue momentum distribution measurements.