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Coupling of (deformed) core and weakly bound neutron

Coupling of (deformed) core and weakly bound neutron. M. Kimura (Hokkaido Univ.) . Introduction. We are now able to access to 1. Weakly bound neutron-rich with A ～ 40 2. Heavier unstable nuclei with N ～ 28, 50,… What will we find there?

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Coupling of (deformed) core and weakly bound neutron

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  1. Coupling of (deformed) core and weakly bound neutron M. Kimura (Hokkaido Univ.)

  2. Introduction We are now able to access to 1. Weakly bound neutron-rich with A～40 2. Heavier unstable nuclei with N ～ 28, 50,… What will we find there? Theoretical predictions by AntisymmetrizedMolecular Dynamics

  3. Description of deformed coreAMD method

  4. AMD Framework A-body Hamiltonian Gogny D1S effective interaction, Exact removal of spurious c.o.m.motion • Variational wave function Variational calculationafter parity projection Single particle wave function is represented by a deformed Gaussian wave packet

  5. AMD Framework AMD model wave function is flexible to describe various kinds of structure (shells & clusters) without assumption (deformed) shells Variation Initial wave function (randomly generated) clustered

  6. AMD Framework 1. Energy variation with the constraint on the Quadrupole deformation b 2. Angular momentum projection • 3. GCM Configuration mixing between the states with different deformation and configurations Solve Hill-Wheeler eq. to obtain eigenvalue and eigenfunction

  7. AMD Framework M. Kimura, Phys.Rev. C 75, 041302 (2007) 1. Energy variation with the constraint on the Quadrupole deformation b 2. Angular momentum projection • 3. GCM G. Neyens, PRC84, 064301 (2011) • Coexistence of many particle-hole states at very small excitation energy has been predicted by AMD • Recent experiments such as p and n-knockout, n-transfer andb-decays revealed corresponding states • Coexistence of many particle-hole states with different deformations • (shape coexisting phenomena) is now establishing Single particle energy and wave function Construct single particle Hamiltonian from variational results and diagonalize it.

  8. Description of weakly bound neutronAMD+RGM methodfor Core + n and 2n systems

  9. AMD + RGM (core + 1n, 2n system) • Solve core + 1n, 2n system (Coupled Channnel Core + n RGM) : Wave function of the core described AMD+GCM method (In the case of the 30Ne+n system, the core is 30Ne. is a linear combination of Jp projected Slater determinants) : Valence neutron (In the case of the Core+2n system, there are two ) : Coefficient of each channels, and relative wave function between the core and valence neutrons (They are the unknown variables (functions) to be calculated by this method)

  10. AMD + RGM (core + 1n, 2n system) • In the practical calculation, the RGC wave function is transformed to the GCM wave functions. (straightforward but CPU demanding ) The core is a linear combination of different shapes (AMD+GCM w.f) = + + … The basis wave functions of AMD+RCM And, we diagonalize total Hamiltonian for Core + n (2n) system

  11. AMD + RGM (core + 1n, 2n system): O isotopes AMD Results (Blue Symbols) • Correct description of neutrondrip-line (Gogny D1S) • Underestimation of even-oddstaggering (Pairing correlation is not enough?) • Underestimation of Sn for 23Oand 24O (1s orbit) • AMD+RGM Results (Green Symbols) • Better staggering • ( (1s1/2)2 and (0d3/2)2 pairs ) • Improvement of the last neutron(s)orbital in 23O and 24O (1s orbit).

  12. AMD + RGM (core + 1n, 2n system): O isotopes AMD Results (Blue Symbols) • Overestimation for light isotopes • Monotonic increase of radii in thecalculation, while 23O and 24Oshow drastic increase in theobservation • AMD+RGM Results (Green Symbols) • Almost no effect for light isotopes(d5/2) dominance • Slight increase in 23O and 24O(1s1/2). But not enough to explain • the observation.

  13. Beyond island of inversion Toward neutron-dripline

  14. 1n Halo of 31Ne(N=21) • Coulomb breakup, and enhanced B(E1) Observed large cross section can be explained with l= 1, 2 • Large Interaction cross section M. Takechi, et. al., Nucl. Phys. A 834, (2010), 412 T. Nakamura, et. al., PRL103, 262501 (2009)

  15. AMD + RGM for 31Ne • Wave function of 30Ne is AMD w.f., relative motion between 30Ne and n is solved • All states below 10MeV of 30Ne are included as the core wave function of 31Ne • AMD result shows particle (n p3/2) + rotor (30Ne(g.s.)) nature • AMD + RGM tends to weak coupling • between 30Ne and neutron Sn=250 keV→ 450keV Talk by Minomo K. Mimono, et al., PRC84, 034602 (2011) K. Mimono, et al., in preparation.

  16. “Parity Inversion” and “Neutron-halo” near drip-line 35Mg and 37Mg • 1n separation energy is around or less than 1MeV • 37Mg is the heaviest odd mass Magnesium QUESTIONS • Island of inversion is extended in this region ? • Neutron Halos?

  17. 35Mg (N=23): (fp)3config. vs. (fp)4(sd)-1config. 1. neutron single particle level density is very large around 0 energy 2. 0p3/2 orbit also intrudes due to the high single particle density and increase of fermi energy (larger neutron #) 3. (fp)3 ,(fp)4(sd)-1 and (fp)5(sd)-2 configuration compete ⇒ possible parity inversion

  18. 35Mg (N=23): (fp)3config. vs. (fp)4(sd)-1config. A. Gade et al., PRC83, 044305 (2011) • (fp)4(sd)-1 becomes the ground state and the parity is inverted. • Stronger n-n correlation in fp shell than sd • Experimental information is not enough

  19. 37Mg (N=25): (fp)5 vs. (fp)6(sd)-1 vs. (sdg)1(fp)6(sd)-2 1. Further increase of single particle level density. 2. 0g9/2 orbit also intrudes across N=28 shell gap ! due to larger neutron # and weak binding 3. (fp)5 ,(fp)6(sd)-1 and (g)1(fp)6(sd)-2 configurations compete 4. 1/2+ state with (g)1(fp)6(sd)-2 comes down

  20. 37Mg (N=25): (fp)5 vs. (fp)6(sd)-1 vs. (sdg)1(fp)6(sd)-2 1. The ground state is normal configuration (end of island of inversion?) 2. Positive parity state with 0g9/2 appears at small excitation energy 3. The ground state density does not reproduce the observed cross section ⇒ Need to improve the tail part of wave function.

  21. 37Mg (N=25): AMD+RGM • Strong deformed core and weak binding • lowers intruding orbit from g9/2 • Need to extract core-n interaction from • RGM • Need to solve resonaces and scattering states : AMD+GCM w.f. of 36Mg l = 0 … + + l = 2 1/2+ gains extra biding energy by RGM and degenerate with 5/2- shows better agreement with the observed Reaction cross section

  22. Summary and Outlook • Summary • Microscopic description of deformed core by AMD • Description of weakly bound neutron by RGM • Better description of Sn and Rrms of Oxygen isotopesThere are still discrepancy between experiments and calculation.(new data for 24O is in need) • Possible parity-inversion in 35Mg • (Interaction dependence) • 2s1/2 neutron configuration with a halo with deformed core of 36MgStrong deformation of the core assists the lowering of 2s1/2 configuration • Outlook • Application of R-matrix method to AMD+RGMPhase shifts, equivalent Core-n local potential, • Development in more efficient calculation method • Application to deformed core + 2n system

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