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?Theoretical predictions by Antisymmetrized Molecular Dynamics

Description of deformed core

AMD method

AMD Framework

Variational wave functionVariational calculation after parity projection

A-body Hamiltonian Gogny D1S effective interaction, Exact removal of spurious c.o.m. motion

Single particle wave function is represented by a deformed Gaussian wave packet

AMD Framework

Initial wave function(randomly generated)

Variation

(deformed)shells

clustered

AMD model wave function is flexible to describe various kinds of

structure (shells & clusters) without assumption

AMD Framework

2. Angular momentum projection

1. Energy variation with the constraint on the Quadrupole deformation b

Solve Hill-Wheeler eq. to obtain eigenvalue and eigenfunction

3. GCM

Configuration mixing between the states with different deformation and configurations

AMD Framework

1. Energy variation with the constraint on the Quadrupole deformation b

Single particle energy and wave function

Construct single particle Hamiltonian from variational results

and diagonalize it.

2. Angular momentum projection3. 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 and b-decays revealed corresponding states

• Coexistence of many particle-hole states with different deformations (shape coexisting phenomena) is now establishing

M. Kimura, Phys.Rev. C 75, 041302 (2007)

Description of weakly bound neutron

AMD+RGM methodfor Core + n and 2n systems

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)

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

AMD + RGM (core + 1n, 2n system): O isotopes

AMD Results (Blue Symbols)• Correct description of neutron

drip-line (Gogny D1S)• Underestimation of even-odd

staggering (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).

AMD Results (Blue Symbols)• Overestimation for light isotopes• Monotonic increase of radii in the

calculation, 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.

AMD + RGM (core + 1n, 2n system): O isotopes

Beyond island of inversion Toward neutron-dripline

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)

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

AMD + RGM for 31Ne

AMD + RGM

config.

0+ × p 3/2 56%

2+ × p 3/2 24%

2+ × f 7/2 9%

1- × s 1/2 5%

AMD

config.

0+ × p 3/2 37%

2+ × p 3/2 41%

2+ × f 7/2 12%

1- × s 1/2 5%

Sn=250 keV → 450keV

Talk by Minomo

K. Mimono, et al., PRC84, 034602 (2011)

K. Mimono, et al., in preparation.

“Parity Inversion” and “Neutron-halo” near drip-line

– 1n separation energy is around or less than 1MeV– 37Mg is the heaviest odd mass MagnesiumQUESTIONS– Island of inversion is extended in this region ?– Neutron Halos?

35Mg and 37Mg

35Mg (N=23): (fp)3 config. vs. (fp)4(sd)-1 config.

1. neutron single particle level density is very large around 0 energy2. 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

35Mg (N=23): (fp)3 config. vs. (fp)4(sd)-1 config.

• (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

A. Gade et al., PRC83, 044305 (2011)

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 binding3. (fp)5 , (fp)6(sd)-1 and (g)1(fp)6(sd)-2 configurations compete4. 1/2+ state with (g)1(fp)6(sd)-2 comes down

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 energy3. The ground state density does not reproduce the observed cross section ⇒ Need to improve the tail part of wave function.

37Mg (N=25): AMD+RGM

: AMD+GCM w.f. of 36Mg

1/2+ gains extra biding energy by RGM and degenerate with 5/2- shows better agreement with the observed Reaction cross section

• 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

l = 0 l = 2+ + …

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+RGM

Phase shifts, equivalent Core-n local potential, • Development in more efficient calculation method• Application to deformed core + 2n system