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Geometry of Two-Proton-Halo Candidate Nucleus . 大石知広 (M2) ° 、 萩野浩一 東北大学大学院・理学研究科・物理学専攻 ( 2009.8.28. 三者若手夏の学校). Introduction (1). nucleus has a t ypical feature of “ Borromean ” nuclei, such that. → unbound,. or. but. → bound as . Introduction (2).

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geometry of two proton halo candidate nucleus

Geometry of Two-Proton-HaloCandidate Nucleus

大石知広(M2)°、萩野浩一

東北大学大学院・理学研究科・物理学専攻

(2009.8.28.三者若手夏の学校)

introduction 1
Introduction (1)

nucleus has a typical feature of

“Borromean” nuclei, such that

→ unbound,

or

but

→ bound as .

introduction 2
Introduction (2)

Two protons are considered to have the

“halo-like” structure around the core .

?

or

Its geometry is an interesting topic,

in connection to

1.di-proton correlation in weakly bound system,

2.two proton emission.

introduction 3
Introduction (3)

For two-neutron-halo nuclei, e.g. :

Ref[1]:K.Hagino, and H.Sagawa, PRC72(‘05)044321

How does Coulomb repulsion affect the

halo-structure?

model 1
Model (1)

Three-body model Hamiltonian:

model 2
Model (2)

Assumption:

(1).This time, I study only the g.s. of :

(2).Core is spherical, and proton-Core interaction

= Woods-Saxon + Coulomb:

model 3
Model (3)

(3).Proton-proton interaction

=δ-interaction + Coulomb:

procedure
Procedure

(1) Solve the single-particle Schrödinger eq:

(2) Using

as basis, diagonalize the total Hamiltonian.

  • Calculate some expectation values,

e.g. ,etc…

and density-distributions of two protons.

parameter setting 1
Parameter-setting (1)

Woods-Saxon potential:

Where . . .

to reproduce energy levels of .

parameter setting 2 a
Parameter-setting (2)a

To determine , I need

(1).energy cutoff :

(2).nn-scattering length:

Ref[2]:H.Esbensen, G.F.Bertsch, and K.Hencken, PRC56(‘97)3054

parameter setting 2 b
Parameter-setting (2)b

※are determined to reproduce the binding energy difference between and :

geometrical properties
Geometrical properties

The total Hamiltonian is diagonalized in the

truncated space, determined by .

I will calculate g.s.properties of .

results 1
Results (1)

Geometrial values:

Ref[3]:C.A.Bertulani, and M.S.Hussein,

PRC76(‘07)051602(R)

Occupation probability:

results 2
Results (2)

Density distribution as a function of and

the angle , weighted with :

summary
Summary

•In the g.s. of , d(5/2)-wave is dominant,

and two protons tend to couple with S=0.

•Both S=0 & S=1 component have radial tail,

characteristic in halo nucleus.

→Coulomb effect?

•The expectation value of angle is .

However, it should be interpreted with a care,

because of the 3-peaked structure of density.

future works
Future works

•Reproduce the resonance energies of for

accuracy of single-particle states.

•Construct excited states, i.e. coupling.

•Study about the dipole-excitation:

or two-proton-emission.