Shape phase transition in neutron-rich even-even light nuclei with Z=20-28

H.B.Bai X.W.Li H.F.Dong W.C.CaoDepartment of Physics, Chifeng University, Chifeng

contentscontents

IntroductionIntroduction

E-GOS MethodE-GOS Method

Results and DiscussionResults and Discussion

ConclusionsConclusions

2 、 The interacting Boson Model (IBM) ：

IBM-3 ：three types of bosons ： proton-proton(π) ； neutron-neutron(υ) ； proton-neutron(δ).

form the isospin T=1 triplet

一、一、 IntroductioIntroductionn1 、 light nuclear

an algebraic model used to study the nuclear collective motions.

nuclear structure theories and astrophsics

c d ddT sd U (5)(18) (U (3) SU (2)) (U (6) O (5) O (3)) (1)U

sc T sd d dd(18) (U (3) SU (2)) (U (6) O (5) O (3)) (2)(6)U O

c dsdT sd ((18) (U (3) SU (2)) (U (6) O (3)) (3)3)SUU

The natural chains of IBM-3 group U(18) ：

The subgroups Ud(5), Osd(6) and SUsd(3) describe vibrational,γ-unstable and rotational nuclei respectively.

3 、 In this paper, we studied the shape phase transition of neutron-rich even-even light nuclei with proton number Z=20-28 by E-GOS method

二、二、 E-GOS MethodE-GOS Method

E-Gamma Over Spin (E-GOS) curves can describe the evolution from vibrational to rotational structure in nuclei .

2I

IE

In IBM-3 model, theoretical yrast energy level for

U(5) limit ：

SU(3) limit ：2

( 1)2IE I IJ

SO(6) limit ： (2 )( 2) ( 2)

4

EE I I I

( 2)E I I

)24(2

)2(2

IJ

IIE

perfect harmonic vibrator ：

an axially symmetric rotor ：

To study the shape and phase evolution, the ratio is introduced

I

IIER

)2(

While spin I goes towards infinite ：

0vibrationR

)2

(42

JRrotation

4

)2(

E

R

0 2 4 6 8 10 12 14 16 18 20 220

50100

150

200

250300

350

400450

500

550600

650

Fig.1 E-GOS curves of vibrational, rotational and gamma-unstable nuclei

su(3)o(6)u(5)

R

Spin(I)

Figure 1 shows these theoretical limits ， the first excited state energy level at 1 MeV.

三、三、 Results and DiscussiResults and Discussionon

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R

R

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R

R R

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40Ca

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42Ca

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44Ca

R

C6Ca

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62Ni

66Ni

68Ni

Fig.2 E-GOS corves of neutron-rich even-even light nuclei with z=20-28

64NiR

24 EE 2 0Q

24 EE 2 0Q

nucleus EE44++/ E/ E22

++ (b) nucleusEE44

++/ / EE22

++(b)

40Ca 1.3519 0.1201 0.3064 52Fe 2.8092

42Ca 1.8058 0.2462 0.6487 54Fe 1.8026 0.1984 0.8035

44Ca 1.9732 0.2670 0.7257 56Fe 2.4645 0.2498 1.0364

46Ca 1.9123 0.1509 0.4225 58Fe 2.5630 0.2607 1.1073

48Ca 1.1754 0.0996 0.2868 60Fe 2 ． 5687

44Ti 2.2659 0.2579 0.7763 56Ni 1.4530

46Ti 2.2598 0.3253 1.0017 58Ni 1.6912 0.18 0.8234

48Ti 2.3347 0.2685 0.8507 60Ni 1.8806 0.2065 0.9663

50Ti 1.7218 0.1671 0.5438 62Ni 1.9915 0.1965 0.9398

52Ti 2.2088 64Ni 1.9388 0.1744 0.8519

48Cr 2.4707 0.3676 1.2704 66Ni 1.8750

50Cr 2.4023 0.2938 1.0433 68Ni 1.4909

52Cr 1.6520 0.2229 0.8126

54Cr 2.1859 0.2523 0.9430

56Cr 2.6650

0Q2 2 0Q

Table 1

)3/()20:2(4 20112 eZREB

20

211 16

5)20:2( QeEB

1 、 the doubly magic nuclei 40Ca, 48Ca and 56Ni:

higher first excited state

E4/E2=1.1754~1.4530

β2=0.0996~0.1201

Q0=0.2868(b) ~ 0.3064(b)

2 、 the singly magic nuclei 42- 46 Ca, 58-66Ni, 50Ti, 52Cr and 54Fe :

E4/E2=1.6912 ~1.9732

β2=0.1509 ~0.2670 Q0=0.4225 (b) ~ 0.7257 (b)

the shape of single magic nuclei is obviously deviated from sphere at low spin. From the E-GOS curve characteristics and the calculated shape parameters, these singly magic nuclei not only have strong shell effect but also have collective motion with increasing valence nucleons.

44Ca :

approaches the U （ 5 ） limit when the spin 6I

the critical point of phase transformation appears when6I

3 、 44.46.48.52Ti are U(5)-SU(3) transitional nuclei and is the8I

critical point for 46 、 48Ti ， for 44 、 46 、 48 Ti ， the vibration characteristics is gradually strengthening with the increase of mass .

4 、 For 48-56Cr are U(5)-SU(3) transitional nuclei, and the vibration characteristics strengthen with the increase of neutron number when 8I

5 、 For 52-60Fe ， these isotoles have complex structre in the low spin.

It is known that the doubly magic nuclei 40,48Ca and 56Ni have higher exciting energies on the first and second excited states ，

In comparison ， 68Ni has also high first and second excited energy levels ，

So ， it should be also a doubly magic nucleus

we infered that N=40 may be a magic number for neutron and 68Ni may be a doubly magic nucleus ？

6 、 68Ni （ Z=28 ， N=40 ） is similar in E-GOS curve to doubly magic nuclei 40,48Ca and 56Ni when 4I

20 22 24 26 28

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5.5

28 30 32 34 36 38 401.0

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4.0

Ex(

MeV

)

Fig.3 The relationship curves between the energy levels of the first and second excited states with the number of neutron

neutron number

I=2

I=4 40-48Ca56-68Ni

I=4

I=2

Ex(

Me

V)

neutron number

四、 Conclusions the doubly magic nuclei have similar E-the doubly magic nuclei have similar E-

GOS curves at the low spin state. GOS curves at the low spin state. the singly magic nuclei have characteristhe singly magic nuclei have characteris

tics of collective motion when the numbtics of collective motion when the number of valence nucleon increases and closer of valence nucleon increases and closes to mid-shell. es to mid-shell.

The isospin effect plays an important rolThe isospin effect plays an important role in the shape phase transition of neutroe in the shape phase transition of neutron-rich even-even light nuclei .n-rich even-even light nuclei .

6868Ni is a doubly magic nucleus. Ni is a doubly magic nucleus.