1. 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.Cao Department of Physics, Chifeng University, Chifeng

2. contents Introduction Introduction E-GOS Method E-GOS Method Results and Discussion Results and Discussion Conclusions Conclusions

3. 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、 Introduction 1 、 light nuclear an algebraic model used to study the nuclear collective motions. nuclear structure theories and astrophsics

4. The natural chains of IBM-3 group U(18) ： The subgroups U d (5), O sd (6) and SU sd (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

5. 二、 E-GOS Method E-Gamma Over Spin (E-GOS) curves can describe the evolution from vibrational to rotational structure in nuclei.

6. In IBM-3 model, theoretical yrast energy level for U(5) limit ： SU(3) limit ： SO(6) limit ： perfect harmonic vibrator ： an axially symmetric rotor ：

7. To study the shape and phase evolution, the ratio is introduced While spin I goes towards infinite ：

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

9. 三、 Results and Discussion

10. nucleus E 4 + / E 2 + (b) nucleus E 4 + / E 2 + (b) 40 Ca1.35190.1201 0.3064 52 Fe2.8092 42 Ca1.80580.2462 0.6487 54 Fe1.80260.19840.8035 44 Ca1.97320.2670 0.7257 56 Fe2.46450.24981.0364 46 Ca1.91230.1509 0.4225 58 Fe2.56300.26071.1073 48 Ca1.17540.0996 0.2868 60 Fe 2 ． 5687 44 Ti2.26590.2579 0.7763 56 Ni1.4530 46 Ti2.25980.3253 1.0017 58 Ni1.69120.180.8234 48 Ti2.33470.2685 0.8507 60 Ni1.88060.20650.9663 50 Ti1.72180.1671 0.5438 62 Ni1.99150.19650.9398 52 Ti2.2088 64 Ni1.93880.17440.8519 48 Cr2.47070.3676 1.2704 66 Ni1.8750 50 Cr2.40230.2938 1.0433 68 Ni1.4909 52 Cr1.65200.2229 0.8126 54 Cr2.18590.2523 0.9430 56 Cr2.6650 Table 1

11. 1 、 the doubly magic nuclei 40 Ca, 48 Ca and 56 Ni: higher first excited state E 4 /E 2 =1.1754~1.4530 β 2 =0.0996~0.1201 Q 0 =0.2868(b) ~ 0.3064(b)

12. 2 、 the singly magic nuclei 42- 46 Ca, 58-66 Ni, 50 Ti, 52 Cr and 54 Fe : E 4 /E 2 =1.6912 ~1.9732 β 2 =0.1509 ~0.2670 Q 0 =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. 44 Ca : approaches the U （ 5 ） limit when the spin the critical point of phase transformation appears when

13. 3 、 44.46.48.52 Ti are U(5)-SU(3) transitional nuclei and is the critical point for 46 、 48 Ti ， for 44 、 46 、 48 Ti ， the vibration characteristics is gradually strengthening with the increase of mass. 4 、 For 48-56 Cr are U(5)-SU(3) transitional nuclei, and the vibration characteristics strengthen with the increase of neutron number when 5 、 For 52-60 Fe ， these isotoles have complex structre in the low spin.

14. It is known that the doubly magic nuclei 40,48 Ca and 56 Ni have higher exciting energies on the first and second excited states ， In comparison ， 68 Ni 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 68 Ni may be a doubly magic nucleus ？ 6 、 68 Ni （ Z=28 ， N=40 ） is similar in E-GOS curve to doubly magic nuclei 40,48 Ca and 56 Ni when

16. 四、 Conclusions the doubly magic nuclei have similar E-GOS curves at the low spin state. the doubly magic nuclei have similar E-GOS curves at the low spin state. the singly magic nuclei have characteristics of collective motion when the number of valence nucleon increases and closes to mid-shell. the singly magic nuclei have characteristics of collective motion when the number of valence nucleon increases and closes to mid-shell. The isospin effect plays an important role in the shape phase transition of neutron-rich even-even light nuclei. The isospin effect plays an important role in the shape phase transition of neutron-rich even-even light nuclei. 68 Ni is a doubly magic nucleus. 68 Ni is a doubly magic nucleus.