SHAPE PHASE TRANSITIONS AND POSSIBLE E(5) SYMMETRY NUCLEI FOR <font>Ti</font> ISOTOPES

Guo, Jian-You; Fang, Xiang Zheng; Sheng, Zong Qiang

doi:10.1142/s0218301308009860

Cited by 9 publications

(8 citation statements)

References 31 publications

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“…This elicites a very large β 2 deformation with the formula. However, in medium-mass and heavy region usage of the formula is siutable [30].…”

Section: Resultsmentioning

confidence: 99%

“…In these studies, 148,150,152 Sm and 128,130,132,134 Ce have been suggested as an example of the possible critical-point nuclei with X(5) symmetry. Beside, Ti isotopes have been examined in the HFB method [29] and RMF model [30] to investigate the critical-point nuclei. In these studies, 48,52,60 Ti and 46,52,60 Ti have been found as to be the possible candidate critical-point nuclei with E(5) symmetry in the RMF model and HFB method, respectively.…”

Section: Introductionmentioning

confidence: 99%

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Shape of Te isotopes in mean-field formalism

Bayram¹,

Yilmaz²

2014

Pramana - J Phys

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“…This elicites a very large β 2 deformation with the formula. However, in medium-mass and heavy region usage of the formula is siutable [30].…”

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Shape of Te isotopes in mean-field formalism

Bayram¹,

Yilmaz²

2014

Pramana - J Phys

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“…Bu simetriler deneysel olarak Ba-134 [8] ve Sm-152 [9] çekirdeklerinin spektrumlarından belirlendi. Genellikle QPT'ler geometrik modellerle [10][11][12] ve cebirsel modellerle [12][13][14][15][16][17][18][19][20] çalışılmasına rağmen teorik çalışmalar RMF modeli [21][22][23][24][25] ve HartreeFock-Bogoliubov (HFB) modeli [3,26,27] ile de gerçekleştirilmiştir. Bu çalışmalarda hem RMF ve hem de HFB modelinde kısıtlı kuadrupol moment değerleri ile elde edilen potansiyel enerji eğrileri hesaplanmaktadır (PEC).…”

Section: Introductionunclassified

124-134Xe Izotopları için Triaxiall RMF Hesaplamaları

Bayram¹,

Akkoyun²,

Şentürk³

2016

CSJ

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Özet. Bu çalışmada çift-çift [124][125][126][127][128][129][130][131][132][133][134] Xe çekirdekleri için Relativistik Ortalama Alan (RMF) Modeli kullanılarak taban durum nükleer özellik hesaplamaları yapılmıştır. Bu çekirdekler için RMF+DDM2 etkileşmesi ile taban durum bağlanma enerjileri için deneysel değerlere çok yakın sonuçlar elde edilmiştir. Triaxiall simetriye dayalı hesaplamalar yapılarak [124][125][126][127][128][129][130][131][132][133][134] Xe izotop zincirinde izotopların taban durum şekilleri üzerine bir analizde sunulmaktadır. Özellikle deneysel olarak 130 Xe çekirdeğinin E(5) simetrisine sahip kritik nokta çekirdeği olduğu iddia edilmektedir. Bu bağlamda Xe izotopları için RMF modeli çerçevesinde elde edilen potansiyel enerji yüzeyleri (PES) kullanılarak E(5) simetrili çekirdek taraması yapılmıştır. Çift-çift [124][125][126][127][128][129][130][131][132][133][134] Xe izotopları için izotop zinciri boyunca şekil evrimi detaylıca tartışılmıştır. Anahtar kelimeler: RMF modeli, Bağlanma enerjisi, Xe izotopları, PES, E(5) simetrisi Triaxiall RMF Calculations for 124-134 Xe IsotopesAbstract. In this study, ground-state nuclear properties of even-even [124][125][126][127][128][129][130][131][132][133][134] Xe nuclei have been calculated by using Relativistic Mean Field (RMF) model. By using RMF+DDM2 interaction the ground-state binding energies of these nuclei have been predicted as very close to experimental values. Also, an analizing on the ground-state shape of [124][125][126][127][128][129][130][131][132][133][134] Xe isotopes is presented by using calculations based on triaxiall symmetry. In particular, 130 Xe nuclei has been pointed out as possible critical point nuclei with E(5) symmetry from experimental studies. For this reason, by using potential energy surfaces (PES) of [124][125][126][127][128][129][130][131][132][133][134] Xe nuclei obtained from RMF model, scanning for E(5) symmetry in this isotopic chain has been done. For even-even 124-134 Xe nuclei, shape evolution has been discussed in detail.

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“…Also, phenomenological mean field models (e.g, Hartree-Fock-Bogoliubov (HFB) method [7,8] and relativistic mean field (RMF) model [9,10,11]) have been used to investigate the critical-point nuclei with E (5) or X (5) symmetry in Ref. [12,13,14,15,16,17,18,19,20]. In these studies, potential energy curves (PECs) obtained from quadrupole constrained calculations have been used for describing the possible critical-point nuclei.…”

Section: Introductionmentioning

confidence: 99%

Consistent empirical physical formulas for potential energy curves of 38–66Ti isotopes by using neural networks

Akkoyun

Bayram

Kara

et al. 2013

Phys. Part. Nuclei Lett.

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8Nuclear shape transition has been actively studied in the past decade. In particular, the 9 understanding of this phenomenon from a microscopic point of view is of great 10 importance. Because of this reason, many works have been employed to investigate shape 11 phase transition in nuclei within the relativistic and non-relativistic mean field models by 12 examining potential energy curves (PECs). In this paper, by using layered feed-forward 13 neural networks (LFNNs), we have constructed consistent empirical physical formulas 14 (EPFs) for the PECs of Ti calculated in Hartree-Fock-Bogoliubov (HFB) method 15 with SLy4 Skyrme forces. It has been seen that the PECs obtained by neural network 16 method are compatible with those of HFB calculations. 18The study of the structural evolution in atomic nuclei with changing numbers of their 2 neutron and proton constituents dates back to the early days of the nuclear physics. In the 3 last decade, a number of theoretical developments have given insights into, and ways to 4 model, this structural evolution, particularly in transitional regions of rapid change [1, 2]. 5These breakthroughs involve the concepts of quantum phase transitions (QPTs) and the 6 critical-point symmetries. A new class of symmetries E(5) and X(5) have been suggested 7 to describe shape phase transitions in atomic nuclei by Iachello [3, 4]. The E(5) critical-8 point symmetry has been found to correspond to the second order transition between U(5) 9 and O(6), while the X(5) critical-point symmetry has been found to correspond to the first 10 order transition between U(5) and SU(3). These symmetries was experimentally 11 identified in the spectrum of 134 Ba [5] and 152 Sm [6]. 12 From theoretical point of view, QPTs have been studied within the Interacting Boson 13 Model (IBM) and the solutions of Bohr-Mottelson differential equations. They are useful 14 representations for describing QPTs in nuclei. Also, phenomenological mean field 15 models (e.g, Hartree-Fock-Bogoliubov (HFB) method [7, 8] and relativistic mean field 16 (RMF) model [9, 10, 11]) have been used to investigate the critical-point nuclei with E(5) energy curves (PECs) obtained from quadrupole constrained calculations have been used 19 for describing the possible critical-point nuclei. Relatively flat PECs are obtained for 20 critical-point nuclei with E(5) symmetry, while in nuclei with X(5) symmetry, PECs with 21 a bump are obtained. It should be noted, however, that one should go beyond a simple 22mean field level for a quantitative analysis of QPT in nuclei. For this purpose, some 23 methods have been utilized in Ref. [21, 22, 23, 24]. The application of these methods for 24 a systematic study of QPT in nuclei is at present still very time-consuming. Therefore, the 25 evolution of the PECs along the isotopic or isotonic chains is important and can be used 26 for qualitative understanding of QPTs in nuclei. 27In Ref. [19], HFB method with SLy4 Skyrme forces have been employed to 28 investigate ground-state properties of even-even 3...

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SHAPE PHASE TRANSITIONS AND POSSIBLE E(5) SYMMETRY NUCLEI FOR Ti ISOTOPES

Cited by 9 publications

References 31 publications

Shape of Te isotopes in mean-field formalism

Shape of Te isotopes in mean-field formalism

124-134Xe Izotopları için Triaxiall RMF Hesaplamaları

Consistent empirical physical formulas for potential energy curves of 38–66Ti isotopes by using neural networks

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