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The Examination of the Halo Nucleus Properties of Li Isotopes According International Journal of Engineering and Technical Research (IJETR) ISSN: 2321-0869 (O) 2454-4698 (P) Volume-8, Issue-3, March 2018 The Examination of the Halo Nucleus Properties of 6-11Li Isotopes According to the Shell Model Dariush Amirhashemi, A.Güneİ Tanir, Kemal KRo Abstract– Halo nuclei are separated into two as two or one The nucleon number in the outside of the core in halo nuclei neutron halo nuclei depending on the nucleon number taking specifies how many halos that nucleus has. For instance; 11Li place in their final orbits. These cores have three mass isotope is a two neutron halo if 9Li is taken as a core. Two configurations as neutron-neutron-core (n+n+c). One neutron neutron halo nuclei have three-mass configuration (n+n+core) halo nuclei have two-mass configuration (n+c). Two mass system [11-12]. One halo nuclei could be explained with two-mass could be reduced to one mass system by accepting the last two neutrons of two halo nuclei called as dineutron as a single (n+core) system [13-14]. particle also by taking the phenomenon of pairing between the In the study, possible different combinations of all Li isotopes 11 nucleons into consideration. In this way, it becomes easier to and Li halo nucleus have been suggested, their ground state solve the cores transforming into one neutron halo state. The and excitation energies have been calculated and their firstly observed core of this mysterious nuclear structure called comparisons have been conducted with experimental studies. as neutron halo is 11Li and it still keeps its secrecy. The purpose of this study is the examination of the halo nucleus properties of 6-11 II. THEORY Li isotopes according to the shell model. To reach this 2.1. Neutron halo purpose in the study, the halo nuclei of all Li isotopes have been Most of the studies related to halo nuclei have been conducted suggested in different possible combinations and the ground states and excitation energies belonging to each state have been on neutron halo. The nuclei taking place in the drip line zone, calculated. which are light, unstable and with neutron excess are generally considered as neutron halo nuclei. There are various Index Terms– Halo nuclei, shell model, 6-11 Li isotopes, nuclei in the neutron halo state, but the nucleus which has excitation energy been studied most is 11Li. The first indication of the halo structure was understood with the study conducted on 11Li I. INTRODUCTION isotope by Tanihata in 1985 for the nuclei close to the neutron 6 11 I4 8 It is known that the neutrons and protons within the atom drip line. The nuclei such as He, Be, Be and He out of the nucleus have been arranged with different combinations. isotopic nuclei whose mass number is 6,8,11 and 14 are also Deviation is observed from the stability zone in the nuclei the important neutron halo nuclei on which studies have been both with neutron excess and proton excess. The zero-energy conducted. Moreover; there are also many nuclei candidate line in Z-N plane is called drip line [1]. In the experimental for the neutron halo in the drip line zone [15]. studies conducted with radioactive nuclear beams, exotic Halo nuclei are separated into two as two or one neutron halo nucleus structures have been met in the nuclei close to the drip nuclei depending on the nucleon number taking place in their 11 line. Some neutrons or protons forming the nucleus may final orbits. For instance; Li isotope becomes two neutron 9 11 classically pass to the forbidden zone. This state that could halos if Li is taken as a core, Be becomes one neutron halo 10 also be considered as nuclear stratosphere zone is called as nucleus if Be is taken as a core. The nuclei with neutron 6 8 14 17 halo state. The excitation energies of the final nucleon or excess such as He, He, Be and B are two neutron halo nucleons are too little in the nuclei close to the drip line nuclei due to the fact that they have two neurons in their final [2-3-4]. If 6-8 MeV in the stable nuclei are met, these are orbital. These nuclei have three mass configurations as around 1 MeV. Neutron intensity distribution also shows a neutron-neutron-core (n+n+c). One neutron halo nuclei have long tail. This situation is the neutron halo state [4-5-6]. two-mass configuration (n+c). Two mass system could be Although the mass intensity of a halo nucleus is too little, it reduced to one mass system by accepting the last two neutrons affects the reaction impact sections very much. These and of two halo nuclei called as dineutron as a single particle also similar properties are the supports sufficient for revealing the by taking the phenomenon of pairing between the nucleons new properties of such nuclei. into consideration. In this way, it becomes easier to solve the The first nucleus observed as the halo nucleus is 11Li nucleus nuclei transforming into one neutron halo state [16]. having neutron halo. The secret structure of 11Li still keeps its 2.2. Binding and Excitation Energies secrecy. Some of the nuclei considered as neutron halo are Binding energy is the negative of the energy necessary to b 6He, 11Be, 14Be and 17B [7-8-9]. The nuclei with neutron separate the E core into its protons and neutrons. The highest excess are called neutron halo (such as 6He, 8He, 14Be, 9Li, value of the binding energy is when the nucleus is in ground 11Li and 11Be) and the nuclei with proton excess are called state. Ex(n) excitation energy of n. excited state is found from b proton halo (such as 14B, 9C, 17F, 17Ne and 12N) [10]. E (n) binding energy. b b Ex(n)=E (n)-E (0) (2.1) Dariush Amirhashemi, SÕnav College, 06520 AnNara; TurNey Eb(0) is the ground state energy. There are many terms A.Güneİ Tanir, Gazi University, Faculty Of Science, 06500 Ankara, contributing to the total binding energy of the nucleus; Turkey b 2 (1) 2 b Kemal Koç, Baskent University, Faculty Of Education, 06530 Ankara, E G (core+ p ) = 2er +E G (r )+E (core) (2.2) Turkey 36 www.erpublication.org The Examination of the Halo Nucleus Properties of 6-11Li Isotopes According to the Shell Model p n Here; 2e r is the negative of the energy necessary for (1p3/2) (1p3/2) , (1,0) state; E b ( 4He +1p ) ()()p e + n e + E 1( p ) + E b ( 4He) extracting two particles from the potential well. It is accepted G 2/3 p3 / 2 p3 / 2 G p3 / 2 that two particles move independently in r orbit. This potential well is not dependent on the number of the particles E b ( 4He) + ()()p e + n e + 1( p ) 2 V 1()2,1( p ) 2 out of the core. 1p3 / 2 1p3 / 2 2/3 2/3 10 The contribution to the binding energy occurring from the mutual interaction of two external-core particles is shown )1( 2 with EG (r ) . This term is not only dependent on r , it is b EG =-0,53(1,2)-3(1,4)+0,2+0,887+1,967-28,297=-30,079MeV also dependent on b J G and TG . E (core) represents the p n binding energy of the particle in the core. (1p3/2) (1p3/2) , (3,0) state; b If the closed shell core is accepted as inert, E (core) term is E b ( 4He +1p ) E b ( 4He) + ()()p e + n e + 1( p )2 V (1,2) (1p ) 2 G 2/3 p3 / 2 p3 / 2 2/3 2/3 30 stable, Hamiltonyen of the system with (core+two nucleons) is; p n (1p3/2) (1p3/2) , (1,0) state; H=Hcore+H12 (2.3) E b E b ( 4He ) + ()()p e + n e + 1( p )2 (1p )2 V (1,2) (1p )2 (1p ) 2 G p 2/3 p 2/3 3 / 2 1/ 2 3 / 2 1/ 2 A A A 10 H [()T k +U (k)]+[ W (,)k l - U (k)] (2.4) kor ¦ ¦ ¦ b k 3 3 k<l k 3 E - 6,1 A - 3B + C + ()()p e + n e G 0 1p3 / 2 1p1 / 2 2 2 A 2 (2.5) H12 ¦[()T k +U (k )]+ [ ¦¦W (,)k l +W )2,1( - ¦U (k )] k k k 1 1l 3 1 (1p )p (1p )n, (2,0) state; Here; H represents the interaction between the core 3/2 3/2 core particles (k=3,...A). If the core is accepted as inert, the b b 4 2 2 2 2 EG E ( He ) + ()()p e1p + n e1p + 1( p3 / 2 ) (1p1/ 2 ) V 1()2,1( p3 / 2 ) (1p1/ 2 ) contribution of Hcore to total energy is stable. H12 term 2/3 2/3 20 expresses the contribution coming from two extra-core particles. E b - 2,1 A - 3B + C + ()()p e + n e If there are more than two nucleons outside the core; for G 0 1p3 / 2 1p1 / 2 p n p n instance, in n particle r shell and m particle l shell, the When (1p3/2) (1p3/2) , (1,0) state and (1p3/2) (1p3/2) , (2,0) binding energy is; states are examined; it is necessary to know the excited states 5 5 E b + r n + l m =E +E b + + +E 1 r nl m (2.6) of He and Li to calculate the binding energies of (p)ep1/2 and G (core ) c (core) ner mel G ( ) (n)ep1/2 (proton and neutron).
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