Halo Or Skin in Zr-Isotopes Harvinder Kaur, Sarabjeet Kaur, and M

Proceedings of the DAE Symp. on Nucl. Phys. 62 (2017) 350

Halo or Skin in Zr-Isotopes Harvinder Kaur, Sarabjeet Kaur, and M. S. Mehta∗ Department of Physics, Rayat Bahra University, Mohali-140 104, INDIA

Introduction to the continuum, the Borromean structure etc. In the past, several theoretical models The information of properties of neutron-rich in relativistic kinematics such as Hartree Bo- (in particular) nuclei in the region away from goliubov with or without the Fock term, Rel- β-stability line is becoming more and more ativistic Mean Field model with hartree ap- clear with the availability of more energetic proximation have been developed for a self- radioactive beams of short-lived nuclei of consistent description of spherical as well as the rare isotope. In the recent decades, deformed halo nuclei. the studies of nuclear structure has made a considerable progress by exploring new phe- nomena that opened up the new frontiers in Very recently, the nuclear reaction cross- sections of 19,20,22C [3] nuclei are measured the field. The density distribution of nucleons 22 is an important observable of nucleus which and it is shown that C nucleus has halo gives information of a nucleus . The density structure. This drip-line nucleus is reported 42,44 distribution of nuclei towards the drip-line is to be two neutron halo nucleus. Also, Mg quite different to the one near the β-stability nuclei which are close to neutron drip-line have been predicted as showing halo structure line. A significant character in nuclei at the 11 19 31 extreme is the existence of nuclear halos and [4, 5]. The nuclei Be, C, Ne are the ex- skins [1]. This exotic property of nuclei in amples of one-neutron halo [6, 7]. Usually, light mass region was first observed by I. halo is the name given to the long extended Tanihata et al. [2], experimentally, in 1985 low density tail in the nuclear matter distri- for 11Li. bution, which results in larger radius. On the other hand, the neutron skin is the significant The definition of a halo nucleus is still be- difference in the values of matter radii for neu- ing debated. The large value of N/Z ratio trons and protons. The neutron skin, qualita- in unstable nuclei produces a large difference tively, describes an excess of neutrons at the in Fermi energy of neutrons and protons, and nuclear surface. Recently, the skin thickness thus, decoupling of neutron and proton distri- is calculated [8] for 208Pb and its correlation butions appears as halos and/ or skins. The with the slope of symmetry energy. halo structure in nuclei can appear when the system reaches the threshold and the role of long-range repulsive force on relative motion In the present work we employ axially de- of particle becomes less. As a result the tail formed relativistic mean field model with NL3 of wave function extends farther away from parameterization to calculate the neutron the region of nuclear interaction, thereby pro- and proton density distributions. ducing an unusual extended region of low nuclear density distribution. The other interest- ing features in nuclei close to neutron drip-line are, for example, the largely extended spatial Formalism density distribution, coupling of bound states The Relativistic Mean Field formalism is used here to investigate the decay properties of superheavy nuclei. The Lagrangian density ∗Electronic address: [email protected] as given by,

Available online at www.sympnp.org/proceedings Proceedings of the DAE Symp. on Nucl. Phys. 62 (2017) 351

-10 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 -1 10 10

-2 132 -2 10 n Zr 10 1 1 p 130 µ µ 2 2 -3 Zr -3 L = ψi{iγ ∂µ − M}ψi + ∂ σ∂µσ − mσσ 10 10 2 2 -4 -4 10 10 1 3 1 4 1 µν 2 3 ) -2 -2 − g σ − g σ − g ψ ψ σ − Ω Ω -3 s i i µν 10 134 136 10 Zr Zr 3 4 4 (fm

n,p -3 -3 1 2 µ 1 µ 2 µ ρ 10 10 + m V Vµ + c3(VµV ) − gwψ γ ψiVµ w i -1 -1 2 4 10 10

-2 -2 1 1 2 138 µν µ µ µ 10 Zr 140 10 − B~ .B~ µν + m R~ .R~ µ − gρψ γ ~τψi.R~ Zr ρ i -3 -3 4 2 10 10

-4 -4 1 (1 − τ3) 10 10 − F µν F − eψ γµ ψ A 0 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 4 µν i 2 i µ r (fm) where ψ is Dirac spinor for nucleon and M is FIG. 1: The density distribution for even-even 130−140 mass of nucleon. The quantities mσ,mω, and Zr nuclei using NL3 parameter set. mρ are the masses of σ, ω, and ρ. The non- linear self interaction coupling of σ mesons is denoted by g2 and g3. In the present calcu- lations, we employ NL3 parameterization for considered here has extended tail as compared meson-baryon coupling. to proton density. The extension in neutron density is ≥ 2.5 fm at the outer region of nu- Results and Discussion clei. Such a long tail indicates the halo (or near halo) nature of these nuclei. At the cen- The halo and/or skin in nuclei is a threshold tral region the neutron density is compara- effect that arises due to a very weak binding tively larger than the proton density, which of the last one or two valence nucleons and shows Coulomb repulsion among protons. In 130−140 hence get decoupled from the rest of nucleons the isotopic series Zr most of the nu- in nucleus. The variation of neutron and clei are spherical or near spherical and oblate proton densities as a function of distance deformed. from the nucleus gives the insight of the distribution of nucleons near the surface of nucleus. The tail part of density distribution is important as far as the skin and halo References structure is concerned. [1] I. Tanihata, J. Phys. G: Nucl. Part. Phys. The baryon density is calculated by the re- 22, 157, (1996). lation given by, [2] I. Tanihata, et al., Phys. Rev. Lett. 55, 2676, (1985). A et al. 104 † [3] K. Tanaka, , Phys. Rev. Lett., , ρv(r) = X ψi (r)ψi(r) 062701, (2010). i=1 [4] L. Li, et al., Phys. Rev. C 85, 024312, The baryon density is the sum of squares of (2012). large and small components of Dirac spinors [5] Zhou, et al., Phys. Rev. C 82, 011301(R), and is normalized to nucleon number. (2010). In the present work, we calculate the neu- [6] T. Nakamura, et. al., Phys. Rev. Lett., tron and proton density distributions for even- 103, 262501, (2009). even Zr-isotopes (130−140Zr) using axially de- [7] A. Di Pietro, et. al., Phys. Rev. Lett., 105, formed relativistic mean field model. The den- 022701, (2010). sity distribution of neutron and proton is plot- [8] M. Warda, M. Centelles, X. Viñas, and X. ted in figure 1. From the figure it is clearly vis- Roca Maza, Acta Phys. Pol. B 43, 209, ible that the neutron density for all isotopes (2012).

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