Proceedings of the DAE Symp. on Nucl. Phys. 63 (2018) 792 Formation of medium heavy mass nuclei through r-process R. R. Swain1, S. K. Patra2,∗ and B. B. Sahu1 1School of Applied Sciences, KIIT Deemed to be University, Bhubaneswar-751024, Odisha, India and 2Institute of Physics, Sachibalaya Marg, Bhubaneswar-751005,India Introduction Theoretical formalism The astrophysical site of the r-process, the The relativistic concept comes from the in- rapid neutron-capture process that makes half teraction of nucleons through mesons. The of the elements heavier than iron, remains quantum hydrodynamics (QHD) [5, 6] says, a long-standing mystery of nucleosynthesis. nucleus can be formed in a system by coupling Upto Fe, the elements are produced by rapid the dirac nucleons with the exchange meson neutron capture process and after that the fu- through an effective Lagrangian. So the La- sion process changes to endothermic process. grangian density is defined in meson-exchange While large uncertainties remain about the model as; site of the r-process and its exact location, L = L + L + L (1) it is thought to occur in environments with N m int a high density of free neutrons. There are LN represents the Lagrangian of free nucleon, a number of astrophysical scenarios suggested µ as possible sites [1, 2]. But the neutron cap- LN = ψ¯(iγµ∂ − m)ψ (2) ture processes depends on neutron flux that are defined by rapid- and slow-process. At Lm consists of the free meson field and elec- high neutron density the r-process takes place tromagnetic field as; very nearer to the drip-line nuclei, whereas s- 1 µ 1 2 2 process has enough time for beta disintegra- Lm = ∂µσ∂ σ − mσ σ (3) tion which helps for the production of nuclei 2 2 nearer to the beta stability line. Here, in this 1 µν 1 2 µ − Ωµν Ω + mω ωµ ω work we are trying to investigate the forma- 2 2 −→ −→ −→ tion of medium heavy mass nuclei i.e. from 1 µν 1 2−→ µ 1 µν − R µν R + mρ ρ µρ − Fµν F Ga-Pd through r-process and determine the 4 2 4 path by using relativistic mean-field (RMF) L represents the Lagrangian of interac- formalism with DD-ME2 force parameter set. int tion part The calculated outcomes are able to corre- late with the macro-microscopic finite range µ −→ µ −→ Lint = −gσψψσ¯ − gωψγ¯ ψωµ − gρψ¯ τ γ ψ. ρ µ(4) droplet model (FRDM) data [3, 4]. So, we −eψγ¯ µψ A study the binding energy (B.E) of the nuclei, µ nuclear radii such as neutron radius (r ), pro- n Results and discussion ton radius (rp), matter radius (rm) to know the structural properties of all the nuclei. As In this paper, we investigate the formation a necessary requirement for the determination of medium-heavy mass nuclei through rapid for the r-process path we calculate the one neutron capture process (r-process) path from neutron separation energy (Sn) as well as two Ga Pd using relativistic mean field formal- neutron separation energy (S2n). ism (RMF) with DDME-2 force parameter set [5],[6]. We calculate the ground state proper- ties such as binding energy, nuclear radii such as neutron radius (rn), proton radius (rp), ∗ Electronic address: [email protected] matter radius (rm), one neutron separation Available online at www.sympnp.org/proceedings Proceedings of the DAE Symp. on Nucl. Phys. 63 (2018) 793 Ga 81−88 83−97 83−103 4.8 r 6 n RMF Ga β Ge β As β r FRDM −→ −→ −→ 4.6 p r 85−104 94−103 95−107 m 4 Seβ Brβ Krβ n 4.4 S −→ −→ −→ 94−102 106−113 107−112 2 Nuclear radii 4.2 Rbβ−→ Srβ−→ Y−→ β 4 0 110−122 111−123 114−124 730 20 Zrβ Nbβ Moβ 45 50 55 60 65 70 45 50 55 60 65 70 −→ −→ −→ − − − − 720 RMF 119 125 126 127 127 128 128 129 15 RMF Tcβ Ruβ Rhβ P d.... FRDM FRDM −→ −→ −→ 710 2n 10 S This r-process path is determined with the 700 B.E. (MeV) 5 approximation that when the two neutron sep- 690 aration energy lies in between 2-4 MeV and is 680 0 45 50 55 60 65 70 45 50 55 60 65 70 N N obtained near the drip line as suggested in Ref. [1]. FIG. 1: Plot of binding energies, nuclear radii, one-neutron separation energy (Sn) and two- Conclusion S neutron separation energy ( 2n) verses neutron In conclusion, the structural properties such number (N) of Ga element as binding energy, nuclear radii for different elements from Ga to Pd nuclei are calculated Pd 5.6 20 by using RMF formalism with DDME-2 force rn r 15 RMF parameter set. The evaluated results are in 5.2 p FRDM r m agreement with FRDM results in the isotopic n 10 4.8 S chain. The one neutron- and two neutron Nuclear radii 5 separation energies are also evaluated from 4.4 0 1200 30 the calculated binding energies. The r-process 50 100 50 100 25 1100 path for the formation of medium mass heavy 20 RMF 1000 FRDM and super-heavy nuclei suggested here may 2n 15 S 900 10 be useful for the future experiment. B.E. (MeV) RMF 800 FRDM 5 0 700 This work is supported by project No. 40 50 60 70 80 90 100 110 40 50 60 70 80 90 100 110 N N SR/FTP/PS-106/2013, SERB, DST, Govt. of India. FIG. 2: Plot of binding energies, nuclear radii, one-neutron separation energy (Sn) and two- S neutron separation energy ( 2n) verses neutron References number (N) of Pd element [1] E M Burbidge, G R Burbidge, Fowler W A and Hoyle F 1957 Rev. Mod. Phys. 29 energies (Sn) and two neutron separation en- 547. ergies (S2n) also shown in figures 1 and 2. We [2] A. G. W. Cameron, Report CRL-41, have compared our calculated results with the Chalk River (1957). available FRDM results [3, 4] and it can be [3] P. Moller, J. R. Nix, W. D. Myers and seen that the evaluated results are in good W. J. Swiatecki, At. Data and Nucl. Data agreement with the FRDM results. Tables 59, 185 (1995) In this r-process, the nucleus Fe or Ni [4] P. Moller, J. R. Nix and K. -L. Kratz, At. captures the neutron until the formation of Data and Nucl. Data Tables 66, 131 (1997) a neutron-rich nuclei. Then this unstable [5] B.D. Serot, J.D. Walecka, Adv. Nucl. neutron-rich nuclei undergoes β-emission and Phys. 16 (1986) 1. formed a less neutron-rich Cu nuclei. Now [6] G.A. Lalazissis, P. Ring, D. Vretenar this procedure continues and built a new (Eds.), Lecture Notes in Physics, Vol. 641, heavier element which is shown below. Springer-Verlag, Heidelberg, 2004. Available online at www.sympnp.org/proceedings.