**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**33090

##### Applying the Crystal Model Approach on Light Nuclei for Calculating Radii and Density Distribution

**Authors:**
A. Amar

**Abstract:**

A new model namely, the crystal model, has been modified to calculate radius and density distribution of light nuclei up to 8Be. The crystal model has been modified according to solid state physics which uses the analogy between nucleon distribution and atoms distribution in the crystal. The model has analytical analysis to calculate the radius where the density distribution of light nuclei has been obtained from the analogy of crystal lattice. The distribution of nucleons over crystal has been discussed in general form. The equation used to calculate binding energy was taken from the solid-state model of repulsive and attractive force. The numbers of the protons were taken to control repulsive force where the atomic number was responsible for the attractive force. The parameter has been calculated from the crystal model was found to be proportional to the radius of the nucleus. The density distribution of light nuclei was taken as a summation of two clusters distribution as in 6Li=alpha+deuteron configuration. A test has been done on the data obtained for radius and density distribution using double folding for d+6,7Li with M3Y nucleon-nucleon interaction. Good agreement has been obtained for both radius and density distribution of light nuclei. The model failed to calculate the radius of 9Be, so modifications should be done to overcome discrepancy.

**Keywords:**
nuclear lattice,
crystal model,
light nuclei,
nuclear density distributions

**References:**

[1] R. Guardiola, I. Moliner , M. A. Nagarajan , “Alpha-cluster model for 8Be and 12C with correlated alpha particles,” Nuclear Physics A 679, 2001, 393–409.

[2] A. Amar, “Spectroscopic information of 6Li from d, 3He and alpha elastically scattered by 6Li,” International Journal of Modern Physics E Vol. 23, No. 08, 1450041, 2014.

[3] Ulf-G. Meißner, Sci. Bull. (2015) 60(1):43–54, Physics & Astronomy, Dean Lee, Ulf-G. Meißner , Keith A. Olive, Mikhail Shifman , and Thomas Vonk,“θ-dependence of light nuclei and nucleosynthesis,” Physical Review Research 2, 033392, 2020.

[4] Dean Lee, Gautam Rupak, “Radiative capture reactions in lattice effective field theory,” Physical Review Letters, PRL111, 032502, 2013.

[5] O. Jensen, G. Hagen, T. Papenbrock, D. Dean, J. Vaagen, “Computation of spectroscopic factors with the coupled-cluster method,” Phys. Rev. C 82, 014310, 2010.

[6] G. Hagen, N. Michel, “Elastic proton scattering of medium mass nuclei from coupled-cluster theory,” Phys. Rev. C 86, 021602, 2012.

[7] Petr Navrátil, R. Roth, S. Quaglioni, “Ab initio many-body calculation of the 7Be(p,g)8B radiative capture,” Phys. Lett. B 704, 379, 2011.

[8] Petr Navrátil, S. Quaglioni, “Ab Initio Many-Body Calculations of the H3(d,n)He4 and He3(d,p)He4 Fusion Reactions,” Phys. Rev. Lett. 108, 042503, 2012.

[9] M. Lage, U.-G. Meißner, and A. Rusetsky,“ A method to measure the antikaon–nucleon scattering length in lattice QCD,” Phys. Lett. B 681, 439, 2009.

[10] V. Bernard, M. Lage, U.-G. Meißner, and A. Rusetsky, “Scalar mesons in a finite volume, J. High Energy Phys. 01, 2011, 019.

[11] H. B. Meyer, “Photodisintegration of a Bound State on the Torus,” arXiv:1202.6675.

[12] R. A. Briceno and Z. Davoudi, “Moving Multi-Channel Systems in a Finite Volume with Application to Proton-Proton Fusion,” arXiv:1204. 1110.

[13] K. M. Nollett, R. Wiringa, “Six-body calculation of the α-deuteron radiative capture cross section,” Phys. Rev. C 84, 024319 83, 041001, 2011.

[14] I. Brida, S. C. Pieper, R. Wiringa, Phys. Rev. C 2011.

[15] Michelle Pine et al., Eur.Phys. J. A, 2013, pp. 49-151.

[16] Ulf-G. Meißner, The 8th International Workshop on Chiral Dynamics, CD2015 29 June 2015 - 03 July 2015 Pisa,Italy.

[17] T. A. Lähde, E. Epelbaum, H. Krebs, D. Lee, U.-G. Meißner and G. Rupak, “Lattice Effective Field Theory for Medium-Mass Nuclei,” Phys. Lett. B 732 (2014) 110 (arXiv:1311.0477 (nucl-th).

[18] B. A. Urazbekov, A. S. Denikin, Eurasian Journal of Physics and Functional Materials, 2018, 2, pp. 17-22.

[19] Yu. N. Eldyshev et al, Sov. Jour. Nucl. Phys. 16, 1973, pp. 282.

[20] A. Amar, O. Hemada, Study an approach of crystal model, World Academy of Science, Engineering and Technology, International Journal of Nuclear and Quantum Engineering,Vol:15, No:2, 2021.

[21] James F. Shackelford, Introduction to Materials Science for engineer, Pearson; 8 edition (April 12, 2014).

[22] I. Angelia, K. P. Marinova, Atomic Data and Nuclear Data Tables 99 2013, pp. 69–95.

[23] Bu Borasoy, Evgeny Epelbaum, Hermann Krebs, Dean Lee, Ulf-G. Meißner, R. Bijker, F. Iachello, Phys. Rev. Lett. 112, 2104, 15, 152501.

[24] Ghahramany et al. Journal of Theoretical and Applied Physics 2012, 6:3, http://www.jtaphys.com/content/6/1/3, New approach to nuclear binding energy in integrated nuclear model.

[25] D. R. Tilley , J. H. Kelley, J. L. Godwina,, D. J. Millener, J. E. Purcell, C. G. Sheua,, H. R. Weller Nuclear Physics A 745, 2004, pp. 155–362.

[26] K. H. Bray T, Mahavir Jain Tt, K. S. Jayaraman, G. Lobianco, G. A. Moss W. T. H. Van Oers And D. O. Wells F. Petrovich, Nuclear Physics A l89, 1972, pp. 35-64.

[27] B. A. Watson, P. P. Singh, and R. E. Segal, Phys. Rev. Vol. 182, No. 4 1969, pp. 977-989.

[28] J. Cook, Nuclear Physics A382, 1982, pp. 61-70; P. E. Hodgson, The Deuteron-Nucleus Optical Potential, Nuclear Physics Laboratory, Oxford, 1966; A. Amar, Int. J. Modern. Phys. E, Vol. 23, No. 8, 2014, 1450041, 3: P. E. Hodgson, Rep. Prog. Phys. 34, 1971, pp. 765.

[29] I. J. Thompson, Fresco 2.0, Department of physics, University of Surrey, Guildford GU2 7XH, England, 2006.

[30] S. Matsuki, S. Yamashita, K. Fukunaga, D.C. Nguyen, N. Fujiwara, T. Yanabu, J, Jpj, 26, (6), 1344, 1969, 06.

[31] J. Arvieux, R, CEA-R-3392 ,1 , 196803.

[32] N. Burtebayeva et al. Acta Physica Polonica B, No. 5, Vol. 46, 2015.