**Commenced**in January 2007

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**Paper Count:**31743

##### Study of Proton-9,11Li Elastic Scattering at 60~75 MeV/Nucleon

**Authors:**
Arafa A. Alholaisi,
Jamal H. Madani,
M. A. Alvi

**Abstract:**

The radial form of nuclear matter distribution, charge and the shape of nuclei are essential properties of nuclei, and hence, are of great attention for several areas of research in nuclear physics. More than last three decades have witnessed a range of experimental means employing leptonic probes (such as muons, electrons etc.) for exploring nuclear charge distributions, whereas the hadronic probes (for example alpha particles, protons, etc.) have been used to investigate the nuclear matter distributions. In this paper, p-^{9,11}Li elastic scattering differential cross sections in the energy range to MeV have been studied by means of Coulomb modified Glauber scattering formalism. By applying the semi-phenomenological Bhagwat-Gambhir-Patil [BGP] nuclear density for loosely bound neutron rich ^{11}Li nucleus, the estimated matter radius is found to be 3.446 *fm* which is quite large as compared to so known experimental value 3.12 *fm*. The results of microscopic optical model based calculation by applying Bethe-Brueckner–Hartree–Fock formalism (BHF) have also been compared. It should be noted that in most of phenomenological density model used to reproduce the p-^{11}Li differential elastic scattering cross sections data, the calculated matter radius lies between 2.964 and 3.55 *fm*. The calculated results with phenomenological BGP model density and with nucleon density calculated in the relativistic mean-field (RMF) reproduces p-^{9}Li and p-^{11}Li experimental data quite nicely as compared to Gaussian- Gaussian or Gaussian-Oscillator densities at all energies under consideration. In the approach described here, no free/adjustable parameter has been employed to reproduce the elastic scattering data as against the well-known optical model based studies that involve at least four to six adjustable parameters to match the experimental data. Calculated reaction cross sections σ_{R} for p-^{11}Li at these energies are quite large as compared to estimated values reported by earlier works though so far no experimental studies have been performed to measure it.

**Keywords:**
Bhagwat-Gambhir-Patil density,
coulomb modified Glauber model,
halo nucleus,
optical limit approximation.

**Digital Object Identifier (DOI):**
doi.org/10.6084/m9.figshare.12489875

**References:**

[1] I. Tanihata, et al. “Measurements of interaction cross sections and nuclear radii in the light p-shell region,” Phys. Rev. Lett., vol. 55, pp. 2676-79, Dec.1985.

[2] I. Tanihata et al. “Determination of the density distribution and the correlation of halo neutrons in 11Li,” Phys. Lett. B, vol. 287, pp. 307-311, Jan.1992.

[3] G. D. Alkhazov, S. L Belostotsky, A. A. Vorobyov, “Scattering of 1 GeV protons on nuclei,” Phys. Reports, vol. 42, pp. 89-144 June 1978.

[4] P. Egelhofaf, “Probing the halo structure of exotic nuclei by direct reactions with radioactive beams,” Nucl. Phys. A, vol. 722, pp. C254-60, July 2003.

[5] A. V. Dobrovolsky et al. “Study of the nuclear matter distribution in neutron-rich Li isotopes,” Nucl. Phys. A, vol. 766, pp. 1-24, Feb. 2006.

[6] J. S. A1-Khalili and J. A. Tostevin, “Matter radii of light halo nuclei,” Phys. Rev. lett., vol. 76, pp. 3903-06, May 1996.

[7] C.B. Moon et al. “Measurements of 11Li+ p and 9Li+ p elastic scatterings at 60 MeV,” Phys. Lett. B, vol. 297, pp. 39-43, Dec. 1992.

[8] M. Y. M. Hassan, M. Y. H. Farag, H. E. H. Esmael and H. M. Maridi, “Microscopic model analysis of 11Li+ p elastic scattering at 62, 68.4, and 75 MeV/nucleon,” Phys. Rev. C, vol. 79, pp. 014612, Jan. 2009.

[9] V.K. Lukyanov et al. “Microscopic analysis of 11Li elastic scattering on protons and breakup processes within the 9Li+2n cluster model,” Phys. Rev. C, vol. 88, pp. 034612, Sept. 2013.

[10] K Spasovaet al. “Microscopic analysis of 11Li elastic scattering on protons and breakup processes within 9Li+ 2n cluster model, “Journal of Physics: Conference Series 2014, vol. 1, p. 012031. IOP Publishing

[11] Manjari Sharma and W. Haider, “Study of 11Li+ p elastic scattering using BHF formalism with three body force, “J. Phys. G: Nucl. and Particle Phys., vol. 45, pp. 045102, March 2018.

[12] S. K. Charagi, S. K Gupta, “Coulomb-modified Glauber model description of heavy-ion reaction cross sections,” Phys. Rev. C, vol. 41, pp. 1610-18 April 1990.

[13] A. Bhagwat, Y. K. Ghambhir and S. H. Patil, “Nuclear densities of Li isotopes,” J. Phys. G: Nucl. Particle Phys., vol. 27, B1-B7, Feb. 2001.

[14] R. J. Glauber, in Lecture on Theoretical Physics vol. 1, ed. by W.E. Brittin, L.C. Dunham (Interscience, New York, 1959), p. 315

[15] B. Abu-Ibrahim, W. Horiuchi, A. Kohama and Y. Suzuki, “Reaction cross sections of carbon isotopes incident on a proton,” Phys. Rev. C, vol. 77, pp. 034607, March 2008.

[16] M.A. Alvi, “Study of Different Forms of Density Distributions in Proton–Nucleus Total Reaction Cross Section and the Effect of Phase in NN Amplitude,” Braz. J. Phys., vol 44, pp. 55–63, Jan. 2014

[17] I. Ahmad, M. A. Abdulmomen, L. A. Al-Khattabi, “Alpha-nucleus total reaction cross section in the rigid projectile model using microscopic N-α amplitude,” Int. J. Modern Phys. E, vol. 10, pp. 43-53, Feb. 2001.

[18] Y. K. Gambhir, S. H. Patil, “Some characteristics of nuclear densities,” Z. Physik A Atomic Nuclei, vol. 324, pp. 9-13, March 1986.

[19] G. Baur and S. Typel, “Direct reactions with exotic nuclei, nuclear structure and astrophysics,” Prog. Part. Nucl. Phys., vol. 59(1), pp. 122-30, July 2007

[20] J S. Karataglidis, P. J. Dortmans, K. Amos, and C. Bennhold, “Alternative evaluations of halos in nuclei,” Phys. Rev. C, vol. 61, pp. 024319, Jan. 2000

[21] Syed Rafi, A. Bhagwat, W. Haider, and Y. K. Gambhir, “Brueckner-Hartree-Fock–based optical potential for proton-4,6,8He and proton-6,7,9,11Li scattering,”Phys. Rev. C, vol. 86, pp. 034612, Sept. 2012.