Surface contours and shapes of Super Heavy Elements

Surface contours and shapes of Super Heavy Elements (SHE) S. Niranjani Department of Information Technology, MOHAMED SATHAK A. J. COLLEGE OF ENGINEERING, Egatur, Chennai – 603 103, India. S. Sudhakar and G. Shanmugam SK INSTITUTE OF HIGHER STUDIES, S-2, Lotus colony, Nandanam, Chennai – 600 035, India www. skhigherstudies. com www. skhigherstudies. org

Introduction ØA superheavy nucleus is one which is doubly magic beyond Pb (Z=82, N=126) and has a spherical shape, according to theoretical predictions. ØWhile the predicted magic number for proton beyond 82 is 114, 120, 124 or 126 according to non-self-consistent, self-consistent and relativistic theories, the neutron magic number after 126 is to be 172 or 184 according to those theories. Ø It is generally conjectured that while the macroscopicmicroscopic method may give the neutron magic number as N=184 correctly, it predicts the proton magic number beyond Pb only as Z=114 which turns out to be questionable. Ø We like to show in this work by surface contours that the spherical doubly magic nucleus after Pb is 310126184 and not 298114 184.

Surface contour ØA contour plot is a two-dimensional version of a threedimensional surface plot. ØGiven a function v=f ( x, y), a surface contour consists of all the curves that connect all the (x, y) points for a constant v. ØIn this work, we use Origin software to generate the contour plots given the values x, y and f(x, y).

Sample contour images Simple Contour lines. The number of contour lines, and the color map, and the format of the table can be modified. Some packages will allow you to smooth the sharp edges of the contour lines. Contour lines are good for black and white figures. The individual contours can be labeled. (Software: Tecplot). Taken from Website under Reference

Shaded Contours. Again, the number of contour lines, and the color map, and the format of the table can be modified. Some packages will blend the colors from one level to the next. No such blending occurs in the following image. Shaded contours work well with grayscale. For better results, set the color map to a grayscale while creating the image, rather than converting the color image to grayscale (either by just printing it out on a gray scale printer or by using various image manipulation tools). (Software: Tecplot). Taken from Website under Reference

Contour Lines Displayed on a Surface. The surface can be rotated to view it from different angles. (Software: Tecplot). Taken from Website under Reference

The Surface Colored by the Contour Values. The surface can be rotated to view it from different angles. Note: the colors from one level to the next are blended. (Software: IBM Data Visualization Explorer). Taken from Website under Reference

The Mesh Colored by the Contour Values. Sometimes, viewing the mesh that has been colored by contour values works quite well. The mesh allows you to see through the surface and view all the data. (Software: IBM Data Visualization Explorer). Taken from Website under Reference

Some packages have the ability to smooth out the sharp corners of contour lines. Instead of just drawing lines, such software pieces together smooth curves called splines. In the following image, the contours on the left are the basic contours, the contours on the right use splines. (Software: PV~Wave). Taken from Website under Reference

Advantages ØEasy detection of areas of rapid change and areas of constant value. ØWell suited to monochrome and gray scale reproduction. ØEasy to annotate within the field. ØWidely used and generally understood by others. ØCan easily be transformed and projected

Synthesis of Super Heavy Elements Recently, at Dubna, two super heavy isotopes 115 X 288 and 115 X 287 have been detected together with their expected alpha decay chains followed by spontaneous fission events [1].

Detection of Super Heavy elements

Details of calculations Our macroscopic-microscopic method essentially has two components for the evaluation of the potential energy of nuclei: A smooth macroscopic liquid-drop model energy part (ELDM). A fluctuating microscopic part consisting of shell and pairing corrections (Eshell and Epair). Thus the total energy E is given by, E(Z, N, ε, )=ELDM(Z, N, ε, ) + Eshell(Z, N, ε, ) + Epair(Z, N, ε, ) ε and being the elongational and the non-axial parameters.

Q values of alpha decay of some very heavy and super heavy nuclei Ap Zp Ad Zd Q (Me. V) Calculated 271 275 279 283 286 290 294 106 108 110 112 114 116 118 267 271 275 279 282 286 290 104 106 108 110 112 114 116 Experimental (Oganessian et al. ) 8. 37 9. 50 9. 75 9. 42 10. 21 10. 63 11. 42 8. 65 9. 44 9. 84 9. 67 10. 35 11. 00 11. 81

Shapes of Super Heavy Elements (taken from [3])

Results using contour plots The results of our calculations are given in the form of Potential Energy Surfaces (normalized to spherical -liquid-drop energy) in the (Q 20, Q 22) plane, plane where Q 20 = Q 0 cos and Q 22=Q 0/√ 2 sin [3].

Figure 1: Potential Energy Surface (normalized to spherical-liquiddrop energy in Me. V) for 82 Pb 208

Figure 2: Potential Energy Surface (normalized to spherical-liquid-drop energy in Me. V) for 114 X 286

Figure 3: Potential Energy Surface (normalized to spherical-liquid-drop energy in Me. V) for 124 X 300

Figure 4: Potential Energy Surface (normalized to spherical-liquid-drop energy in Me. V) for 126 X 310

References: [1] G. Shanmugam, S. Sudhakar and S. Niranjani Phys. Rev. C 72, 034310(2005) and references therein. [2] G. Shanmugam, S. Sudhakar, S. Niranjani and D. K. Mohapatra, submitted to Phys. Rev. C (2005). [3] S. Cwiok, P. H. Heenen and W. Nazarewicz, Nature 433, 705 (2005). Websites: http: //www. msi. umn. edu/user_support/scivis/techniques/contours. html