Post #19-My High School Research Paper

This is my research paper about the spontaneous fission of even-mass rutherfordium and seaborgium isotopes that I wrote for my AP English Literature class in senior year. This got a low B-, because the topic wasn't "debatable". He wrote a comment on my paper that I got a higher score than I deserved, but he acknowledged the good academic-style writing of it. Other students in my class discussed ethical issues and  other controversial topics, and some got high A grades. I have always been curious about why the specific isotopes of rutherfordium and seaborgium had such short spontaneous fission half-lives ever since I compiled my first isotope catalog, and so I took advantage of this opportunity to research the origin of the short half-lives. I really wish I could have researched the stabilizing effect of odd amounts of neutrons and/or protons in superheavy nuclei, but I had three other AP classes and I worked 25 hours a week at this point in my life. Here's the paper I wrote, including MLA citations:

Nate Kloepfer

Mr. Andrus

AP English Lit

4 April 2014

Rapid Spontaneous Fission of Even-Even Rutherfordium and Seaborgium Isotopes

        Looking at a sequential list of isotopes of the elements rutherfordium and seaborgium, it is hard for one not to notice the short half-lives of the isotopes with even amounts of neutrons and protons. For example, the half-life of even-even rutherfordium-258 is 0.012 seconds, as compared to the half-lives of rutherfordium-257 and -259, are 4.7 seconds and 2.8 seconds, respectively (“Isotopes of Rutherfordium” 1). The origin of the short half-life of rutherfordium-258, and other light even-even isotopes of rutherfordium and seaborgium, is their rapid spontaneous fission. The even-even isotopes of rutherfordium and seaborgium have comparably short fission half-lives because of incomplete nucleon shell effects of the two elements, the destabilizing nature of unpaired nucleons, and the smaller fission barriers that come with added protons.

        One of the origins of the short spontaneous fission half-lives of rutherfordium and seaborgium is the incomplete nucleonic shells that these nuclei have. As a general rule, nuclei with complete nuclear shells are stabilized more against spontaneous fission than comparable nuclei with incomplete nuclear shells (Somerville 8). The dominant nuclear subshells in the rutherfordium-seaborgium region of nuclear map are neutron numbers N=152 and N=162, and proton numbers Z=100, Z=102, and Z=108 (“Study of Fission Barriers” 1). The listed stabilized proton numbers do not include Z=104 (rutherfordium) or Z=106 (seaborgium), suggesting that Z=104,106 proton number is an incomplete nuclear subshell that destabilizes the nuclei against fission.

        The absence of unpaired nucleons in the even-even isotopes of rutherfordium and seaborgium contributes to their comparably short spontaneous fission half-lives. The presence of an odd amount of protons or neutrons increase the fission half-lives by at least one order of magnitude, and the fission half-lives of odd-odd nuclei increase by up to 8 orders of magnitude (“Exploring the Island” 1). The reason behind the enhanced stability of nuclei with odd amounts of nucleons is due to nuclear pairing effects. The absence of unpaired nucleons in even-even isotopes results in more rapid spontaneous fission ("The New Isotope 270110"). Like splitting wood with the grain, paired nucleons in the even-even isotopes of rutherfordium and seaborgium cause them to fission easily.

        The primary reason why the even-even isotopes of rutherfordium and seaborgium have short spontaneous fission half-lives is the presence of smaller fission barriers. To calculate the fission barriers, nuclear binding energy is graphed as a function of deformation (“Study of Fission Barriers” 2). The results of plotting the fission barriers for even-even superheavy nuclei suggest an overall lowering of both fission barriers as the proton number increases from Z=100 to Z=110 (“Study of Fission Barriers” 4). A lower fission barrier means less resistance to fission, and thus shorter half-lives. The collapse of the outer, more deformed fission barrier in the isotopes of rutherfordium destabilize the nuclei to spontaneous fission. The second fission barrier is nonexistant for seaborgium isotopes and heavier (Hulet 13). The second fission barrier is important to the stability of superheavy nuclei, because it means that the nucleus must undergo a greater deformation to fission. If a proton-rich nucleus lacks a second fission barrier, the Coloumb force overwhelms the Strong nuclear force much more easily, and the nucleus fissions. Thus the rapid fission of rutherfordium and seaborgium.

        The factors of incomplete subshells, small fission barriers, and the absence of unpaired nucleons all work together to make the even-even isotopes of rutherfordium and seaborgium very unstable to spontaneous fission. The proton subshells of Z=102 and Z=108 mostly confine the fissioning nuclides to Z=104 (rutherfordium) and Z=106 (seaborgium), while the decreasing fission barriers of the increasingly proton-rich nuclei further shortens the half-lives. The instability is confined to the even-even isotopes of rutherfordium and seaborgium, because of the absence of unpaired nucleons. Thus the nuclei rutherfordium-254, 256, 258, 260, 262, and seaborgium-258, 260, 262, 264, and 266 all have dominant fission decay modes with short half-lives.

Works Cited

Hulet, E. K. "SciTech Connect:." SciTech Connect:. Lawrence Livermore National Laboratory,

n.d. Web.

Hofmann, Sigurd, F. Heßberger, and et al. "The new isotope 270110 and its decay products

266Hs and 262Sg."link.springer.com. The European Physical Journal A - Hadrons and Nuclei, n.d. Web. 18 Mar 2014. <link.springer.com/article/10.1007/s10050017013>.

Hofmann, Sigurd. "Viewpoint: Exploring the island of superheavy elements." physics.aps.org.

N.p., 09 Apr 2010. Web. 18 Mar 2014. <http://physics.aps.org/articles/v3/31?referer=apshome>.

"Isotopes of Rutherfordium." Wikipedia. Wikimedia Foundation, 15 Mar. 2014. Web.

Staszczak, A., J. Dobaczewski, and W. Nazarewicz. "Self-Consistent Study of Fission Barriers of

Even-Even Superheavy Nuclei." phys.utk.edu. PDF. N.p.: n.p., 2008.

Somerville, Lawrence P. "Lawrence Berkeley National Laboratory. "Observation of New

Spontaneous Fission Activities From Elements 100 To 105 [eScholarship]. N.p., 07 July 2010. Web.