San José State University
Thayer Watkins
Silicon Valley
& Tornado Alley

Some Preliminary Analyses of the Measured
Electric Quadrupole Moments of Nuclides

The electric quadrupole moment measures the deviation of the shape of a nucleus from spherical symmetry. The alpha module model of nuclear structure indicates that equal and exactly filled shells of neutrons and protons should appear dynamically as spheres. Therefore excess neutrons or excess protons in a nucleus might contribute an asymmetry to the dynamic shape of a nucleus.

The excess number of neutrons (XSn) is defined as (n−p) for n>p and otherwise 0. Likewise the excess number of protons XSp is (p−n) for p>n and 0 otherwise.

The electric quadrupole moment is expressed in barns, which is 10-28 m². (This unit comes from an American folk saying that someone who is a poor shot could not hit the broadside of a barn. The broadside of a barn became the expression for a large area. When some physicist was informed of some atomic or subatomic area he exclaimed, "Why that is as big as a barn!" The term stuck and was defined formally as 10-28 m².

From the tables of N.J. Stone there were found 316 measured electric quadrupole moments (QM). The first regression equation estimated was

QM = c0 + c1XSn + c2XSp

The results were

QM = -0.06663 + 0.01961XSn + 0.06663XSp
                      (5.9)                (0.1)

The number in parentheses below a coefficient is its t-ratio, the coefficient divided by its standard deviation. For a coefficient to be significantly different from zero at the 95 percent level of confidence its t-ratio must be 2 or greater in magnitude. As can be seen the influence of the number of excess protons is not significantly different from zero. The number of excess neutrons is a significant influence,

With the excess number of protons removed the regression equation is

QM = -0.06538 + 0.019567XSn

The coefficient of determination (R²) for this equation is only 10 percent. Only 10 percent of the variation in QM is explained by variations in XSn. The excess number of neutrons is part of the explanation of the electric quadrupole moment but only a small part. The expanation must, however, be in terms of the numbers of neutrons and proton.

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