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4.8 Nuclei and particles

4.8.1 Size of atomic nuclei

The majority of atomic nuclei are approximately spherical in shape and it is sufficient for many purposes to describe them using a spherically symmetric matter distribution with rms radius,

R = r0A1/3

where r₀ ≈ 1.2 fm and A is the mass number.
       A more accurate expression for the nuclear rms radius, obtained from the liquid drop model of the nucleus, is given by the expression (Myers, 1983)

R =

(1.15 + 1.8A −2/3 − 1.2A−4/3)A1/3

Although it is customary to describe the nucleus as having a radius, this does not, of course, correspond to a sharp cut-off with a finite density of nucleons inside and zero density outside. A frequently used approximation to the actual nucleon density in spherically symmetric nuclei is

	ρ = ρ0		1 + exp		r − c		−1
					a

where c, the radius at which the density drops to ρ₀, is ≈ 1.1A^1/3 fm, the nuclear surface thickness parameter a ≈ 0.6 fm does not depend strongly on nuclear size and ρ₀ ≈ 0.17 nucleon fm⁻³.

Some nuclei display a nucleon density distribution that deviates appreciably from spherical symmetry. A first indication of the magnitude of such a deviation can be obtained from the ground state quadrupole moment Q of a nucleus. If the nucleus is considered a uniformly charged ellipsoid of rotation with average radius R, then a first estimate of the deviation from average in the direction of symmetry ΔR is

	ΔR	≈	83Q
	R		ZR2

where Z is the atomic number of the nucleus, Q is in barns and R in fm. The ground state electric quadrupole moments of nuclei are tabulated in several standard text books, e.g. Lederer (1978).

References

W. F. Myers and K. H. Schmidt (1983) Nuclear Physics, A410, 61.
C. M. Lederer and V. Shirley (1978) Table of Isotopes, Wiley, New York.

M.R.Sené

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