An independent‐particle model of scientific salaries

During recent years there has been a remarkable correlation or explanation of a wide variety of experimental nuclear data in terms of the socalled independent‐particle model (IPM) of the nucleus. This model, which encompasses both the shell model and the optical model, views a nucleon which interacts with the many other nucleons in a complex nucleus as interacting with the nucleus as a whole via an IPM potential. For nucleon‐nuclear interactions the potentials which have been inferred by phenomenologists from a vast amount of data have the general form shown in Fig. 1. Here the vertical scale represents the IPM potential of a nucleon interacting with the nucleus as a whole and the horizontal scale represents the radial distance (r) from the center of the nucleus. The curves shown represent IPM potentials used to represent typical nuclei with mass numbers $\text{A\hspace{0.17em}=\hspace{0.17em}50,}$ 100, 150, 200, and 250. A convenient and frequently used form function for representing nuclear potentials is the Saxon potential $$\text{f(r)\hspace{0.17em}=\hspace{0.17em}{1+}\exp {\mathrm{[(r-R)/d]\}}}^{\text{−1}},$$ where R represents the radial distance to the point at which the potential reduces in magnitude to 0.5 of its central value and d is a parameter which determines the diffuseness or surface thickness of the potential. Experimental data with beams of deuterons, alpha particles, other nuclei, as well as pions and K mesons, all scattered by heavy nuclei, seem to be accounted for quite readily in terms of the optical‐model form of the IPM. The success of the IPM seems so broad that one might be tempted to apply it to a great variety of physical phenomena and even sociological phenomena.

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