Abstract
The composite particle representation theory (CPRT) proposed by Wu and Feng is examined by comparing its results to the shell-model calculations of Wildenthal and Chung for the s-d shell nuclei $^{20}\mathrm{O}$, $^{20}\mathrm{F}$, and $^{20}\mathrm{Ne}$. Each identical nucleon pair is treated in the CPRT as a boson. In all cases, the CPRT results are identical to the shell model. It was found that by evaluating the normalizations and the error sums of the CPRT wave functions, the spurious states, a subject of vital importance for any mapping theory, can be and are correctly removed. This shows that the composite particle representation is equivalent to the conventional representation in quantum mechanics. Thus the CPRT can provide an exact theoretical framework to treat particle clusters as ideal bosons (or fermions, depending on the nature of the clusters) in a many-body system, and is particularly useful for any quantum systems where clusterization dominates.
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