The mathematical framework concerning a class of α-
cluster
matter was studied from a full microscopic point of view on the basis of generator coordinate space. It is shown that all of the microscopic kernels can be attributed to those of one-dimensional α-
cluster
matter, if the image of a simple lattice is adopted as one of the models for the α-
cluster
matter. In other words, the problems of α-
cluster
matter were solved directly after those of an α-
cluster
chain. Furthermore, the analytical formulae for most of the kernels were written using the aid of computer derivations of the matrices. Results concerning α-
cluster
matter reproduce the bulk properties of ordinary nuclear matter fairly well. The volume and surface terms in Weizacker's mass formula are discussed within the framework of this model.
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