A Unified Theory of the Nucleus - download pdf or read online

By K. Wildermuth, Y.C. Tang

ISBN-10: 3322852555

ISBN-13: 9783322852557

ISBN-10: 3528083735

ISBN-13: 9783528083731

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Extra info for A Unified Theory of the Nucleus

Sample text

7. Construction of Generalized Cluster Wave Functions In the following subsections, we shall give a description of the Jastrow factor, together with a discussion of Jacobi and parameter coordinates which are useful in connection with generalized cluster wave functions. 7a. Introduction of Jacobi Coordinates To satisfy requirement (ii) mentioned above, it is necessary to have the center-of-mass coordinates clearly separated out. For this purpose, we shaH introduce the so-called Jacobi coordinate system.

7d. Summary In this section it is shown that the method of generalized cluster wave functions allows us to construct angular-momentum eigenfunctions of general type for a many-nucleon system. By using Jacobi coordinates as variables, we can, for instance, choose the radial dependence of the spatial parts of the wave functions describing the internal and relative motions of the clusters in a very flexible way without affecting the angular-momentum eigenvalues for the many-nucleon wave functions.

RH) = A S{15o (a;) 150 (a;)x(R') Z(R~) x [8(rl-r;Pj(r2-r~) ... 56) where the delta function 8 (fj - i) includes the spin and isobaric-spin coordinates of the nucleon i as well as its spatial coordinates, i. 57) dr' =dr', d 1"; ... d r~ is a differential volume element in the combined space, spin, 8 (rj - I I I I and and isospin space. The antisymmetrization is carried out on the nucleon coordinates I" I, ••• , r H and not on the primed parameter coordinates which are distinct from the nucleon coordinates.

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A Unified Theory of the Nucleus by K. Wildermuth, Y.C. Tang


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