By K. Wildermuth, Y.C. Tang

ISBN-10: 3322852555

ISBN-13: 9783322852557

ISBN-10: 3528083735

ISBN-13: 9783528083731

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From eq. 2) one sees that the wave function l/J represents a continuous linear superposition of trial functions (or basis wave functions as we shall often call them) of the form A {¢(a) 8 (R - R'H(s, t)}, with variational amplitudes given by F (R'). The variation of l/J is given by S 8l/J = 8 F(R')A {¢(a) 8 (R - R') Hs, tn dR'. 4) Upon substituting eqs. 6) = 1 with Te being the kinetic-energy operator of the total center of mass. 7) 44 4. Formulation of a Unified Microscopic Nuclear Structure and Reaction Theory where /1 denotes the reduced mass and ER denotes the total kinetic energy of the neutron and the 0: cluster at large separation in the center-of-mass system.

The same is true also for the corresponding rand r states. t For the explicit construction of these wave functions, see reference IKA 591. 30 3. 14 3- Fig. 4. Energy levels of 16 0. ----0+ POSITIVE - PARITY LEVELS NEGATIVE - PARITY LEVELS Our considerations show that the lowest measured negative-parity levels of 16 0 should have 1" :: r, 1-, and 2- (see fig. 4). As one might expect, the 2 -level lies above the land 3 -levels, because there the 12C cluster has to be in its first excited state. The pen· etrating-orbit argument no longer suffices to give ordering of the 1- and r levels, since there is large cluster overlapping in both these states and other more subtle and complicated effects connected with the Pauli principle come into play.

That means if the considered cluster function is an eigenfunction of the operator J2, the parity operator, and so on, before the introduction of this anti-correlation factor, it will remain so after the introduction of such a factor. If fik (Iri - rk I) is chosen to have the same form for all nucleon pairs, then I/JJ of eq. 60) is symmetric in all nucleon coordinates and does not have to be included in the antisymmetrization process. One consequence of this is that our discussions about equivalences between different cluster functions remain valid even after the introduction of this factor.

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

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