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**

**Example text**

Also, using arguments similar to those applied to the states in 7Li, one sees immediately that the two T = I 6Li states considered here have even parity. As is seen from fig. 3, these qualitative conclusions do agree with the experimental level scheme. Level spectra of 6He and 6Be in the low-excitation region are similar to the T = I level spectrum of 6Li as shown in fig. 3. The ground states of both these nuclei have 1" = 0+. In 6Be, the states are not stable with respect to particle decay, due to the large number of protons present.

3). To make this more clear, let us write eq. 3) = R~ -R~. As has been mentioned previously, the antisymmetrization operator A operates only on the unprimed nucleon coordinates, but not on the primed parameter coordinates R'. 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'.

25) I~ ~(if A{ [(xI+iyd+(x2+ iY2)+ ... -(xs+iYs)- ... -(xs+iYs)]4 i i~1 8 X exp (- rr )0: 1 ... 7Ts } . The term [(XI + iYI) + ... ]4 in eq. 25) is a sum of many terms of the form (XI + iYI )nl (X2 + iY2)n 2 ... (xx + iYs)ns, where nl, ... , ns take on integral values from 0 to 4, subject to the condition that nl + n2 + ... + ns = 4. In accordance with the Pauli principle, only those terms which correspond to four nucleons in the I p shell (whose wave functions, besides their exponential factors, are proportional to Xi + iYi) and four nucleons in the I s shell (whose wave functions, besides their exponential factors, are constants) with the proper spin and isospin configuration are different from zero.

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

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